,transcrib]'s ,note ,m9or typographical errors & irregul>ities h be5 correct$4 ,footnotes h be5 numb]$ sequ5tially )9 *apt]s & mov$ to ! end ( ea* *apt]4 ,,! ,,logic ,,( ,,*ance ,,an ,,essay ,,on ,,! ,,f\ndations ,,& ,,prov9ce ,,( ,,! ,,!ory ,,( ,,probability1 ,,) ,,especial ,,ref]5ce ,,to ,,its ,,logical ,,be>+s ,,& ,,its ,,application ,,to ,,moral ,,& ,,social ,,sci5ce ,,& ,,to ,,/ati/ics1 ,,by ,,john ,,v5n1 ,sc4,d41 ,f4,r4,s41 ,,fell[ ,,& ,,lectur] ,,9 ,,! ,,moral ,,sci5ces1 ,,gonville ,,& ,,caius ,,college1 ,,cambridge4 ,,late ,,exam9] ,,9 ,,logic ,,& ,,moral ,,philosophy ,,9 ,,! ,,univ]sity ,,( ,,london4 ,s c>eful ( ! type %e seems ,s c>eless ( ! s+le life4 ,,?ird ,,edition1 ,,re-,,writt5 ,,& ,,enl>g$4 ,london3 ,,macmillan ,,& ,,co4 ,,& ,,new ,,york #ahhh ,all ,rights res]v$4 ,fir/ ,edition pr9t$ #ahff4 ,second ,edition #ahgf4 ,?ird ,edition #ahhh4 ,,preface ,,to ,,fir/ ,,edition ,any "w on ,probability by a ,cambridge man w be s likely to h its scope & its g5]al treatm5t ( ! subject prejudg$1 t x may be well to /ate at ! outset t ! foll[+ ,essay is 9 no s5se ma!matical4 ,n only1 to quote a common b (t5 delusive assurance1 w 'no k ( ma!matics beyond ! simple rules ( ,ari?metic' be requir$ to und]/& ^! pages1 b x is n int5d$ t any su* k %\ld be acquir$ by ! process ( read+ !m4 ,( ! two or ?ree occasions on :i* algebraical =mul occur !y w n be f\nd to =m any ess5tial "p ( ! text4 ,! sci5ce ( ,probability occupies at pres5t a some:at anomal\s position4 ,x is impossible1 ,i ?9k1 n to obs]ve 9 x "s ( ! m>ks & consequ5t disadvantages ( a sectional /udy4 ,by a small body ( ard5t /ud5ts x has be5 cultivat$ ) great assiduity1 & ! results !y h obta9$ w always be reckon$ among ! mo/ extraord9>y products ( ma!matical g5ius4 ,b by ! g5]al body ( ?9k+ m5 its pr9ciples seem to be reg>d$ ) indiff]5ce or suspicion4 ,su* p]sons may admire ! +5uity display$1 & be /ruck ) ! pr(undity ( _m ( ! calculations1 b !re seems to !m1 if ,i may s express x1 an unreality ab\t ! :ole treatm5t ( ! subject4 ,to _m p]sons ! m5tion ( ,probability sugge/s little else ?an ! notion ( a set ( rules1 v +5i\s & pr(\nd rules no d\bt1 ) :i* ma!maticians amuse !mselves by sett+ & solv+ puzzles4 ,x mu/ be admitt$ t "s gr\nd has be5 giv5 = su* an op9ion4 ,! examples commonly select$ by writ]s on ! subject1 ?\gh v well adapt$ to illu/rate its rules1 are = ! mo/ "p ( a special & peculi> "*1 su* z ^? relat+ to dice & c>ds4 ,:5 !y h se>*$ = illu/rations drawn f ! practical bus9ess ( life1 !y h v g5]ally1 b un=tunately1 hit ^u j ! sort ( in/ances :i*1 z ,i %all endeav\r to %[ h]eaft]1 are among ! v wor/ t c\ld be *os5 = ! purpose4 ,x is sc>cely possible = any unprejudic$ p]son to read :at has be5 writt5 ab\t ! cr$ibility ( witnesses by em95t writ]s1 )\t 8 exp]i5c+ an inv9cible di/ru/ ( ! pr9ciples :i* !y adopt4 ,to say t ! rules ( evid5ce sometimes giv5 by su* writ]s are brok5 9 practice1 w\ld sc>cely be correct2 = ! rules are ( su* a k9d z g5]ally to defy any attempt to appeal to !m 9 practice4 ,?is suppos$ want ( h>mony betwe5 ,probability & o!r bran*es ( ,philosophy is p]fectly errone\s4 ,x arises f ! belief t ,probability is a bran* ( ma!matics try+ to intrude itself on to gr\nd :i* does n altoge!r belong to x4 ,i %all endeav\r to %[ t ?is belief is unf\nd$4 ,to answ] correctly ! sort ( que/ions to :i* ! sci5ce introduces u does g5]ally dem& "s k ( ma!matics1 (t5 a great k1 b ! discussion ( ! fundam5tal pr9ciples on :i* ! rules are bas$ does n necess>ily require any su* qualification4 ,que/ions might arise 9 o!r sci5ces1 9 ,geology1 = example1 :i* c\ld only be answ]$ by ! aid ( ari?metical calculations4 ,9 su* a case any "o w\ld admit t ! ari?metic 0 extrane\s & accid5tal4 ,h[ev] _m que/ions ( ?is k9d !re might be "h1 ^? p]sons :o d n c>e to "w out special results = !mselves might /ill h an accurate k ( ! pr9ciples ( ! sci5ce1 & ev5 consid]able acqua9tance ) ! details ( x4 ,! same holds true 9 ,probability2 its connection ) ma!matics1 ?\gh c]ta9ly f> clos] ?an t ( mo/ o!r sci5ces1 is /ill ( mu* ! same k9d4 ,x is pr9cipally :5 we wi% to "w out results = ourselves t ma!matical k is requir$2 )\t su* k ! /ud5t may /ill h a firm grasp ( ! pr9ciples & ev5 see 8 way to _m ( ! d]ivative results4 ,! op9ion t ,probability1 in/ead ( be+ a bran* ( ! g5]al sci5ce ( evid5ce :i* happ5s to make mu* use ( ma!matics1 is a portion ( ma!matics1 errone\s z x is1 has yet be5 v disadvantage\s to ! sci5ce 9 sev]al ways4 ,/ud5ts ( ,philosophy 9 g5]al h !nce conceiv$ a prejudice aga9/ ,probability1 :i* has = ! mo/ "p det]r$ !m f exam9+ x4 ,z soon z a subject comes to be consid]$ 'ma!matical' its claims seem g5]ally1 by ! mass ( read]s1 to be ei!r on ! "o h& sc\t$ or at lea/ c\rte\sly reject$1 or on ! o!r to be bl9dly accept$ ) all _! assum$ consequ5ces4 ,( imp>tial & lib]al criticism x obta9s little or no?+4 ,! consequ5ces ( ?is /ate ( ?+s h be51 ,i ?9k1 disa/r\s to ! /ud5ts !mselves ( ,probability4 ,no sci5ce c safely be ab&on$ entirely to its own devotees4 ,its details ( c\rse c only be /udi$ by ^? :o make x _! special occupation1 b its g5]al pr9ciples are sure to be cramp$ if x is n expos$ occasionally to ! free criticism ( ^? ^: ma9 culture has be5 ( a m g5]al "*4 ,probability has be5 v mu* ab&on$ to ma!maticians1 :o z ma!maticians h g5]ally be5 unwill+ to treat x ?or\ghly4 ,!y h work$ out its results1 x is true1 ) wond]ful acut5ess1 & ! greate/ +5uity has be5 %[n 9 solv+ v>i\s problems t arose1 & d$uc+ subord9ate rules4 ,& ?is 0 all t !y c\ld 9 fairness be expect$ to d4 ,any subject :i* has be5 discuss$ by su* m5 z ,laplace & ,poisson1 & on :i* !y h exhau/$ all _! p[]s ( analysis1 c\ld n fail to be pr(\ndly treat$1 s f> z x fell )9 _! prov9ce4 ,b f ?is prov9ce ! real pr9ciples ( ! sci5ce h g5]ally be5 exclud$1 or s meagrely discuss$ t !y _h bett] h be5 omitt$ altoge!r4 ,treat+ ! subject z ma!maticians su* writ]s h naturally tak5 x up at ! po9t :]e _! ma!matics w\ld be/ come into play1 & t ( c\rse has n be5 at ! f\ndations4 ,9 ! works ( mo/ writ]s ^u ! subject we %\ld se>* 9 va9 = any?+ l a critical discussion ( ! fundam5tal pr9ciples ^u :i* its rules re/1 ! class ( enquiries to :i* x is mo/ prop]ly applicable1 or ! relation x be>s to ,logic & ! g5]al rules ( inductive evid5ce4 ,?is want ( precision z to ultimate pr9ciples is p]fectly compatible "h1 z x is 9 ! dep>tm5ts ( ,morals & ,politics1 ) a g5]al agreem5t on processes & results4 ,b x is1 to say ! lea/1 unphilosophical1 & d5otes a /ate ( ?+s 9 :i* positive error is always liable to arise :5ev] ! process ( controv]sy =ces u to appeal to ! f\ndations ( ! sci5ce4 ,) reg>d to ! rem>ks 9 ! la/ few p>agraphs1 prom95t exceptions mu/ be made 9 ! case ( two rec5t works at lea/4#a ,! fir/ ( ^! is ,pr(essor de ,morgan's ,=mal ,logic4 ,he has !re giv5 an inve/igation into ! f\ndations ( ,probability z conceiv$ by him1 & no?+ c be m complete & precise ?an 8 /atem5t ( pr9ciples1 & 8 d$uctions f !m4 ,if ,i c\ld at all agree ) ^! pr9ciples !re w\ld h be5 no necessity = ! foll[+ essay1 z ,i c\ld n hope to add any?+ to _! f\ndation1 & %\ld be f> inde$ f rivall+ 8 lucid /atem5t ( !m4 ,b 9 8 s*eme ,probability is reg>d$ v mu* f ! ,conceptuali/ po9t ( view2 z /at$ 9 ! preface1 he consid]s t ,probability is conc]n$ ) =mal inf]5ces 9 :i* ! premises are ent]ta9$ ) a conviction %ort ( absolute c]ta9ty4 ,) ?is view ,i _c agree4 ,z ,i h ent]$ into criticism ( "s po9ts ( 8 s*eme 9 "o ( ! foll[+ *apt]s1 & %all h occasion frequ5tly to ref] to 8 "w1 ,i ne$ say no m ab\t x "h4 ,! o!r "w to :i* ,i ref] is ! pr(\nd ,laws ( ,?\ght ( ! late ,pr(essor ,boole1 to :i* some:at simil> rem>ks may 9 "p be appli$4 ,ow+ h[ev] to 8 peculi> treatm5t ( ! subject1 ,i h sc>cely any:]e come into contact ) any ( 8 express$ op9ions4 ,! view ( ! prov9ce ( ,probability adopt$ 9 ?is ,essay diff]s s radically f t ( mo/ o!r writ]s on ! subject1 & especially f t ( ^? j ref]r$ to1 t ,i h ?\ght x bett]1 z reg>ds details1 to avoid all criticism ( ! op9ions ( o!rs1 except :]e conflict 0 unavoidable4 ,) reg>d to t radical diff]5ce itself ,bacon's rem>k applies1 beh9d :i* ,i mu/ %elt] myself f any *ange ( presumption4--,quod ad univ]salem i/am repreh5sionem att9et1 c]tissimum v]e e/ rem reputanti1 eam et magis probabilem esse et magis mode/am1 quam si facta fuisset ex p>te4 ,almo/ ! only writ] :o seems to me to h express$ a j view ( ! nature & f\ndation ( ! rules ( ,probability is ,mr ,mill1 9 8 ,sy/em ( ,logic4#b ,8 treatm5t ( ! subject is h[ev] v brief1 & a consid]able portion ( ! space :i* he has devot$ to x is occupi$ by ! discussion ( "o or two special examples4 ,!re are moreov] "s errors1 z x seems to me1 9 :at he has writt51 :i* w be ref]r$ to 9 "s ( ! foll[+ *apt]s4 ,! ref]5ce to ! "w j m5tion$ w s]ve to convey a g5]al idea ( ! view ( ,probability adopt$ 9 ?is ,essay4 ,) :at may be call$ ! ,mat]ial view ( ,logic z oppos$ to ! ,=mal or ,conceptuali/1--) t :i* reg>ds x z tak+ cognisance ( laws ( ?+s & n ( ! laws ( our own m9ds 9 ?9k+ ab\t ?+s1--,i am 9 entire accordance4 ,( ! prov9ce ( ,logic1 reg>d$ f ?is po9t ( view1 & "u its wide/ aspect1 ,probability may1 9 my op9ion1 be consid]$ to be a portion4 ,! pr9cipal objects ( ?is ,essay are to asc]ta9 h[ great a portion x comprises1 :]e we are to draw ! b\nd>y betwe5 x & ! contigu\s bran*es ( ! g5]al sci5ce ( evid5ce1 :at are ! ultimate f\ndations ^u :i* its rules re/1 :at ! nature ( ! evid5ce !y are capable ( af=d+1 & to :at class ( subjects !y may mo/ fitly be appli$4 ,t ! sci5ce ( ,probability1 on ?is view ( x1 conta9s some?+ m important ?an ! results ( a sy/em ( ma!matical assumptions1 is obvi\s4 ,i am conv9c$ moreov] t x c & ought to be r5d]$ bo? int]e/+ & intelligible to ord9>y read]s :o h any ta/e = philosophy4 ,9 o!r words1 if ! l>ge & gr[+ body ( read]s :o c f9d pleasure 9 ! /udy ( books l ,mill's ,logic & ,:ewell's ,inductive ,sci5ces1 turn ) av]sion f a "w on ,probability1 ! cause 9 ! latt] case mu/ lie ei!r 9 ! view ( ! subject or 9 ! mann] & /yle ( ! book4 ,i take ?is opportunity ( ?ank+ sev]al fri5ds1 among/ :om ,i mu/ especially m5tion ,mr ,todhunt]1 ( ,/ ,john's ,college1 & ,mr ,h4 ,sidgwick1 ( ,tr9ity ,college1 = ! tr\ble !y h k9dly tak5 9 look+ ov] ! pro(-%eets1 :il/ ?is "w 0 pass+ ?r\gh ! ,press4 ,to ! =m] 9 p>ticul> my ?anks are due = ?us add+ to ! obligations :i* ,i1 z an old pupil1 already ow$ him1 by tak+ an am\nt ( tr\ble1 9 mak+ sugge/ions & corrections = ! b5efit ( ano!r1 :i* few w\ld c>e to take = any?+ b a "w ( _! own4 ,8 ext5sive k ( ! subject1 & 8 extremely accurate judgm5t1 r5d] ! s]vice he has ?us af=d$ me ( ! greate/ possible value4 ,,gonville ,,& ,,caius ,,college ,septemb] #ahff4 #a4 ,i am "h speak+1 ( c\rse1 ( ^? only :o h expressly treat$ ( ! f\ndations ( ! sci5ce4 ,mr ,todhunt]'s admirable "w on ! ,hi/ory ( ! ,!ory ( ,probability be+1 z ! "n d5otes1 ma9ly hi/orical1 su* enquiries h n directly fall5 )9 8 prov9ce4 #b4 ,?is rem>k1 & t at ! comm5cem5t ( ! la/ p>agraph1 hav+ be5 misund]/ood1 ,i ought to say t ! only s5se 9 :i* orig9ality is claim$ = ?is ,essay is 9 ! ?or\gh work+ out ( ! ,mat]ial view ( ,logic z appli$ to ,probability4 ,i h giv5 a pretty full discussion ( ! g5]al pr9ciples ( ?is view 9 ! t5? *apt]1 & h !re po9t$ out "s ( ! peculi>ities to :i* x leads4 ,,preface ,,to ,,second ,,edition ,! pr9cipal reason = designat+ ?is volume a second edition consi/s 9 ! fact t ! great] portion ( :at may be t]m$ ! fir/ edition is incorporat$ into x4 ,besides v>i\s omissions 7pr9cipally :]e ! =m] treatm5t has s9ce seem$ to me ne$lessly prolix71 ,i h add$ new matt]1 n mu* inf]ior 9 am\nt to ! :ole ( ! orig9al "w4 ,9 addition1 moreov]1 to ^! alt]ations 9 ! matt]1 ! g5]al arrangem5t ( ! subject z reg>ds ! successive *apt]s has be5 completely *ang$2 ! =m] arrangem5t hav+ be5 7z x n[ seems to me7 ju/ly object$ to z defici5t & awkw>d 9 me?od4 ,aft] say+ ?is1 x ought to be expla9$ :e!r any *ange ( g5]al view or results w be f\nd 9 ! pres5t treatm5t4 ,! g5]al view ( ,probability adopt$ is q un*ang$1 fur!r read+ & reflection hav+ only confirm$ me 9 ! conviction t ?is is ! s\nde/ & mo/ fruitful way ( reg>d+ ! subject4 ,x is ! m necess>y to say ?is1 z to a cursory read] x might seem o!rwise2 ow+ to my hav+ endeav\r$ to avoid ! ne$lessly polemical tone :i*1 z is (t5 ! case ) ^? :o are mak+ _! fir/ essay 9 writ+ ^u any subject1 0 d\btless too prom95t 9 ! =m] edition4 ,i h n ?\ght x necess>y1 ( c\rse1 except 9 "o or two cases1 to indicate po9ts ( detail :i* x has seem$ necess>y to correct4 ,a numb] ( new discussions h be5 introduc$ ^u topics :i* 7 b little or n at all treat$ be=e4 ,! pr9cipal ( ^! ref] to ! nature & physical orig9 ( ,laws ( ,error 7,*4 ,,ii472 ! g5]al view ( ,logic1 & consequ5tly ( ,probability1 t]m$ ! ,mat]ial view1 adopt$ "h 7,*4 ,x472 a brief hi/ory & criticism ( ! v>i\s op9ions held on ! subject ( ,modality 7,*4 ,,xii472 ! logical pr9ciples und]ly+ ! me?od ( ,lea/ ,squ>es 7,*4 ,,xiii472 & ! practices ( ,insurance & ,gambl+1 s f> z ! pr9ciples involv$ 9 !m are conc]n$ 7,*4 ,,xv474 ,! ,*apt] on ! ,cr$ibility ( ,extraord9>y ,/ories is also ma9ly new2 ?is 0 ! portion ( ! =m] "w :i* has s9ce seem$ to me ! lea/ satisfactory1 b ow+ to ! extreme intricacy ( ! subject ,i am f> f feel+ ?or\ghly satisfi$ ) x ev5 n[4 ,i h aga9 to ?ank sev]al fri5ds = ! assi/ance !y h s k9dly af=d$4 ,among/ ^! ,i mu/ prom95tly m5tion ,mr ,c4 ,j4 ,monro1 late fell[ ( ,tr9ity4 ,x is only ! tru? to say t ,i h d]iv$ m assi/ance f 8 sugge/ions & criticisms ?an has be5 consci\sly obta9$ f all o!r ext]nal s\rces toge!r4 ,mu* ( ?is criticism has be5 giv5 privately 9 lett]s1 & notes on ! pro(-%eets2 b "o ( ! mo/ elaborate ( 8 discussions ( ! subject 0 communicat$ to ! ,cambridge ,philosophical ,society "s ye>s ago2 z x 0 n publi%$1 h[ev]1 ,i am un=tunately unable to ref] ! read] to x4 ,i ought to add t he is n 9 any way committ$ to any ( my op9ions ^u ! subject1 f "s ( :i* 9 fact he m or less diss5ts4 ,i am also mu* indebt$ to ,mr ,j4 ,w4 ,l4 ,glai%]1 also ( ,tr9ity ,college1 = _m h9ts & ref]5ces to v>i\s publications ^u ! subject ( ,lea/ ,squ>es1 & = c>eful criticism 7giv5 9 ! mid/ ( mu* o!r lab\r7 ( ! *apt] 9 :i* t subject is treat$4 ,i ne$ n add t1 l e "o else :o has _h to discuss ! subject ( ,probability dur+ ! la/ t5 ye>s1 ,i h made con/ant use ( ,mr ,todhunt]'s ,hi/ory4 ,i may take ?is opportunity ( add+ t a consid]able portion ( ! t5? *apt] has rec5tly appe>$ 9 ! ,janu>y numb] ( ,m9d1 & t ! sub/ance ( sev]al *apt]s1 especially 9 ! m logical p>ts1 has =m$ "p ( my ord9>y lectures 9 ,cambridge2 ! f\ndation & logical treatm5t ( ,probability be+ n[ expressly includ$ 9 ! ,s*$ule ( ,subjects = ! ,moral ,sci5ces ,tripos4 ,m>* #ahgf4 ,,preface ,,to ,,?ird ,,edition ,! pres5t edition has be5 revis$ ?r\gh\t1 & 9 fact rewritt54 ,?ree *apt]s are new1 viz4 ! fif? 7,on ! conception ( ,r&omness7 & ! eighte5? & n9ete5? 7,on ! nature1 & on ! employm5t1 ( ,av]ages74 ,! eigh?1 t5?1 elev5?1 & fifte5? *apt]s h be5 reca/1 & mu* new matt] add$1 & num]\s alt]ations made 9 ! rema9+ portions4#a ,on ! o!r h& ?ree *apt]s ( ! la/ edition h be5 ne>ly or entirely omitt$4 ,^! alt]ations d n imply any appreciable *ange ( view on my "p z to ! f\ndations & prov9ce ( ,probability4 ,"s ( !m are ( c\rse due to ! necess>y *anges involv$ 9 ! attempt to write up to date ^u a subject :i* has n be5 /ation>y dur+ ! la/ elev5 ye>s4 ,= in/ance ! greatly increas$ int]e/ n[ tak5 9 :at may be call$ ! ,!ory ( ,/ati/ics has r5d]$ x desirable to g mu* m fully into ! ,nature & treatm5t ( ,laws ( ,error4 ,! omissions are ma9ly due to a wi% to avoid increas+ ! bulk ( ?is volume m ?an is actually necess>y1 & to a feel+ t ! portions treat+ specially ( ,inductive ,logic 7:i* occupi$ "s space 9 ! la/ edition7 w\ld be m suitable to a regul> "w on t subject4 ,i am at pres5t engag$ on su* a "w4 ,! publications :i* ,i h _h occasion to notice h mo/ly appe>$ 9 v>i\s sci5tific j\rnals4 ,! pr9cipal au?ors ( ^! h be5 ,mr ,f4 ,galton & ,mr ,f4 ,y4 ,edgewor?3 to ! latt] ( :om ,i am also p]sonally mu* oblig$ = _m discussions1 oral & writt51 & = 8 k9dness 9 look+ ?r\gh ! pro(-%eets4 ,8 publi%$ articles are too num]\s = sep>ate m5tion "h1 b ,i may say g5]ally1 9 addition to ! obligations specially notic$1 t ,i h be5 consid]ably indebt$ to !m 9 writ+ ! la/ two *apt]s4 ,two au?ors ( works ( a some:at m sub/antial "*1 viz4 ,pr(4 ,lexis & ,von ,kries1 only came "u my notice un=tunately aft] ?is "w 0 already 9 ! pr9t]'s h&s4 ,) ! latt] ( ^! au?ors ,i f9d myself 9 clos] agreem5t ?an ) mo/ o!rs1 9 respect ( 8 g5]al conception & treatm5t ( ,probability4 ,decemb] #ahhg4 #a4 ,i h indicat$ ! new *apt]s & sections by pr9t+ !m 9 italics 9 ! ,table ( ,cont5ts4 ,,table ,,( ,,cont5ts4#a #a4 ,*apt]s & sections :i* are ne>ly or entirely new are pr9t$ 9 italics4 ,,"p ,i4 ,,physical ,,f\ndations ,,( ,,! ,,sci5ce ,,( ,,probability4 ,*h4 ,i-,v4 ,,*apt] ,i4 ,,! ,,s]ies ,,( ,,probability4 #a1 #b4 ,di/9ction betwe5 ! proportional propositions ( ,probability1 & ! propositions ( ,logic4 #c1 #d4 ,! =m] are be/ reg>d$ z pres5t+ a s]ies ( individuals1 #e4 ,:i* may occur 9 any ord] ( "t1 #f1 #g4 ,& :i* pres5t !mselves 9 gr\ps4 #h4 ,comp>ison ( ! above ) ! ord9>y phraseology4 #i1 #aj4 ,^! s]ies ultimately fluctuate1 #aa4 ,especially 9 ! case ( moral & social ph5om5a1 #ab4 ,?\gh 9 ! case ( games ( *ance ! fluctuation is practically inappreciable4 #ac1 #ad4 ,9 ?is latt] case only c rigor\s inf]5ces be drawn4 #ae1 #af4 ,! ,pet]sburg ,problem4 ,,*apt] ,,ii4 ,,arrangem5t ,,& ,,=mation ,,( ,,! ,,s]ies4 ,,laws ,,( ,,error4 #a1 #b4 ,indication ( ! nature ( a ,law ( ,error or ,div]g5ce4 #c4 ,is !re necess>ily b "o su* law1 #d4 ,applicable to widely di/9ct classes ( ?+s8 #e1 #f4 ,?is _c be prov$ directly by /ati/ics2 #g1 #h4 ,:i* 9 c]ta9 cases %[ actual asymmetry4 #i1 #aj4 ,nor d$uctively2 #aa4 ,nor by ! ,me?od ( ,lea/ ,squ>es4 #ab4 ,di/9ction betwe5 ,laws ( ,error & ! ,me?od ( ,lea/ ,squ>es4 #ac4 ,suppos$ exi/5ce ( types4 #ad-af4 ,homog5e\s & het]og5e\s classes4 #ag1 #ah4 ,! type 9 ! case ( human /ature1 c4 #ai1 #bj4 ,! type 9 m5tal *>act]i/ics4 #ba1 #bb4 ,applications ( ! =ego+ pr9ciples & results4 ,,*apt] ,,iii4 ,,orig9 ,,or ,,process ,,( ,,causation ,,( ,,! ,,s]ies4 #a4 ,! causes consi/ ( 7#a7 'objects1' #b1 #c4 ,:i* may or may n be di/+ui%able into natural k9ds1 #d-f4 ,& 7#b7 'ag5cies4' #g4 ,requisites dem&$ 9 ! above3 #h1 #i4 ,consequ5ces ( _! abs5ce4 #aj4 ,:]e are ! requir$ causes f\nd8 #aa1 #ab4 ,n 9 ! direct results ( human w4 #ac-ae4 ,exam9ation ( app>5t exceptions4 #af-ah4 ,fur!r analysis ( "s natural causes4 ,,*apt] ,,iv4 ,,h[ ,,to ,,discov] ,,& ,,prove ,,! ,,s]ies4 #a4 ,! data ( ,probability are e/abli%$ by exp]i5ce2 #b4 ,?\gh 9 practice mo/ problems are solv$ d$uctively4 #c-g4 ,me*anical in/ance to %[ ! inadequacy ( any priori pro(4 #h4 ,! ,pr9ciple ( ,suffici5t ,reason inapplicable4 #i4 ,evid5ce ( actual exp]i5ce4 #aj1 #aa4 ,fur!r exam9ation ( ! causes4 #ab1 #ac4 ,di/9ction betwe5 ! succession ( physical ev5ts & ! ,doctr9e ( ,comb9ations4 #ad1 #ae4 ,rem>ks ( ,laplace on ?is subject4 #af4 ,b]n\lli's ,!orem2 #ag1 #ah4 ,its inapplicability to social ph5om5a4 #ai4 ,summation ( prec$+ results4 ,,*apt] ,v4 ,,! ,,conception ,,( ,,r&omness4 #a4 ,g5]al ,indication4 #b-e4 ,! po/ulate ( ultimate uni=m di/ribution at "o /age or ano!r4 #f4 ,?is area ( di/ribution mu/ be f9ite3 #g1 #h4 ,geometrical illu/rations 9 support3 #i4 ,c we conceive any exception "h8 #aj1 #aa4 ,exp]im5tal det]m9ation ( ! r&om "* :5 ! ev5ts are _m3 #ab4 ,correspond+ det]m9ation :5 !y are few4 #ac1 #ad4 ,illu/ration f ! con/ant 4 #ae1 #af4 ,conception ( a l9e drawn at r&om4 #ag4 ,graphical illu/ration4 ,,"p ,,ii4 ,,logical ,,sup]/ructure ,,on ,,! ,,above ,,physical ,,f\ndations4 ,*h4 ,,vi-,,xiv4 ,,*apt] ,,vi4 ,,measurem5t ,,( ,,belief4 #a1 #b4 ,prelim9>y rem>ks4 #c1 #d4 ,are we accurately consci\s ( gradations ( belief8 #e4 ,probability only conc]n$ ) "p ( ?is enquiry4 #f4 ,difficulty ( measur+ our belief2 #g4 ,ow+ to intrusion ( emotions1 #h4 ,& complexity ( ! evid5ce4 #i4 ,& :5 measur$1 is x always correct8 #aj1 #aa4 ,di/9ction betwe5 logical & psy*ological views4 #ab-af4 ,analogy ( ,=mal ,logic fails to %[ t we c ?us deta* & measure our belief4 #ag4 ,app>5t evid5ce ( popul> language to ! contr>y4 #ah4 ,h[ is full belief ju/ifi$ 9 inductive enquiry8 #ai-bc4 ,attempt to %[ h[ p>tial belief may be simil>ly ju/ifi$4 #bd-bh4 ,ext5sion ( ?is explanation to cases :i* _c be repeat$ 9 exp]i5ce4 #bi4 ,c o!r emotions besides belief be ?us measur$8 #cj4 ,errors ?us aris+ 9 connection ) ! ,pet]sburg ,problem4 #ca1 #cb4 ,! emotion ( surprise is a p>tial exception4 #cc1 #cd4 ,objective & subjective phraseology4 #ce4 ,! def9ition ( probability1 #cf4 ,introduces ! notion ( a 'limit'1 #cg4 ,& implies1 vaguely1 "s degree ( belief4 ,,*apt] ,,vii4 ,,! ,,rules ,,( ,,inf]5ce ,,9 ,,probability4 #a4 ,nature ( ^! inf]5ces4 #b4 ,inf]5ces by addition & subtraction4 #c4 ,inf]5ces by multiplication & division4 #d-f4 ,rule = indep5d5t ev5ts4 #g4 ,o!r rules sometimes introduc$4 #h4 ,all ! above rules may be int]pret$ subjectively1 i4e4 9 t]ms ( belief4 #i-aa4 ,rules ( s-call$ ,inv]se ,probability4 #ab1 #ac4 ,nature ( ! assumption involv$ 9 !m3 #ad-af4 ,arbitr>y "* ( ?is assumption4 #ag1 #ah4 ,physical illu/rations4 ,,*apt] ,,viii4 ,,! ,,rule ,,( ,,succession4 #a4 ,reasons = desir+ "s su* rule3 #b4 ,?\gh x c\ld sc>cely belong to ,probability4 #c4 ,di/9ction betwe5 ,probability & ,induction4 #d1 #e4 ,impossibility ( r$uc+ ! v>i\s rules ( ! latt] "u "o head4 #f4 ,/atem5t ( ! ,rule ( ,succession2 #g4 ,pro( (f]$ = x4 #h4 ,is x a /rict rule ( inf]5ce8 #i4 ,or is x a psy*ological pr9ciple8 ,,*apt] ,,ix4 ,,induction4 #a-e4 ,/atem5t ( ! ,inductive problem1 & orig9 ( ! ,inductive inf]5ce4 #f4 ,relation ( ,probability to ,induction4 #g-i4 ,! two are sometimes m]g$ into "o4 #aj4 ,ext5t to :i* causation is ne$$ 9 ,probability4 #aa-ac4 ,difficulty ( ref]r+ an individual to a class3 #ad4 ,?is difficulty b slight 9 ,logic1 #ae1 #af4 ,b leads to p]plexity 9 ,probability3 #ag-ba4 ,mild =m ( ?is p]plexity2 #bb1 #bc4 ,s]i\s =m4 #bd-bg4 ,illu/ration f ,life ,insurance4 #bh1 #bi4 ,mean+ ( '! value ( a life'4 #cj1 #ca4 ,successive specialization ( ! classes to :i* objects are ref]r$4 #cb4 ,summ>y ( results4 ,,*apt] ,x4 ,,*ange1 ,,causation ,,& ,,design4 #a4 ,old ,!ological objection to ,*ance4 #b-d4 ,sci5tific v]sion ( ! same4 #e4 ,/ati/ics 9 ref]5ce to ,free-w4 #f-h4 ,inconclusiv5ess ( ! common argum5ts "h4 #i1 #aj4 ,*ance z oppos$ to ,physical ,causation4 #aa4 ,*ance z oppos$ to ,design 9 ! case ( num]ical con/ants4 #ab-ad4 ,!oretic solution betwe5 ,*ance & ,design4 #ae4 ,illu/ration f ! dim5sions ( ! ,pyramid4 #af1 #ag4 ,discussion ( c]ta9 difficulties "h4 #ah1 #ai4 ,illu/ration f ,psy*ical ,ph5om5a4 #bj4 ,arbu?nott's ,problem ( ! proportion ( ! sexes4 #ba-bc4 ,r&om or design$ di/ribution ( ! />s4 7,note on ! proportion ( ! sexes47 ,,*apt] ,,xi4 ,,mat]ial ,,& ,,=mal ,,logic4 #a1 #b4 ,broad di/9ction betwe5 ^! views2 #b1 #c4 ,difficulty ( adh]+ consi/5tly to ! objective view2 #d4 ,especially 9 ! case ( ,hypo!ses4 #e4 ,! d\btful /age ( our facts is only occasional 9 ,inductive ,logic4 #f-i4 ,b normal & p]man5t 9 ,probability4 #aj1 #aa4 ,consequ5t difficulty ( avoid+ ,conceptuali/ phraseology4 ,,*apt] ,,xii4 ,,consequ5ces ,,( ,,! ,,di/9ctions ,,( ,,! ,,previ\s ,,*apt]4 #a1 #b4 ,probability has no relation to "t4 #c1 #d4 ,butl] & ,mill on ,probability be=e & aft] ! ev5t4 #e4 ,o!r attempts at expla9+ ! difficulty4 #f-h4 ,:at is really meant by ! di/9ction4 #i4 ,orig9 ( ! common mi/ake4 #aj-ab4 ,examples 9 illu/ration ( ?is view1 #ac4 ,is ,probability relative8 #ad4 ,:at is really meant by ?is expression4 #ae4 ,objections to t]m+ ,probability relative4 #af1 #ag4 ,9 suitable examples ! difficulty sc>cely pres5ts itself4 ,,*apt] ,,xiii4 ,,on ,,modality4 #a4 ,v>i\s s5ses ( ,modality2 #b4 ,hav+ mo/ly "s relation to ,probability4 #c4 ,modality mu/ be recogniz$4 #d4 ,sometimes relegat$ to ! pr$icate1 #e1 #f4 ,sometimes incorrectly reject$ altoge!r4 #g1 #h4 ,common practical recognition ( x4 #i-aa4 ,modal propositions 9 ,logic & 9 ,probability4 #ab4 ,ari/otelian view ( ! ,modals2 #ac1 #ad4 ,f\nd$ on ext9ct philosophical views2 #ae4 ,b long & widely ma9ta9$4 #af4 ,kant's g5]al view4 #ag-ai4 ,! numb] ( modal divisions admitt$ by v>i\s logicians4 #bj4 ,influ5ce ( ! !ory ( ,probability4 #ba1 #bb4 ,modal syllogisms4 #bc4 ,popul> modal phraseology4 #bd-bf4 ,probable & ,dialectic syllogisms4 #bg1 #bh4 ,modal difficulties occur 9 ,jurisprud5ce4 #bi1 #cj4 ,propos$ /&>ds ( legal c]ta9ty4 #ca4 ,reject$ =mally 9 ,engli% ,law1 b possibly recogniz$ practically4 #cb4 ,h[1 if s1 x might be det]m9$4 ,,*apt] ,,xiv4 ,,fallacies4 #a-c4 7,i47 ,errors 9 judg+ ( ev5ts aft] !y h happ5$4 #d-g4 ,v v>i\s judgm5ts may be ?us involv$4 #h1 #i4 7,,ii47 ,confusion betwe5 r&om & pick$ selections4 #aj1 #aa4 7,,iii47 ,undue limitation ( ! notion ( ,probability4 #ab-af4 7,,iv47 ,d\ble or ,quits3 ! ,m>t+ale4 #ag1 #ah4 ,physical illu/ration4 #ai1 #bj4 7,v47 ,inadequate realization ( l>ge numb]s4 #ba-bd4 ,production ( works ( art by *ance4 #be4 ,illu/ration f doctr9e ( h]$ity4 #bf-cj4 7,,vi47 ,confusion betwe5 ,probability & ,induction4 #ca-cc4 7,,vii47 ,undue neglect ( small *ances4 #cd1 #ce4 7,,viii47 ,judg+ by ! ev5t 9 ,probability & 9 ,induction4 ,,"p ,,iii4 ,,v>i\s ,,applications ,,( ,,! ,,!ory ,,( ,,probability4 ,*h4 ,,xv-,,xix4 ,,*apt] ,,xv4 ,,insurance ,,& ,,gambl+4 #a1 #b4 ,! c]ta9ties & unc]ta9ties ( life4 #c-e4 ,insurance a means ( dim9i%+ ! unc]ta9ties4 #f1 #g4 ,gambl+ a means ( increas+ !m4 #h1 #i4 ,v>i\s =ms ( gambl+4 #aj1 #aa4 ,comp>ison betwe5 ^! practices4 #ab-ad4 ,pro(s ( ! disadvantage ( gambl+3-- 7#a7 on ari?metical gr\nds3 #ae1 #af4 ,illu/ration f family names4 #ag4 7#b7 f ! 'moral expectation'4 #ah1 #ai4 ,inconclusiv5ess ( ^! pro(s4 #bj-bb4 ,broad] que/ions rais$ by ^! attempts4 ,,*apt] ,,xvi4 ,,application ,,( ,,probability ,,to ,,te/imony4 #a1 #b4 ,d\btful applicability ( ,probability to te/imony4 #c4 ,conditions ( su* applicability4 #d4 ,reasons = ! above conditions4 #e1 #f4 ,are ^! conditions fulfill$ 9 ! case ( te/imony8 #g4 ,! appeal "h is n directly to /ati/ics4 #h1 #i4 ,illu/rations ( ! above4 #aj1 #aa4 ,is any application ( ,probability to te/imony valid8 ,,*apt] ,,xvii4 ,,cr$ibility ,,( ,,extraord9>y ,,/ories4 #a4 ,improbability be=e & aft] ! ev5t4 #b1 #c4 ,does ! rejection ( ?is lead to ! conclusion t ! cr$ibility ( a /ory is indep5d5t ( its nature8 #d4 ,g5]al & special cr$ibility ( a witness4 #e-h4 ,di/9ction betwe5 alt]native & op5 que/ions1 & ! usual rules = application ( te/imony to ea* ( ^!4 #i4 ,discussion ( an objection4 #aj1 #aa4 ,te/imony ( wor?less witnesses4 #ab-ad4 ,common practical ways ( reg>d+ su* problems4 #ae4 ,extraord9>y /ories n necess>ily less probable4 #af-ah4 ,mean+ ( ! t]m extraord9>y1 & its di/9ction f miracul\s4 #ai1 #bj4 ,comb9ation ( te/imony4 #ba1 #bb4 ,sci5tific mean+ ( a miracle4 #bc1 #bd4 ,two di/9ct prepossessions 9 reg>d to miracles1 & ! logical consequ5ces ( ^!4 #be4 ,difficulty ( discuss+ by our rules cases 9 :i* arbitr>y int]f]5ce c be po/ulat$4 #bf1 #bg4 ,consequ5t inappropriat5ess ( _m argum5ts4 ,,*apt] ,,xviii4 ,,on ,,! ,,nature ,,& ,,use ,,( ,,an ,,av]age1 ,,& ,,on ,,! ,,diff]5t ,,k9ds ,,( ,,av]age4 #a4 ,prelim9>y rude notion ( an av]age1 #b4 ,m precise quantitative notion1 yield+ 7#a7 ! ,ari?metical ,av]age1 #c4 7#b7 ! ,geometrical4 #d4 ,9 asymmetrical curves ( error ! ari?metic av]age mu/ be di/+ui%$ f1 #e4 7#c7 ! ,maximum ,ord9ate av]age1 #f4 7#d7 & ! ,m$ian4 #g4 ,diagram 9 illu/ration4 #h-aj4 ,av]age dep>ture f ! av]age1 consid]$ "u ! above heads1 & "u t ( #aa4 7#e7 ,! 7av]age (7 ,mean ,squ>e ( ,error1 #ab-ad4 ,! objects ( tak+ av]ages4 #ae4 ,mr ,galton's practical me?od ( det]m9+ ! av]age4 #af1 #ag4 ,no di/9ction betwe5 ! av]age & ! mean4 #ah-bj4 ,di/9ction betwe5 :at is necess>y & :at is exp]im5tal "h4 #ba1 #bb4 ,!oretical defects 9 ! det]m9ation ( ! 'errors'4 #bc4 ,practical escape f ^!4 7,note ab\t ! units 9 ! expon5tial equation & integral47 ,,*apt] ,,xix4 ,,! ,,!ory ,,( ,,! ,,av]age ,,z ,a ,,means ,,( ,,approximation ,,to ,,! ,,tru?4 #a-d4 ,g5]al indication ( ! problem3 i4e4 an inv]se "o requir+ ! previ\s consid]ation ( a direct "o4 ,i4 ,! direct problem3--giv5 ! c5tral value & law ( disp]sion ( ! s+le errors1 to det]m9e ^? ( ! av]ages4 #f-bj4 #f4 7i7 ,! law ( disp]sion may be det]m9able priori1 #g4 7ii7 or exp]im5tally1 by /ati/ics4 #h1 #i4 ,!nce to det]m9e ! modulus ( ! error curve4 #aj-ad4 ,num]ical example to illu/rate ! nature & am\nt ( ! contraction ( ! modulus ( ! av]age-error curve4 #ae4 ,?is curve is ( ! same g5]al k9d z t ( ! s+le errors2 #af4 ,equally symmetrical1 #ag1 #ah4 ,& m heap$ up t[>ds ! c5tre4 #ai1 #bj4 ,algebraic g5]alization ( ! =ego+ results4 ,,ii4 ,! inv]se problem3--giv5 b a few ( ! errors to det]m9e _! c5tre & law1 & !nce to draw ! above d$uctions4 #ba-be4 #bb1 #bc4 ,! actual calculations are ! same z be=e1 #bd4 ,) ! extra dem& t we mu/ det]m9e h[ probable are ! results4 #be4 ,summ>y4 ,,iii4 ,consid]ation ( ! same que/ions z appli$ to c]ta9 peculi> laws ( error4 #bf-cg4 #bf4 7i7 ,all errors equally probable4 #bg1 #bh4 7ii7 ,c]ta9 peculi> laws ( error4 #bi1 #cj4 ,fur!r analysis ( ! reasons = tak+ av]ages4 #ca-ce4 ,illu/rative examples4 #cf1 #cg4 ,curves ) d\ble c5tre & abs5ce ( symmetry4 #ch1 #ci4 ,conclusion4 ,,! ,,logic ,,( ,,*ance4 ,,*apt] ,i4 ,,on ,,c]ta9 ,,k9ds ,,( ,,gr\ps ,,or ,,s]ies ,,z ,,! ,,f\ndation ,,( ,,probability4 #a4 ,x is sometimes n easy to give a cle> def9ition ( a sci5ce at ! outset1 s z to set its scope & prov9ce be=e ! read] 9 a few words4 ,9 ! case ( ^? sci5ces :i* are m imm$iately & directly conc]n$ ) :at are t]m$ objects1 r ?an ) :at are t]m$ processes1 ?is difficulty is n inde$ s s]i\s4 ,if ! read] is already famili> ) ! objects1 a simple ref]5ce to !m w give him a tol]ably accurate idea ( ! direction & nature ( 8 /udies4 ,ev5 if he be n famili> ) !m1 !y w /ill be (t5 to "s ext5t connect$ & associat$ 9 8 m9d by a "n1 & ! m]e utt]ance ( ! "n may ?us convey a fair am\nt ( prelim9>y in=mation4 ,?is is m or less ! case ) _m ( ! natural sci5ces2 we c (t5 tell ! read] be=eh& exactly :at he is go+ to /udy4 ,b :5 a sci5ce is conc]n$1 n s mu* ) objects directly1 z ) processes & laws1 or :5 x takes = ! subject ( its enquiry "s comp>atively obscure feature drawn f ph5om5a :i* h little or no?+ else 9 common1 ! difficulty ( giv+ prelim9>y in=mation becomes great]4 ,recogniz$ classes ( objects h !n to be disreg>d$ & ev5 brok5 up1 & an entirely novel arrangem5t ( ! objects to be made4 ,9 su* cases x is ! /udy ( ! sci5ce t fir/ gives ! sci5ce its unity1 = till x is /udi$ ! objects ) :i* x is conc]n$ 7 probably nev] ?\ght ( toge!r4 ,"h a def9ition _c be giv5 at ! outset1 & ! process ( obta9+ x may become by comp>ison some:at labori\s4 ,! sci5ce ( ,probability1 at lea/ on ! view tak5 ( x 9 ! foll[+ pages1 is ( ?is latt] description4 ,! read] :o is at pres5t unacqua9t$ ) ! sci5ce _c be at once in=m$ ( its scope by a ref]5ce to objects ) :i* he is already famili>4 ,he w h to be tak5 9 h&1 z x 71 & "s little "t & tr\ble w h to be exp5d$ 9 direct+ 8 att5tion to our subject-matt] be=e he c be expect$ to "k x4 ,to d ?is w be our fir/ task4 #b4 ,9 /udy+ ,nature1 9 any =m1 we are cont9ually com+ into possession ( in=mation :i* we sum up 9 g5]al propositions4 ,n[ 9 v _m cases ^! g5]al propositions are nei!r m nor less c]ta9 & accurate ?an ! details :i* !y embrace & ( :i* !y are compos$4 ,we are assum+ at pres5t t ! tru? ( ^! g5]alizations is n disput$2 z a matt] ( fact !y may re/ on weak evid5ce1 or !y may be unc]ta9 f _! be+ widely ext5d$ by induction2 :at is meant is1 t :5 we resolve !m into _! compon5t p>ts we h precisely ! same assurance ( ! tru? ( ! details z we h ( t ( ! :ole4 ,:5 ,i "k1 = in/ance1 t all c[s rum9ate1 ,i feel j z c]ta9 t any p>ticul> c[ or c[s rum9ate z t ! :ole class does4 ,i may be "r or wrong 9 my orig9al /atem5t1 & ,i may h obta9$ x by any conceivable mode 9 :i* tru?s c be obta9$2 b :atev] ! value ( ! g5]al proposition may be1 t ( ! p>ticul>s is nei!r great] nor less4 ,! process ( inf]r+ ! p>ticul> f ! g5]al is n accompani$ by ! slighte/ dim9ution ( c]ta9ty4 ,if "o ( ^! 'imm$iate inf]5ces' is ju/ifi$ at all1 x w be equally "r 9 e case4 ,b x is by no means necess>y t ?is *>act]i/ic %\ld exi/ 9 all cases4 ,!re is a class ( imm$iate inf]5ces1 almo/ unrecogniz$ inde$ 9 logic1 b con/antly drawn 9 practice1 ( :i* ! *>act]i/ic is1 t z !y increase 9 p>ticul>ity !y dim9i% 9 c]ta9ty4 ,let me assume t ,i am told t "s c[s rum9ate2 ,i _c inf] logically f ?is t any p>ticul> c[ does s1 ?\gh ,i %\ld feel "s way remov$ f absolute disbelief1 or ev5 indiff]5ce to ass5t1 ^u ! subject2 b if ,i saw a h]d ( c[s ,i %\ld feel m sure t "s ( !m 7 rum9ant ?an ,i did ( ! s+le c[1 & my assurance w\ld increase ) ! numb]s ( ! h]d ab\t :i* ,i _h to =m an op9ion4 ,"h !n we h a class ( ?+s z to ! individuals ( :i* we feel q 9 unc]ta9ty1 :il/ z we embrace l>g] numb]s 9 our ass]tions we atta* great] weight to our inf]5ces4 ,x is ) su* classes ( ?+s & su* inf]5ces t ! sci5ce ( ,probability is conc]n$4 #c4 ,9 ! =ego+ rem>ks1 :i* are int5d$ to be purely prelim9>y1 we h n be5 able altoge!r to avoid "s ref]5ce to a subjective elem5t1 viz4 ! degree ( our c]ta9ty or belief ab\t ! ?+s :i* we are suppos$ to contemplate4 ,! read] may be aw>e t by "s writ]s ?is elem5t is reg>d$ z ! subject-matt] ( ! sci5ce4 ,h5ce x w h to be discuss$ 9 a future *apt]4 ,z h[ev] ,i d n agree ) ! op9ion ( ! writ]s j m5tion$1 at lea/ z reg>ds treat+ ?is elem5t z "o ( prim>y importance1 no fur!r allusion w be made to x "h1 b we w pass on at once to a m m9ute inve/igation ( t di/9ctive *>act]i/ic ( c]ta9 classes ( ?+s :i* 0 introduc$ to notice 9 ! la/ section4 ,9 ^! classes ( ?+s1 :i* are ^? ) :i* ,probability is conc]n$1 ! fundam5tal conception :i* ! read] has to fix 9 8 m9d z cle>ly z possible1 is1 ,i take x1 t ( a s]ies4 ,b x is a s]ies ( a peculi> k9d1 "o ( :i* no bett] comp5di\s description c be giv5 ?an t :i* is conta9$ 9 ! /atem5t t x comb9es individual irregul>ity ) aggregate regul>ity4 ,?is is a /atem5t :i* w probably ne$ "s explanation4 ,let u recur to an example ( ! k9d already allud$ to1 select+ "o :i* %all be 9 accordance ) exp]i5ce4 ,"s *ildr5 w n live to ?irty4 ,n[ if ?is proposition is to be reg>d$ z a purely indef9ite or1 z x w\ld be t]m$ 9 logic1 'p>ticul>' proposition1 no d\bt ! notion ( a s]ies does n obvi\sly pres5t itself 9 connection ) x4 ,x conta9s a /atem5t ab\t a c]ta9 unkn[n proportion ( ! :ole1 & t is all4 ,b x is n ) ^! purely indef9ite propositions t we %all be conc]n$4 ,let u suppose ! /atem5t1 on ! contr>y1 to be ( a num]ical "*1 & to ref] to a giv5 proportion ( ! :ole1 & we %all !n f9d x difficult to exclude ! notion ( a s]ies4 ,we %all f9d x1 ,i ?9k1 impossible to d s z soon z we set be=e u ! aim ( obta9+ accurate1 or ev5 mod]ately correct inf]5ces4 ,:at1 = in/ance1 is ! mean+ ( ! /atem5t t two new-born *ildr5 9 ?ree fail to atta9 ! age ( sixty-?ree8 ,x c]ta9ly does n decl>e t 9 any giv5 bat* (1 say1 ?irty1 we %all f9d j tw5ty t fail3 :atev] might be ! /rict mean+ ( ! words1 ?is is n ! import ( ! /atem5t4 ,x r contemplates our exam9ation ( a l>ge numb]1 ( a long succession ( in/ances1 & /ates t 9 su* a succession we %all f9d a num]ical proportion1 n inde$ fix$ & accurate at fir/1 b :i* t5ds 9 ! long run to become s4 ,9 e k9d ( example ) :i* we %all be conc]n$ we %all f9d ?is ref]5ce to a l>ge numb] or succession ( objects1 or1 z we %all t]m x1 s]ies ( !m4 ,a few additional examples may s]ve to make ?is pla94 ,let u suppose t we toss up a p5ny a great _m times2 ! results ( ! successive ?r[s may be conceiv$ to =m a s]ies4 ,! sep>ate ?r[s ( ?is s]ies seem to occur 9 utt] disord]2 x is ?is disord] :i* causes our unc]ta9ty ab\t !m4 ,sometimes head comes1 sometimes tail comes2 sometimes !re is a repetition ( ! same face1 sometimes n4 ,s long z we conf9e our obs]vation to a few ?r[s at a "t1 ! s]ies seems to be simply *aotic4 ,b :5 we consid] ! result ( a long succession we f9d a m>k$ di/9ction2 a k9d ( ord] beg9s gradually to em]ge1 & at la/ assumes a di/9ct & /rik+ aspect4 ,we f9d 9 ?is case t ! heads & tails occur 9 ab\t equal numb]s1 t simil> repetitions ( diff]5t faces d s also1 & s on4 ,9 a ^w1 not)/&+ ! individual disord]1 an aggregate ord] beg9s to prevail4 ,s aga9 if we are exam9+ ! l5g? ( human life1 ! diff]5t lives :i* fall "u our notice compose a s]ies pres5t+ ! same features4 ,! l5g? ( a s+le life is famili>ly unc]ta91 b ! av]age duration ( a bat* ( lives is becom+ 9 an almo/ equal degree famili>ly c]ta94 ,! l>g] ! numb] we take out ( any mix$ cr[d1 ! cle>] become ! symptoms ( ord]1 ! m ne>ly w ! av]age l5g? ( ea* select$ class be ! same4 ,^! few cases w s]ve z simple examples ( a prop]ty ( ?+s :i* c be trac$ almo/ ev]y:]e1 to a great] or less ext5t1 ?r\gh\t ! :ole field ( our exp]i5ce4 ,fires1 %ipwrecks1 yields ( h>ve/1 bir?s1 m>riages1 suicides2 x sc>cely seems to matt] :at feature we s+le out = obs]vation4#a ,! irregul>ity ( ! s+le in/ances dim9i%es :5 we take a l>ge numb]1 & at la/ seems = all practical purposes to disappe>4 ,9 speak+ ( ! effect ( ! av]age 9 ?us dim9i%+ ! irregul>ities :i* pres5t !mselves 9 ! details1 ! att5tion ( ! /ud5t mu/ be prom95tly direct$ to ! po9t1 t x is n ! absolute b ! relative irregul>ities :i* ?us t5d to dim9i% )\t limit4 ,?is idea w be famili> en\gh to ! ma!matician1 b to o!rs x may require "s reflection 9 ord] to grasp x cle>ly4 ,! absolute div]g5ces & irregul>ities1 s f> f dim9i%+1 %[ a disposition to increase1 & ?is 7x may be7 )\t limit1 ?\gh _! relative importance %[s a correspond+ disposition to dim9i% )\t limit4 ,?us 9 ! case ( toss+ a p5ny1 if we take a few ?r[s1 say t51 x is decid$ly unlikely t !re %\ld be a diff]5ce ( six betwe5 ! numb]s ( heads & tails2 t is1 t !re %\ld be z _m z eight heads & !re=e z few z two tails1 or vice v]s4 ,b take a ?\s& ?r[s1 & x becomes 9 turn exce$+ly likely t !re %\ld be z mu* z1 or m ?an1 a diff]5ce ( six betwe5 ! respective numb]s4 ,on ! o!r h& ! proportion ( heads to tails 9 ! case ( ! ?\s& ?r[s w be v mu* ne>] to unity1 9 mo/ cases1 ?an :5 we only took t54 ,9 o!r words1 ! long] a game ( *ance cont9ues ! l>g] are ! spells & runs ( luck 9 !mselves1 b ! less _! relative proportions to ! :ole am\nts involv$4 #d4 ,9 speak+ z above ( ev5ts or ?+s z to ! details ( :i* we "k little or no?+1 x is n ( c\rse impli$ t our ignorance ab\t !m is complete & univ]sal1 or1 :at comes to ! same ?+1 t irregul>ity may be obs]v$ 9 all _! qualities4 ,all t is meant is t !re are "s qualities or m>ks 9 !m1 ! exi/5ce ( :i* we are n able to pr$icate ) c]ta9ty 9 ! individuals4 ,) reg>d to all _! o!r qualities !re may be ! utmo/ uni=mity1 & consequ5tly ! mo/ complete c]ta9ty4 ,! irregul>ity 9 ! l5g? ( human life is notori\s1 b no "o d\bts ! exi/5ce ( su* organs z a he>t & bra9s 9 any p]son :om he happ5s to meet4 ,& ev5 9 ! qualities 9 :i* ! irregul>ity is obs]v$1 !re are (t51 inde$ g5]ally1 positive limits )9 :i* x w be f\nd to be conf9$4 ,no p]son1 = in/ance1 c calculate :at may be ! l5g? ( any p>ticul> life1 b we feel p]fectly c]ta9 t x w n /ret* out to #aej ye>s4 ,! irregul>ity ( ! individual in/ances is only %[n 9 c]ta9 respects1 z e4g4 ! l5g? ( ! life1 & ev5 9 ^! respects x has its limits4 ,! same rem>k w apply to mo/ ( ! o!r examples ) :i* we %all be conc]n$4 ,! disord] 9 fact is n univ]sal & unlimit$1 x only prevails 9 c]ta9 directions & up to c]ta9 po9ts4 #e4 ,9 speak+ z above ( a s]ies1 x w h>dly be necess>y to po9t out t we d n imply t ! objects !mselves :i* compose ! s]ies mu/ occur successively 9 "t2 ! s]ies may be =m$ simply by _! com+ 9 succession "u our notice1 :i* z a matt] ( fact !y may d 9 any ord] :atev]4 ,a regi/] ( mortality1 = in/ance1 may be made up ( dea?s :i* took place simultane\sly or successively2 or1 we might if we pleas$ arrange ! dea?s 9 an ord] q di/9ct f ei!r ( ^!4 ,?is is entirely a matt] ( indiff]5ce2 9 all ^! cases ! s]ies1 = any purposes :i* we ne$ take into acc\nt1 may be reg>d$ z be+ ( precisely ! same description4 ,! objects1 be x rememb]$1 are giv5 to u 9 nature2 ! ord] "u :i* we view !m is our own private arrangem5t4 ,?is is m5tion$ "h simply by way ( caution1 ! mean+ ( ?is ass]tion w become m pla9 9 ! sequel4 ,i am aw>e t ! ^w 's]ies' 9 ! application ) :i* x is us$ "h is liable to "s miscon/ruction1 b ,i _c f9d any bett] ^w1 or inde$ any z suitable 9 all respects4 ,z rem>k$ above1 ! ev5ts ne$ n necess>ily h occurr$ 9 a regul> sequ5ce ( "t1 ?\gh !y (t5 w h done s4 ,9 _m cases 7= in/ance1 ! ?r[s ( a p5ny or a die7 !y really d occur 9 succession2 9 o!r cases 7= in/ance1 ! heights ( m51 or ! duration ( _! lives71 :atev] may h be5 ! ord] ( _! actual occurr5ce1 !y are commonly br\ght "u our notice 9 succession by be+ arrang$ 9 /ati/ical tables4 ,9 all cases alike our processes ( inf]5ce involve ! necessity ( exam9+ "o aft] ano!r ( ! memb]s :i* compose ! gr\p1 or at lea/ ( be+ prep>$ to d ?is1 if we are to be 9 a position to ju/ify our inf]5ces4 ,! =ce ( ^! consid]ations w come out 9 ! c\rse ( ! inve/igation 9 ,*apt] ,,vi4 ,! late ,leslie ,ellis#b has express$ :at seems to me a sub/antially simil> view 9 t]ms ( g5us & species1 in/ead ( speak+ ( a s]ies4 ,he says1 ,:5 individual cases are consid]$1 we h no conviction t ! ratios ( frequ5cy ( occurr5ce dep5d on ! circum/ances common to all ! trials4 ,on ! contr>y1 we recognize 9 ! det]m9+ circum/ances ( _! occurr5ce an extrane\s elem5t1 an elem5t1 t is1 extrane\s to ! idea ( ! g5us & species4 ,cont+5cy & limitation come 9 7s to speak7 toge!r2 & bo? alike disappe> :5 we consid] ! g5us 9 its entirety1 or 7:i* is ! same ?+7 9 :at may be call$ an ideal & practically impossible realization ( all :i* x pot5tially conta9s4 ,if ?is be grant$1 x seems to foll[ t ! fundam5tal pr9ciple ( ! ,!ory ( ,probabilities may be reg>d$ z includ$ 9 ! foll[+ /atem5t1--,! conception ( a g5us implies t ( num]ical relations among ! species subord9at$ to x4 ,z rem>k$ above1 ?is appe>s a sub/antially simil> doctr9e to t expla9$ 9 ?is *apt]1 b ,i d n ?9k t ! t]ms g5us & species are by any means s well fitt$ to br+ out ! conception ( a t5d5cy or limit z :5 we speak ( a s]ies1 & ,i !re=e mu* pref] ! latt] expression4 #f4 ,! read] w n[ h 9 8 m9d ! conception ( a s]ies or gr\p ( ?+s or ev5ts1 ab\t ! individuals ( :i* we "k b little1 at lea/ 9 c]ta9 respects1 :il/ we f9d a cont9ually increas+ uni=mity z we take l>g] numb]s "u our notice4 ,?is is def9ite en\gh to po9t out tol]ably cle>ly ! k9d ( ?+s ) :i* we h to deal1 b x is n suffici5tly def9ite = purposes ( accurate ?\ght4 ,we mu/ !re=e attempt a some:at clos] analysis4 ,!re are c]ta9 phrases s commonly adopt$ z to h become "p ( ! te*nical vocabul>y ( ! subject1 su* z an 'ev5t' & ! 'way 9 :i* x c happ54' ,?us ! act ( ?r[+ a p5ny w\ld be call$ an ev5t1 & ! fact ( its giv+ head or tail w\ld be call$ ! way 9 :i* ! ev5t happ5$4 ,if we 7 discuss+ tables ( mortality1 ! =m] t]m w\ld d5ote ! m]e fact ( dea?1 ! latt] ! age at :i* x occurr$1 or ! way 9 :i* x 0 br\ght ab\t1 or :atev] else 9 x might be ! p>ticul> circum/ance "u discussion4 ,?is phraseology is v conv5i5t1 & w (t5 be made use ( 9 ?is "w1 b )\t explanation x may lead to confusion4 ,= 9 _m cases ! way 9 :i* ! ev5t happ5s is ( su* great relative importance1 t accord+ z x happ5s 9 "o way or ano!r ! ev5t w\ld h a diff]5t "n2 9 o!r words1 x w\ld n 9 ! two cases be nom9ally ! same ev5t4 ,! phrase !re=e w h to be consid]ably /ret*$ be=e x w conv5i5tly cov] all ! cases to :i* we may h to apply x4 ,if = in/ance we 7 contemplat+ a s]ies ( human be+s1 male & female1 x w\ld s\nd odd to call _! humanity an ev5t1 & _! sex ! way 9 :i* ! ev5t happ5$4 ,if we recur h[ev] to any ( ! classes ( objects already ref]r$ to1 we may see our pa? t[>ds obta9+ a m accurate conception ( :at we want4 ,x w easily be se5 t 9 e "o ( !m !re is a mixture ( simil>ity & dissimil>ity2 !re is a s]ies ( ev5ts :i* h a c]ta9 numb] ( features or attributes 9 common1--)\t ?is !y w\ld n be class$ toge!r4 ,b !re is also a di/9ction exi/+ among/ !m2 a c]ta9 numb] ( o!r attributes are to be f\nd 9 "s & are n to be f\nd 9 o!rs4 ,9 o!r words1 ! individuals :i* =m ! s]ies are comp\nd1 ea* be+ made up ( a collection ( ?+s or attributes2 "s ( ^! ?+s exi/ 9 all ! memb]s ( ! s]ies1 o!rs are f\nd 9 "s only4 ,s f> !re is no?+ peculi> to ! sci5ce ( ,probability2 t 9 :i* ! di/9ctive *>act]i/ic consi/s is ?is2--t ! occasional attributes1 z di/+ui%$ f ! p]man5t1 are f\nd on an ext5d$ exam9ation to t5d to exi/ 9 a c]ta9 def9ite proportion ( ! :ole numb] ( cases4 ,we _c tell 9 any giv5 in/ance :e!r !y w be f\nd or n1 b z we g on exam9+ m cases we f9d a gr[+ uni=mity4 ,we f9d t ! proportion ( in/ances 9 :i* !y are f\nd to in/ances 9 :i* !y are want+1 is gradually subject to less & less comp>ative v>iation1 & approa*es cont9ually t[>ds "s app>5tly fix$ value4 ,! above is ! mo/ compreh5sive =m ( description2 z a matt] ( fact ! gr\ps w 9 _m cases take a f> simpl] =m2 !y may appe>1 e4g4 simply z a succession ( ?+s ( ! same k9d1 say human be+s1 ) or )\t an occasional attribute1 say t ( be+ left-h&$4 ,we are us+ ! ^w attribute1 ( c\rse1 9 its wide/ s5se1 int5d+ x to include e di/9ctive feature t c be obs]v$ 9 a ?+1 f ess5tial qualities d[n to ! m]e/ accid5ts ( "t & place4 #g4 ,on exam9+ our s]ies1 !re=e1 we %all f9d t x may be/ be conceiv$1 n necess>ily z a succession ( ev5ts happ5+ 9 diff]5t ways1 b z a succession ( gr\ps ( ?+s4 ,^! gr\ps1 on be+ analys$1 are f\nd 9 e case to be resolvable into collections ( sub/ances & attributes4 ,t :i* gives its unity to ! succession ( gr\ps is ! fact ( "s ( ^! sub/ances or attributes be+ common to ! :ole succession2 t :i* gives _! di/9ction to ! gr\ps 9 ! succession is ! fact ( "s ( !m conta9+ only a portion ( ^! sub/ances & attributes1 ! o!r portion or portions be+ occasionally abs5t4 ,s und]/ood1 our phraseology may be made to embrace e class ( ?+s ( :i* ,probability c take acc\nt4 #h4 ,x w be easily se5 t ! ord9>y expression 7viz4 ! 'ev5t1' & ! 'way 9 :i* x happ5s'7 may be includ$ 9 ! above4 ,:5 ! occasional attributes are unimportant ! p]man5t ones are suffici5t to fix & appropriate ! "n1 ! pres5ce or abs5ce ( ! o!rs be+ simply d5ot$ by "s modification ( ! "n or ! addition ( "s pr$icate4 ,we may !re=e 9 all su* cases speak ( ! collection ( attributes z '! ev5t1'--! same ev5t ess5tially1 t is--only say+ t x 7s z to pres]ve its nom9al id5tity7 happ5s 9 diff]5t ways 9 ! diff]5t cases4 ,:5 ! occasional attributes h[ev] are important1 or compose ! majority1 ?is way ( speak+ becomes less appropriate2 language is some:at /ra9$ by our imply+ t two extremely diff]5t assemblages are 9 reality ! same ev5t1 ) a diff]5ce only 9 its mode ( happ5+4 ,! phrase is h[ev] a v conv5i5t "o1 & ) ?is caution aga9/ its be+ misund]/ood1 x w frequ5tly be made use ( "h4 #i4 ,a s]ies ( ! above-m5tion$ k9d is1 ,i appreh5d1 ! ultimate basis ^u :i* all ! rules ( ,probability mu/ be bas$4 ,x is ess5tial to a cle> compreh5sion ( ! subject to h c>ri$ our analysis up to ?is po9t1 b any attempt at fur!r analysis into ! intimate nature ( ! ev5ts compos+ ! s]ies1 is n requir$4 ,x is altoge!r unnecess>y1 = in/ance1 to =m any op9ion ^u ! que/ions discuss$ 9 metaphysics z to ! indep5d5t exi/5ce ( sub/ances4 ,we h discov]$1 on exam9ation1 a s]ies compos$ ( gr\ps ( sub/ances & attributes1 or ( attributes alone4 ,at su* a s]ies we /op1 & !nce inve/igate our rules ( inf]5ce2 into :at ^! sub/ances or attributes w\ld !mselves be ultimately analys$1 if tak5 9 h& by ! psy*ologi/ or metaphysician1 x is no bus9ess ( ours to enquire "h4 #aj4 ,! /age !n :i* we h n[ rea*$ is t ( hav+ discov]$ a quantity ( ?+s 7!y prove on analysis to be gr\ps ( ?+s7 :i* are capable ( be+ classifi$ toge!r1 & are be/ reg>d$ z con/itut+ a s]ies4 ,! di/9ctive peculi>ity ( ?is s]ies is our f9d+ 9 x an ord]1 gradually em]g+ out ( disord]1 & %[+ 9 "t a m>k$ & unmi/akeable uni=mity4 ,! impression :i* may possibly be d]iv$ f ! description ( su* a s]ies1 & :i* ! read] w probably already ent]ta9 if he h /udi$ ,probability be=e1 is t ! gradual evolution ( ?is ord] is indef9ite1 & its approa* !re=e to p]fection unlimit$4 ,& _m ( ! examples commonly select$ c]ta9ly t5d to confirm su* an impression4 ,b 9 ref]5ce to ! !ory ( ! subject x is1 ,i am conv9c$1 an error1 & "o liable to lead to mu* confusion4 ,! l9es :i* h be5 prefix$ z a motto to ?is "w1 ,s c>eful ( ! type %e seems1 s c>eless ( ! s+le life1 are soon aft] correct$ by ! ass]tion t ! type itself1 if we reg>d x = a long "t1 *anges1 & !n vani%es & is succe$$ by o!rs4 ,s 9 ,probability2 t uni=mity :i* is f\nd 9 ! long run1 & :i* pres5ts s great a contra/ to ! individual disord]1 ?\gh durable is n ev]la/+4 ,keep on wat*+ x long en\gh1 & x w be f\nd almo/ inv>iably to fluctuate1 & 9 "t may prove z utt]ly irr$ucible to rule1 & !re=e z incapable ( pr$iction1 z ! individual cases !mselves4 ,! full be>+ ( ?is fact ^u ! !ory ( ! subject1 & ^u c]ta9 common modes ( calculation connect$ ) x1 w appe> m fully 9 "s ( ! foll[+ *apt]s2 at pres5t we w conf9e ourselves to v briefly e/abli%+ & illu/rat+ x4 ,let u take1 = example1 ! av]age duration ( life4 ,?is1 provid$ our data are suffici5tly ext5sive1 is kn[n to be tol]ably regul> & uni=m4 ,?is fact has be5 already indicat$ 9 ! prec$+ sections1 & is a tru? inde$ ( :i* ! popul> m9d has a tol]ably cle> grasp at ! pres5t day4 ,b a v little consid]ation w %[ t !re may be a sup]ior z well z an inf]ior limit to ! ext5t )9 :i* ?is uni=mity c be obs]v$2 9 o!r words :il/ we may fall into error by tak+ too few in/ances we may also fail 9 our aim1 ?\gh 9 a v diff]5t way & f q diff]5t reasons1 by tak+ too _m4 ,at ! pres5t "t ! av]age duration ( life 9 ,engl& may be1 say1 =ty ye>s2 b a c5tury ago x 0 decid$ly less2 sev]al c5turies ago x 0 presumably v mu* less2 :il/ if we possess$ /ati/ics ref]r+ to a /ill e>li] population ( ! c\ntry we %\ld probably f9d t !re has be5 s9ce t "t a /ill m m>k$ improvem5t4 ,:at may be ! future t5d5cy no man c say = c]ta94 ,x may be1 & we hope t x w be ! case1 t ow+ to sanit>y & o!r improvem5ts1 ! duration ( life w g on increas+ /eadily2 x is at lea/ conceivable1 ?\gh d\btless incr$ible1 t x %\ld d s )\t limit4 ,on ! o!r h&1 & ) mu* m likelihood1 ?is duration might gradually t5d t[>ds "s fix$ l5g?4 ,or1 aga91 x is p]fectly possible t future g5]ations might pref] a %ort & a m]ry life1 & !re=e r$uce _! av]age longevity4 ,! duration ( life _c b dep5d to "s ext5t ^u ! g5]al ta/es1 habits & employm5ts ( ! p1 t is ^u ! ideal :i* !y consci\sly or unconsci\sly set be=e !m1 & he w\ld be a ra% man :o %\ld und]take to pr$ict :at ?is ideal w be "s c5turies h5ce4 ,all t x is "h necess>y h[ev] to indicate is1 t ?is p>ticul> uni=mity 7z we h hi!rto call$ x1 9 ord] to m>k its relative "*7 has v>i$1 &1 "u ! influ5ce ( future eddies 9 op9ion & practice1 may v>y /ill2 & ?is to any ext5t1 & ) any degree ( irregul>ity4 ,to borr[ a t]m f ,a/ronomy1 we f9d our uni=mity subject to :at might be call$ an irregul> secul> v>iation4 #aa4 ,! above is a fair typical in/ance4 ,if we _h tak5 a less simple feature ?an ! l5g? ( life1 or "o less closely connect$ ) :at may be call$ by comp>ison ! great p]man5t uni=mities ( nature1 we %\ld h f\nd ! peculi>ity "u notice exhibit$ 9 a f> m /rik+ degree4 ,! dea?s f small-pox1 = example1 or ! in/ances ( duell+ or accusations ( wit*craft1 if exam9$ dur+ a few successive decades1 might h %[n a v tol]able degree ( uni=mity4 ,b ^! uni=mities h ris5 possibly f z]o2 aft] v>i\s & v great fluctuations seem t5d+ t[>ds z]o aga91 at lea/ 9 ?is c5tury2 & may1 = any?+ we "k1 und]go /ill m rapid fluctuations 9 future4 ,n[ ^! examples mu/ be reg>d$ z be+ only extreme ones1 & n su* v extreme ones1 ( :at is ! almo/ univ]sal rule 9 nature4 ,i %all endeav\r to %[ t ev5 ! few app>5t exceptions1 su* z ! proportions betwe5 male & female bir?s1 c41 may n be1 & probably 9 reality are n1 /rictly speak+1 exceptions4 ,a type1 t is1 :i* %all be 9 ! fulle/ s5se ( ! words1 p]si/5t & inv>iable is sc>cely to be f\nd 9 nature4 ,! full import ( ?is conclusion w be se5 9 future *apt]s4 ,att5tion is only direct$ "h to ! important inf]5ce t1 al?\gh /ati/ics are notori\sly ( no value unless !y are 9 suffici5t numb]s1 yet x does n foll[ b t 9 c]ta9 cases we may h too _m ( !m4 ,if !y are made too ext5sive1 !y may aga9 fall %ort1 at lea/ = any p>ticul> "t or place1 ( _! greate/ atta9able accuracy4 #ab4 ,^! natural uni=mities !n are f\nd at l5g? to be subject to fluctuation4 ,n[ contra/ ) !m any ( ! uni=mities af=d$ by games ( *ance2 ^! latt] seem to %[ no trace ( secul> fluctuation1 h[ev] long we may cont9ue our exam9ation ( !m4 ,criticisms w be (f]$1 9 ! c\rse ( ! foll[+ *apt]s1 ^u "s ( ! common attempts to prove priori t !re mu/ be ?is fixity 9 ! uni=mity 9 "q1 b ( its exi/5ce !re c sc>cely be mu* d\bt4 ,p5ce give heads & tails ab\t equally (t5 n[1 z !y did :5 !y 7 fir/ toss$1 & z we believe !y w cont9ue to d1 s long z ! pres5t ord] ( ?+s cont9ues4 ,! fixity ( ^! uni=mities may n be z absolute z is commonly suppos$1 b no am\nt ( exp]i5ce :i* we ne$ take into acc\nt is likely 9 any appreciable degree to int]f]e ) !m4 ,h5ce ! obvi\s contra/1 t1 :]eas natural uni=mities at l5g? fluctuate1 ^? af=d$ by games ( *ance seem fix$ = ev]4 #ac4 ,"h !n are s]ies app>5tly ( two diff]5t k9ds4 ,!y are alike 9 _! initial irregul>ity1 alike 9 _! subsequ5t regul>ity2 x is 9 :at we may t]m _! ultimate =m t !y beg9 to div]ge f ea* o!r4 ,! "o t5ds )\t any irregul> v>iation t[>ds a fix$ num]ical proportion 9 its uni=mity2 9 ! o!r ! uni=mity is f\nd at la/ to fluctuate1 & to fluctuate1 x may be1 9 a mann] utt]ly irr$ucible to rule4 ,z ?is *apt] is int5d$ to be little m ?an explanatory & illu/rative ( ! f\ndations ( ! sci5ce1 ! rem>k may be made "h 7= :i* subsequ5t ju/ification w be (f]$7 t x is 9 ! case ( s]ies ( ! =m] k9d only t we are able to make any?+ :i* c be int]pret$ into /rict sci5tific inf]5ces4 ,we %all be able h[ev] 9 a g5]al way to see ! k9d & ext5t ( error t w\ld be committ$ if1 9 any example1 we 7 to sub/itute an imag9>y s]ies ( ! =m] k9d = any actual s]ies ( ! latt] k9d :i* exp]i5ce may pres5t to u4 ,! two s]ies are ( c\rse to be z alike z possible 9 all respects1 except t ! v>iable uni=mity has be5 replac$ by a fix$ "o4 ,! diff]5ce !n betwe5 !m w\ld n appe> 9 ! initial /age1 = 9 t /age ! di/9ctive *>act]i/ics ( ! s]ies ( ,probability are n app>5t2 all is !re irregul>ity1 & x w\ld be z impossible to %[ t !y 7 alike z t !y 7 diff]5t2 we c only say g5]ally t ea* %[s ! same k9d ( irregul>ity4 ,nor w\ld x appe> 9 ! next subsequ5t /age1 = ! real v>iability ( ! uni=mity has n = "s "t scope to make itself p]ceiv$4 ,x w\ld only be 9 :at we h call$ ! ultimate /age1 :5 we suppose ! s]ies to ext5d = a v long "t1 t ! diff]5ce w\ld beg9 to make itself felt4#c ,! proportion ( p]sons1 = example1 :o die ea* ye> at ! age ( six mon?s is1 :5 ! numb]s exam9$ are on a small scale1 utt]ly irregul>2 x becomes h[ev] regul> :5 ! numb]s exam9$ are on a l>g] scale2 b if we cont9u$ our obs]vation = a v great l5g? ( "t1 or ov] a v great ext5t ( c\ntry1 we %\ld f9d ?is regul>ity itself *ang+ 9 an irregul> way4 ,! sub/itution j m5tion$ is really equival5t to say+1 ,let u assume t ! regul>ity is fix$ & p]man5t4 ,x is mak+ a hypo!sis :i* may n be altoge!r consi/5t ) fact1 b :i* is =c$ ^u u = ! purpose ( secur+ precision ( /atem5t & def9ition4 #ad4 ,! full mean+ & be>+ ( su* a sub/itution w only become app>5t 9 "s ( ! subsequ5t *apt]s1 b x may be po9t$ out at once t x is 9 ?is way only t we c ) p]fect /rictness introduce ! notion ( a 'limit' into our acc\nt ( ! matt]1 at any rate 9 ref]5ce to _m ( ! applications ( ! subject to purely /ati/ical enquiries4 ,we say t a c]ta9 proportion beg9s to prevail among ! ev5ts 9 ! long run2 b !n on look+ clos] at ! facts we f9d t we h to express ourselves hypo!tically1 & to say t if pres5t circum/ances rema9 z !y are1 ! long run w %[ its *>act]i/ics )\t di/urbance4 ,:51 z is (t5 ! case1 we "k no?+ accurately ( ! circum/ances by :i* ! succession ( ev5ts is br\ght ab\t1 b h /rong reasons to suspect t ^! circum/ances are likely to und]go "s *ange1 !re is really no?+ else to be done4 ,we c only introduce ! conception ( a limit1 t[>ds :i* ! numb]s are t5d+1 by assum+ t ^! circum/ances d n *ange2 9 o!r words1 by sub/itut+ a s]ies ) a fix$ uni=mity = ! actual "o ) ! v>y+ uni=mity4#d #ae4 ,if ! read] w /udy ! foll[+ example1 "o well kn[n to ma!maticians "u ! "n ( ! ,pet]sburg#e problem1 he w f9d t x s]ves to illu/rate sev]al ( ! consid]ations m5tion$ 9 ?is *apt]4 ,x s]ves especially to br+ out ! facts t ! s]ies ) :i* we are conc]n$ mu/ be reg>d$ z indef9itely ext5sive 9 po9t ( numb] or duration2 & t :5 s reg>d$ c]ta9 s]ies1 b c]ta9 s]ies only 7! "o 9 "q be+ a case 9 po9t71 take advantage ( ! indef9ite range to keep on produc+ individuals 9 x ^: deviation f ! previ\s av]age has no f9ite limit :atev]4 ,:5 rightly view$ x is a v simple problem1 b x has giv5 rise1 at "o "t or ano!r1 to a good deal ( confusion & p]plexity4 ,! problem may be /at$ ?us3--a p5ny is toss$ up2 if x gives head ,i receive "o p\nd2 if heads twice runn+ two p\nds2 if heads ?ree times runn+ f\r p\nds1 & s on2 ! am\nt to be receiv$ d\bl+ e "t t a fre% head succe$s4 ,t is1 ,i am to g on z long z x cont9ues to give a succession ( heads1 to reg>d ?is succession z a 'turn' or set1 & !n take ano!r turn1 & s on2 & = ea* su* turn ,i am to receive a paym5t2 ! occurr5ce ( tail be+ und]/ood to yield no?+1 9 fact be+ omitt$ f our consid]ation4 ,h[ev] _m times head may be giv5 9 succession1 ! numb] ( p\nds ,i may claim is f\nd by rais+ two to a p[] "o less ?an t numb] ( times4 ,"h !n is a s]ies =m$ by a succession ( ?r[s4 ,we w assume1--:at _m p]sons w consid] to admit ( demon/ration1 & :at c]ta9ly exp]i5ce confirms )9 consid]able limits1--t ! r>ity ( ^! 'runs' ( ! same face is 9 direct proportion to ! am\nt ,i receive = !m :5 !y d occur4 ,9 o!r words1 if we reg>d only ! occasions on :i* ,i receive paym5ts1 we %all f9d t e o!r "t ,i get "o p\nd1 once 9 f\r times ,i get two p\nds1 once 9 eight times f\r p\nds1 & s on )\t any end4 ,! "q is !n ask$1 :at ought ,i to pay = ?is privilege8 ,at ! risk ( a slight anticipation ( ! results ( a subsequ5t *apt]1 we may assume t ?is is equival5t to ask+1 :at am\nt paid ea* "t w\ld on ! av]age leave me nei!r w9n] nor los]8 ,9 o!r words1 :at is ! av]age am\nt ,i %\ld receive on ! above t]ms8 ,!ory pron\nces t ,i ought to give an inf9ite sum3 t is1 no f9ite sum1 h[ev] great1 w\ld be an adequate equival5t4 ,& ?is is really q intelligible4 ,!re is a s]ies ( indef9ite l5g? be=e me1 & ! long] ,i cont9ue to "w x ! ri*] are my returns1 & ?is )\t any limit :atev]4 ,x is true t ! v ri* hauls are extremely r>e1 b /ill !y d come1 & :5 !y come !y make x up by _! great] ri*ness4 ,on e occasion on :i* p h devot$ !mselves to ! pursuit 9 "q1 !y made acqua9tance1 ( c\rse1 ) b a limit$ portion ( ?is s]ies2 b ! s]ies on :i* we base our calculation is unlimit$2 & ! inf]5ces usually drawn z to ! sum :i* ought 9 ! long run to be paid = ! privilege 9 "q are 9 p]fect accordance ) ?is supposition4 ,! common =m ( objection is giv5 9 ! reply1 t s f> f pay+ an inf9ite sum1 no s5sible man w\ld give any?+ approa*+ to #ej = su* a *ance4 ,probably n1 because no man w\ld see en\gh ( ! s]ies to make x wor? 8 :ile4 ,:at mo/ p]sons =m _! practical op9ion ^u1 is su* small portions ( ! s]ies z !y h actually se5 or c reasonably expect4 ,n[ 9 any su* portion1 say "o :i* embraces #ajj turns1 ! longe/ succession ( heads w\ld n am\nt on ! av]age to m ?an sev5 or eight4 ,?is is obs]v$1 b x is =gott5 t ! =mula :i* produc$ ^!1 w\ld1 if x _h great] scope1 keep on produc+ bett] & bett] ones )\t any limit4 ,h5ce x arises t "s p]sons are p]plex$1 because ! conduct !y w\ld adopt1 9 ref]5ce to ! curtail$ portion ( ! s]ies :i* !y are practically likely to meet )1 does n f9d its ju/ification 9 inf]5ces :i* are necess>ily bas$ ^u ! s]ies 9 ! complet5ess ( its inf9itude4 #af4 ,?is w be m cle>ly se5 by consid]+ ! v>i\s possibilities1 & ! scope requir$ 9 ord] to exhau/ !m1 :5 we conf9e ourselves to a limit$ numb] ( ?r[s4 ,beg9 ) ?ree4 ,?is yields eight equally likely possibilities4 ,9 f\r ( ^! cases ! ?r[] />ts ) tail & !re=e loses3 9 two he ga9s a s+le po9t 7i4e4 #a72 9 "o he ga9s two po9ts1 & 9 "o he ga9s f\r po9ts4 ,h5ce 8 total ga9 be+ eight p\nds a*iev$ 9 f\r diff]5t cont+5cies1 8 av]age ga9 w\ld be two p\nds4 ,n[ suppose he be all[$ to g z f> z n ?r[s1 s t we h to contemplate #bn possibilities4 ,all ( ^! h to be tak5 into acc\nt if we wi% to consid] :at happ5s on ! av]age4 ,x w readily be se5 t1 :5 all ! possible cases h be5 reckon$ once1 8 total ga9 w be 7reckon$ 9 p\nds71 #bn-#b #bn-#cb #bn-#dbb 444 #bbn-#c #bn-#b #bn-#a1 viz4 7n #a7 #bn-#b4 ,?is be+ spread ov] #bn-#a diff]5t occasions ( ga9 8 av]age ga9 w be #a_/b 7n #a74 ,n[ :5 we are ref]r+ to av]ages x mu/ be rememb]$ t ! m9imum numb] ( diff]5t occurr5ces necess>y 9 ord] to ju/ify ! av]age is t :i* enables ea* ( !m to pres5t itself once4 ,a man proposes to /op %ort at a succession ( t5 heads4 ,well & good4 ,we tell him t 8 av]age ga9 w be #e4 #ajs4 #j;d43 b we also impress ^u him t 9 ord] to ju/ify ?is /atem5t he mu/ comm5ce to toss at lea/ #ajbd times1 = 9 no less numb] c all ! cont+5cies ( ga9 & loss be exhibit$ & balanc$4 ,if he proposes to rea* an av]age ga9 ( #bj1 he w require to be prep>$ to g up to #ci ?r[s1 ,to ju/ify ?is paym5t he mu/ comm5ce to ?r[ #bci times1 i4e4 ab\t a million million times4 ,n be=e he has accompli%$ ?is w he be 9 a position to prove to any sceptic t ?is is ! true av]age value ( a 'turn' ext5d+ to #ci successive tosses4 ,( c\rse if he elects to toss to all et]nity we mu/ adopt ! l9e ( explanation :i* alone is possible :]e que/ions ( inf9ity 9 respect ( numb] & magnitude are involv$4 ,we _c tell him to pay d[n 'an inf9ite sum1' = ?is has no /rict mean+4 ,b we tell him t1 h[ev] mu* he may cons5t to pay ea* "t runs ( heads occur1 he w atta9 at la/ a /age 9 :i* he w h won back 8 total paym5ts by 8 total receipts4 ,h[ev] l>ge n may be1 if he p]sev]es 9 try+ #bn times he may h a true av]age receipt ( #a_/b 7n #a7 p\nds1 & if he cont9ues long en\gh onw>ds he w h x4 ,! problem w recur = consid]ation 9 a future *apt]4 #a4 ,! foll[+ /ati/ics w give a fair idea ( ! wide range ( exp]i5ce ov] :i* su* regul>ity is f\nd to exi/3 ,z illu/rations ( equal am\nts ( fluctuation f totally dissimil> causes1 take ! dea?s 9 ! ,we/ di/rict ( ,london 9 sev5 ye>s 7fluctuation #ac4ff71 & (f5ces aga9/ ! p]son 7fluctuation #ac4fa72 or dea?s f apoplexy 7fluctuation #e4ed71 & (f5ces aga9/ prop]ty1 )\t viol5ce 7fluctuation #e4dh72 or /ud5ts regi/]$ at ! ,college ( ,surgeons 7fluctuation #a4he71 & ! numb] ( p\nds ( manufactur$ tobacco tak5 = home consumption 7fluctuation #a4hi72 or out-door paup]s 7fluctuation #c4de7 & tonnage ( ,briti% vessels ent]$ 9 balla/ 7fluctuation #c4dc71 c4 ,extract$ f a pap] 9 ! ,j\rnal ( ! ,/ati/ical ,society1 by ,mr ,guy1 ,m>*1 #aheh2 ! 'fluctuation' "h giv5 is a measure ( ! am\nt ( irregul>ity1 t is ( dep>ture f ! av]age1 e/imat$ 9 a way :i* w be describ$ h]eaft]4 #b4 ,transactions ( ! ,cambridge ,philosophical ,society1 ,vol4 ,,ix4 p4 #fje4 ,repr9t$ 9 ! collect$ edition ( 8 writ+s1 p4 #ej4 #c4 ,we might express x ?us3--a few in/ances are n suffici5t to display a law at all2 a consid]able numb] w suffice to display x2 b x takes a v great numb] to e/abli% t a *ange is tak+ place 9 ! law4 #d4 ,! ma!matician may illu/rate ! nature ( ?is sub/itution by ! analogies ( ! 'circle ( curvature' 9 geometry1 & ! 'in/antane\s ellipse' 9 a/ronomy4 ,9 ! cases 9 :i* ^! conceptions are made use ( we h a ph5om5on :i* is cont9u\sly v>y+ & also *ang+ its rate ( v>iation4 ,we take x at "s giv5 mom5t1 suppose its rate at t mom5t to be fix$1 & !n complete its c>e] on t supposition4 #e4 ,s call$ f its fir/ ma!matical treatm5t appe>+ 9 ! ,comm5t>ii ( ! ,pet]sburg ,academy2 a v>iety ( notices ^u x w be f\nd 9 ,mr ,todhunt]'s ,hi/ory ( ! ,!ory ( ,probability4 ,,*apt] ,,ii4 ,,fur!r ,,discussion ,,^u ,,! ,,nature ,,( ,,! ,,s]ies ,,m5tion$ ,,9 ,,! ,,la/ ,,*apt]4 #a4 ,9 ! c\rse ( ! la/ *apt] ! nature ( a p>ticul> k9d ( s]ies1 t namely1 :i* mu/ be consid]$ to con/itute ! basis ( ! sci5ce ( ,probability1 has receiv$ a suffici5tly g5]al explanation = ! prelim9>y purpose ( introduction4 ,"o might inde$ say m ?an ?is2 = ! *>act]i/ics :i* 7 !re po9t$ out are really suffici5t 9 !mselves to give a fair g5]al idea ( ! nature ( ,probability1 & ( ! sort ( problems ) :i* x deals4 ,b 9 ! conclud+ p>agraphs an indication 0 giv5 t ! s]ies ( ?is k9d1 z !y actually occur 9 nature or z ! results ( m or less artificial production1 are seldom or nev] f\nd to occur 9 su* a simple =m z might possibly be expect$ f :at _h previ\sly be5 said2 b t !y are almo/ always se5 to be associat$ toge!r 9 gr\ps aft] a some:at complicat$ fa%ion4 ,a full] discussion ( ?is topic mu/ n[ be und]tak54 ,we w take = exam9ation an in/ance ( a k9d ) :i* ! inve/igations ( ,quetelet w h s]v$ to famili>ize "s read]s4 ,suppose t we measure ! heights ( a great _m adult m5 9 any t[n or c\ntry4 ,^! heights w ( c\rse lie betwe5 c]ta9 extremes 9 ea* direction1 & if we cont9ue to accumulate our measures x w be f\nd t !y t5d to lie cont9u\sly betwe5 ^! extremes2 t is to say1 t "u ^? circum/ances no int]m$iate height w be f\nd to be p]man5tly unrepres5t$ 9 su* a collection ( measurem5ts4 ,n[ suppose ^! heights to be m>%all$ 9 ! ord] ( _! magnitude4 ,:at we always f9d is some?+ ( ! foll[+ k9d2--ab\t ! middle po9t betwe5 ! extremes1 a l>ge numb] ( ! results w be f\nd cr[d$ toge!r3 a little on ea* side ( ?is po9t !re w /ill be an excess1 b n to s great an ext5t2 & s on1 9 "s dim9i%+ scale ( proportion1 until z we get t[>ds ! extreme results ! numb]s ?9 (f & become relatively exce$+ly small4 ,! po9t to :i* att5tion is "h direct$ is n ! m]e fact t ! numb]s ?us t5d to dim9i% f ! middle 9 ea* direction1 b1 z w be m fully expla9$ directly1 ! law accord+ to :i* ?is progressive dim9ution takes place4 ,! ^w 'law' is "h us$ 9 its ma!matical s5se1 to express ! =mula connect+ toge!r ! two elem5ts 9 "q1 namely1 ! height itself1 & ! relative numb] t are f\nd ( t height4 ,we %all h to enquire :e!r "o ( ^! elem5ts is a function ( ! o!r1 &1 if s1 :at function4 #b4 ,aft] :at 0 said 9 ! la/ *apt]1 x ne$ h>dly be insi/$ ^u t ! int]e/ & significance ( su* inve/igations z ^! are almo/ entirely dep5d5t ^u ! /ati/ics be+ v ext5sive4 ,9 "o or o!r ( ,quetelet's works on ,social ,physics#a w be f\nd a selection ( measurem5ts ( almo/ e elem5t :i* ! physical frame ( man c furni%3--8 height1 8 weight1 ! muscul> p[] ( v>i\s limbs1 ! dim5sions ( almo/ e "p & organ1 & s on4 ,"s ( ! mo/ ext5sive ( ^! express ! heights ( #be1jjj ,f$]al soldi]s f ! ,army ( ! ,potomac1 & ! circumf]5ces ( ! *e/s ( #egch ,scot* militia m5 tak5 _m ye>s ago4 ,^? :o wi% to consult a l>ge rep]tory ( su* /ati/ics _c be ref]r$ to any bett] s\rces ?an to ^! & o!r works by ! same au?or4#b ,int]e/+ & valuable1 h[ev]1 z are ,quetelet's /ati/ical inve/igations 7& mu* ( ! importance n[ des]v$ly atta*$ to su* enquiries is1 p]haps1 ow+ m to 8 ef=ts ?an to ^? ( any o!r p]son71 ,i _c b feel conv9c$ t !re is mu* 9 :at he has writt5 ^u ! subject :i* is errone\s & confus+ z reg>ds ! f\ndations ( ! sci5ce ( ,probability1 & ! philosophical que/ions :i* x involves4 ,^! errors are n by any means conf9$ to him1 b = v>i\s reasons !y w be bett] discuss$ 9 ! =m ( a criticism ( 8 explicit or implicit expression ( !m1 ?an 9 any m indep5d5t way4 #c4 ,9 ! fir/ place !n1 he always1 or almo/ always1 assumes t !re c be b "o & ! same law ( arrangem5t = ! results ( our obs]vations1 measurem5ts1 & s on1 9 ^! /ati/ical enquiries4 ,t is1 he assumes t :5ev] we get a gr\p ( su* magnitudes clu/]+ ab\t a mean1 & gr[+ less frequ5t z !y dep>t f t mean1 we %all f9d t ?is dim9ution ( frequ5cy takes place accord+ to "o inv>iable law1 :atev] may be ! nature ( ^! magnitudes1 & :atev] ! process by :i* !y may h be5 obta9$4 ,t su* a uni=mity z ?is %\ld prevail among/ _m & v>i\s classes ( ph5om5a w\ld probably seem surpris+ 9 any case4 ,b ! full significance ( su* a fact z ?is 7if inde$ x 7 a fact7 only becomes app>5t :5 att5tion is direct$ to ! pr(\nd di/9ctions 9 ! nature & orig9 ( ! ph5om5a :i* are ?us suppos$ to be h>moniz$ by be+ br\ght "u "o compreh5sive pr9ciple4 ,?is w be bett] appreciat$ if we take a brief glance at "s ( ! pr9cipal classes into :i* ! ?+s ) :i* ,probability is *iefly conc]n$ may be divid$4 ,^! are ( a ?ree-fold k9d4 #d4 ,9 ! fir/ place !re are ! v>i\s comb9ations1 & runs ( luck1 af=d$ by games ( *ance4 ,suppose a h&ful1 consi/+ ( t5 co9s1 7 toss$ up a great _m times 9 succession1 & ! results 7 tabulat$4 ,:at we %\ld obta9 w\ld be some?+ ( ! foll[+ k9d4 ,9 a c]ta9 proportion ( cases1 & ^! ! mo/ num]\s ( all1 we %\ld f9d t we got five heads & five tails2 9 a some:at less proportion ( cases we %\ld h1 z equally frequ5t results1 f\r heads six tails1 & f\r tails six heads2 & s on 9 a cont9ually dim9i%+ proportion until at l5g? we came d[n1 9 a v small relative numb] ( cases1 to n9e heads "o tail1 & n9e tails "o head2 :il/ ! lea/ frequ5t results possible w\ld be ^? :i* gave all heads or all tails4#c ,"h ! /ati/ical elem5ts "u consid]ation are1 z reg>ds _! orig9 at any rate1 optional or br\ght ab\t by human *oice4 ,!y w\ld1 !re=e1 be commonly describ$ z be+ ma9ly artificial1 b _! results ultimately altoge!r a matt] ( *ance4 ,aga91 9 ! second place1 we might take ! accurate measurem5ts--i4e4 ! actual magnitudes !mselves1--( a great _m natural objects1 belong+ to ! same g5us or class2 su* z ! cases1 already ref]r$ to1 ( ! heights1 or o!r *>act]i/ics ( ! inhabitants ( any di/rict4 ,"h human volition or int]v5tion ( any k9d seem to h little or no?+ to d ) ! matt]4 ,x is optional ) u to collect ! measures1 b ! ?+s measur$ are q outside our control4 ,!y w\ld !re=e be commonly describ$ z be+ altoge!r ! production ( nature1 & x w\ld n be suppos$ t 9 /rictness *ance _h any?+ :atev] to d ) ! matt]4 ,9 ! ?ird place1 ! result at :i* we are aim+ may be "s fix$ magnitude1 "o & ! same 9 ea* ( our successive attempts1 s t if our measurem5ts 7 rigidly accurate we %\ld m]ely obta9 ! same result repeat$ ov] & ov] aga94 ,b s9ce all our me?ods ( atta9+ our aims are practically subject to innum]able imp]fections1 ! results actually obta9$ w dep>t m or less1 9 almo/ e case1 f ! real & fix$ value :i* we are try+ to secure4 ,!y w be sometimes m wide ( ! m>k1 sometimes less s1 ! worse attempts be+ ( c\rse ! less frequ5t4 ,if a man aims at a t>get he w seldom or nev] hit x precisely 9 ! c5tre1 b 8 good %ots w be m#d num]\s ?an 8 bad ones4 ,"h aga91 !n1 we h a s]ies ( magnitudes 7i4e4 ! deflections ( ! %ots f ! po9t aim$ at7 clu/]+ ab\t a mean1 b produc$ 9 a v diff]5t way f ^? ( ! la/ two cases4 ,9 ?is in/ance ! elem5ts w\ld be commonly reg>d$ z only p>tially ! results ( human volition1 & *ance !re=e z be+ only a co-ag5t 9 ! effects produc$4 ,) ^! mu/ be class$ :at may be call$ e/imates1 z di/+ui%$ f measurem5ts4 ,by ! latt] are g5]ally und]/ood ! results ( a c]ta9 am\nt ( me*anism or manipulation2 by ! =m] we may und]/& ^? cases 9 :i* ! magnitude 9 "q is det]m9$ by direct obs]vation or introspection4 ,! int]e/ & importance ( ?is class1 s f> z sci5tific pr9ciples are conc]n$1 dates ma9ly f ! inve/igations ( ,fe*n]4 ,its *ief field is naturally to be f\nd among/ psy*ological data4 ,o!r classes ( ?+s1 besides ^? allud$ to above1 might readily be giv54 ,^! h[ev] are ! classes ab\t :i* ! mo/ ext5sive /ati/ics are obta9able1 or to :i* ! mo/ practical importance & int]e/ are atta*$4 ,! pr(\nd di/9ctions :i* sep>ate _! orig9 & "* are obvi\s4 ,if !y all really did display precisely ! same law ( v>iation x w\ld be a mo/ rem>kable fact1 po9t+ d\btless to "s deep-seat$ id5tity und]ly+ ! v>i\s ways1 app>5tly s widely di/9ct1 9 :i* !y _h be5 br\ght ab\t4 ,! que/ions n[ to be discuss$ are3 ,is x ! case1 ) any consid]able degree ( rig\r1 t only "o law ( di/ribution does really prevail8 &1 9 s f> z ?is is s1 h[ does x come to pass8 #e4 ,9 support ( an affirmative answ] to ! =m] ( ^! two que/ions1 sev]al diff]5t k9ds ( pro( are1 or might be1 (f]$4 7,i47 ,= "o plan we may make a direct appeal to exp]i5ce1 by collect+ sets ( /ati/ics & obs]v+ :at is _! law ( di/ribution4 ,z rem>k$ above1 ?is has be5 done 9 a great v>iety ( cases1 & 9 "s in/ances to a v consid]able ext5t1 by ,quetelet & o!rs4 ,8 rese>*es h made x abundantly conv9c+ t _m classes ( ?+s & processes1 diff]+ widely 9 _! nature & orig91 d nev]!less appe> to con=m ) a consid]able degree ( accuracy to "o & ! same#e law4 ,at lea/ ?is is made pla9 = ! m c5tral values1 = ^? t is :i* are situat$ mo/ ne>ly ab\t ! mean4 ,) reg>d to ! extreme values !re is1 on ! o!r h&1 "s difficulty4 ,= in/ance 9 ! arrangem5ts ( ! heights ( a numb] ( m51 ^! extremes are r a /umbl+-block2 inde$ x has be5 propos$ to reject !m f bo? ends ( ! scale on ! plea t !y are mon/rosities1 ! fact be+ t _! relative numb]s d n seem to be by any means ^? :i* !ory w\ld assign4#f ,su* a plan ( rejection is h[ev] q unau?oriz$1 = ^! dw>fs & giants are born into ! _w l _! m normally siz$ bre?r51 & h precisely z mu* "r z any o!rs to be includ$ 9 ! =mul we draw up4 ,besides ! in/ance ( ! heights ( m51 o!r classes ( obs]vations ( a some:at simil> "* h be5 already ref]r$ to z collect$ & arrang$ by ,quetelet4 ,f ! nature ( ! case1 h[ev]1 !re are n _m appropriate ones at h&2 = :5 our object is1 n to illu/rate a law :i* c be o!rwise prov$1 b to obta9 actual direct pro( ( x1 ! collection ( obs]vations & measurem5ts ought to be made ^u su* a l>ge scale z to det] any b ! mo/ p]sev]+ comput]s f und]go+ ! requisite lab\r4 ,"s ( ! rem>ks made 9 ! c\rse ( ! note on ! opposite page w s]ve to illu/rate ! difficulties :i* w\ld lie 9 ! way ( su* a mode ( pro(4 ,we are speak+ "h1 x mu/ be und]/ood1 only ( symmetrical curves3 if !re is asymmetry1 i4e4 if ! ,law ( ,error is diff]5t on diff]5t sides ( ! mean1--a comp>atively v small numb] ( obs]vations w\ld suffice to detect ! fact4 ,b1 grant$ symmetry & rapid decrease ( frequ5cy on ea* side ( ! mean1 we c\ld g5]ally select "s "o species ( ! expon5tial curve :i* %\ld pretty closely repres5t our /ati/ics 9 ! neighb\rhood ( ! mean4 ,t is1 :]e ! /ati/ics are num]\s we c\ld secure agreem5t2 & :]e we c\ld n secure agreem5t ! /ati/ics w\ld be comp>atively s sc>ce t we %\ld h to cont9ue ! obs]vations = a v long "t 9 ord] to prove ! disagreem5t4 #f4 ,all[+ ! v>i\s /ati/ics su* cr$it z !y des]ve1 = _! ext5t1 appropriat5ess1 accuracy & s on1 ! g5]al conclusion :i* w on ! :ole be drawn by almo/ e "o :o takes ! tr\ble to consult !m1 is t !y d1 9 l>ge "p1 con=m approximately to "o type or law1 at any rate = all except ! extreme values4 ,s mu* z ?is mu/ be fully admitt$4 ,b t !y d n1 inde$ we may say t !y _c1 always d s 9 ! case ( ! extreme values1 w become obvi\s on a little consid]ation4 ,9 "s ( ! classes ( ?+s to :i* ! law is suppos$ to apply1 = example1 ! successions ( heads & tails 9 ! ?r[s ( a p5ny1 !re is no limit to ! magnitude ( ! fluctuations :i* may & w occur4 ,po/ulate z long a succession ( heads or ( tails z we please1 & if we c\ld only live & toss long en\gh = x we %\ld succe$ 9 gett+ x at l5g?4 ,9 o!r cases1 includ+ _m ( ! applications ( ,probability to natural ph5om5a1 !re c h>dly fail to be su* limits4 ,deviations exce$+ a c]ta9 range may n be m]ely improbable1 t is ( v r>e occurr5ce1 b !y may (t5 f ! nature ( ! case be actually impossible4 ,& ev5 :5 !y are n actually impossible x may frequ5tly appe> on exam9ation t !y are only r5d]$ possible by ! occasional introduction ( ag5cies :i* are n suppos$ to be available 9 ! production ( ! m ord9>y or int]m$iate values4 ,:51 = in/ance1 we are mak+ obs]vations ) any k9d ( in/rum5t1 ! nature ( its con/ruction may put an absolute limit ^u ! possible am\nt ( error4 ,& ev5 if !re be n an absolute limit "u all k9ds ( usage x may nev]!less be ! case t !re is "o "u fair & prop] usage2 x be+ ! case t only :5 ! in/rum5t is design$ly or c>elessly tamp]$ ) w any new causes ( div]g5ce be introduc$ :i* 7 n conf9$ )9 ! old limits4 ,suppose1 = in/ance1 t a man is fir+ at a m>k4 ,8 wor/ %ots mu/ be suppos$ to be br\ght ab\t by a comb9ation ( su* causes z 7 act+1 or prep>$ to act1 9 e o!r case2 ! extreme in/ance ( :at we may ?us t]m 'fair usage' be+ :5 a numb] ( di/9ct causes h happ5$ to conspire toge!r s z to t5d 9 ! same direction1 in/ead (1 z 9 ! o!r cases1 m or less neutraliz+ "o ano!r's "w4 ,b ! aggregate effect ( su* causes may well be suppos$ to be limit$4 ,! man w n dis*>ge 8 %ot ne>ly at "r angles to ! true l9e ( fire unless "s entirely new cause comes 91 z by "s unusual circum/ance hav+ di/ract$ 8 att5tion1 or by 8 hav+ _h "s spasmodic seizure4 ,b influ5ces ( ?is k9d 7 n suppos$ to h be5 available be=e2 & ev5 if !y 7 we are tak+ a bold /ep 9 assum+ t ^! occasional great di/urbances are subject to ! same k9d ( laws z are ! aggregates ( innum]able little ones4 ,we _c inde$ lay mu* /ress ^u an example ( ?is la/ k9d1 z comp>$ ) ^? 9 :i* we c see = c]ta9 t !re is a fix$ limit to ! range ( error4 ,x is !re=e (f]$ r = illu/ration ?an = pro(4 ,! enorm\s1 9 fact inconceivable magnitude ( ! numb]s expressive ( ! *ance ( v r>e comb9ations1 su* z ^? 9 "q1 has su* a bewild]+ effect ^u ! m9d t "o may be sometimes apt to conf\nd ! impossible ) ! high] degrees ( ! m]ely ma!matically improbable4 #g4 ,at ! "t ! fir/ edition ( ?is essay 0 compos$ writ]s on ,/ati/ics 71 ,i ?9k1 /ill = ! mo/ "p "u ! influ5ce ( ,quetelet1 & incl9$ to ov]value 8 au?ority on ?is p>ticul> subject3 ( late h[ev] att5tion has be5 repeat$ly drawn to ! necessity ( tak+ acc\nt ( o!r laws ( arrangem5t ?an ! b9omial or expon5tial4 ,mr ,galton1 = in/ance1--to :om e bran* ( ! !ory ( /ati/ics owes s mu*1--has insi/$#g t ! assumption :i* lies at ! basis ( ! well-kn[n law ( ',frequ5cy ( ,error'444 is incorrect 9 _m gr\ps ( vital & social ph5om5a4444 ,= example1 suppose we endeav\r to mat* a t9t2 ,fe*n]'s law1 9 its approximative & simple/ =m ( s5sation log /imulus1 tells u t a s]ies ( t9ts1 9 :i* ! quantities ( :ite scatt]$ on a black gr\nd are z #a1 #b1 #d1 #h1 #af1 #cb1 c41 w appe> to ! eye to be sep>at$ by equal int]vals ( t9t4 ,!re=e1 9 mat*+ a grey t conta9s #h portions ( :ite1 we are j z likely to err by select+ "o t has #af portions z "o t has #d portions4 ,9 ! fir/ case !re w\ld be an error 9 excess1 ( #h2 9 ! second !re w\ld be an error1 9 defici5cy1 ( #d4 ,!re=e1 an error ( ! same magnitude 9 excess or 9 defici5cy is n equally probable4 ,! consequ5ces ( ?is assumption are work$ out 9 a rem>kable pap] by ,dr ,d4 ,mc,alister1 to :i* allusion w h to be made aga9 h]eaft]4 ,all t conc]ns u "h to po9t out is t :5 ! results ( /ati/ics ( ?is "* are arrang$ graphically we d n get a curve :i* is symmetrical on bo? sides ( a c5tral axis4 #h4 ,m rec5tly1 ,mr ,f4 ,y4 ,edgewor? 79 a report ( a ,committee ( ! ,briti% ,association appo9t$ to enquire into ! v>iation ( ! monet>y /&>d7 has urg$ ! same consid]ations 9 respect ( prices ( commodities4 ,he gives a numb] ( /ati/ics drawn f ! prices ( twelve commodities dur+ ! two p]iods #aghb-ahbj1 #ahbj-ahfe4 ,! maximum & m9imum entry = ea* s]ies hav+ be5 not$1 x is f\nd t ! numb] ( entries above ! 'middle po9t1' half-way betwe5 ! maximum & m9imum1#h is 9 e in/ance less ?an half ! total numb] ( entries 9 ! s]ies4 ,9 ! tw5ty-f\r trials !re is n a s+le exception to ! rule1 & 9 v few cases ev5 an approa* to an exception4 ,we may presume !n t ! curves are ( ! lop-sid$ "* indicat$ by ! accompany+ diagram4 ,! same facts are also asc]ta9$ 9 respect to place v>iations z di/+ui%$ f "t v>iations4 ,to ^! may be add$ "s /ati/ics ( my own1 ref]r+ to ! heights ( ! b>omet] tak5 at ! same h\r on m ?an #djjj successive days 7v4 ,nature1 ,sept4 #b1 #ahhg74 ,s f> z ^! g !y %[ a m>k$ asymmetry ( arrangem5t4 ,9 fact x appe>s to me t ?is want ( symmetry ought to be look$ = 9 all cases 9 :i* ! ph5om5a "u measurem5t are ( a '"o-sid$' "*2 9 ! s5se t !y are measur$ on "o side only ( a c]ta9 fix$ po9t f :i* _! possibility is suppos$ to />t4 ,= n only is x impossible = !m to fall bel[ ?is po9t3 long be=e !y rea* x ! influ5ce ( its proximity is felt 9 enhanc+ ! difficulty & importance ( ! same am\nt ( absolute diff]5ce4 ,look at a table ( /atures1 = in/ance1 ) a mean value ( #fi in*es4 ,a dim9ution ( ?ree feet 77 ?is possible7 is mu* m influ5tial1--c\nts = mu* m1 9 e s5se ( ! t]m1--?an an addition ( ! same am\nt2 = ! =m] does n d\ble ! mean1 :ile ! latt] m ?an halves x4 ,rev]t to an illu/ration4 ,if a va/ numb] ( petty influ5c+ circum/ances ( ! k9d already describ$ 7 to act ^u a sw++ p5dulum we %\ld expect ! deflections 9 ea* direction to display symmetry2 b if !y 7 to act ^u a spr+ we %\ld n expect su* a result4 ,any ph5om5a ( :i* ! latt] is ! m appropriate illu/ration c h>dly be expect$ to range !mselves ) symmetry ab\t a mean4#i #i4 7,,ii47 ,! la/ rem>ks w sugge/ ano!r k9d ( pro( :i* might be (f]$ to e/abli% ! inv>iable nature ( ! law ( error4 ,x is ( a direct d$uctive k9d1 n appeal+ imm$iately to /ati/ics1 b involv+ an enquiry into ! actual or assum$ nature ( ! causes by :i* ! ev5ts are br\ght ab\t4 ,imag9e t ! ev5t "u consid]ation is br\ght to pass1 9 ! fir/ place1 by "s fix$ cause1 or gr\p ( fix$ causes4 ,if ?is compris$ all ! influ5c+ circum/ances ! ev5t w\ld inv>iably happ5 9 precisely ! same way3 !re w\ld be no errors or deflections :atev] to be tak5 acc\nt (4 ,b n[ suppose t !re 7 also an enorm\s numb] ( v small causes :i* t5d$ to produce deflections2 t ^! causes act$ 9 entire indep5d5ce ( "o ano!r2 & t ea* ( ! lot told z (t51 9 ! long run1 9 "o direction z 9 ! opposite4 ,x is easy#aj to see1 9 a g5]al way1 :at w\ld foll[ f ^! assumptions4 ,9 a v few cases ne>ly all ! causes w\ld tell 9 ! same direction2 9 o!r words1 9 a v few cases ! deflection w\ld be extreme4 ,9 a great] numb] ( cases1 h[ev]1 x w\ld only be ! mo/ "p ( !m t w\ld tell 9 "o direction1 :il/ a few did :at !y c\ld to c\nt]act ! re/2 ! result be+ a comp>atively l>g] numb] ( some:at small] deflections4 ,s on1 9 increas+ numb]s1 till we approa* ! middle po9t4 ,"h we %all h a v l>ge numb] ( v small deflections3 ! cases 9 :i* ! oppos$ influ5ces j succe$ 9 balanc+ "o ano!r1 s t no error :atev] is produc$1 be+1 ?\gh actually infrequ5t1 relatively ! mo/ frequ5t ( all4 ,n[ if all deflections f a mean 7 br\ght ab\t 9 ! way j indicat$ 7an indication :i* mu/ suffice = ! pres5t7 we %\ld always h "o & ! same law ( arrangem5t ( frequ5cy = ^! deflections or errors1 viz4 ! expon5tial#aa law m5tion$ 9 #e4 #aj4 ,x may be readily admitt$ f :at we "k ab\t ! production ( ev5ts t some?+ resembl+ ^! assumptions1 & !re=e some?+ resembl+ ! consequ5ces :i* foll[ f !m1 is really secur$ 9 a v great numb] ( cases4 ,b al?\gh ?is may prevail approximately1 x is 9 ! highe/ degree improbable t x c\ld ev] be secur$1 ev5 artificially1 ) any?+ approa*+ to rigid accuracy4 ,= "o ?+1 ! causes ( deflection w seldom or nev] be really indep5d5t ( "o ano!r4 ,"s ( !m w g5]ally be ( a k9d su* t ! supposition t sev]al are sway+ 9 "o direction1 may affect ! capacity ( ea* to produce t full effect :i* x w\ld h be5 capable ( if x _h be5 left to d its "w alone4 ,9 ! common example1 = in/ance1 ( fir+ at a m>k1 s long z we consid] ! case ( ! tol]ably good %ots ! effect ( ! w9d 7"o ( ! causes ( error7 w be approximately ! same :atev] may be ! precise direction ( ! bullet4 ,b :5 a %ot is consid]ably wide ( ! m>k ! w9d c no long] be reg>d$ z act+ at "r angles to ! l9e ( flight1 & its effect 9 consequ5ce w n be precisely ! same z be=e4 ,9 o!r words1 ! causes "h are n /rictly indep5d5t1 z !y 7 assum$ to be2 & consequ5tly ! results to be attribut$ to ea* are n absolutely un9flu5c$ by ^? ( ! o!rs4 ,d\btless ! effect is trifl+ "h1 b ,i appreh5d t if we 7 c>efully to scrut9ize ! modes 9 :i* ! sev]al elem5ts ( ! total cause conspire toge!r1 we %\ld f9d t ! assumption ( absolute indep5d5ce 0 haz>d\s1 n to say unw>rantable1 9 a v great numb] ( cases4 ,^! brief rem>ks ^u ! process by :i* ! deflections are br\ght ab\t mu/ suffice = ! pres5t purpose1 z ! subject w receive a full] inve/igation 9 ! c\rse ( ! next *apt]4 ,accord+1 !re=e1 to ! be/ consid]ation :i* c at ! pres5t /age be af=d$ to ?is subject1 we may draw a simil> conclusion f ?is d$uctive l9e ( argum5t z f ! direct appeal to /ati/ics4 ,! same g5]al result seems to be e/abli%$2 namely1 t approximately1 ) suffici5t accuracy = all practical purposes1 we may say t an exam9ation ( ! causes by :i* ! deflections are g5]ally br\ght ab\t %[s t !y are mo/ly ( su* a "* z w\ld result 9 giv+ u ! commonly accept$ ',law ( ,error1' z x is t]m$4#ab ,! two l9es ( enquiry1 !re=e1 )9 ! limits assign$1 af=d ea* o!r a decid$ mutual confirmation4 #aa4 7,,iii47 ,!re /ill rema9s a ?ird1 indirect & ma!matical l9e ( pro(1 :i* might be (f]$ to e/abli% ! conclusion t ! ,law ( ,error is always "o & ! same4 ,x may be ma9ta9$ t ! recogniz$ & univ]sal employm5t ( "o & ! same me?od1 t kn[n to ma!maticians & a/ronom]s z ! ,me?od ( ,lea/ ,squ>es1 9 all mann] ( diff]5t cases ) v satisfactory results1 is compatible only ) ! supposition t ! errors to :i* t me?od is appli$ mu/ be gr\p$ accord+ to "o inv>iable law4 ,if all 'laws ( error' 7 n ( "o & ! same type1 t is1 if ! relative frequ5cy ( l>ge & small div]g5ces 7su* z we h be5 speak+ (7 7 n arrang$ accord+ to "o patt]n1 h[ c\ld "o me?od or rule equally suit !m all8 ,9 ord] to pres]ve a cont9uity ( treatm5t1 "s notice mu/ be tak5 ( ?is enquiry "h1 ?\gh1 z 9 ! case ( ! la/ argum5t1 any ?or\gh discussion ( ! subject is impossible at ! pres5t /age4 ,= "o ?+1 x w\ld involve too mu* employm5t ( ma!matics1 or at any rate ( ma!matical conceptions1 to be suitable = ! g5]al plan ( ?is treatise3 ,i h accord+ly devot$ a special *apt] to ! consid]ation ( x4 ,! ma9 reason1 h[ev]1 aga9/ discuss+ ?is argum5t "h1 is1 t to d s w\ld involve ! anticipation ( a totally diff]5t side ( ! sci5ce ( ,probability f t hi!rto treat$ (4 ,?is mu/ be especially insi/$ ^u1 z ! neglect ( x involves mu* confusion & "s error4 ,dur+ ^! e>li] *apt]s we h be5 entirely occupi$ ) lay+ :at may be call$ ! physical f\ndations ( ,probability4 ,we h done no?+ else ?an e/abli%1 9 "o way or ano!r1 ! exi/5ce ( c]ta9 gr\ps or arrangem5ts ( ?+s :i* are f\nd to pres5t !mselves 9 nature2 we h endeav\r$ to expla9 h[ !y come to pass1 & we h illu/rat$ _! pr9cipal *>act]i/ics4 ,b ^! are m]ely ! f\ndations ( ,inf]5ce1 we h n yet said a ^w ^u ! logical processes :i* are to be erect$ ^u ^! f\ndations4 ,we h n !re=e ent]$ yet ^u ! logic ( *ance4 #ab4 ,n[ ! way 9 :i* ! ,me?od ( ,lea/ ,squ>es is sometimes spok5 ( t5ds to conceal ! magnitude ( ?is di/9ction4 ,writ]s h reg>d$ x z synonym\s ) ! ,law ( ,error1 :]eas ! fact is t ! two are n only totally di/9ct ?+s b t !y h sc>cely ev5 any necess>y connection ) ea* o!r4 ,! ,law ( ,error is ! /atem5t ( a physical fact2 x simply assigns1 ) m or less ( accuracy1 ! relative frequ5cy ) :i* errors or deviations ( any k9d are f\nd 9 practice to pres5t !mselves4 ,x belongs !re=e to :at may be t]m$ ! physical f\ndations ( ! sci5ce4 ,! ,me?od ( ,lea/ ,squ>es1 on ! o!r h&1 is n a law at all 9 ! sci5tific s5se ( ! t]m4 ,x is simply a rule or direction in=m+ u h[ we may be/ proce$ to treat any gr\p ( ^! errors :i* may be set be=e u1 s z to extract ! true result at :i* !y h be5 aim+4 ,cle>ly !re=e x belongs to ! inf]5tial or logical "p ( ! subject4 ,x _c inde$ be d5i$ t ! me?ods we employ mu/ h "s connection ) ! arrangem5t ( ! facts to :i* !y are appli$2 b ! two ?+s are none ! less di/9ct 9 _! nature1 & 9 ?is case ! connection does n seem at all a necess>y "o1 b at mo/ "o ( propriety & conv5i5ce4 ,! ,me?od ( ,lea/ ,squ>es is usually appli$1 no d\bt1 to ! mo/ famili> & common =m ( ! ,law ( ,error1 namely ! expon5tial =m ) :i* we h be5 rec5tly occupi$4 ,b o!r =ms ( laws ( error may exi/1 &1 if !y did1 ! me?od 9 "q might equally well be appli$ to !m4 ,i am n ass]t+ t x w\ld necess>ily be ! be/ me?od 9 e case1 b x w\ld be a possible "o2 inde$ we may g fur!r & say1 z w be %[n 9 a future *apt]1 t x w\ld be a good me?od 9 almo/ e case4 ,b its p>ticul> m]its or dem]its d n int]f]e ) its possible employm5t 9 e case 9 :i* we may *oose to resort to x4 ,x w be se5 !re=e1 ev5 f ! few rem>ks t c be made ^u ! subject "h1 t ! fact t "o & ! same me?od is v commonly employ$ ) satisfactory results af=ds little or no pro( t ! errors to :i* x is appli$ mu/ be arrang$ accord+ to "o fix$ law4 #ac4 ,s mu* !n = ! attempt to prove ! preval5ce1 9 all cases1 ( ?is p>ticul> law ( div]g5ce4 ,! next po9t 9 ,quetelet's treatm5t ( ! subject :i* des]ves att5tion z errone\s or confus+1 is ! doctr9e ma9ta9$ by him & o!rs z to ! exi/5ce ( :at he t]ms a type 9 ! gr\ps ( ?+s 9 "q4 ,?is is a n unnatural consequ5ce f "s ( ! data & conclusions ( ! la/ few p>agraphs4 ,ref] back to two ( ! ?ree classes ( ?+s already m5tion$ 9 #d4 ,if x really 7 ! case t 9 arrang+ 9 ord] a s]ies ( incorrect obs]vations or attempts ( our own1 & a collection ( natural objects belong+ to "s "o & ! same species or class1 we f\nd t ! law ( _! div]g5ce 0 9 ea* case id5tical 9 ! long run1 we %\ld be naturally dispos$ to apply ! same expression ',law ( ,error' to bo? in/ances alike1 ?\gh 9 /rictness x c\ld only be appropriate to ! =m]4 ,:5 we p]=m an op]ation ourselves ) a cle> consci\sness ( :at we are aim+ at1 we may q correctly speak ( e deviation f ?is z be+ an error2 b :5 ,nature pres5ts u ) a gr\p ( objects ( any k9d1 x is us+ a r bold metaphor to speak 9 ?is case also ( a law ( error1 z if %e _h be5 aim+ at some?+ all ! "t1 & _h l ! re/ ( u miss$ h] m>k m or less 9 almo/ e in/ance4#ac ,suppose we make a long succession ( attempts to measure accurately ! precise height ( a man1 we %\ld f "o cause or ano!r seldom or nev] succe$ 9 do+ s ) absolute accuracy4 ,b we h no "r to assume t ^! imp]fect measurem5ts ( ours w\ld be f\nd s to deviate accord+ to "o p>ticul> law ( error z to pres5t ! precise c\nt]p>t ( a s]ies ( actual heights ( diff]5t m51 suppos+ t ^! latt] 7 assign$ ) absolute precision4 ,:at might be ! actual law ( error 9 a s]ies ( direct measurem5ts ( any giv5 magnitude c\ld h>dly be ass]t$ be=eh&1 & probably ! attempt to det]m9e x by exp]i5ce has n be5 made suffici5tly (t5 to enable u to asc]ta9 x2 b ^u g5]al gr\nds x seems by no means c]ta9 t x w\ld foll[ ! s-call$ expon5tial law4 ,be ?is h[ev] z x may1 x is r a lic5ce ( language to talk z if nature _h be5 at "w 9 ! same way z "o ( u2 aim+ 7ineffectually = ! mo/ "p7 at a giv5 result1 t is at produc+ a man end[$ ) a c]ta9 /ature1 proportions1 & s on1 :o might !re=e be reg>d$ z ! typical man4 #ad4 ,/at$ z above1 namely1 t !re is a fix$ inv>iable human type to :i* all individual specim5s ( humanity may be reg>d$ z hav+ be5 meant to atta91 b f :i* !y h deviat$ 9 "o direction or ano!r2 accord+ to a law ( deviation capable ( priori det]m9ation1 ! doctr9e is little else ?an absurd4 ,b if we look some:at clos] at ! facts ( ! case1 & ! probable explanation ( ^! facts1 we may see our way to an important tru?4 ,! facts1 on ! au?ority ( ,quetelet's /ati/ics 7! great int]e/ & value ( :i* mu/ be frankly admitt$71 are v briefly z foll[s3 if we take any elem5t ( our physical frame :i* admits ( accurate measurem5t1 say ! height1 & det]m9e ?is measure 9 a great numb] ( diff]5t individuals belong+ to any tol]ably homog5e\s class ( p1 we %all f9d t ^! heights d admit ( an ord]ly arrangem5t ab\t a mean1 aft] ! fa%ion :i* has be5 already repeat$ly m5tion$4 ,:at is meant by a homog5e\s class8 is a p]t95t & significant enquiry1 b apply+ ?is condition to any simple cases its mean+ is readily /at$4 ,x implies t ! mean 9 "q w be diff]5t accord+ to ! nationality ( ! p]sons "u measurem5t4 ,accord+ to ,quetelet1#ad 9 ! case ( ,engli%m5 ! mean is ab\t #e ft4 #i 942 = ,belgians ab\t #e ft4 #g 942 = ! ,fr5* ab\t #e ft4 #d 94 ,x ne$ h>dly be add$ t ^! measures are ^? ( adult males4 #ae4 ,x may fairly be ask$ "h :at w\ld h be5 ! consequ5ce1 _h we1 in/ead ( keep+ ! ,engli% & ! ,fr5* ap>t1 mix$ ! results ( our measurem5ts ( !m all toge!r8 ,! "q is an important "o1 z x w oblige u to und]/& m cle>ly :at we mean by homog5e\s classes4 ,! answ] t w\ld usually be giv5 to x1 ?\gh sub/antially correct1 is some:at too decisive & summ>y4 ,x w\ld be said t we are "h mix+ di/9ctly het]og5e\s elem5ts1 & t 9 consequ5ce ! resultant law ( error w be by no means ( ! simple "* previ\sly exhibit$4 ,s f> z su* an answ] is to be admitt$ its gr\nds are easy to appreciate4 ,9 accordance ) ! usual law ( error ! div]g5ces f ! mean gr[ cont9u\sly less num]\s z !y increase 9 am\nt4 ,n[1 if we mix up ! ,fr5* & ,engli% heights1 :at w foll[8 ,beg9n+ f ! ,engli% mean ( #e feet #i in*es1 ! heights w at fir/ foll[ almo/ entirely ! law det]m9$ by ^! ,engli% conditions1 = at ?is po9t ! ,engli% data are v num]\s1 & ! ,fr5* by comp>ison v few4 ,b1 z we beg9 to approa* ! ,fr5* mean1 ! numb]s w cease to %[ t cont9ual dim9ution :i* !y %\ld %[1 accord+ to ! ,engli% scale ( arrangem5t1 = "h ! ,fr5* data are 9 turn v num]\s1 & ! ,engli% by comp>ison few4 ,! result ( su* a comb9ation ( het]og5e\s elem5ts is illu/rat$ by ! figure annex$1 ( c\rse 9 a v exagg]at$ =m4 ,figure3 ,sup]position ( two ,gaussians4 #af4 ,9 ! above case ! nature ( ! het]og5eity1 & ! reasons :y ! /ati/ics %\ld be s collect$ & arrang$ z to avoid x1 seem$ tol]ably obvi\s4 ,x w be se5 /ill m pla9ly if we take a p>allel case drawn f artificial proce$+s4 ,suppose t aft] a man _h fir$ a few ?\s& %ots at a c]ta9 spot1 say a waf] fix$ some:]e on a wall1 ! position ( ! spot at :i* he aims 7 %ift$1 & he fir$ a few ?\s& m %ots at ! waf] 9 its new position4 ,n[ let u collect & arrange all ! %ots ( bo? s]ies 9 ! ord] ( _! dep>ture f ei!r ( ! c5tres1 say ! new "o4 ,"h we %\ld really be m+l+ toge!r two discordant sets ( elem5ts1 ei!r ( :i*1 if kept ap>t f ! o!r1 w\ld h be5 ( a simple & homog5e\s "*4 ,we %\ld f9d1 9 consequ5ce1 t ! resultant law ( error betray$ its composite or het]og5e\s orig9 by a gl>+ dep>ture f ! cu/om>y =m1 some:at aft] ! fa%ion indicat$ 9 ! above diagram4 ,! in/ance ( ! ,engli% & ,fr5* heights resembles ! "o j giv51 b falls f> %ort ( x 9 ! /r+5cy ) :i* ! requisite conditions are secur$4 ,! fact is we h n "h got ! mo/ suitable requirem5ts1 viz4 a gr\p consi/+ ( a few fix$ causes supplem5t$ by innum]able little di/urb+ influ5ces4 ,:at we call a nation is really a highly artificial body1 ! memb]s ( :i* are subject to a consid]able numb] ( local or occasional di/urb+ causes4 ,among/ ,fr5*m5 7 includ$1 presumably1 ,bretons1 ,prov5als1 ,alsatians1 & s on1 ?us comm+l+ di/9ctions :i*1 ?\gh less ?an ^? betwe5 ,fr5* & ,engli%1 reg>d$ z :oles1 are v f> f be+ insignificant4 ,& to ^! diff]5ces ( race mu/ be add$ o!r di/urbances1 also highly important1 dep5d5t ^u v>y+ climate1 food & occupation4 ,x is pla91 !re=e1 t :atev] objections exi/ aga9/ confus+ toge!r ,fr5* & ,engli% /ati/ics1 exi/ also1 ?\gh ( c\rse 9 a less degree1 aga9/ confus+ toge!r ^? ( ! v>i\s prov9cial & o!r compon5ts :i* make up ! ,fr5* p4 #ag4 ,out ( ! great v>iety ( important causes :i* influ5ce ! height ( m51 x is probable t ^? :i* mo/ ne>ly fulfil ! ma9 conditions requir$ by ! ',law ( ,error' are ^? ab\t :i* we "k ! lea/4 ,^u ! effects ( food & employm5t1 obs]vation has some?+ to say1 b ^u ! purely physiological causes by :i* ! height ( ! p>5ts influ5ces ! height ( ! (fspr+1 we h probably no?+ :i* des]ves to be call$ k4 ,p]haps ! be/ supposition we c make is "o :i*1 9 accordance ) ! say+ t 'l bre$s l'1 w\ld assume t ! purely physiological causes repres5t ! con/ant elem5t2 t is1 giv5 a homog5e\s race ( p to beg9 )1 :o freely int]m>ry1 & are subject to l circum/ances ( climate1 food1 & occupation1 ! /&>d w\ld rema9 on ! :ole con/ant4#ae ,9 su* a case ! man :o possess$ ! mean height1 mean weight1 mean /r5g?1 & s on1 might !n be call$1 9 a sort ( way1 a 'type'4 ,! deviations f ?is type w\ld !n be produc$ by innum]able small influ5ces1 p>tly physiological1 p>tly physical & social1 act+ = ! mo/ "p indep5d5tly ( "o ano!r1 & result+ 9 a ,law ( ,error ( ! usual description4 ,"u su* re/rictions & explanations z ^!1 !re seems to be no reasonable objection to speak+ ( a ,fr5* or ,engli% type or mean4 ,b x mu/ always be rememb]$ t "u ! pres5t circum/ances ( e political nation1 ^! some:at het]og5e\s bodies might be subdivid$ into v>i\s small] gr\ps1 ea* ( :i* w\ld frequ5tly exhibit ! *>act]i/ics ( su* a type 9 an ev5 m m>k$ degree4 #ah4 ,on ?is po9t ! reports ( ! ,an?ropometrical ,committee1 already ref]r$ to1 are mo/ in/ructive4 ,!y illu/rate ! ext5t to :i* ?is subdivision c\ld be c>ri$ out1 & prove1--if any pro( 7 necess>y1--t ! discov]y ( ,quetelet's homme moy5 w\ld lead u a long *ase4 ,s f> z _! results g ! mean ',engli%' /ature 79 in*es7 is #fg4ff4 ,b ?is is compos$ ( ,scot*1 ,iri%1 ,engli% & ,wel% con/itu5ts1 ! sep>ate means ( ^! be+1 respectively2 #fh4ga1 #fg4ij1 #fg4cf1 & #ff4ff4 ,b ^! aga9 may be subdivid$2 = c>eful obs]vation %[s t ! mean ,engli% /ature is di/9ctly great] 9 c]ta9 di/ricts 7e4g4 ! ,nor?-,ea/]n c\nties7 ?an 9 o!rs4 ,!n aga9 ! mean ( ! pr(essional classes is consid]ably great] ?an t ( ! lab\r]s2 & t ( ! hone/ & intellig5t is v mu* great] ?an t ( ! crim9al & lunatic con/itu5ts ( ! population4 ,&1 s f> z ! obs]vations are ext5sive en\gh = ! purpose1 x appe>s t e *>act]i/ic 9 respect ( ! gr\p+ ab\t a mean :i* c be detect$ 9 ! m ext5sive ( ^! classes c be detect$ also 9 ! n>r[]4 ,nor is !re any reason to suppose t ! same process ( subdivision c\ld n be c>ri$ out z mu* f>!r z we *ose to prolong x4 #ai4 ,x ne$ h>dly be add$ to ! above rem>ks t no "o :o gives ! slighte/ adhesion to ! ,doctr9e ( ,evolution c\ld reg>d ! type1 9 ! above qualifi$ s5se ( ! t]m1 z possess+ any real p]man5ce & fixity4 ,if ! con/ant causes1 :atev] !y may be1 rema9 un*ang$1 & if ! v>iable ones cont9ue 9 ! long run to balance "o ano!r1 ! results w cont9ue to clu/] ab\t ! same mean4 ,b if ! con/ant ones und]go a gradual *ange1 or if ! v>iable ones1 in/ead ( balanc+ ea* o!r suff] "o or m ( _! numb] to beg9 to acquire a prepond]at+ influ5ce1 s z to put a sort ( bias ^u _! aggregate effect1 ! mean w at once beg91 s to say1 to %ift its gr\nd4 ,& hav+ once begun to %ift1 x may cont9ue to d s1 to :atev] ext5t we recognize t ,species are v>iable & ,developm5t is a fact4 ,x is z if ! po9t on ! t>get at :i* we aim1 in/ead ( be+ fix$1 7 sl[ly *ang+ its position z we cont9ue to fire at x2 *ang+ almo/ c]ta9ly to "s ext5t & tempor>ily1 & n improbably to a consid]able ext5t & p]man5tly4 #bj4 ,our examples ?r\gh\t ?is *apt] h be5 almo/ exclusively drawn f physical *>act]i/ics1 :e!r ( man or ( inanimate ?+s2 b x ne$ n be suppos$ t we are necess>ily conf9$ to su* in/ances4 ,mr ,galton1 = in/ance1 has propos$ to ext5d ! same pr9ciples ( calculation to m5tal ph5om5a1 ) a view to _! m accurate det]m9ation4 ,! objects to be ga9$ by s do+ belong r to ! inf]5tial "p ( our subject1 & w be bett] indicat$ fur!r on2 b !y d n involve any di/9ct pr9ciple4 ,l o!r attempts to apply ! me?ods ( sci5ce 9 ! region ( ! m9d1 ?is proposal has met ) "s opposition2 ) v slight reason1 z x seems to me4 ,t our m5tal qualities1 if !y c\ld be submitt$ to accurate measurem5t1 w\ld be f\nd to foll[ ! usual ,law ( ,error1 may be assum$ )\t mu* hesitation4 ,! kn[n ext5t ( ! correlation ( m5tal & bodily *>act]i/ics gives high probability to ! supposition t :at is prov$ to prevail1 at any rate approximately1 among/ mo/ bodily elem5ts :i* h be5 submitt$ to measurem5t1 w prevail also among/ ! m5tal elem5ts4 ,to :at ext5t su* measurem5ts c\ld be c>ri$ out practically1 is ano!r matt]4 ,x does n seem to me t x c\ld be done ) mu* success2 p>tly because our m5tal qualities are s closely connect$ )1 inde$ s run into "o ano!r1 t x is impossible to isolate !m = purposes ( comp>ison4#af ,?is is to "s ext5t inde$ a difficulty 9 bodily measurem5ts1 b x is f> m s 9 ^? ( ! m9d1 :]e we c h>dly get beyond :at c be call$ a good guess4 ,! doctr9e1 !re=e1 t m5tal qualities foll[ ! n[ famili> law ( arrangem5t c sc>cely be gr\nd$ ^u any?+ m ?an a /rong analogy4 ,/ill ?is analogy is q /rong en\gh to ju/ify u 9 accept+ ! doctr9e & all ! conclusions :i* foll[ f x1 9 s f> z our e/imates & measurem5ts c be reg>d$ z tru/wor?y4 ,!re seems !re=e no?+ unreasonable 9 ! attempt to e/abli% a sy/em ( natural classification ( mank9d by arrang+ !m into a c]ta9 numb] ( gr\ps above & bel[ ! av]age1 ea* gr\p be+ int5d$ to correspond to c]ta9 limits ( excell5cy or defici5cy4#ag ,all t is necess>y = su* a purpose is t ! rate ( dep>ture f ! mean %\ld be tol]ably con/ant "u widely diff]5t circum/ances3 9 ?is case ?r\gh\t all ! races ( man4 ,( c\rse if ! law ( div]g5ce is ! same z t :i* prevails 9 inanimate nature we h a /ill wid] & m natural sy/em ( classification at h&1 & "o :i* ought to be famili>1 m or less1 to e "o :o has ?us to e/imate qualities4 #ba4 ,p]haps "o ( ! be/ illu/rations ( ! legitimate application ( su* pr9ciples is to be f\nd 9 ,mr ,galton's "w on ,h]$it>y ,g5ius4 ,inde$ ! full =ce & purport ( "s ( 8 reason+s !re c h>dly be appreciat$ except by ^? :o are famili> ) ! conceptions :i* we h be5 discuss+ 9 ?is *apt]4 ,we c only af=d space to notice "o or two po9ts1 b ! /ud5t w f9d 9 ! p]usal1 ( at any rate ! m argum5tive p>ts1 ( t volume#ah an int]e/+ illu/ration ( ! doctr9es n[ "u discussion4 ,= "o ?+ x may be safely ass]t$1 t no "o unfamili> ) ! ,law ( ,error w\ld ev] 9 ! lea/ appreciate ! excessive rapidity ) :i* ! sup]ior degrees ( excell5ce t5d to become sc>ce4 ,e "o1 ( c\rse1 c see at once1 9 a num]ical way at lea/1 :at is involv$ 9 be+ '"o ( a million'2 b !y w\ld n at all und]/&1 h[ v little extra sup]iority is to be look$ = 9 ! man :o is '"o ( two million'4 ,!y w\ld conf\nd ! m]e num]ical di/9ction1 :i* seems 9 "s way to imply d\ble excell5ce1 ) ! intr9sic sup]iority1 :i* w\ld mo/ly be repres5t$ by a v small fractional advantage4 ,to be '"o ( t5 million' s\nds v gr&1 b if ! qualities "u consid]ation c\ld be e/imat$ 9 !mselves )\t ! k ( ! va/ly wid] area f :i* ! selection _h be5 made1 & 9 fre$om !re=e f any consequ5t num]ical bias1 p w\ld be surpris$ to f9d :at a v slight comp>ative sup]iority 01 z a rule1 ?us obta9$4 #bb4 ,! po9t j m5tion$ is an important "o 9 argum5ts f /ati/ics4 ,if1 = in/ance1 we f9d a small gr\p ( p]sons1 connect$ toge!r by blood-relation%ip1 & all possess+ "s m5tal *>act]i/ic 9 m>k$ sup]iority1 mu* dep5ds ^u ! comp>ative r>ity ( su* excell5ce :5 we are endeav\r+ to decide :e!r or n ! common possession ( ^! qualities 0 accid5tal4 ,su* a decision c nev] be m ?an a r\gh "o1 b if x is to be made at all ?is consid]ation mu/ ent] z a factor4 ,aga91 :5 we are comp>+ "o nation ) ano!r1#ai say ! ,a!nian ) any mod]n ,european p1 does ! popul> m9d at all appreciate :at sort ( evid5ce ( g5]al sup]iority is impli$ by ! production1 out ( "o nation1 ( su* a gr\p z c be compos$ ( ,socrates1 ,plato1 & a few ( _! contempor>ies8 ,9 ?is latt] case we are also1 x %\ld be rem>k$1 employ+ ! ',law ( ,error' 9 a second way2 = we are assum+ t :]e ! extremes are great s w also ! means be1 9 o!r words we are assum+ t e am\nt ( dep>ture f ! mean occurs ) a 7r\ghly7 calculable degree ( relative frequ5cy4 ,h[ev] g5]ally ?is tru? may be accept$ 9 a vague way1 its evid5ce c only be appreciat$ by ^? :o "k ! reasons :i* c be giv5 9 its fav\r4 ,b ! same pr9ciples w also supply a caution 9 ! case ( ! la/ example4 ,!y rem9d u t1 = ! m]e purpose ( comp>ison1 ! av]age man ( any gr\p or class is a mu* bett] object = selection ?an ! em95t "o4 ,!re may be great] difficulties 9 ! way ( detect+ him1 b :5 we h done s we h got possession ( a secur] & m /able basis ( comp>ison4 ,he is select$1 by ! nature ( ! case1 f ! mo/ num]\s /ratum ( 8 society2 ! em95t man f a ?9ly occupi$ /ratum4 ,9 accordance !re=e ) ! n[ famili> laws ( av]ages & ( l>ge numb]s ! fluctuations among/ ! =m] w g5]ally be v few & small 9 comp>ison ) ^? among/ ! latt]4 #a4 ,essai de ,physique ,sociale1 #ahfi4 ,an?ropomtrie1 #ahgj4 #b4 ,z reg>ds lat] /ati/ics on ! same subject ! read] c ref] to ! ,reports ( ! ,an?ropometrical ,committee ( ! ,briti% ,association 7#ahgi1 #ahhj1 #ahha1 #ahhc2--;especially ?is la/74 ,^! reports seem to me to repres5t a great advance on ! results obta9$ by ,quetelet1 & fully to ju/ify ! claim ( ! ,secret>y 7,mr ,c4 ,rob]ts7 t _! /ati/ics are unique 9 range & numb]s4 ,!y embrace n m]ely milit>y recruits--l mo/ ( ! previ\s tables--b almo/ e class & age1 & bo? sexes4 ,moreov] !y ref] n only to /ature b to a numb] ( o!r physical *>act]i/ics4 #c4 ,z e ma!matician kn[s1 ! relative numb]s ( ea* ( ^! possible ?r[s are giv5 by ! successive t]ms ( ! expansion ( 7#a #a7aj1 viz4 #a1 #aj1 #de1 #abj1 #baj1 #beb1 #baj1 #abj1 #de1 #aj1 #a4 #d4 ,t is !y w be m d5sely aggregat$4 ,if a space ! size ( ! bull's-eye be exam9$ 9 ea* successive circle1 ! numb] ( %ot m>ks :i* x conta9s w be successively less4 ,! actual numb] ( %ots :i* /rike ! bull's-eye w n be ! greate/1 s9ce x cov]s s mu* less surface ?an any ( ! o!r circles4 #e4 ,commonly call$ ! expon5tial law2 its equation be+ ( ! =m y ,ae-hx#b4 ,! curve correspond+ to x cuts ! axis ( y at "r angles 7express+ ! fact t ne> ! mean !re are a l>ge numb] ( values approximately equal72 aft] a "t x beg9s to slope away rapidly t[>ds ! axis ( x 7express+ ! fact t ! results soon beg9 to gr[ less common z we rec$e f ! mean72 & ! axis ( x is an asymptote 9 bo? directions 7express+ ! fact t no magnitude1 h[ev] remote f ! mean1 is /rictly impossible2 t is1 e deviation1 h[ev] excessive1 w h to be enc\nt]$ at l5g? )9 ! range ( a suffici5tly long exp]i5ce74 ,! curve is obvi\sly symmetrical1 express+ ! fact t equal deviations f ! mean1 9 excess & 9 defect1 t5d to occur equally (t5 9 ! long run4 ,figure3 ,gaussian normal di/ribution4 ,a r\gh graphic repres5tation ( ! curve is giv5 above4 ,= ! b5efit ( ^? unfamili> ) ma!matics "o or two brief rem>ks may be "h app5d$ conc]n+ "s ( its prop]ties4 7#a7 ,x mu/ n be suppos$ t all specim5s ( ! curve are simil> to "o ano!r4 ,! dott$ l9es are equally specim5s ( x4 ,9 fact1 by v>y+ ! ess5tially arbitr>y units 9 :i* x & y are respectively e/imat$1 we may make ! portion t[>ds ! v]tex ( ! curve z obtuse or z acute z we please4 ,?is consid]ation is ( importance2 = x rem9ds u t1 by v>y+ "o ( ^! arbitr>y units1 we c\ld get an 'expon5tial curve' :i* %\ld tol]ably closely resemble any symmetrical curve ( error1 provid$ t ?is latt] recogniz$ & 0 f\nd$ ^u ! assumption t extreme div]g5ces 7 excessively r>e4 ,h5ce x w\ld be difficult1 by m]e obs]vation1 to prove t ! law ( error 9 any giv5 case 0 n expon5tial2 unless ! /ati/ics 7 v ext5sive1 or ! actual results dep>t$ consid]ably f ! expon5tial =m4 7#b7 ,x is q impossible by any graphic repres5tation to give an adequate idea ( ! excessive rapidity ) :i* ! curve aft] a "t approa*es ! axis ( x4 ,at ! po9t ,r1 on our scale1 ! curve w\ld approa* )9 ! fifte5-?\s&? "p ( an in* f ! axis ( x1 a di/ance :i* only a v good microscope c\ld detect4 ,:]eas 9 ! hyp]bola1 e4g4 ! rate ( approa* ( ! curve to its asymptote is cont9ually decreas+1 x is "h j ! rev]se2 ?is rate is cont9ually increas+4 ,h5ce ! two1 viz4 ! curve & ! axis ( x1 appe> to ! eye1 aft] a v %ort "t1 to m]ge into "o ano!r4 #f4 ,z by ,quetelet3 not$1 among/ o!rs1 by ,h]s*el1 ,essays1 page #dji4 #g4 ,proc4 ,r4 ,soc4 ,oct4 #ba1 #ahgi4 #h4 ,we are "h consid]+1 rememb]1 ! case ( a f9ite am\nt ( /ati/ics2 s t !re are actual limits at ea* end4 #i4 ,x mu/ be admitt$ t exp]i5ce has n yet 7,i believe7 %[n ?is asymmetry 9 respect ( heights4 #aj4 ,! above reason+ w probably be accept$ z valid at ?is /age ( enquiry4 ,b 9 /rictness1 assumptions are made "h1 :i* h[ev] ju/ifiable !y may be 9 !mselves1 involve some:at ( an anticipation4 ,!y dem&1 & 9 a future *apt] w receive1 clos] scrut9y & criticism4 #aa4 ,a def9ite num]ical example ( ?is k9d ( conc5tration ( frequ5cy ab\t ! mean 0 giv5 9 ! note to #d4 ,x 0 ( a b9omial =m1 consi/+ ( ! successive t]ms ( ! expansion ( 7#a #a7m4 ,n[ x may be %[n 7,quetelet1 ,lett]s1 p4 #bfc2 ,liagre1 ,calcul des ,probabilits1 #cd7 t ! expansion ( su* a b9omial1 z m becomes indef9itely great1 approa*es z its limit ! expon5tial =m2 t is1 if we take a numb] ( equidi/ant ord9ates proportional respectively to #a1 m1 m7m - #a7_/7ab7 c41 & connect _! v]tices1 ! figure we obta9 approximately repres5ts "s =m ( ! curve y ,ae-hx#b1 & t5ds to become id5tical ) x1 z m is increas$ )\t limit4 ,9 o!r words1 if we suppose ! errors to be produc$ by a limit$ numb] ( f9ite1 equal & indep5d5t causes1 we h an approximation to ! expon5tial ,law ( ,error1 :i* m]ges into id5tity z ! causes are increas$ 9 numb] & dim9i%$ 9 magnitude )\t limit4 ,jevons has giv5 7,pr9ciples ( ,sci5ce1 p4 #cha7 a diagram drawn to scale1 to %[ h[ rapid ?is approximation is4 ,"o po9t mu/ be c>efully rememb]$ "h1 z x is frequ5tly ov]look$ 7by ,quetelet1 = in/ance74 ,! coeffici5ts ( a b9omial ( two equal t]ms--z 7#a #a7m1 9 ! prec$+ p>agraph--are symmetrical 9 _! arrangem5t f ! fir/1 & v spe$ily become indi/+ui%able 9 7graphical7 outl9e f ! f9al expon5tial =m4 ,b if1 on ! o!r h&1 we 7 to consid] ! successive t]ms ( su* a b9omial z 7#a #d7m 7:i* are proportional to ! relative *ances ( #j1 #a1 #b1 #c1 444 failures 9 m v5tures1 ( an ev5t :i* has "o *ance 9 its fav\r to f\r aga9/ x7 we %\ld h an unsymmetrical succession4 ,if h[ev] we suppose m to increase )\t limit1 z 9 ! =m] supposition1 ! unsymmetry gradually disappe>s & we t5d t[>ds precisely ! same expon5tial =m z if we _h begun ) two equal t]ms4 ,! only diff]5ce is t ! position ( ! v]tex ( ! curve is no long] 9 ! c5tre3 9 o!r words1 ! likelie/ t]m or ev5t is n an equal numb] ( successes & failures b successes & failures 9 ! ratio ( #a to #d4 #ab4 ',law ( ,error' is ! usual te*nical t]m = :at has be5 else:]e spok5 ( above z a ,law ( ,div]g5ce f a mean4 ,x is 9 /rictness only appropriate 9 ! case ( "o1 namely ! ?ird1 ( ! ?ree classes ( ph5om5a m5tion$ 9 #d1 b by a conv5i5t g5]alization x is equally appli$ to ! o!r two2 s t we t]m ! am\nt ( ! div]g5ce f ! mean an 'error' 9 e case1 h[ev] x may h be5 br\ght ab\t4 #ac4 ,?is h[ev] seems to be ! purport1 ei!r by direct ass]tion or by implication1 ( two elaborate works by ,quetelet1 viz4 8 ,physique ,sociale & 8 ,an?ropomtrie4 #ad4 ,he sc>cely1 h[ev]1 pr(esses to give ^! z an accurate measure ( ! mean height1 nor does he always give precisely ! same measure4 ,practically1 none b soldi]s be+ measur$ 9 any great numb]s1 ! ,engli% /ature did n af=d accurate data on any l>ge scale4 ,! /ati/ics giv5 a few pages fur!r on are probably f> m tru/wor?y4 #ae4 ,?is /atem5t w receive "s explanation & correction 9 ! next *apt]4 #af4 ,i am n speak+ "h ( ! n[ famili> results ( ,psy*ophysics1 :i* are ma9ly occupi$ ) ! measurem5t ( p]ceptions & o!r simple /ates ( consci\sness4 #ag4 ,p]haps ! be/ brief acc\nt ( ,mr ,galton's me?od is to be f\nd 9 a pap] 9 ,m9d 7,july1 #ahhj7 on ! /ati/ics ( ,m5tal ,imag]y4 ,! subject "u comp>ison "h--viz4 ! relative p[]1 possess$ by diff]5t p]sons1 ( rais+ cle> visual images ( objects no long] pres5t to u--is "o :i* x seems impossible to 'measure'1 9 ! ord9>y s5se ( ! t]m4 ,b by arrang+ all ! answ]s 9 ! ord] 9 :i* ! faculty 9 "q seems to be possess$ we c1 ) "s approa* to accuracy1 select ! middlemo/ p]son 9 ! r[ & use him z a basis ( comp>ison ) ! correspond+ p]son 9 any o!r bat*4 ,& simil>ly ) ^? :o occupy o!r relative positions ?an t ( ! middlemo/4 #ah4 ,i ref] to ! introductory & conclud+ *apt]s3 ! bulk ( ! book is1 f ! nature ( ! case1 ma9ly occupi$ ) /ati/ical & biographical details4 #ai4 ,see ,galton's ,h]$it>y ,g5ius1 pp4 #ccf-cej1 ,on ! comp>ative wor? ( diff]5t races4 ,,*apt] ,,iii4 ,,on ,,! ,,causal ,,process ,,by ,,:i* ,,! ,,gr\ps ,,or ,,s]ies ,,( ,,probability ,,are ,,br\ght ,,ab\t4 #a4 ,9 discuss+ ! "q :e!r all ! v>i\s gr\ps & s]ies ) :i* ,probability is conc]n$ are ( precisely "o & ! same type1 we made "s exam9ation ( ! process by :i* !y are naturally produc$1 b we mu/ n[ ent] a little m into ! details ( ?is process4 ,all ev5ts are ! results ( num]\s & complicat$ antec$5ts1 f> too num]\s & complicat$ 9 fact = x to be possible = u to det]m9e or take !m all into acc\nt4 ,n[1 ?\gh x is /rictly true t we c nev] det]m9e !m all1 !re is a broad di/9ction betwe5 ! case ( ,induction1 9 :i* we c make out en\gh ( !m1 & ) suffici5t accuracy1 to satisfy a reasonable c]ta9ty1 & ,probability1 9 :i* we _c d s4 ,to ,induction we %all return 9 a future *apt]1 & !re=e no m ne$ be said ab\t x "h4 ,we %all f9d x conv5i5t to beg9 ) a division :i*1 ?\gh n pret5d+ to any philosophical accuracy1 w s]ve z a prelim9>y guide4 ,x is ! simple division into objects1 & ! ag5cies :i* affect !m4 ,all ! ph5om5a ) :i* ,probability is conc]n$ 7z inde$ mo/ ( ^? ) :i* sci5ce ( any k9d is conc]n$7 are ! product ( c]ta9 objects natural & artificial1 act+ "u ! influ5ce ( c]ta9 ag5cies natural & artificial4 ,9 ! toss+ ( a p5ny1 = in/ance1 ! objects w\ld be ! p5ny or p5ce :i* 7 successively ?r[n2 ! ag5cies w\ld be ! act ( ?r[+1 & ev]y?+ :i* comb9$ directly or indirectly ) ?is to make any p>ticul> face come upp]mo/4 ,?is is a simple & intelligible division1 & c easily be s ext5d$ 9 mean+ z to embrace e class ( objects ) :i* we are conc]n$4 ,n[ if1 9 any two or m cases1 we _h ! same object1 or objects indi/+ui%ably alike1 & if !y 7 expos$ to ! influ5ce ( ag5cies 9 all respects precisely alike1 we %\ld expect ! results to be precisely simil>4 ,by "o ( ! applications ( ! famili> pr9ciple ( ! uni=mity ( nature we %\ld be confid5t t exact lik5ess 9 ! antec$5ts w\ld be foll[$ by exact lik5ess 9 ! consequ5ts4 ,if ! same p5ny1 or simil> p5ce1 7 ?r[n 9 exactly ! same way1 we %\ld inv>iably f9d t ! same face falls upp]mo/4 #b4 ,:at we actually f9d is1 ( c\rse1 v f> remov$ f ?is4 ,9 ! case ( ! objects1 :5 !y are artificial con/ructions1 e4g4 dice1 p5ce1 c>ds1 x is true t !y are purposely made z ne>ly z possible indi/+ui%ably alike4 ,we ei!r use ! same ?+ ov] & ov] aga9 or diff]5t ones made accord+ to precisely ! same model4 ,b 9 natural objects no?+ ( ! sort prevails4 ,9 fact :5 we come to exam9e !m1 we f9d reproduc$ 9 !m precisely ! same *>act]i/ics z ^? :i* pres5t !mselves 9 ! f9al result :i* we 7 ask$ to expla91 s t unless we exam9e !m a /age fur!r back1 z we %all h to d to "s ext5t at any rate1 we seem to be m]ely po/ulat+ aga9 ! v peculi>ity ( ! ph5om5a :i* we 7 und]tak+ to expla94 ,!y w be f\nd1 = in/ance1 to consi/ ( l>ge classes ( objects1 ?r\gh\t all ! individual memb]s ( :i* a g5]al resemblance ext5ds4 ,suppose t we 7 consid]+ ! l5g? ( life4 ,! objects "h are ! human be+s1 or t select$ class ( !m1 ^: lives we are consid]+4 ,! resemblance exi/+ among !m is to be f\nd 9 ! /r5g? & s\ndness ( _! pr9cipal vital organs1 toge!r ) all ! circum/ances :i* collectively make up :at we call ! goodness ( _! con/itutions4 ,x is true t mo/ ( ^! circum/ances d n admit ( any approa* to actual measurem5t2 b1 z 0 po9t$ out 9 ! la/ *apt]1 v _m ( ! circum/ances :i* d admit ( su* measurem5t h be5 measur$1 & f\nd to display ! *>act]i/ics 9 "q4 ,h5ce1 f ! kn[n analogy & correlation betwe5 our v>i\s organs1 !re c be no reasonable d\bt t if we c\ld arrange human con/itutions 9 g5]al1 or ! v>i\s elem5ts :i* compose !m 9 p>ticul>1 9 ! ord] ( _! /r5g?1 we %\ld f9d j su* an aggregate regul>ity & j su* gr\p+s ab\t ! mean1 z ! f9al result 7viz4 9 ?is case ! l5g? ( _! lives7 pres5ts to our notice4 #c4 ,x w be obs]v$ !re=e t = ?is purpose ! exi/5ce ( natural k9ds or gr\ps is necess>y4 ,9 our games ( *ance ( c\rse ! same die may be ?r[n1 or a c>d be drawn f ! same pack1 z (t5 z we please2 b _m ( ! ev5ts :i* occur to human be+s ei!r _c be repeat$ at all1 or n (t5 en\gh to secure 9 ! case ( ! s+le individual any suffici5t /ati/ical uni=mity4 ,su* regul>ity z we trace 9 nature is ow+1 mu* m ?an is (t5 suspect$1 to ! arrangem5t ( ?+s 9 natural k9ds1 ea* ( !m conta9+ a l>ge numb] ( individuals4 ,7 ea* k9d ( animals or vegetables limit$ to a s+le pair1 or ev5 to b a few pairs1 !re w\ld n be mu* scope left = ! collection ( /ati/ical tables among/ !m4 ,or to take a less viol5t supposition1 if ! numb]s 9 ea* natural class ( objects 7 mu* small] ?an !y are at pres5t1 or ! diff]5ces betwe5 _! v>ieties & sub-species mu* m m>k$1 ! consequ5t difficulty ( extract+ f !m any suffici5t l5g? ( /ati/ical tables1 ?\gh n fatal1 might be v s]i\s4 ,a l>ge numb] ( objects 9 ! class1 toge!r ) t g5]al simil>ity :i* entitles ! objects to be fairly compris$ 9 "o class1 seem to be important conditions = ! applicability ( ! !ory ( ,probability to any ph5om5on4 ,some?+ analog\s to ?is excessive paucity ( objects 9 a class w\ld be f\nd 9 ! attempt to apply special ,insurance (fices to ! case ( ^? trades :]e ! numb]s are v limit$1 & ! employm5t s dang]\s z to put !m 9 a class by !mselves4 ,if an insurance society 7 />t$ = ! workm5 9 gunp[d] mills alone1 a premium w\ld h to be *>g$ to avoid possible ru91 s high z to illu/rate ! extreme paucity ( appropriate /ati/ics4 #d4 ,s mu* 7at pres5t7 = ! objects4 ,if we turn to :at we h t]m$ ! ag5cies1 we f9d mu* ! same ?+ aga9 "h4 ,by ! adju/m5t ( _! relative int5sity1 & ! respective frequ5cy ( _! occurr5ce1 ! total effects :i* !y produce are f\nd to be also tol]ably uni=m4 ,x is ( c\rse conceivable t ?is %\ld h be5 o!rwise4 ,x might h be5 f\nd t ! second gr\p ( conditions s exactly correct$ ! =m] z to conv]t ! m]ely g5]al uni=mity into an absolute "o2 or x might h be5 f\nd1 on ! o!r h&1 t ! second gr\p %\ld aggravate or di/urb ! influ5ce ( ! =m] to su* an ext5t z to de/roy all ! uni=mity ( its effects4 ,practically nei!r is ! case4 ,! second condition simply v>ies ! details1 leav+ ! uni=mity on ! :ole ( precisely ! same g5]al description z x 0 be=e4 ,or if ! objects 7 suppos$ to be absolutely alike1 z 9 ! case ( successive ?r[s ( a p5ny1 x may s]ve to br+ ab\t a uni=mity4 ,analysis w %[ ^! ag5cies to be ?us made up ( an almo/ inf9ite numb] ( diff]5t compon5ts1 b x w detect ! same peculi>ity t we h s (t5 _h occasion to ref] to1 p]vad+ almo/ all ^! compon5ts4 ,! proportions 9 :i* !y are comb9$ w be f\nd to be ne>ly1 ?\gh n q1 ! same2 ! int5sity ) :i* !y act w be ne>ly ?\gh n q equal4 ,& !y w all unite & bl5d into a m & m p]fect regul>ity z we proce$ to take ! av]age ( a l>g] numb] ( in/ances4 ,take1 = in/ance1 ! l5g? ( life4 ,z we h se51 ! con/itutions ( a v l>ge numb] ( p]sons select$ at r&om w be f\nd to pres5t mu* ! same feature2 g5]al uni=mity accompani$ by individual irregul>ity4 ,n[ :5 ^! p]sons g out into ! _w1 !y are expos$ to a v>iety ( ag5cies1 ! collective influ5ce ( :i* w assign to ea* ! l5g? ( life allott$ to him4 ,^! ag5cies are ( c\rse innum]able1 & _! mutual int]action complicat$ beyond all p[] ( analysis to extricate4 ,ea* effect becomes 9 its turn a cause1 is int]wov5 inextricably ) an indef9ite numb] ( o!r causes1 & reacts ^u ! f9al result4 ,climate1 food1 clo?+1 are "s ( ^! ag5cies1 or r comprise aggregate gr\ps ( !m4 ,! nature ( a man's "w is also important4 ,"o man ov]works himself1 ano!r foll[s an unheal?y trade1 a ?ird exposes himself to infection1 & s on4 ,! result ( all ?is int]action betwe5 :at we h ?us call$ objects & ag5cies is t ! f9al outcome pres5ts ! same g5]al *>act]i/ics ( uni=mity z may be detect$ sep>ately 9 ! two con/itu5t elem5ts4 ,or r1 z we %all proce$ pres5tly to %[1 x does s 9 ! great majority ( cases4 #e4 ,x may be object$ t su* an explanation z ! above does n really am\nt to any?+ des]v+ ( ! "n1 = t in/ead ( expla9+ h[ a p>ticul> /ate ( ?+s is caus$ x m]ely po9ts out t ! same /ate exi/s else:]e4 ,!re is a uni=mity discov]$ 9 ! objects at ! /age :5 !y are commonly submitt$ to calculation2 we !n grope ab\t among/ ! causes ( !m1 & aft] all only discov] a precisely simil> uni=mity exi/+ among/ ^! causes4 ,?is is to "s ext5t true1 = ?\gh "p ( ! objection c be remov$1 x mu/ always rema9 ! case t ! f\ndations ( an objective sci5ce w re/ 9 ! la/ resort ^u ! m]e fact t ?+s are f\nd to be ( su* & su* a "*4 #f4 ,?is division1 into objects & ! ag5cies :i* affect !m1 is m]ely int5d$ = a r\gh practical arrangem5t1 suffici5t to po9t out to ! read] ! imm$iate nature ( ! causes :i* br+ ab\t our famili> uni=mities4 ,if we g back a /ep fur!r1 x might fairly be ma9ta9$ t !y may be r$uc$ to "o1 namely1 to ! ag5cies4 ,! objects1 z we h t]m$ !m1 are n an orig9al creation 9 ! /ate 9 :i* we n[ f9d !m4 ,no "o supposes t :ole gr\ps or classes 7 br\ght into exi/5ce simultane\sly1 ) all _! g5]al resemblances & p>ticul> diff]5ces fully develop$4 ,ev5 if x 7 ! case t ! fir/ p>5ts ( ea* natural k9d _h be5 specially creat$1 in/ead ( be+ develop$ out ( pre-exi/+ =ms1 x w\ld /ill be true t among/ ! numb]s ( ea* t n[ pres5t !mselves ! *>act]i/ic diff]5ces & resemblances are ! result ( :at we h t]m$ ag5cies4 ,take1 = in/ance1 a s+le *>act]i/ic only1 say ! height2 :at det]m9es ?is z we f9d x 9 any giv5 gr\p ( m58 ,p>tly1 no d\bt1 ! nature ( _! own food1 clo?+1 employm5t1 & s on1 especially 9 ! e>lie/ ye>s ( _! life2 p>tly also1 v likely1 simil> conditions & circum/ances on ! "p ( _! p>5ts at "o "t or ano!r4 ,no "o1 ,i presume1 9 ! pres5t /ate ( k1 w\ld attempt to enum]ate ! rema9+ causes1 or ev5 to give any indication ( _! exact nature2 b at ! same "t few w\ld ent]ta9 any d\bt t ag5cies ( ?is g5]al description h be5 ! det]m9+ causes at "w4 ,if x be ask$ aga91 ,into :at may ^! ag5cies !mselves be ultimately analys$8 ! answ] to ?is "q1 9 s f> z x involves any detail$ exam9ation ( !m1 w\ld be =eign to ! plan ( ?is essay4 ,9 s f> z any g5]al rem>ks1 applicable to ne>ly all classes alike ( su* ag5cies1 are call$ =1 we are l$ back to ! po9t f :i* we />t$ 9 ! previ\s *apt]1 :5 we 7 discuss+ :e!r !re is necess>ily "o fix$ law accord+ to :i* all our s]ies are =m$4 ,we !re saw t e ev5t might be reg>d$ z be+ br\ght ab\t by a comp>atively few important causes1 ( ! k9d :i* comprises all ( :i* ord9>y obs]vation takes any notice1 & an indef9itely num]\s gr\p ( small causes1 too num]\s1 m9ute1 & unc]ta9 9 _! action = u to be able to e/imate !m or inde$ to take !m individually into acc\nt at all4 ,! important ones1 x is true1 may also 9 turn be !mselves conceiv$ to be made up ( aggregates ( small compon5ts1 b !y are /ill be/ reg>d$ z be+ by comp>ison simple & di/9ct1 = _! compon5t p>ts act mo/ly 9 gr\ps collectively1 appe>+ & disappe>+ toge!r1 s t !y possess ! ess5tial *>act]i/ics ( unity4 #g4 ,n[1 broadly speak+1 x appe>s to me t ! mo/ suitable conditions = ,probability are ^!3 t ! important causes %\ld be by comp>ison fix$ & p]man5t1 & t ! rema9+ ones %\ld on ! av]age cont9ue to act z (t5 9 "o direction z 9 ! o!r4 ,?is !y may d 9 two ways4 ,9 ! fir/ place we may be able to pr$icate no?+ m ( !m ?an ! m]e fact t !y act#a z (t5 9 "o direction z ! o!r2 :at we %\ld !n obta9 w\ld be m]ely ! simple /ati/ical uni=mity t is describ$ 9 ! fir/ *apt]4 ,b x may be ! case1 & 9 practice g5]ally is s m or less approximately1 t ^! m9or causes act also 9 indep5d5ce ( "o ano!r4 ,:at we !n get is a gr\p ( uni=mities su* z 0 expla9$ & illu/rat$ 9 ! second *apt]4 ,e possible comb9ation ( ^! causes !n occurr+ ) a regul> degree ( frequ5cy1 we f9d "o peculi> k9d ( uni=mity exhibit$1 n m]ely 9 ! m]e fact ( excess & defect 7( :atev] may be ! v>iable quality 9 "q71 b also 9 e p>ticul> am\nt ( excess & defect4 ,h5ce1 9 ?is case1 we get :at "s writ]s t]m a 'mean' or 'type1' in/ead ( a simple av]age4 ,= in/ance1 suppose a man ?r[+ a quoit at a m>k4 ,"h our fix$ causes are 8 /r5g?1 ! weight ( ! quoit1 & ! int5tion ( aim+ at a giv5 po9t4 ,^! we mu/ ( c\rse suppose to rema9 un*ang$1 if we are to obta9 any su* uni=mity z we are seek+4 ,! m9or & v>iable causes are all ^? innum]able little di/urb+ influ5ces ref]r$ to 9 ! la/ *apt]4 ,x might conceivably be ! case t we 7 only able to asc]ta9 t ^! act$ z (t5 9 "o direction z 9 ! o!r2 :at we %\ld !n f9d 0 t ! quoit t5d$ to fall %ort ( ! m>k z (t5 z beyond x4 ,b ow+ to ^! little causes be+ mo/ly indep5d5t ( "o ano!r1 & m or less equal 9 _! influ5ce1 we f9d also t e am\nt ( excess & defect pres5ts ! same g5]al *>act]i/ics1 & t 9 a l>ge numb] ( ?r[s ! quantity ( div]g5ces f ! m>k1 ( any giv5 am\nt1 is a tol]ably det]m9ate function1 accord+ to a regul> law1 ( t am\nt ( div]g5ce4#b #h4 ,! necessity ( ! conditions j h9t$ at w be/ be se5 by a ref]5ce to cases 9 :i* any ( !m happ5 to be miss+4 ,?us we "k t ! l5g? ( life is on ! :ole tol]ably regul>1 & s are ! numb]s ( ^? :o die 9 successive ye>s or c5turies ( mo/ ( ! common] diseases4 ,b x does n seem to be ! case ) all diseases4 ,:at1 = in/ance1 ( ! ,sweat+ ,sickness1 ! ,black ,dea?1 ! ,asiatic ,*ol]a8 ,! two =m] ei!r d n recur1 or1 if !y d1 recur 9 su* a mild =m z n to des]ve ! same "n4 ,:at 9 fact ( any ( ! diseases :i* are epidemic r ?an endemic8 ,all ^! h _! causes d\btless1 & w\ld be produc$ aga9 by ! recurr5ce ( ! conditions :i* caus$ !m be=e4 ,b "s ( !m app>5tly d n recur at all4 ,!y seem to h dep5d$ ^u su* r>e conditions t _! occurr5ce 0 almo/ unique4 ,& ( ^? :i* d recur ! c\rse is frequ5tly s ecc5tric & irregul>1 (t5 s mu* dep5d5t ^u human w or want ( w1 z to entirely deprive _! results 7t is1 ! annual numb] ( dea?s :i* !y cause7 ( ! /ati/ical uni=mity ( :i* we are speak+4 ,! explanation probably is t "o ( ! pr9cipal causes 9 su* cases is :at we commonly call contagion4 ,if s1 we h at once a cause :i* s f> f be+ fix$ is subject to ! utmo/ v>iability4 ,/r+5t caution may de/roy x1 c>elessness may aggravate x to any ext5t4 ,! w ( man1 z f9d+ its expression ei!r on ! "p ( gov]nm5t1 ( doctors1 or ( ! public1 may make ( x pretty ne>ly :at is wi%$1 ?\gh aga9/ ! possibility ( its entrance into any community no precautions c absolutely insure u4 #i4 ,if x be repli$ t ?is want ( /ati/ical regul>ity only arises f ! fact ( our hav+ conf9$ ourselves to too limit$ a "t1 & t we %\ld f9d irregul>ity disappe> "h1 z else:]e1 if we kept our tables op5 long en\gh1 we %all f9d t ! answ] w sugge/ ano!r case 9 :i* ! requisite conditions = ,probability are want+4 ,su* a reply w\ld only be conclusive ^u ! supposition t ! ways & ?\ghts ( m5 are 9 ! long run inv>iable1 or if v>iable1 subject to p]iodic *anges only4 ,on ! assumption ( a /eady progress 9 society1 ei!r = ! bett] or ! worse1 ! argum5t falls to ! gr\nd at once4 ,f :at we "k ( ! c\rse ( ! _w1 ^! fe>ful pe/s ( ! pa/ may be consid]$ z solit>y ev5ts 9 our hi/ory1 or at lea/ ev5ts :i* w n be repeat$4 ,no cont9u$ uni=mity w\ld !re=e be f\nd 9 ! dea?s :i* !y occasion1 ?\gh ! regi/r>'s books 7 kept op5 = a ?\s& ye>s4 ,! reason "h is probably to be s\ght 9 ! gradual alt]ation ( ^? indef9itely num]\s conditions :i* we t]m collectively progress or civilization4 ,e little circum/ance ( ?is k9d has "s be>+ ^u ! liability ( any "o to cat* a disease4 ,b :5 a k9d ( sl[ & /eady tide sets 91 9 consequ5ce ( :i* ^! influ5ces no long] rema9 at ab\t ! same av]age /r5g?1 w>r+ on ab\t equal t]ms ) ho/ile influ5ces1 b on ! contr>y %[ a /eady t5d5cy to increase _! p[]1 ! /ati/ics w1 ) consequ5t /ead9ess & p]man5ce1 take ! impress ( su* a *ange4 #aj4 ,briefly !n1 if we 7 ask$ :]e ! di/9ctive *>act]i/ics ( ,probability are mo/ prom95tly to be f\nd1 & :]e !y are mo/ prom95tly abs5t1 we might say t 7#a7 !y prevail pr9cipally 9 ! prop]ties ( natural k9ds1 bo? 9 ! ultimate & 9 ! d]ivative or accid5tal prop]ties4 ,9 all ! *>act]i/ics ( natural species1 9 all !y d & 9 all :i* happ5s to !m1 s f> z x dep5ds ^u _! prop]ties1 we seldom fail to detect ?is regul>ity4 ,?us 9 m52 _! height1 /r5g?1 weight1 ! age to :i* !y live1 ! diseases ( :i* !y die2 all pres5t a well-kn[n uni=mity4 ,life insurance tables (f] ! mo/ famili> in/ance ( ! importance ( ^! applications ( ,probability4 7#b7 ,! same peculi>ity prevails aga9 9 ! =ce & frequ5cy ( mo/ natural ag5cies4 ,w9d & wea!r are se5 to lose _! prov]bial irregul>ity :5 exam9$ on a l>ge scale4 ,man's "w !re=e1 :5 op]at$ on by su* ag5cies z ^!1 ev5 ?\gh x _h be5 made 9 diff]5t cases absolutely alike to beg9 )1 aft]w>ds %[s only a g5]al regul>ity4 ,i may s[ exactly ! same am\nt ( se$ 9 my field e ye>4 ,! yield may "o ye> be mod]ate1 ! next ye> be abundant ?r\gh fav\rable wea!r1 & !n aga9 9 turn be de/roy$ by hail4 ,b 9 ! long run ^! irregul>ities w be equaliz$ 9 ! result ( my crops1 because !y are equaliz$ 9 ! p[] & frequ5cy ( ! productive ag5cies4 ,! bus9ess ( und]writ]s1 & (fices :i* insure ! crops aga9/ hail1 w\ld fall "u ?is class2 ?\gh1 z already rem>k$1 !re is no v pr(\nd di/9ction betwe5 !m & ! =m] class4 ,! read] mu/ be rem9d$ aga9 t ?is fixity is only tempor>y1 t is1 t ev5 "h ! s]ies belong to ! class ( ^? :i* possess a fluctuat+ type4 ,^? inde$ :o believe 9 ! fixity ( natural species w h ! be/ *ance ( f9d+ a s]ies ( ! really p]man5t type among/ !m1 ?\gh ev5 !y w admit t "s *ange 9 ! *>act]i/ic is atta9able 9 l5g? ( "t4 ,9 ! case ( ! pr9cipal natural ag5cies1 x is ( c\rse inconte/able t ! pres5t av]age is ref]able to ! pres5t geological p]iod only4 ,our av]age temp]ature & av]age ra9fall h 9 =m] times be5 widely diff]5t f :at !y n[ are1 & d\btless w be s aga94 ,any full] inve/igation ( ! process by :i*1 on ! ,!ory ( ,evolution1 out ( a primeval simplicity & uni=mity ! pres5t v>iety 0 educ$1 h>dly belongs to ! scope ( ! pres5t "w3 at mo/1 a few h9ts mu/ suffice4 #aa4 ,! above1 !n1 are in/ances ( natural objects & natural ag5cies4 ,!re seems reason to believe t x is 9 su* ?+s only1 z di/+ui%$ f ?+s artificial1 t ! prop]ty 9 "q is to be f\nd4 ,?is is an ass]tion t w ne$ "s discussion & explanation4 ,two in/ances1 9 app>5t opposition1 w at once occur to ! m9d ( "s read]s2 "o ( :i*1 f its great intr9sic importance1 & ! o!r1 f ! frequ5cy ( ! problems :i* x furni%es1 w dem& a few m9utes' sep>ate exam9ation4 7#a7 ,! fir/ ( ^! is ! already m5tion$ case ( in/rum5tal obs]vations4 ,9 ! use ( a/ronomical & o!r in/rum5ts ! utmo/ possible degree ( accuracy is (t5 desir$1 a degree :i* _c be reasonably hop$ = 9 any "o s+le obs]vation4 ,:at we d !re=e 9 ^! cases is to make a l>ge numb] ( successive obs]vations :i* are naturally f\nd to diff] some:at f ea* o!r 9 _! results2 by means ( ^! ! true value 7z expla9$ 9 a future *apt]1 on ! ,me?od ( ,lea/ ,squ>es7 is to be det]m9$ z accurately z possible4 ,! subjects !n ( calculation "h are a c]ta9 numb] ( elem5ts1 slightly incorrect elem5ts1 giv5 by successive obs]vations4 ,are n ^! obs]vations artificial1 or ! direct product ( volunt>y ag5cy8 ,c]ta9ly n3 or r1 ! answ] dep5ds on :at we und]/& by volunt>y4 ,:at is really int5d$ & aim$ at by ! obs]v]1 is ( c\rse1 p]fect accuracy1 t is1 ! true obs]vation1 or ! volunt>y /eps & prelim9>ies on :i* ?is obs]vation dep5ds4 ,:e!r volunt>y or n1 ?is result only c be call$ int5tional4 ,b ?is result is n obta9$4 ,:at we actually get 9 its place is a s]ies ( deviations f x1 conta9+ results m or less wide ( ! tru?4 ,n[ by :at are ^! deviations caus$8 ,by j su* ag5cies z we h be5 consid]+ 9 "s ( ! e>li] sections 9 ?is *apt]4 ,heat & its irregul> w>p+ influ5ce1 draughts ( air produc+ _! correspond+ effects1 du/ & consequ5t friction 9 "o "p or ano!r1 ! slight di/ortion ( ! in/rum5t by /ra9s or ! sl[ unev5 contraction :i* cont9ues long aft] ! metal 0 ca/2 ^! & su* z ^! are "s ( ! causes :i* div]t u f ! tru?4 ,besides ?is gr\p1 !re are o!rs :i* c]ta9ly d dep5d ^u human ag5cy1 b :i* are n1 /rictly speak+1 volunt>y4 ,!y are su* z ! irregul> action ( ! muscles1 inability to make our v>i\s organs & memb]s execute precisely ! purposes we h 9 m9d1 p]haps diff]5t rates 9 ! rapidity ( ! n]v\s curr5ts1 or 9 ! response to /imuli1 9 ! same or diff]5t obs]v]s4 ,! effect produc$ by "s ( ^!1 & ! all[ance t has 9 consequ5ce to be made1 are becom+ famili> ev5 to ! outside _w "u ! "n ( ! 'p]sonal equation' 9 a/ronomical1 psy*ophysical1 & o!r obs]vations4 #ab4 7#b7 ,! o!r example1 allud$ to above1 is ! /ock "o ( c>ds & dice4 ,"h1 z 9 ! la/ case1 ! result is remotely volunt>y1 9 ! s5se t delib]ate volition pres5ts itself at "o /age4 ,b subsequ5tly to ?is /age1 ! result is produc$ or affect$ by s _m involunt>y ag5cies t x owes its *>act]i/ic prop]ties to ^!4 ,! turn+ up1 = example1 ( a p>ticul> face ( a die is ! result ( volunt>y ag5cy1 b x is n an imm$iate result4 ,t p>ticul> face 0 n *os51 ?\gh ! fact ( its be+ *os5 0 ! remote consequ5ce ( an act ( *oice4 ,!re has be5 an int]m$iate *aos ( conflict+ ag5cies1 :i* no "o c calculate be=e or di/+ui% aft]w>ds4 ,^! ag5cies seem to %[ a uni=mity 9 ! long run1 & !nce to produce a simil> uni=mity 9 ! result4 ,! draw+ ( a c>d f a pack is inde$ m directly volitional1 z 9 cutt+ = p>tn]s 9 a game ( :i/4 ,b no "o cont9ues to d ?is long )\t hav+ ! pack well %uffl$ 9 ! int]val1 :]eby a ho/ ( involunt>y influ5ces are let 94 #ac4 ,! once />tl+ b n[ famili> uni=mities exhibit$ 9 ! cases ( suicides & misdirect$ lett]s1 d n belong to ! same class4 ,! f9al resolution1 or want ( x1 :i* leads to ^! results1 is 9 ea* case inde$ an important +r$i5t 9 ! individual's action or omission2 b1 9 s f> z volition has any?+ to d ) ! results z a :ole1 x in/antly di/urbs !m4 ,if ! voice ( ! ,legislature speaks out1 or any great prea*] or morali/ succe$s 9 det]r+1 or any impressive example 9 influ5c+1 our moral /ati/ics are in/antly tamp]$ )4 ,"s fur!r discussion w be devot$ to ?is subject 9 a future *apt]2 x ne$ only be rem>k$ "h t 7always exclud+ su* common or g5]al influ5ce z ^? j m5tion$7 ! av]age volition1 pot5t z x is 9 ea* sep>ate case1 is on ! :ole sway$ by non-volunt>y conditions1 su* z ^? ( heal?1 ! casualties ( employm5t1 c41 9 fact ! v>i\s circum/ances :i* influ5ce ! l5g? ( a man's life4 #ad4 ,su* di/9ctions z ^? j insi/$ on may seem to "s p]sons to be ne$less1 b s]i\s errors h occasionally aris5 f ! neglect ( !m4 ,! imm$iate products ( man's m9d1 s f> inde$ z we c make an attempt to obta9 !m1 d n seem to possess ?is ess5tial *>act]i/ic ( ,probability4 ,_! *>act]i/ic seems r to be1 ei!r p]fect ma!matical accuracy or utt] want ( x1 ei!r law unfail+ or m]e caprice4 ,if1 e4g41 we f9d ! trees 9 a =e/ gr[+ 9 /raight l9es1 we unhesitat+ly conclude t !y 7 plant$ by man z !y /&4 ,x is true on ! o!r h&1 t if we f9d !m n regul>ly plant$1 we _c conclude t !y 7 n plant$ by man2 p>tly because ! plant] may h work$ )\t a plan1 p>tly because ! subsequ5t irregul>ities br\ght on by nature may h obscur$ ! plan4 ,practically ! m9d has to "w by ! aid ( imp]fect in/rum5ts1 & is subject$ to _m h9drances ?r\gh v>i\s & conflict+ ag5cies1 & by ^! means ! "w loses its orig9al prop]ties4 ,suppose1 = in/ance1 t a man1 in/ead ( produc+ num]ical results by imp]fect obs]vations or by ! ca/ ( dice1 7 to select !m at fir/ h& = himself by simply ?9k+ ( !m at once2 :at sort ( s]ies w\ld he obta98 ,x w\ld be ab\t z difficult to obta9 9 ?is way any su* s]ies z ^? appropriate to ,probability z x w\ld be to keep 8 he>t or pulse work+ regul>ly by direct acts ( volition1 suppos+ t he _h ! requisite control ov] ^! organs4 ,b ! m]e sugge/ion is absurd4 ,a man mu/ h an object 9 ?9k+1 he mu/ ?9k accord+ to a rule or =mula2 b unless he takes "s natural s]ies z a copy1 he w nev] be able to con/ruct "o m5tally :i* %all p]man5tly imitate ! orig9als4 ,or take ano!r product ( human ef=ts1 9 :i* ! int5tion c be execut$ ) tol]able success4 ,:5 any "o builds a h\se1 !re are _m slight di/urb+ influ5ces at "w1 su* z %r9k+ ( bricks & mort>1 settl+ ( f\ndations1 c4 ,b ! effect :i* ^! di/urbances are able to produce is s inappreciably small1 t we may fairly consid] t ! result obta9$ is ! direct product ( ! m9d1 ! accurate realization ( its int5tion4 ,:at is ! consequ5ce8 ,e h\se 9 ! r[1 if design$ by "o man & at "o "t1 is ( exactly ! same height1 wid?1 c4 z its neighb\rs2 or if !re are v>iations !y are few1 def9ite1 & regul>4 ,! result (f]s no resemblance :atev] to ! heights1 weights1 c4 ( a numb] ( m5 select$ at r&om4 ,! build] probably _h "s regul> design 9 contemplation1 & he has succe$$ 9 execut+ x4 #ae4 ,x may be repli$ t if we ext5d our obs]vations1 say to ! h\ses ( a l>ge city1 we %all !n detect ! prop]ty "u discussion4 ,! diff]5t heights ( a great numb]1 :5 gr\p$ toge!r1 might be f\nd to resemble ^? ( a great numb] ( human be+s "u simil> treatm5t4 ,some?+ ( ?is k9d might n improbably be f\nd to be ! case1 ?\gh ! resemblance w\ld be f> f be+ a close "o4 ,b to raise ?is "q is to get on to diff]5t gr\nd1 = we 7 speak+ 7z rem>k$ above7 n ( ! "w ( diff]5t m9ds ) _! diff]5t aims1 b ( t ( "o m9d4 ,9 a multiplicity ( designs1 !re may be t v>iable uni=mity1 = :i* we may look 9 va9 9 a s+le design4 ,! heights :i* ! diff]5t build]s contemplat$ might be f\nd to gr\p !mselves into some?+ ( ! same k9d ( uni=mity z t :i* prevails 9 mo/ o!r ?+s :i* !y %\ld und]take to d indep5d5tly4 ,we might !n trace ! action ( ! same two conditions1--a uni=mity 9 ! multitude ( _! diff]5t designs1 a uni=mity also 9 ! inf9ite v>iety ( ! influ5ces :i* h modifi$ ^? designs4 ,b ?is is a v diff]5t ?+ f say+ t ! "w ( "o man w %[ su* a result z ?is4 ,! diff]5ce is mu* l t betwe5 ! tread ( a ?\s& m5 :o are /epp+ )\t ?9k+ ( ea* o!r1 & _! tread :5 !y are drill$ into a regim5t4 ,9 ! =m] case !re is ! work+1 9 "o way or ano!r1 ( a ?\s& m9ds2 9 ! latt]1 ( "o only4 ,! inve/igations ( ?is & ! =m] *apt] con/itute a suffici5tly close exam9ation into ! detail$ causes by :i* ! peculi> =m ( /ati/ical results ) :i* we are conc]n$ is actually produc$1 to s]ve ! purpose ( a "w :i* is occupi$ ma9ly ) ! me?ods ( ! ,sci5ce ( ,probability4 ,! great importance1 h[ev]1 ( c]ta9 /ati/ical or sociological enquiries w dem& a recurr5ce 9 a future *apt] to "o p>ticul> application ( ^! /ati/ics1 viz4 to ^? conc]n$ ) "s classes ( human actions4 #af4 ,! only important addition to1 or modification (1 ! =ego+ rem>ks :i* ,i h f\nd occasion to make is due to ,mr ,galton4 ,he has rec5tly po9t$ out1--& 0 ,i believe ! fir/ to d s1--t 9 c]ta9 cases "s analysis ( ! causal processes c be effect$1 & is 9 fact absolutely necess>y 9 ord] to acc\nt = ! facts obs]v$4 ,take1 = in/ance1 ! heights ( ! population ( any c\ntry4 ,if ! di/ribution or disp]sion ( ^! ab\t _! mean value 7 left to ! unimp$$ action ( ^? myriad productive ag5cies allud$ to above1 we %\ld c]ta9ly obta9 su* an arrangem5t 9 ! po/]ity ( any "o g5]ation z _h already be5 exhibit$ 9 ! p>5ts4 ,t is1 we %\ld f9d repeat$ 9 ! previ\s /age ! same k9d ( ord] z we 7 try+ to acc\nt = 9 ! foll[+ /age4 ,b !n1 z ,mr ,galton insi/s1 if su* ag5cies act$ freely & indep5d5tly1 ?\gh we %\ld get ! same k9d ( arrangem5t or di/ribution1 we %\ld n get ! same degree ( x3 !re w\ld1 on ! contr>y1 be a t5d5cy t[>ds fur!r disp]sion4 ,! 'curve ( facility' 7v4 ! diagram on p4 #bi7 w\ld belong to ! same class1 b w\ld h a diff]5t modulus4 ,we %all see ?is at once if we take = comp>ison a case 9 :i* simil> ag5cies "w _! way )\t any c\nt]action :atev]4 ,suppose1 = in/ance1 t a l>ge numb] ( p]sons1 ^: =tunes 7 equal to beg9 )1 7 to comm5ce gambl+ or bett+ cont9ually = "s small sum4 ,if we exam9e _! circum/ances aft] successive int]vals ( "t1 we %\ld expect to f9d _! =tunes di/ribut$ accord+ to ! same g5]al law1--i4e4 ! n[ famili> law 9 "q1--b we %\ld also expect to f9d t ! poore/ ones 7 slightly poor]1 & ! ri*e/ ones slightly ri*]1 on ea* successive occasion4 ,we %all see m ab\t ?is 9 a future *apt] 7on ,gambl+71 b x may be tak5 = grant$ "h t !re is no?+ 9 ! laws ( *ance to resi/ ?is t5d5cy t[>ds int5sify+ ! extremes4 ,n[ x is f\nd1 on ! contr>y1 9 ! case ( vital ph5om5a1--= in/ance 9 t ( height1 & presumably ( mo/ ( ! o!r qualities :i* are 9 any way *>act]i/ic ( natural k9ds1--t !re is1 ?r\gh a numb] ( successive g5]ations1 a rem>kable degree ( fixity4 ,! tall m5 are n tall]1 & ! %ort m5 are n %ort]1 p] c5t4 ( ! population 9 successive g5]ations3 always suppos+ ( c\rse t "s g5]al *ange ( circum/ances1 su* z climate1 diet1 c4 has n set 94 ,!re mu/ !re=e "h be "s cause at "w :i* t5ds1 s to say1 to draw 9 ! extremes & ?us to *eck ! o!rwise cont9ually increas+ disp]sion4 #ag4 ,! facts 7 fir/ te/$ by c>eful exp]im5t4 ,at ! date ( ,mr ,galton's orig9al pap] on ! subject1#c !re 7 no available /ati/ics ( heights ( human be+s2 s a physical elem5t admitt+ ( c>eful exp]im5t 7viz4 ! size or weight ( c]ta9 se$s7 0 accurately e/imat$4 ,f ^! data ! actual am\nt ( rev]sion f ! extremes1 t is1 ( ! slight pressure cont9ually put ^u ! extreme memb]s ) ! result ( cr[d+ !m back t[>ds ! mean1 0 det]m9$1 & ?is 0 comp>$ ) :at !ory w\ld require 9 ord] to keep ! *>act]i/ics ( ! species p]man5tly fix$4 ,s9ce !n1 /ati/ics h be5 obta9$ to a l>ge ext5t :i* deal directly ) ! heights ( human be+s4 ,! g5]al conclusion at :i* we arrive is t !re are sev]al causes at "w :i* are nei!r slight nor indep5d5t4 ,!re is1 = in/ance1 ! obs]v$ fact t ! extremes are z a rule n equally f]tile ) ! means1 nor equally capable ( resi/+ dea? & disease4 ,h5ce z reg>ds _! m]e numb]s1 !re is a t5d5cy = !m some:at to ?9 out4 ,!n aga9 !re is a di/9ct positive cause 9 respect ( 'rev]sion4' ,n only are ! (fspr+ ( ! extremes less num]\s1 b ^! (fspr+ also t5d to clu/] ab\t a mean :i* is1 s to say1 %ift$ a little t[>ds ! true c5tre ( ! :ole gr\p2 i4e4 t[>ds ! mean (fspr+ ( ! mean p>5ts4 #ah4 ,= a full discussion ( ^! *>act]i/ics1 & = a v>iety ( mo/ +5i\s illu/rations ( _! mode ( ag5cy & ( _! comp>ative efficacy1 ! read] may be ref]r$ to ,mr ,galton's orig9al articles4 ,= our pres5t purpose x w suffice to say t ^! *>act]i/ics t5d t[>ds ma9ta9+ ! fixity ( species2 & t ?\gh !y d n affect :at may be call$ ! g5]al nature ( ! 'probability curve' or 'law ( facility'1 !y d det]m9e its precise value 9 ! cases 9 "q4 ,if1 inde$1 x be ask$ :y !re is no ne$ = any su* corrective influ5ce 9 ! case (1 say1 fir+ at a m>k3 ! answ] is t !re is no op5+ = x except :]e a cumulative influ5ce is introduc$4 ,! reason :y ! =tunes ( our bett+ p>ty %[$ an ev] increas+ div]g5cy1 & :y "s special correction 0 ne$$ 9 ord] to av]t su* a t5d5cy 9 ! case ( vital ph5om5a1 0 t ! new />t+-po9t at e /ep 0 slightly det]m9$ by ! results ( ! previ\s /ep4 ,! man :o has lo/ a %ill+ "o "t />ts1 next "t1 worse (f by j a %ill+2 &1 b = ! corrections we h be5 indicat+1 ! man :o 0 born tall w\ld1 s to say1 ?r[ (f 8 desc5dants f a vantage gr\nd ( sup]ior height4 ,! true p>allel 9 ! case ( ! m>ksm5 w\ld be to suppose t _! new po9ts ( aim 7 always %ift$ a little 9 ! direction ( ! la/ div]g5ce4 ,! spread+ out ( ! %ot-m>ks w\ld !n cont9ue )\t limit1 j z w\ld ! div]g5ce ( =tunes ( ! suppos$ gambl]s4 #a4 ,z /at$ above1 ?is is really little m ?an a re-/atem5t1 a /age fur!r back1 ( ! exi/5ce ( ! same k9d ( uni=mity z t :i* we are call$ ^u to expla9 9 ! concrete details pres5t$ to u 9 exp]i5ce4 #b4 ,x w\ld seem 9 fact t 9 co>se & rude obs]vations ! errors proce$ f a v few pr9cipal causes1 & 9 consequ5ce our hypo!sis z to ! ,expon5tial ,law ( ,error w probably repres5t ! facts only imp]fectly1 & ! frequ5cy ( ! errors w only approximate r\ghly & vaguely to ! law :i* foll[s f x4 ,b :5 a/ronom]s1 n cont5t ) ! degree ( accuracy !y _h rea*$1 prosecut$ _! rese>*es into ! rema9+ s\rces ( error1 !y f\nd t n ?ree or f\r1 b a great numb] ( m9or s\rces ( error ( ne>ly co-ord9ate importance began to reveal !mselves1 hav+ be5 till !n mask$ & ov]%ad[$ by ! grav] errors :i* _h be5 n[ approximately remov$4444 ,!re 7 errors ( graduation1 & _m o!rs 9 ! contraction ( in/rum5ts2 o!r errors ( _! adju/m5ts2 errors 7te*nically s call$7 ( obs]vation2 errors f ! *anges ( temp]ature1 ( wea!r1 f slight irregul> motions & vibrations2 9 %ort1 ! ?\s& m9ute di/urb+ influ5ces ) :i* mod]n a/ronom]s are famili>4 7,extract$ f a pap] by ,mr ,cr(ton 9 ! ,vol4 ( ! ,philosophical ,transactions = #ahgj1 p4 #agg47 #c4 ,typical ,laws ( ,h]$ity2 read be=e ! ,royal ,in/itution1 ,feb4 #i1 #ahgg4 ,see also ,j\rnal ( ! ,an?rop4 ,in/4 ,nov4 #ahhe4 ,,*apt] ,,iv4 ,,on ,,! ,,modes ,,( ,,e/abli%+ ,,& ,,det]m9+ ,,! ,,exi/5ce ,,& ,,num]ical ,,proportions ,,( ,,! ,,*>act]i/ic ,,prop]ties ,,( ,,our ,,s]ies ,,or ,,gr\ps4 #a4 ,at ! po9t :i* we h n[ rea*$1 we are suppos$ to be 9 possession ( s]ies or gr\ps ( a c]ta9 k9d1 ly+ at ! bottom1 z "o may say1 & =m+ ! f\ndation on :i* ! ,sci5ce ( ,probability is to be erect$4 ,we h describ$ ) suffici5t p>ticul>ity ! *>act]i/ics ( su* a s]ies1 & h indicat$ ! process by :i* x is1 z a rule1 actually br\ght ab\t 9 nature4 ,! next enquiries :i* h to be successively made are1 h[ 9 any p>ticul> case we are to e/abli% _! exi/5ce & det]m9e _! special "* & prop]ties8 & secondly1#a :5 we h obta9$ !m1 9 :at mode are !y to be employ$ = logical purposes8 ,! answ] to ! =m] enquiry does n seem difficult4 ,exp]i5ce is our sole guide4 ,if we want to discov] :at is 9 reality a s]ies ( ?+s1 n a s]ies ( our own conceptions1 we mu/ appeal to ! ?+s !mselves to obta9 x1 = we _c f9d mu* help else:]e4 ,we _c tell h[ _m p]sons w be born or die 9 a ye>1 or h[ _m h\ses w be burnt or %ips wreck$1 )\t actually c\nt+ !m4 ,:5 we ?us speak ( 'exp]i5ce' we mean to employ ! t]m 9 its wide/ signification2 we mean exp]i5ce supplem5t$ by all ! aids :i* inductive or d$uctive logic c af=d4 ,:51 = in/ance1 we h f\nd ! s]ies :i* comprises ! numb]s ( p]sons ( any assign$ class :o die 9 successive ye>s1 we h no hesitation 9 ext5d+ x "s way into ! future z well z into ! pa/4 ,! ju/ification ( su* a proc$ure mu/ be s\ght 9 ! ord9>y canons ( ,induction4 ,z a special discussion w be giv5 ^u ! connection betwe5 ,probability & ,induction1 no m ne$ be said ^u ?is subject "h2 b no?+ w be f\nd !re at v>iance ) ! ass]tion j made1 t ! s]ies we employ are ultimately obta9$ by exp]i5ce only4 #b4 ,9 _m cases x is und\bt$ly true t we d n resort to direct exp]i5ce at all4 ,if ,i want to "k :at is my *ance ( hold+ t5 trumps 9 a game ( :i/1 ,i d n enquire h[ (t5 su* a ?+ has occurr$ be=e4 ,if all ! inhabitants ( ! globe 7 to divide !mselves up into :i/ p>ties !y w\ld h to keep on at x = a great _m ye>s1 if !y want$ to settle ! "q satisfactorily 9 t way4 ,:at we d ( c\rse is to calculate algebraically ! proportion ( possible comb9ations 9 :i* t5 trumps c occur1 & take ?is z ! answ] to our problem4 ,s aga91 if ,i want$ to "k ! *ance ( ?r[+ six ) a die ^: faces 7 unequal1 x w\ld be a "q if my be/ way w\ld n be to calculate geometrically ! solid angle subt5d$ at ! c5tre ( gravity by ! opposite face1 & ! ratio ( ?is to ! :ole surface ( a sph]e w\ld repres5t suffici5tly closely ! *ance requir$4 ,x is q true t 9 su* examples z ! above1 especially ! =m] "o1 nobody w\ld ev] ?9k ( appeal+ to /ati/ics4 ,?is w\ld be a t$i\s process to adopt :51 z "h1 ! me*anical & o!r conditions ^u :i* ! production ( ! ev5ts dep5d are comp>atively few1 det]m9ate1 & admit ( isolat$ consid]ation1 :il/ ! enorm\s numb] ( comb9ations :i* c be con/ruct$ out ( !m causes an enorm\s consequ5t multiplicity ( ways 9 :i* ! ev5ts c possibly happ54 ,h5ce1 9 practice1 priori det]m9ation is (t5 easy1 :il/ po/]iori appeal to exp]i5ce w\ld be n m]ely t$i\s b utt]ly impracticable4 ,?is1 comb9$ ) ! frequ5t simplicity & attractiv5ess ( su* examples :5 d$uctively treat$1 has made !m v popul>1 & produc$ ! impression 9 _m qu>t]s t !y are ! prop] typical in/ances to illu/rate ! !ory ( *ance4 ,:]eas1 _h ! sci5ce be5 conc]n$ ) ^? k9ds ( ev5ts only :i* 9 practice are commonly made subjects ( insurance1 probably no o!r view w\ld ev] h be5 tak5 ?an t x 0 bas$ ^u direct appeal to exp]i5ce4 #c4 ,:51 h[ev]1 we look a little clos]1 we f9d t !re is no occasion = su* a %>p di/9ction z t app>5tly impli$ betwe5 ! two classes ( examples j indicat$4 ,9 su* cases z ^? ( dice & c>ds1 ev51 9 :i* we appe> to reason directly f ! det]m9+ conditions1 or possible v>iety ( ! ev5ts1 r ?an f actual obs]vation ( _! occurr5ce1 we %all f9d t ?is proc$ure is only valid by ! help ( a tacit assumption :i* c nev] be det]m9$ o!rwise ?an by direct exp]i5ce4 ,x is1 no d\bt1 an exce$+ly natural & obvi\s assumption1 & "o :i* is cont9ually d]iv+ fre% weight f e-day obs]vation1 b x is "o :i* ought n to be admitt$ )\t consid]ation4 ,z ?is is a v important matt]1 n s mu* 9 itself z 9 connection ) ! light :i* x ?r[s ^u ! !ory ( ! subject1 we w ent] into a some:at detail$ exam9ation ( x4 ,let u take a v simple example1 t ( toss+ up a p5ny4 ,suppose t ,i am contemplat+ a succession ( two ?r[s2 ,i c see t ! only possible ev5ts are#b ,,hh1 ,,ht1 ,,?1 ,,tt4 ,s mu* is c]ta94 ,we are moreov] tol]ably well conv9c$ f exp]i5ce t ^! ev5ts occur1 9 ! long run1 ab\t equally (t54 ,?is is ( c\rse admitt$ on all h&s4 ,b on ! view commonly ma9ta9$1 x is cont5d$ t we might h kn[n ! fact be=eh& on gr\nds :i* are applicable to an indef9ite numb] ( o!r & m complex cases4 ,! =m 9 :i* ?is view w\ld g5]ally be advanc$ is1 t we are enabl$ to /ate be=eh& t ! f\r ?r[s above m5tion$ are equally likely4 ,if 9 return we ask :at is meant by ! expression 'equally likely'1 x appe>s t !re are two & only two possible =ms ( reply4 ,"o ( ^! seeks ! explanation 9 ! /ate ( m9d ( ! obs]v]1 ! o!r seeks x 9 "s *>act]i/ic ( ! ?+s obs]v$4 7#a7 ,x might1 = in/ance1 be said on ! "o h&1 t :at is meant is t ! f\r ev5ts contemplat$ are equally easy to imag9e1 or1 m accurately1 t our expectation or belief 9 _! occurr5ce is equal4 ,we c\ld h>dly be cont5t ) ?is reply1 = ! fur!r enquiry w\ld imm$iately be urg$1 ,on :at gr\nd is ?is to be believ$8 ,:at are ! *>act]i/ics ( ev5ts ( :i* our expectation is equal8 ,if we cons5t$ to give an answ] to ?is fur!r enquiry1 we %\ld be l$ to ! second =m ( reply1 to be notic$ directly2 if we did n cons5t we %\ld1 x seems1 be admitt+ t ,probability 0 only a portion ( ,psy*ology1 conf9$ !re=e to consid]+ /ates ( m9d 9 !mselves1 r ?an 9 _! ref]5ce to facts1 viz4 z be+ true or false4 ,we %\ld1 t is1 be ceas+ to make x a sci5ce ( inf]5ce ab\t ?+s4 ,?is po9t w h to be gone into m ?or\ghly 9 ano!r *apt]2 b x is impossible to direct att5tion too prom95tly to ! fact t ,logic 7& !re=e ,probability z a bran* ( ,logic7 is n conc]n$ ) :at m5 d believe1 b ) :at !y ought to believe1 if !y are to believe correctly4 7#b7 ,9 ! o!r =m ( reply ! explanation ( ! phrase 9 "q w\ld be s\ght1 n 9 a /ate ( m9d1 b 9 a quality ( ! ?+s contemplat$4 ,we might assign ! foll[+ z ! mean+1 viz4 t ! ev5ts really w\ld occur ) equal frequ5cy 9 ! long run4 ,! gr\nd ( ?is ass]tion w\ld probably be f\nd 9 pa/ exp]i5ce1 & x w\ld d\btless be impossible s to frame ! answ] z to exclude ! notion ( our belief altoge!r4 ,b /ill !re is a broad di/9ction betwe5 seek+ an equality 9 ! am\nt ( our belief1 z be=e1 & 9 ! frequ5cy ( occurr5ce ( ! ev5ts !mselves1 z "h4 #d4 ,:5 we h got z f> z ?is x c readily be %[n t an appeal to exp]i5ce _c be long evad$4 ,= c ! ass]tion 9 "q 7viz4 t ! ?r[s ( ! p5ny w occur equally (t57 be safely made priori8 ,^? :o consid] t x c seem h>dly to h fully fac$ ! difficulties :i* meet !m4 ,= :5 we beg9 to enquire s]i\sly :e!r ! p5ny w really d :at is expect$ ( x1 we f9d t re/rictions h to be introduc$4 ,9 ! fir/ place x mu/ be an ideal co91 ) its sides equal & fair4 ,?is re/riction is p]fectly intelligible2 ! /udy ( solid geometry enables u to idealize a p5ny into a circul> or cyl9drical lam9a4 ,b ?is condition by itself is n suffici5t1 o!rs are want$ z well4 ,! p5ny 0 suppos$ to be toss$ up1 z we say 'at r&om4' ,:at is meant by ?is1 & h[ is ?is process to be idealiz$8 ,to ask ?is is to introduce no idle subtlety2 = x w\ld sc>cely be ma9ta9$ t ! heads & tails w\ld get _! fair *ances if1 imm$iately be=e ! ?r[+1 we 7 s to place ! co9 9 our h&s z to />t x always ) ! same side upw>ds4 ,! diff]5ce t w\ld result 9 consequ5ce1 slight z its cause is1 w\ld t5d 9 "t to %[ itself 9 ! results4 ,or1 if we p]si/$ 9 />t+ ) ea* ( ! two sides alt]nately upw>ds1 w\ld ! long] repetitions ( ! same side get _! fair *ance8 ,p]haps x w be repli$ t if we ?9k no?+ :atev] ab\t ^! matt]s all w come "r ( its own accord4 ,x may1 & d\btless w be s1 b ?is is fall+ back ^u exp]i5ce4 ,x is "h1 !n1 t we f9d ourselves re/+ on ! exp]im5tal assumption above m5tion$1 & :i* inde$ _c be avoid$4 ,= suppose1 la/ly1 t ! circum/ances ( nature1 or my bodily or m5tal con/itution1 7 su* t ! same side always is />t$ upw>ds1 or inde$ t !y are />t$ 9 any arbitr>y ord] ( our own8 ,well1 x w be repli$1 x w\ld n !n be a fair trial4 ,if we press 9 ?is way = an answ] to su* enquiries1 we %all f9d t ^! tacit re/rictions are really no?+ else ?an a mode ( secur+ an exp]im5tal result4 ,!y are only ano!r way ( say+1 ,let a s]ies ( actions be p]=m$ 9 su* a way z to secure a sequ5ce ( a p>ticul> k9d1 viz41 ( ! k9d describ$ 9 ! previ\s *apt]s4 #e4 ,an int]m$iate way ( evad+ ! direct appeal to exp]i5ce is sometimes f\nd by def9+ ! probability ( an ev5t z be+ measur$ by ! ratio :i* ! numb] ( cases fav\rable to ! ev5t be>s to ! total numb] ( cases :i* are possible4 ,?is seems a some:at loose & ambigu\s way ( speak+4 ,x is cle>ly n en\gh to c\nt ! numb] ( cases m]ely1 !y mu/ also be valu$1 s9ce x is n c]ta9 t ea* is equally pot5t 9 produc+ ! effect4 ,?is1 ( c\rse1 w\ld nev] be d5i$1 b suffici5t importance does n seem to be atta*$ to ! fact t we h really no o!r way ( valu+ !m except by e/imat+ ! effects :i* !y actually d1 or w\ld produce4 ,in/ead ( ?us appeal+ to ! proportion ( cases fav\rable to ! ev5t1 x is f> bett] 7at lea/ z reg>ds ! f\ndation ( ! sci5ce1 = we are n at ?is mom5t discuss+ ! practical me?od ( facilitat+ our calculations7 to appeal at once to ! proportion ( cases 9 :i* ! ev5t actually occurs4 #f4 ,! rem>ks above made w apply1 ( c\rse1 to mo/ ( ! o!r common examples ( *ance2 ! ?r[+ ( dice1 draw+ ( c>ds1 ( balls f bags1 c4 ,9 ! la/ case1 = in/ance1 "o w\ld naturally be incl9$ to suppose t a ball :i* _h j be5 put back w\ld !reby h a bett] *ance ( com+ out aga9 next "t1 s9ce x w be m 9 ! way = t purpose4 ,h[ is ?is to be prev5t$8 ,if we design$ly ?ru/ x to ! middle or bottom ( ! o!rs1 we may ov]do ! precaution2 & are 9 any case introduc+ human design1 t elem5t s ess5tially ho/ile to all t we und]/& by *ance4 ,if we 7 to tru/ to a good %ake sett+ matt]s "r1 we may easily be deceiv$2 = %ak+ ! bag c h>dly d m ?an dim9i% ! disposition ( ^? balls :i* 7 already 9 ea* o!r's neighb\rhood1 to rema9 s4 ,9 ! consequ5t int]action ( ea* ^u all1 ! arrangem5t 9 :i* !y />t _c b leave its impress to "s ext5t ^u _! f9al positions4 ,9 all su* cases1 !re=e1 if we scrut9ize our language1 we %all f9d t any suppos$ priori mode ( /at+ a problem is little else ?an a comp5di\s way ( say+1 ,let means be tak5 = obta9+ a giv5 result4 ,s9ce x is ^u ?is result t our inf]5ces ultimately re/1 x seems simpl] & m philosophical to appeal to x at once z ! gr\ndwork ( our sci5ce4 #g4 ,let u aga9 take ! in/ance ( ! toss+ ( a p5ny1 & exam9e x some:at m m9utely1 to see :at c be actually prov$ ab\t ! results we %all obta94 ,we are will+ to give ! p5ce fair treatm5t by assum+ t !y are p]fect1 t is1 t 9 ! long run !y %[ no pref]5ce = ei!r head or tail2 ! "q !n rema9s1 ,w ! repetitions ( ! same face obta9 ! proportional %>es to :i* !y are entitl$ by ! usual int]pretations ( ! !ory8 ,putt+ !n1 z be=e1 = ! sake ( brevity1 ,h = head1 & ,,hh = heads twice runn+1 we are br\ght to ?is issue2--,giv5 t ! *ance ( ,h is #a_/b1 does x foll[ necess>ily t ! *ance ( ,,hh 7) two p5ce7 is #a_/d8 ,to say no?+ ( ',h t5 times' occurr+ once 9 #ajbd times 7) t5 p5ce71 ne$ x occur at all8 ,! ma!maticians1 = ! mo/ "p1 seem to ?9k t ?is conclusion foll[s necess>ily f fir/ pr9ciples2 to me x seems to re/ ^u no m c]ta9 evid5ce ?an a reasonable ext5sion by ,induction4 ,tak+ !n ! possible results :i* c be obta9$ f a pair ( p5ce1 :at d we f9d8 ,f\r diff]5t results may foll[1 namely1 7#a7 ,,ht1 7#b7 ,,hh1 7#c7 ,,?1 7#d7 ,,tt4 ,if x c be prov$ t ^! f\r are equally probable1 t is1 occur equally (t51 ! commonly accept$ conclusions w foll[1 = a precisely simil> argum5t w\ld apply to all ! l>g] numb]s4 #h4 ,! pro( usually advanc$ makes use ( :at is call$ ! ,pr9ciple ( ,suffici5t ,reason4 ,x takes ?is =m2--,"h are f\r k9ds ( ?r[s :i* may happ52 once admit t ! sep>ate elem5ts ( !m1 namely1 ,h & ,t1 happ5 equally (t51 & x w foll[ t ! above comb9ations w also happ5 equally (t51 = no reason c be giv5 9 fav\r ( "o ( !m t w\ld n equally hold 9 fav\r ( ! o!rs4 ,to a c]ta9 ext5t we mu/ admit ! validity ( ! pr9ciple = ! purpose4 ,9 ! case ( ! ?r[s giv5 above1 x w\ld be valid to prove ! equal frequ5cy ( 7#a7 & 7#c7 & also ( 7#b7 & 7#d72 = !re is no diff]5ce exi/+ betwe5 ^! pairs except :at is introduc$ by our own notation4#c ,,? is ! same z ,,ht1 except 9 ! ord] ( ! occurr5ce ( ! symbols ,h & ,t1 :i* we d n take into acc\nt4 ,b ei!r ( ! pair 7#a7 & 7#c7 is diff]5t f ei!r ( ! pair 7#b7 & 7#d74 ,transpose ! notation1 & !re w\ld /ill rema9 "h a di/9ction :i* ! m9d c recognize4 ,a succession ( ! same ?+ twice runn+ is di/+ui%$ f ! conjunction ( two diff]5t ?+s1 by a di/9ction :i* does n dep5d ^u our arbitr>y notation only1 & w\ld rema9 entirely unalt]$ by a *ange 9 ?is notation4 ,! pr9ciple !re=e ( ,suffici5t ,reason1 if admitt$1 w\ld only prove t d\blets ( ! two k9ds1 = example 7#b7 & 7#d71 occur equally (t51 b x w\ld n prove t !y mu/ ea* occur once 9 f\r times4 ,x _c be prov$ inde$ 9 ?is way t !y ne$ ev] occur at all4 #i4 ,! =mula1 !n1 n be+ demon/rable priori1 7z might h be5 conclud$17 c x be obta9$ by exp]i5ce8 ,to a c]ta9 ext5t x c2 ! pres5t exp]i5ce ( mank9d 9 p5ce & dice seems to %[ t ! small] successions ( ?r[s d really occur 9 ab\t ! proportions assign$ by ! !ory4 ,b h[ ne>ly !y d s no "o c say1 = ! am\nt ( "t & tr\ble to be exp5d$ be=e we c\ld feel t we h v]ifi$ ! fact1 ev5 = small numb]s1 is v great1 :il/ = l>ge numb]s x w\ld be simply intol]able4 ,! exp]im5t ( ?r[+ (t5 en\gh to obta9 'heads t5 times' has be5 actually p]=m$ by two or ?ree p]sons1 & ! results are giv5 by ,de ,morgan1 & ,jevons4#d ,?is1 h[ev]1 be+ only suffici5t on ! av]age to give 'heads t5 times' a s+le *ance1 ! evid5ce is v slight2 x w\ld take a consid]able numb] ( su* exp]im5ts to set ! matt] ne>ly at re/4 ,any su* rule1 !n1 z t :i* we h j be5 discuss+1 :i* pr(esses to describe :at w take place 9 a long succession ( ?r[s1 is only conclusively prov$ by exp]i5ce )9 v n>r[ limits1 t is1 = small repetitions ( ! same face2 )9 limits less n>r[1 inde$1 we feel assur$ t ! rule _c be flagrantly 9 error1 o!rwise ! v>iation w\ld be almo/ sure to be detect$4 ,f ?is we feel /rongly incl9$ to inf] t ! same law w hold ?r\gh\t4 ,9 o!r words1 we are incl9$ to ext5d ! rule by ,induction & ,analogy4 ,/ill !re are s _m in/ances 9 nature ( propos$ laws :i* hold )9 n>r[ limits b get egregi\sly a/ray :5 we attempt to pu% !m to great l5g?s1 t we mu/ give at be/ b a qualifi$ ass5t to ! tru? ( ! =mula4 #aj4 ,! object ( ! above reason+ is simply to %[ t we _c be c]ta9 t ! rule is true4 ,let u n[ turn = a m9ute to consid] ! causes by :i* ! succession ( heads & tails is produc$1 & we may p]haps see reasons to make u /ill m d\btful4 ,x has be5 already po9t$ out t 9 calculat+ probabilities priori1 z x is call$1 we are only able to d s by introduc+ re/rictions & suppositions :i* are 9 reality equival5t to assum+ ! expect$ results4 ,we use words :i* 9 /rictness mean1 ,let a giv5 process be p]=m$2 b an analysis ( our language1 & an exam9ation ( v>i\s tacit suppositions :i* make !mselves felt ! mom5t !y are n compli$ )1 soon %[ t our real mean+ is1 ,let a s]ies ( a giv5 k9d be obta9$2 x is to ?is s]ies only1 & n to ! conditions ( its production1 t all our subsequ5t calculations prop]ly apply4 ,! physical process be+ p]=m$1 we want to "k :e!r any?+ resembl+ ! contemplat$ s]ies really w be obta9$4 ,n[ if ! p5ny 7 inv>iably set ! same side upp]mo/1 & ?r[n ) ! same velocity ( rotation & to ! same height1 c4--9 a ^w1 subject$ to ! same conditions1--x w\ld always come d[n ) ! same side upp]mo/4 ,practically1 we "k t no?+ ( ?is k9d occurs1 = ! individual v>iations 9 ! results ( ! ?r[s are endless4 ,/ill !re w be an av]age ( ^! conditions1 ab\t :i* ! ?r[s w be f\nd1 z x 71 to clu/] mu* m ?ickly ?an else:]e4 ,we %\ld be incl9$ !re=e to inf] t if ! same side 7 always set upp]mo/ !re w\ld really be a dep>ture f ! sort ( s]ies :i* we ord9>ily expect4 ,9 a v l>ge numb] ( ?r[s we %\ld probably beg9 to f9d1 "u su* circum/ances1 t ei!r head or tail 0 hav+ a pref]5ce %[n to x4 ,if s1 w\ld n simil> effects be f\nd to be connect$ ) ! way 9 :i* we />t$ ea* successive pair ( ?r[s8 ,accord+ z we *ose to make a practice ( putt+ ,,hh or ,,tt upp]mo/1 might !re n be a di/urbance 9 ! proportion ( successions ( two heads or two tails8 ,foll[+ out ?is tra9 ( reason+1 x w\ld seem to po9t ) "s likelihood to ! conclusion t 9 ord] to obta9 a s]ies ( ! k9d we expect1 we %\ld h to dispose ! antec$5ts 9 a simil> s]ies at ! />t4 ,! *anges & *ances produc$ by ! act ( ?r[+ might introduce inf9ite individual v>iations1 & yet !re might be f\nd1 9 ! v long run1 to be a close simil>ity betwe5 ^! two s]ies4 #aa4 ,?is is1 to a c]ta9 ext5t1 only %ift+ ! difficulty1 ,i admit2 = ! claim =m]ly advanc$ ab\t ! possibility ( prov+ ! proportions ( ! ?r[s 9 ! =m] s]ies1 w probably n[ be repeat$ 9 fav\r ( ^? 9 ! latt]4 ,/ill ! "q is v mu* n>r[$1 = we h r$uc$ x to a s]ies ( volunt>y acts4 ,a man may put :atev] side he pleases upp]mo/4 ,he may act consci\sly1 z ,i h said1 or he may ?9k no?+ :atev] ab\t ! matt]1 t is1 ?r[ at r&om2 if s1 x w probably be ass]t$ by _m t he w involunt>ily produce a s]ies ( ! k9d 9 "q4 ,x may be s1 or x may n2 x does n seem t !re are any easily accessible data by :i* to decide4 ,all t ,i am conc]n$ ) "h is to %[ ! likelihood t ! commonly receiv$ result does 9 reality dep5d ^u ! fulfilm5t ( a c]ta9 condition at ! outset1 a condition :i* x is c]ta9ly optional ) any "o to fulfil or n z he pleases4 ,! %ort successions d\btless w take c>e ( !mselves1 ow+ to ! inf9ite complications produc$ by ! casual v>iations 9 ?r[+2 b ! long ones may suff]1 unless _! int]e/ be consci\sly or unconsci\sly reg>d$ at ! outset4 #ab4 ,! advice1 ',only try long en\gh1 & y w soon] or lat] get any result t is possible1' is plausible1 b x re/s only on ,induction & ,analogy2 ma!matics d n prove x4 ,z has be5 repeat$ly /at$1 !re are two di/9ct views ( ! subject4 ,ei!r we may1 on ! "o h&1 take a s]ies ( symbols1 call !m heads & tails2 ,h1 ,t1 c42 & make ! assumption t ea* ( ^!1 & ea* pair ( !m1 & s on1 w occur 9 ! long run ) a regulat$ degree ( frequ5cy4 ,we may !n calculate _! v>i\s comb9ations1 & ! consequ5ces t may be drawn f ! data assum$4 ,?is is a purely algebraical process2 x is infallible2 & !re is no limit :atev] to ! ext5t to :i* x may be c>ri$4 ,?is way ( look+ at ! matt] may be1 & und\bt$ly %\ld be1 no?+ m ?an ! c\nt]p>t ( :at ,i h call$ ! sub/itut$ or idealiz$ s]ies :i* g5]ally has to be introduc$ z ! basis ( our calculation4 ,! dang] to be gu>d$ aga9/ is t ( reg>d+ x too purely z an algebraical conception1 & !nce ( s9k+ into ! v natural errors bo? ( too readily evolv+ x out ( our own consci\sness1 & too freely pu%+ x to unw>rant$ l5g?s4 ,or on ! o!r h&1 we may consid] t we are treat+ ( ! behavi\r ( ?+s2--balls1 dice1 bir?s1 dea?s1 c42 & draw+ inf]5ces ab\t !m4 ,b1 !n1 :at 7 9 ! =m] in/ance all[able assumptions1 become "h propositions to be te/$ by exp]i5ce4 ,n[ ! :ole !ory ( ,probability z a practical sci5ce1 9 fact z any?+ m ?an an algebraical tru?1 dep5ds ( c\rse ^u !re be+ a close correspond5ce betwe5 ^! two views ( ! subject1 9 o!r words1 ^u our sub/itut$ s]ies be+ kept 9 accordance ) ! actual s]ies4 ,exp]i5ce abundantly proves t1 betwe5 consid]able limits1 9 ! example 9 "q1 !re does exi/ su* a correspond5ce4 ,b let no "o attempt to en=ce our ass5t to e remote d$uction t ma!maticians c draw f _! =mul4 ,:5 ?is is attempt$ ! di/9ction j trac$ becomes prom95t & important1 & we h to *oose our side4 ,ei!r we g ov] to ! ma!matics1 & s lose all "r ( discussion ab\t ! ?+s2 or else we take "p ) ! ?+s1 & s defy ! ma!matics4 ,we d n "q ! =mal accuracy ( ! latt] )9 _! own prov9ce1 b ei!r we dismiss !m z some:at irrelevant1 z apply+ to data ( ^: correctness we _c be c]ta91 or we take ! lib]ty ( remodell+ !m s z to br+ !m into accordance ) facts4 #ac4 ,a critic ( any doctr9e c h>dly be consid]$ to h done mu* m ?an half 8 duty :5 he has expla9$ & ju/ifi$ 8 gr\nds = object+ to x4 ,x /ill rema9s = him to indicate1 if only 9 a few words1 :at he consid]s its legitimate functions & position to be1 = x c seldom happ5 t he reg>ds x z absolutely wor?less or unmean+4 ,i %\ld say1 !n1 t :5 ,probability is ?us divorc$ f direct ref]5ce to objects1 z x sub/antially is by n be+ f\nd$ ^u exp]i5ce1 x simply resolves itself into ! common algebraical or ari?metical doctr9e ( ,p]mutations & ,comb9ations4#e ,! consid]ations ^u :i* ^! dep5d are purely =mal & necess>y1 & c be fully reason$ out )\t any appeal to exp]i5ce4 ,we !re />t f pure consid]ations ( numb] or magnitude1 & we t]m9ate ) !m1 hav+ only ari?metical calculations to connect !m toge!r4 ,i wi%1 = in/ance1 to f9d ! *ance ( ?r[+ heads ?ree times runn+ ) a p5ny4 ,all ,i h to d is fir/ to asc]ta9 ! possible numb] ( ?r[s4 ,p]mutations tell me t ) two ?+s ?us 9 "q 7viz4 head & tail7 & ?ree times to p]=m ! process1 !re are eight possible =ms ( ! result4 ,( ^! eight "o only be+ fav\rable1 ! *ance 9 "q is pron\nc$ to be "o-eigh?4 ,n[ ?\gh x is q true t ! actual calculation ( e *ance problem mu/ be ( ! above "*1 viz4 an algebraical or ari?metical process1 yet !re is1 x seems to me1 a broad & important di/9ction betwe5 a mat]ial sci5ce :i* employs ma!matics1 & a =mal "o :i* consi/s ( no?+ b ma!matics4 ,:5 we cut ourselves (f f ! necessity ( any appeal to exp]i5ce1 we are reta9+ only ! int]m$iate or calculat+ "p ( ! inve/igation2 we may talk ( dice1 or p5ce1 or c>ds1 b ^! are really only names we *oose to give to our symbols4 ,! ,h's & ,t's ) :i* we deal h no be>+ on objective occurr5ces1 b are j l ! x's & y's ) :i* ! re/ ( algebra deals4 ,probability 9 fact1 :5 s treat$1 seems to be absolutely no?+ else ?an a sy/em ( appli$ ,p]mutations & ,comb9ations4 ,x w n[ readily be se5 h[ n>r[ is ! range ( cases to :i* any purely d$uctive me?od ( treatm5t c apply4 ,x is almo/ entirely conf9$ to su* employm5ts z games ( *ance1 &1 z already po9t$ out1 c only be reg>d$ z really tru/wor?y ev5 !re1 by ! help ( v>i\s tacit re/rictions4 ,?is alone w\ld be conclusive aga9/ ! !ory ( ! subject be+ re/$ ^u su* a basis4 ,! exp]im5tal me?od1 on ! o!r h&1 is1 9 ! same !oretical s5se1 ( univ]sal application4 ,x w\ld include ! ord9>y problems furni%$ by games ( *ance1 z well z ^? :]e ! dice are load$ & ! p5ce are n p]fect1 & also ! indef9itely num]\s applications ( /ati/ics to ! v>i\s k9ds ( social ph5om5a4 #ad4 ,! p>ticul> view ( ! d$uctive "* ( ,probability above discuss$1 c\ld sc>cely h intrud$ itself into any o!r examples ?an ^? ( ! nature ( games ( *ance1 9 :i* ! conditions ( occurr5ce are by comp>ison few & simple1 & are am5able to accurate num]ical det]m9ation4 ,b a doctr9e1 :i* is 9 reality little else ?an ! same !ory 9 a slightly disguis$ =m1 is v preval5t1 & has be5 appli$ to tru?s ( ! mo/ purely empirical "*4 ,?is doctr9e w be be/ introduc$ by a quotation f ,laplace4 ,aft] speak+ ( ! irregul>ity & unc]ta9ty ( nature z x appe>s at fir/ sight1 he goes on to rem>k t :5 we look clos] we beg9 to detect a /rik+ regul>ity :i* seems to sugge/ a design1 & :i* "s h consid]$ a pro( ( ,provid5ce4 ,b1 on reflection1 x is soon p]ceiv$ t ?is regul>ity is no?+ b ! developm5t ( ! respective probabilities ( ! simple ev5ts1 :i* ought to occur m frequ5tly accord+ z !y are m probable4#f ,if ?is rem>k _h be5 made ab\t ! succession ( heads & tails 9 ! ?r[+ up ( a p5ny1 x w\ld h be5 intelligible4 ,x w\ld simply mean ?is3 t ! con/itution ( ! body 0 su* t we c\ld anticipate ) "s confid5ce :at ! result w\ld be :5 x 0 treat$ 9 a c]ta9 way1 & t exp]i5ce w\ld ju/ify our anticipation 9 ! long run4 ,b appli$ z x is 9 a m g5]al =m to ! facts ( nature1 x seems really to h b little mean+ 9 x4 ,let u te/ x by an in/ance4 ,amid/ ! irregul>ity ( individual bir?s1 we f9d t ! male *ildr5 are to ! female1 9 ! long run1 9 ab\t ! proportion ( #ajf to #ajj4 ,n[ if we 7 told t !re is no?+ 9 ?is b ! developm5t ( _! respective probabilities1 w\ld !re be any?+ 9 su* a /atem5t b a some:at pret5ti\s re-/atem5t ( ! fact already ass]t$8 ,! probability is no?+ b t proportion1 & is unque/ionably 9 ?is case d]iv$ f no o!r s\rce b ! /ati/ics !mselves2 9 ! above rem>k ! attempt seems to be made to inv]t ?is process1 & to d]ive ! sequ5ce ( ev5ts f ! m]e num]ical /atem5t ( ! proportions 9 :i* !y occur4 #ae4 ,x w v likely be repli$ t by ! probability above m5tion$ is meant1 n ! m]e num]ical proportion betwe51 ! bir?s1 b "s fact 9 our con/itution ^u :i* ?is proportion dep5ds2 t j z !re 0 a relation ( equality betwe5 ! two sides ( ! p5ny1 :i* produc$ ! ultimate equality 9 ! numb] ( heads & tails1 s !re may be some?+ 9 our con/itution or circum/ances 9 ! proportion ( #ajf to #ajj1 :i* produces ! obs]v$ /ati/ical result4 ,:5 ?is some?+1 :atev] x might be1 0 discov]$1 ! obs]v$ numb]s might be suppos$ capable ( be+ det]m9$ be=eh&4 ,ev5 if ?is 7 ! case1 h[ev]1 x mu/ n be =gott5 t !re c\ld h>dly fail to be1 9 comb9ation ) su* causes1 o!r concurr5t conditions 9 ord] to produce ! ultimate result2 j z besides ! %ape ( ! p5ny1 we _h also to take into acc\nt ! nature ( ! 'r&omness' ) :i* x 0 toss$4 ,:at ^! may be1 no "o at pres5t c und]take to say1 = ! be/ physiologi/s seem indispos$ to haz>d ev5 a guess ^u ! subject4#g ,b )\t go+ into p>ticul>s1 "o may ass]t ) "s confid5ce t ^! conditions _c well be altoge!r indep5d5t ( ! heal?1 circum/ances1 mann]s & cu/oms1 c4 7to express oneself 9 ! vague/ way7 ( ! p>5ts2 & if once ^! influ5c+ elem5ts are introduc$1 ev5 z v m9ute factors1 ! results cease to be dep5d5t only on fix$ & p]man5t conditions4 ,we are at once lett+ 9 o!r conditions1 :i*1 if !y also possess ! *>act]i/ics t di/+ui% ,probability 7an exce$+ly que/ionable assumption71 mu/ h t fact specially prov$ ab\t !m4 ,t ?is %\ld be ! case inde$ seems n m]ely que/ionable1 b almo/ c]ta9ly impossible2 = ^! conditions p>tak+ ( ! nature ( :at we t]m g5]ally1 ,progress & ,civilization1 _c be expect$ to %[ any p]man5t disposition to hov] ab\t an av]age4 #af4 ,! read] :o is famili> ) ,probability is ( c\rse acqua9t$ ) ! celebrat$ !orem ( ,james ,b]n\lli4 ,?is !orem1 ( :i* ! examples j adduc$ are m]ely p>ticul> cases1 is g5]ally express$ some:at z foll[s3--9 ! long run all ev5ts w t5d to occur ) a relative frequ5cy proportional to _! objective probabilities4 ,) ! ma!matical pro( ( ?is !orem we ne$ n tr\ble ourselves1 z x lies outside ! prov9ce ( ?is "w2 b inde$ if !re is any value 9 ! =ego+ criticism1 ! basis on :i* ! ma!matics re/ is faulty1 ow+ to !re be+ really no?+ :i* we c ) propriety call an objective probability4 ,if "o might judge by ! int]pretation & uses to :i* ?is !orem is sometimes expos$1 we %\ld reg>d x z "o ( ! la/ rema9+ relics ( ,realism1 :i* aft] be+ bani%$ else:]e /ill manages to l+] 9 ! remote prov9ce ( ,probability4 ,x w\ld be an illu/ration ( ! invet]ate t5d5cy to objectify our conceptions1 ev5 9 cases :]e ! conceptions _h no "r to exi/ at all4 ,a uni=mity is obs]v$2 sometimes1 z 9 games ( *ance1 x is f\nd to be s connect$ ) ! physical con/itution ( ! bodies employ$ z to be capable ( be+ inf]r$ be=eh&2 ?\gh ev5 "h ! connection is by no means s necess>y z is commonly suppos$1 ow+ to ! fact t 9 addition to ^! bodies !mselves we h also to take into acc\nt _! relation to ! ag5cies :i* influ5ce !m4 ,?is con/itution is !n conv]t$ into an 'objective probability'1 suppos$ to develop into ! sequ5ce :i* exhibits ! uni=mity4 ,f9ally1 ?is v que/ionable objective probability is assum$ to exi/1 ) ! same faculty ( developm5t1 9 all ! cases 9 :i* uni=mity is obs]v$1 h[ev] little resemblance !re may be betwe5 ^! & games ( *ance4 #ag4 ,h[ utt]ly inappropriate any su* conception is 9 mo/ ( ! cases 9 :i* we f9d /ati/ical uni=mity1 w be obvi\s on a mom5t's consid]ation4 ,! obs]v$ ph5om5a are g5]ally ! product1 9 ^! cases1 ( v num]\s & complicat$ antec$5ts4 ,! numb] ( crimes1 = in/ance1 annually committ$ 9 any society1 is a function among/ o!r ?+s1 ( ! /rictness ( ! law1 ! morality ( ! p1 _! social condition1 & ! vigilance ( ! police1 ea* ( ^! elem5ts be+ 9 itself almo/ inf9itely complex4 ,n[1 z a result ( all ^! ag5cies1 !re is "s degree ( uni=mity2 b :at has be5 call$ above ! *ange ( type1 :i* x soon] or lat] t5ds to display1 is unmi/akeable4 ,! av]age annual numb]s d n %[ a /eady gradual approa* t[>ds :at might be consid]$ 9 "s s5se a limit+ value1 b1 on ! contr>y1 fluctuate 9 a way :i*1 h[ev] x may dep5d ^u causes1 %[s none ( ! p]man5t uni=mity :i* is *>act]i/ic ( games ( *ance4 ,?is fact1 comb9$ ) ! obvi\s arbitr>9ess ( s+l+ out1 f among/ ! _m & v>i\s antec$5ts :i* produc$ ! obs]v$ regul>ity1 a few only1 :i* %\ld con/itute ! objective probability 7if we took all1 ! ev5ts be+ absolutely det]m9$1 !re w\ld be no occasion = an appeal to probability 9 ! case71 w\ld h be5 suffici5t to prev5t any "o f assum+ ! exi/5ce ( any su* ?+1 unless ! mi/ak5 analogy ( o!r cases _h pr$ispos$ him to seek = x4 ,!re is a famili> practical =m ( ! same error1 ! t5d5cy to :i* may n improbably be d]iv$ f a simil> !oretical s\rce4 ,x is t ( cont9u+ to accumulate our /ati/ical data to an excessive ext5t4 ,if ! type 7 absolutely fix$ we c\ld n possibly h too _m /ati/ics2 ! long] we *ose to take ! tr\ble ( collect+ !m ! m accurate our results w\ld be4 ,b if ! type is *ang+1 9 o!r words1 if "s ( ! pr9cipal causes :i* aid 9 _! production h1 9 reg>d to _! pres5t degree ( int5sity1 /rict limits ( "t or space1 we %all d h>m r ?an good if we ov]/ep ^! limits4 ,! dang] ( /opp+ too soon is easily se51 b 9 avoid+ x we mu/ n fall into ! opposite error ( go+ on too long1 & s gett+ ei!r gradually or sudd5ly "u ! influ5ce ( a *ang$ set ( circum/ances4 #ah4 ,?is *apt] 0 int5d$ to be devot$ to a consid]ation1 n ( ! processes by :i* nature produces ! s]ies ) :i* we are conc]n$1 b ( ! !oretic basis ( ! me?ods by :i* we c det]m9e ! exi/5ce ( su* s]ies4 ,b x is n possible to keep ! two enquiries ap>t1 = "h1 at any rate1 ! old maxim prevails t to "k a ?+ we mu/ "k its causes4 ,recur = a m9ute to ! consid]ations ( ! la/ *apt]4 ,we !re saw t !re 0 a l>ge class ( ev5ts1 ! conditions ( production ( :i* c\ld be said to consi/ ( 7#a7 a comp>atively few ne>ly un*angeable elem5ts1 & 7#b7 a va/ numb] ( indep5d5t & v *angeable elem5ts4 ,at lea/ if !re 7 any o!r elem5ts besides ^!1 we are assum$ ei!r to make special all[ance = !m1 or to omit !m f our enquiry4 ,n[ 9 c]ta9 cases1 su* z games ( *ance1 ! un*angeable elem5ts may )\t practical error be reg>d$ z really un*angeable ?r\gh\t any range ( "t & space4 ,h5ce1 z a result1 ! d$uctive me?od ( treatm5t becomes 9 _! case at once ! mo/ simple1 natural1 & conclusive2 b1 z a fur!r consequ5ce1 ! /ati/ics ( ! ev5ts1 if we *oose to appeal to !m1 may be collect$ ad libitum ) bett] & bett] approximation to tru?4 ,on ! o!r h&1 9 all social applications ( ,probability1 ! un*angeable causes c only be reg>d$ z really un*angeable "u _m qualifications4 ,we "k little or no?+ ( !m directly2 !y are (t5 9 reality num]\s1 indet]m9ate1 & fluctuat+2 & x is only "u ! gu>antee ( /r+5t re/rictions ( "t & place1 t we c ) any safety attribute to !m suffici5t fixity to ju/ify our !ory4 ,h5ce1 z a result1 ! d$uctive me?od1 "u :atev] "n x may g1 becomes totally inapplicable bo? 9 !ory & practice2 &1 z a fur!r consequ5ce1 ! appeal to /ati/ics has to be made ) ! caution 9 m9d t we %all d mis*ief r ?an good if we g on collect+ too _m ( !m4 #ai4 ,! results ( ! la/ two *apt]s may be summ$ up z foll[s3--,we h ext5d$ ! conception ( a s]ies obta9$ 9 ! fir/ *apt]2 = we h f\nd t ^! s]ies are mo/ly pres5t$ to u 9 gr\ps4 ,^! gr\ps are f\nd ^u exam9ation to be =m$ ^u approximately ! same type ?r\gh\t a v wide & v>i$ range ( exp]i5ce2 ! causes ( ?is agreem5t we discuss$ & expla9$ 9 "s detail4 ,:51 h[ev]1 we ext5d our exam9ation by suppos+ ! s]ies to run to a v great l5g?1 we f9d t !y may be divid$ into two classes sep>at$ by important di/9ctions4 ,9 "o ( ^! classes 7t conta9+ ! results ( games ( *ance7 ! conditions ( production1 & consequ5tly ! laws ( /ati/ical occurr5ce1 may be practically reg>d$ z absolutely fix$2 & ! ext5t ( ! div]g5ces f ! mean seem to "k no f9ite limit4 ,9 ! o!r class1 on ! contr>y 7conta9+ ! bulk ( ord9>y /ati/ical enquiries71 ! conditions ( production v>y ) m or less rapidity1 & s 9 consequ5ce d ! results4 ,moreov] x is (t5 impossible t v>iations f ! mean %\ld exce$ a c]ta9 am\nt4 ,! =m] we may t]m ideal s]ies4 ,x is !y alone :i* %[ ! requisite *>act]i/ics ) any close approa* to accuracy1 & to make ! !ory ( ! subject t5able1 we h really to sub/itute "o ( ?is k9d = "o ( ! less p]fect ones ( ! o!r class1 :5 ^! latt] are "u treatm5t4 ,! =m] class h1 h[ev]1 be5 too exclusively consid]$ by writ]s on ! subject2 & conceptions appropriate only to !m1 & n always ev5 to !m1 h be5 import$ into ! o!r class4 ,x is 9 ?is way t a g5]al t5d5cy to an excessive d$uctive or priori treatm5t ( ! sci5ce has be5 enc\rag$4 #a4 ,?is latt] enquiry belongs to :at may be t]m$ ! m purely logical "p ( ?is volume1 & is ent]$ on 9 ! c\rse ( ,*apt] ,,vi4 #b4 ,= ! use ( ^? n acqua9t$ ) ! common notation employ$ 9 ?is subject1 x may be rem>k$ t ,,hh is simply an abbreviat$ way ( say+ t ! two successive ?r[s ( ! p5ny give head2 ,,ht t ! fir/ ( !m gives head1 & ! second tail2 & s on ) ! rema9+ symbols4 #c4 ,i am endeav\r+ to treat ?is rule ( ,suffici5t ,reason 9 a way t %all be legitimate 9 ! op9ion ( ^? :o accept x1 b !re seem v great d\bts :e!r a contradiction is n involv$ :5 we attempt to extract results f x4 ,if ! sides are absolutely alike1 h[ c !re he any diff]5ce betwe5 ! t]ms ( ! s]ies8 ,! succession seems !n r$uc$ to a dull uni=mity1 a m]e it]ation ( ! same ?+ _m times2 ! s]ies we contemplat$ has disappe>$4 ,if ! sides are n absolutely alike1 :at becomes ( ! applicability ( ! rule8 #d4 ,=mal ,logic1 p4 #ahe4 ,pr9ciples ( ,sci5ce1 p4 #bjh4 #e4 ,! close connection betwe5 ^! subjects is well indicat$ 9 ! title ( ,mr ,:itwor?'s treatise1 ,*oice & ,*ance4 #f4 ,essai ,philosophique4 ,ed4 #ahbe1 p4 #gd4 #g4 ,an op9ion prevail$ r at "o "t 7quot$ & support$ by ,quetelet among/ o!rs7 t ! relative ages ( ! p>5ts _h some?+ to d ) ! sex ( ! (fspr+4 ,if ?is 7 s1 x w\ld q be> out ! above rem>ks4 ,z a matt] ( fact1 x %\ld be obs]v$1 t ! proportion ( #ajf to #ajj does n seem by any means univ]sal 9 all c\ntries or at all times4 ,= v>i\s /ati/ical tables on ! subject see ,quetelet1 ,physique ,sociale1 ,vol4 ,i4 #aff1 #agc1 #bch4 ,,*apt] ,v4 ,,! ,,conception ,,r&omness ,,& ,,its ,,sci5tific ,,treatm5t4 #a4 ,!re is a t]m ( frequ5t occurr5ce 9 treatises on ,probability1 & :i* we h already _h repeat$ occasion to employ1 viz4 ! designation r&om appli$ to an ev5t1 z 9 ! expression 'a r&om di/ribution'4 ,! sci5tific conception involv$ 9 ! correct use ( ?is t]m is1 ,i appreh5d1 no?+ m ?an t ( aggregate ord] & individual irregul>ity 7or app>5t irregul>ity71 :i* has be5 already describ$ 9 ! prec$+ *apt]s4 ,a brief discussion ( ! requisites 9 ?is sci5tific conception1 & 9 p>ticul> ( ! nature & "s ( ! reasons = ! dep>ture f ! popul> conception1 may s]ve to cle> up "s ( ! pr9cipal rema9+ difficulties :i* att5d ?is "p ( our subject4 ,! orig9al1#a & /ill popul>1 signification ( ! t]m is ( c\rse widely diff]5t f ! sci5tific4 ,:at x looks to is ! orig91 n ! results1 ( ! r&om p]=mance1 & x has ref]5ce r to ! s+le action ?an to a gr\p or s]ies ( actions4 ,?us1 :5 a man draws a b[ 'at a v5ture'1 or 'at r&om'1 we mean only to po9t out ! aimless "* ( ! p]=mance2 we are contra/+ x ) ! def9ite int5tion to hit a c]ta9 m>k4 ,b x is none ! less true1 z already po9t$ out1 t we c only apply processes ( inf]5ce to su* p]=mances z ^! :5 we reg>d !m z be+ capable ( frequ5t1 or r ( indef9itely ext5d$ repetition4 ,beg9 ) an illu/ration4 ,p]haps ! be/ typical example t we c give ( ! sci5tific mean+ ( r&om di/ribution is af=d$ by ! arrangem5t ( ! drops ( ra9 9 a %[]4 ,no "o c give a guess :]eab\ts at any in/ant a drop w fall1 b we "k t if we put out a %eet ( pap] x w gradually become uni=mly spott$ ov]2 & t if we 7 to m>k out any two equal areas on ! pap] ^! w\ld gradually t5d to be /ruck equally (t54 #b4 ,i4 ,any attempt to draw inf]5ces f ! assumption ( r&om arrangem5t mu/ po/ulate ! occurr5ce ( ?is p>ticul> /ate ( ?+s at "s /age or o!r4 ,b !re is (t5 consid]able difficulty1 lead+ occasionally to "s arbitr>9ess1 9 decid+ ! p>ticul> /age at :i* x ought to be introduc$4 7#a7 ,?us1 9 _m ( ! problems discuss$ by ma!maticians1 we look z entirely to ! results obta9$1 & ?9k z little ( ! actual process by :i* !y are obta9$1 z :5 we are reg>d+ ! arrangem5t ( ! drops ( ra94 ,a simple example ( ?is k9d w\ld be ! foll[+4 ,a pawn1 diamet] ( base "o in*1 is plac$ at r&om on a *ess-bo>d1 ! diamet] ( ! squ>es ( :i* is "o in* & a qu>t]3 f9d ! *ance t its base %all lie across "o ( ! int]sect+ l9es4 ,"h we may imag9e ! pawns to be s to say ra9$ d[n v]tically ^u ! bo>d1 & ! "q is to f9d ! ultimate proportion ( ^? :i* meet a b\nd>y l9e to ! total ( ^? :i* fall4 ,! problem !re=e becomes a m]ely geometrical "o1 viz4 to det]m9e ! ratio ( a c]ta9 area on ! bo>d to ! :ole area4 ,! det]m9ation ( ?is ratio is all t ! ma!matician ev] takes into acc\nt4 ,n[ take ! foll[+4 ,a /raight brittle rod is brok5 at r&om 9 two places3 f9d ! *ance t ! pieces c make a triangle4#b ,s9ce ! only condition = mak+ a triangle ) ?ree /raight l9es is t ea* two %all be great] ?an ! ?ird1 ! problem seems to involve ! same g5]al conception z 9 ! =m] case4 ,we mu/ conceive su* rods break+ at "o pair ( spots aft] ano!r1--no "o c tell precisely :]e1--b %[+ ! same ultimate t5d5cy to di/ribute ^! spots ?r\gh\t ! :ole l5g? uni=mly4 ,z 9 ! la/ case1 ! ma!matician ?9ks ( no?+ b ?is f9al result1 & pays no he$ to ! process by :i* x may be br\ght ab\t4 ,accord+ly ! problem is aga9 r$uc$ to "o ( m5suration1 ?\gh ( a some:at m complicat$ "*4 #c4 7#b7 ,9 ano!r class ( cases we h to contemplate an int]m$iate process r ?an a f9al result2 b ! same conception has to be introduc$ "h1 ?\gh x is n[ appli$ to ! =m] /age1 & 9 consequ5ce w n 9 g5]al apply to ! latt]4 ,= in/ance3 a %ot is fir$ at r&om f a gun ^: maximum range 7i4e4 at #de elevation7 is #cjjj y>ds3 :at is ! *ance t ! actual range %all exce$ #bjjj y>ds8 ,! ultimately uni=m 7or r&om7 di/ribution "h is commonly assum$ to apply to ! v>i\s directions 9 :i* ! gun c be po9t$2 all possible directions above ! horizontal be+ equally repres5t$ 9 ! long run4 ,we h !re=e to contemplate a surface ( uni=m di/ribution1 b x w be ! surface1 n ( ! gr\nd1 b ( a hemisph]e ^: c5tre is occupi$ by ! man :o fires4 ,! ultimate di/ribution ( ! bullets on ! spots :]e !y /rike ! gr\nd w n be uni=m4 ,! problem is 9 fact to discov] ! law ( v>iation ( ! d5sity ( di/ribution4 ,! above is1 ,i presume1 ! treatm5t g5]ally adopt$ 9 solv+ su* a problem4 ,b !re seems no absolute necessity = any su* p>ticul> *oice4 ,x is surely op5 to any "o to ma9ta9#c t 8 conception ( ! r&omness ( ! fir+ is assign$ by say+ t x is likely t a man %\ld beg9 by fac+ t[>ds any po9t ( ! compass indiff]5tly1 & !n proce$ to raise 8 gun to any angle indiff]5tly4 ,! /age ( ultimately uni=m di/ribution "h has rec$$ a /ep fur!r back4 ,x is n assign$ directly to ! surface ( an imag9>y hemisph]e1 b to ! l9es ( altitude & azimu? drawn on t surface4 ,accord+ly1 ! di/ribution ov] ! hemisph]e itself w n n[ be uni=m1--!re w be a comp>ative cr[d+ up t[>ds ! pole1--& ! ultimate di/ribution ov] ! gr\nd w n be ! same z be=e4 #d4 ,difficulties ( ?is k9d1 aris+ out ( ! unc]ta9ty z to :at /age %\ld be select$ = t ( uni=m di/ribution1 w occasionally pres5t !mselves4 ,= in/ance3 let a book be tak5 at r&om out ( a bookcase2 :at is ! *ance ( hitt+ ^u "s assign$ volume8 ,i h>dly "k h[ ?is "q w\ld commonly be treat$4 ,if we 7 to set our man opposite ! middle ( ! %elf & inquire :at w\ld g5]ally happ5 9 practice1 suppos+ him bl9dfold$1 !re _c be mu* d\bt t ! volumes w\ld n be select$ equally (t54 ,on ! contr>y1 x is likely t !re w\ld be a t5d5cy to increas$ frequ5cy ab\t a c5tre indicat$ by ! height ( 8 %\ld]1 & 7unless he be left-h&$7 a trifle to ! "r ( ! po9t exactly opposite 8 />t+ po9t4 ,if ! "q 7 "o :i* x 7 really wor? :ile to "w out on ^! l9es we %\ld be l$ a long way back4 ,j z we imag9$ our rifleman's position 7on ! second supposition7 to be det]m9$ by two indep5d5t coord9ates ( assum$ cont9u\s & equal facility1 s we might conceive our mak+ ! attempt to analyse ! man's movem5ts into a c]ta9 numb] ( indep5d5t con/itu5ts4 ,we might suppose all ! v>i\s directions f 8 />t+ po9t1 along ! gr\nd1 to be equally likely2 & t :5 he rea*es ! %elves ! r&om motion ( 8 h& is to be regulat$ aft] ! fa%ion ( a %ot dis*>g$ at r&om4 ,! above w\ld be "o way ( sett+ ab\t ! /atem5t ( ! problem4 ,b ! read] w und]/& t all :i* ,i am "h propos+ to ma9ta9 is t 9 ^!1 z 9 e simil> case1 we always enc\nt]1 "u ?is conception ( 'r&omness'1 at "s /age or o!r1 ?is po/ulate ( ultimate uni=mity ( di/ribution ov] "s assign$ magnitude3 ei!r "t2 or space1 l9e>1 sup]ficial1 or solid4 ,b ! selection ( ! /age at :i* ?is is to be appli$ may give rise to consid]able difficulty1 & ev5 arbitr>9ess ( *oice4 #e4 ,"s ye>s ago !re 0 a v int]e/+ discussion ^u ?is subject c>ri$ on 9 ! ma!matical "p ( ! ,educational ,times 7see1 especially1 ,vol4 ,,vii474 ,z n unfrequ5tly happ5s 9 ma!matics !re 0 an almo/ entire accord among/ ! v>i\s writ]s z to ! assumptions practically to be made 9 any p>ticul> case1 & !re=e z to ! conclusion to be drawn1 comb9$ ) a v consid]able am\nt ( diff]5ce z to ! axioms & def9itions to be employ$4 ,?us ,mr ,m4 ,w4 ,cr(ton1 ) ! sub/antial agreem5t ( ,mr ,woolh\se1 laid x d[n unhesitat+ly t at r&om has a v cle> & def9ite mean+2 "o :i* _c be bett] convey$ ?an by ,mr ,wilson's def9ition1 'accord+ to no law'2 & 9 ?is s5se alone ,i mean to use x4 ,accord+ to any sci5tific int]pretation ( 'law' ,i %\ld h said t :]e !re 0 no law !re c\ld be no inf]5ce4 ,b ultimate t5d5cy t[>ds equality ( di/ribution is z mu* tak5 = grant$ by ,mr ,cr(ton z by any "o else3 9 fact he makes ?is a d$uction f 8 def9ition3--,z ?is inf9ite sy/em ( p>allels are drawn accord+ to no law1 !y are z ?ickly dispos$ along any "p ( ! common p]p5dicul> z along any o!r 7,,vii4 p4 #he74 ,mr ,cr(ton holds t any k9d ( unequal di/ribution w\ld imply law1--,if ! po9ts on a plane t5d$ to become d5s] 9 any "p ( ! plane ?an 9 ano!r1 !re mu/ be "s law attract+ !m !re 7ib4 p4 #hd74 ,! same view is en=c$ 9 8 pap] on ,local ,probability 79 ! ,phil4 ,trans41 ,vol4 #aeh74 ,surely if !y t5d to become equally d5se ?is is j z mu* a case ( regul>ity or law4 ,x may be rem>k$ t :]ev] any s]i\s practical consequ5ces turn ^u duly secur+ ! desir$ r&omness1 x is always s contriv$ t no design or awkw>dness or unconsci\s "o-sid$ness %all di/urb ! result4 ,! pr9cipal case 9 po9t "h is ( c\rse af=d$ by games ( *ance4 ,:at we want1 :5 we toss a die1 is to secure t all numb]s f #a to #f %all be equally (t5 repres5t$ 9 ! long run1 b t no p]son %all be able to pr$ict ! individual occurr5ce4 ,we might1 9 our /atem5t ( a problem1 z easily po/ulate 'a numb] ?\ght ( at r&om' z 'a %ot fir$ at r&om'1 b no "o w\ld risk 8 *ances ( ga9 & loss on ! supposition t ?is w\ld be done ) cont9u$ fairness4 ,accord+ly1 we con/ruct a die ^: sides are accurately alike1 & x is f\nd t we may d almo/ :at we l ) ?is1 at any previ\s /age to t ( its issue f ! dice box on to ! table1 )\t int]f]+ ) ! r&om nature ( ! result4 #f4 ,,ii4 ,ano!r *>act]i/ic 9 :i* ! sci5tific conception seems to me to dep>t f ! popul> or orig9al signification is ! foll[+4 ,! area ( di/ribution :i* we take into acc\nt mu/ be a f9ite or limit$ "o4 ,! necessity = ?is re/riction may n be obvi\s at fir/ sight1 b ! consid]ation ( "o or two examples w s]ve to indicate ! po9t at :i* x makes itself felt4 ,suppose t "o 7 ask$ to *oose a numb] at r&om1 n f a f9ite range1 b f ! inexhau/ible possibilities ( enum]ation4 ,9 ! popul> s5se ( ! t]m1--i4e4 ( utt]+ a numb] )\t paus+ to *oose1--!re is no difficulty4 ,b a mom5t's consid]ation w %[ t no arrangem5t ev5 t5d+ t[>ds ultimately uni=m di/ribution c be secur$ 9 ?is way4 ,no av]age c\ld be /ruck ) ev] increas+ /ead9ess4 ,s ) spatial inf9ity4 ,we c rationally speak ( *oos+ a po9t at r&om 9 a giv5 /raight l9e1 area1 or volume4 ,b if we suppose ! l9e to h no end1 or ! selection to be made 9 inf9ite space1 ! basis ( ultimate t5d5cy t[>ds :at may be call$ ! equally ?ick deposit ( our r&om po9ts fails u utt]ly4 ,simil>ly 9 any o!r example 9 :i* "o ( ! magnitudes is unlimit$4 ,suppose ,i fl+ a /ick at r&om 9 a horizontal plane aga9/ a r[ ( iron rail+s & inquire = ! *ance ( its pass+ ?r\gh )\t t\*+ !m4 ,! problem be>s "s analogy to t ( ! *essm51 & s f> z ! motion ( translation ( ! /ick is conc]n$ 7if we beg9 ) ?is7 x pres5ts no difficulty4 ,b z reg>ds ! rotation x is o!rwise4 ,= any assign$ l9e> velocity !re is a c]ta9 angul> velocity bel[ :i* ! /ick may pass ?r\gh )\t contact1 b above :i* x _c4 ,& inasmu* z ! =m] range is limit$ & ! latt] is unlimit$1 we enc\nt] ! same impossibility z be=e 9 endeav\r+ to conceive a uni=m di/ribution4 ,( c\rse we might evade ?is p>ticul> difficulty by beg9n+ ) an e/imate ( ! angul> velocity1 :5 we %\ld h to repeat :at has j be5 said1 mutatis mut&is1 9 ref]5ce to ! l9e> velocity4 #g4 ,i am ( c\rse aw>e t !re are a v>iety ( problems curr5t :i* seem to conflict ) :at has j be5 said1 b !y w all submit to explanation4 ,= in/ance2 ,:at is ! *ance t ?ree /raight l9es1 tak5 or drawn at r&om1 %all be ( su* l5g?s z w admit ( _! =m+ a triangle8 ,!re are two ways 9 :i* we may reg>d ! problem4 ,we may1 = "o ?+1 />t ) ! assumption ( ?ree l9es n great] ?an a c]ta9 l5g? n1 & !n det]m9e t[>ds :at limit ! *ance t5ds z n increases unceas+ly4 ,or1 we may ma9ta9 t ! "q is m]ely "o ( relative proportion ( ! ?ree l9es4 ,we may !n />t ) any magnitude we please to repres5t "o ( ! l9es 7= simplicity1 say1 ! longe/ ( !m71 & consid] t all possible %apes ( a triangle w be repres5t$ by v>y+ ! l5g?s ( ! o!r two4 ,9 ei!r case we get a def9ite result )\t ne$ to make an attempt to conceive any r&om selection f ! inf9ity ( possible l5g?4 ,s 9 :at is call$ ! ?ree-po9t problem3--,?ree po9ts 9 space are select$ at r&om2 f9d ! *ance ( _! =m+ an acute-angl$ triangle4 ,:at is done is to />t ) a clos$ volume1--say a sph]e1 f its sup]ior simplicity1--f9d ! *ance 7on ! assumption ( uni=m di/ribution )9 ?is volume72 & !n conceive ! cont9ual enl>gem5t )\t limit ( ?is sph]e4 ,s reg>d$ ! problem is p]fectly consi/5t & intelligible1 ?\gh ,i fail to see :y x %\ld be t]m$ a r&om selection 9 space r ?an 9 a sph]e4 ,( c\rse if we />t$ ) a diff]5t volume1 say a cube1 we %\ld get a diff]5t result2 & x is !re=e cont5d$ 7e4g4 by ,mr ,cr(ton 9 ! ,educational ,times1 z already ref]r$ to7 t inf9ite space is m naturally & appropriately reg>d$ z t5d$ t[>ds by ! enl>gem5t ( a sph]e ?an by t ( a cube or any o!r figure4 ,aga93 ,a gr\p ( integ]s is tak5 at r&om2 %[ t ! numb] ?us tak5 is m likely to be odd ?an ev54 ,:at we d 9 answ]+ ?is is to />t ) any f9ite numb] n1 & %[ t ( all ! possible comb9ations :i* c be made )9 ?is range !re are m odd ?an ev54 ,s9ce ?is is true irrespective ( ! magnitude ( n1 we are apt to speak z if we c\ld conceive ! selection be+ made at r&om f ! true inf9ity contemplat$ 9 num]ation4 #h4 ,:]e ^! conditions _c be secur$ !n x seems to me t ! attempt to assign any f9ite value to ! probability fails4 ,= in/ance1 9 ! foll[+ problem1 propos$ by ,mr ,j4 ,m4 ,wilson1 ,?ree /raight l9es are drawn at r&om on an inf9ite plane1 & a f\r? l9e is drawn at r&om to int]sect !m3 f9d ! probability ( its pass+ ?r\gh ! triangle =m$ by ! o!r ?ree 7,ed4 ,times1 ,repr9t1 ,vol4 ,v4 p4 #hb71 he (f]s ! foll[+ solution3 ,( ! f\r l9es1 two mu/ & two mu/ n pass )9 ! triangle =m$ by ! rema9+ ?ree4 ,s9ce all are drawn at r&om1 ! *ance t ! la/ drawn %\ld pass ?r\gh ! triangle =m$ by ! o!r ?ree is consequ5tly #a_/b4 ,i quote ?is solution because x seems to me to illu/rate ! difficulty to :i* ,i want to call att5tion4 ,z ! problem is word$1 a triangle is suppos$ to be assign$ by ?ree /raight l9es4 ,h[ev] l>ge x may be1 its size be>s no f9ite ratio :atev] to ! indef9itely l>g] area outside x2 &1 s f> z ,i c put any intelligible con/ruction on ! supposition1 ! *ance ( draw+ a f\r? r&om l9e :i* %\ld happ5 to int]sect ?is f9ite area mu/ be reckon$ z z]o4 ,! problem ,mr ,wilson has solv$ seems to me to be a q diff]5t "o1 viz4 ,giv5 f\r int]sect+ /raight l9es1 f9d ! *ance t we %\ld1 at r&om1 select "o t passes ?r\gh ! triangle =m$ by ! o!r ?ree4 ,! same difficulty seems to me to turn up 9 mo/ o!r attempts to apply ?is conception ( r&omness to real inf9ity4 ,! foll[+ seems an exact analogue ( ! above problem3--,a numb] is select$ at r&om1 f9d ! *ance t ano!r numb] select$ at r&om %all be great] ?an ! =m]2--! answ] surely mu/ be t ! *ance is unity1 viz4 c]ta9ty1 because ! range above any assign$ numb] is inf9itely great] ?an t bel[ x4 ,or1 express$ 9 ! only language 9 :i* ,i c und]/& ! t]m 'inf9ity'1 :at ,i mean is ?is4 ,if ! fir/ numb] be m & ,i am re/rict$ to select+ up to n 7n m7 !n ! *ance ( exce$+ m is n - m 3 n2 if ,i am re/rict$ to #bn !n x is #bn - m 3 #bn & s on4 ,t is1 h[ev] l>ge n & m may be ! expression is always intelligible2 b1 m be+ *os5 fir/1 n may be made z mu* l>g] ?an m z we please3 i4e4 ! *ance may be made to approa* z ne> to unity z we please4 ,i _c b ?9k t !re is a simil> fallacy 9 ,de ,morgan's admirably sugge/ive pap] on ,inf9ity 7,camb4 ,phil4 ,trans4 ,vol4 #aa47 :5 he is discuss+ ! ?ree-po9t problem3--i4e4 giv5 ?ree po9ts tak5 at r&om f9d ! *ance t !y %all =m an acute-angl$ triangle4 ,all t he %[s is1 t if we />t ) "o side z giv5 & consid] ! subsequ5t possible positions ( ! opposite v]tex1 !re are inf9itely z _m su* positions :i* w\ld =m an acute-angl$ triangle z an obtuse3 b1 z be=e1 ?is is solv+ a diff]5t problem4 #i4 ,! ne>e/ approa* ,i c make t[>ds true indef9ite r&omness1 or r&om selection f true indef9it5ess1 is z foll[s4 ,suppose a circle ) a tang5t l9e ext5d$ indef9itely 9 ea* direction4 ,n[ f ! c5tre draw radii at r&om2 9 o!r words1 let ! semicircumf]5ce :i* lies t[>ds ! tang5t be ultimately uni=mly int]sect$ by ! radii4 ,let ^! radii be !n produc$ s z to int]sect ! tang5t l9e1 & consid] ! di/ribution ( ^! po9ts ( int]section4 ,we %all obta9 9 ! result "o *>act]i/ic ( our r&om di/ribution2 i4e4 no portion ( ?is tang5t1 h[ev] small or h[ev] remote1 b w f9d itself 9 ! position ultimately ( any small portion ( ! pavem5t 9 our suppos$ cont9ual ra9fall4 ,t is1 any su* elem5t>y pat* w become m & m closely dott$ ov] ) ! po9ts ( int]section4 ,b ! o!r ess5tial *>act]i/ic1 viz4 t ( ultimately uni=m di/ribution1 w be miss+4 ,!re w be a special =m ( di/ribution1--:at 9 fact w h to be discuss$ 9 a future *apt] "u ! designation ( a 'law ( error'1--by virtue ( :i* ! conc5tration w t5d to be greate/ at a c]ta9 po9t 7t ( contact ) ! circle71 & w ?9 out f "h 9 ea* direction accord+ to an easily calculat$ =mula4 ,! exi/5ce ( su* a /ate ( ?+s z ?is is q oppos$ to ! conception ( true r&omness4 #aj4 ,,iii4 ,ap>t f def9itions & :at comes ( !m1 p]haps ! mo/ important "q connect$ ) ! conception ( ,r&omness is ?is3 ,h[ 9 any giv5 case are we to det]m9e :e!r an obs]v$ arrangem5t is to be consid]$ a r&om "o or n8 ,?is "q w h to be m fully discuss$ 9 a future *apt]1 b we are already 9 a position to see our way ?r\gh "s ( ! difficulties involv$ 9 x4 7#a7 ,if ! ev5ts or objects "u consid]ation are suppos$ to be cont9u$ indef9itely1 or if we "k en\gh ab\t ! mode 9 :i* !y are br\ght ab\t to detect _! ultimate t5d5cy1--or ev51 %ort ( ?is1 if !y are num]\s en\gh to be beyond practical c\nt+1--!re is no great difficulty4 ,we are simply confront$ ) a "q ( fact1 to be settl$ l o!r que/ions ( fact4 ,9 ! case ( ! ra9-drops1 wat* two equal squ>es ( pavem5t or o!r surfaces1 & note :e!r !y come to be m & m d5sely uni=mly & ev5ly spott$ ov]3 if !y d1 !n ! arrangem5t is :at we call a r&om "o4 ,if ,i want to "k :e!r a tobacco-pipe really breaks at r&om1 & w\ld !re=e s]ve z an illu/ration ( ! problem propos$ "s pages back1 ,i h only to drop en\gh ( !m & see :e!r pieces ( all possible l5g?s are equally repres5t$ 9 ! long run4 ,or1 ,i may argue d$uctively1 f :at ,i "k ab\t ! /r5g? ( mat]ials & ! molecul> con/itution ( su* bodies1 z to :e!r fractures ( small & l>ge pieces are all equally likely to occur4 #aa4 ,! read]'s att5tion mu/ be c>efully direct$ to a s\rce ( confusion "h1 aris+ out ( a c]ta9 cross-division4 ,:at we are n[ discuss+ is a "q ( fact1 viz4 ! nature ( a c]ta9 ultimate arrangem5t2 we are n discuss+ ! p>ticul> way 9 :i* x is br\ght ab\t4 ,9 o!r words1 ! anti!sis is betwe5 :at is & :at is n r&om3 x is n betwe5 :at is r&om & :at is design$4 ,z we %all see 9 a few mom5ts x is q possible t an arrangem5t :i* is ! result1--if ev] any?+ 7 s1--( 'design'1 may nev]!less pres5t ! unmi/akeable /amp ( r&omness ( arrangem5t4 ,consid] a case :i* has be5 a good deal discuss$1 & to :i* we %all rev]t aga93 ! arrangem5t ( ! />s4 ,! "q "h is r complicat$ by ! fact t we "k no?+ ab\t ! actual mutual positions ( ! />s1 all t we c take cognizance ( be+ _! app>5t or visible places z project$ ^u ! surface ( a suppos$ sph]e4 ,appeal+ to :at alone we c ?us obs]ve1 x is obvi\s t ! arrangem5t1 z a :ole1 is n ( ! r&om sort4 ,! ,milky ,way & ! o!r resolvable nebul1 z !y pres5t !mselves to u1 are z obvi\s an infraction ( su* an arrangem5t z w\ld be ! occurr5ce "h & !re ( pat*es ( gr\nd 9 a ra9fall :i* receiv$ a va/ numb] m drops ?an ! spaces surr\nd+ !m4 ,if we leave ^! exceptional areas out ( ! "q & consid] only ! />s :i* are visible by ! nak$ eye or by slight telescopic p[]1 x seems equally c]ta9 t ! arrangem5t is1 = ! mo/ "p1 a fairly repres5tative r&om "o4 ,by ?is we mean no?+ m ?an ! fact t :5 we m>k (f any numb] ( equal areas on ! visible sph]e ^! are f\nd to conta9 approximately ! same numb] ( />s4 ,! actual arrangem5t ( ! />s 9 space may also be ( ! same "*3 t is1 ! app>5tly d5s] aggregation may be app>5t only1 aris+ f ! fact t we are look+ ?r\gh regions :i* are n m ?ickly occupi$ b are m]ely m ext5sive4 ,! alt]native be=e u1 9 fact1 is ?is4 ,if ! :ole volume1 s to say1 ( ! />ry heav5s is tol]ably regul> 9 %ape1 !n ! arrangem5t ( ! />s is n ( ! r&om ord]2 if t volume is v irregul> 9 %ape1 x is possible t ! arrangem5t )9 x may be ?r\gh\t ( t ord]4 #ab4 7#b7 ,:5 ! arrangem5t 9 "q includes b a comp>atively small numb] ( ev5ts or objects1 x becomes mu* m difficult to det]m9e :e!r or n x is to be designat$ a r&om "o4 ,9 fact we h to %ift our gr\nd1 & to decide n by :at has be5 actually obs]v$ b by :at we h reason to conclude w\ld be obs]v$ if we c\ld cont9ue our obs]vation mu* long]4 ,?is introduces :at is call$ ',inv]se ,probability'1 viz4 ! det]m9ation ( ! nature ( a cause f ! nature ( ! obs]v$ effect2 a "q :i* w be fully discuss$ 9 a future *apt]4 ,b "s introductory rem>ks may be conv5i5tly made "h4 ,e problem ( ,probability1 z ! subject is "h und]/ood1 introduces ! conception ( an ultimate limit1 & !re=e presupposes an indef9ite possibility ( repetition4 ,:5 we h only a f9ite numb] ( occurr5ces be=e u1 direct evid5ce ( ! "* ( _! arrangem5t fails u1 & we h to fall back ^u ! nature ( ! ag5cy :i* produces !m4 ,& z ! numb] becomes small] ! confid5ce ) :i* we c e/imate ! nature ( ! ag5cy becomes gradually less4 ,beg9 ) an int]m$iate case4 ,!re is a small lawn1 spr9kl$ ov] ) daisies3 is ?is a r&om arrangem5t8 ,we feel "s confid5ce t x is s1 on m]e inspection2 mean+ by ?is t 7negatively7 no trace ( any regul> patt]n c be disc]n$ & 7affirmatively7 t if we take any mod]ately small area1 say a squ>e y>d1 we %all f9d mu* ab\t ! same numb] ( ! plants includ$ 9 x4 ,b we c help ourselves by an appeal to ! kn[n ag5cy ( di/ribution "h4 ,we "k t ! daisy spreads by se$1 & consid]+ ! effect ( ! w9d & ! cont9u$ sweep+ & m[+ ( ! lawn we c detect causes at "w :i* are analog\s to ^? by :i* ! deal+ ( c>ds & ! toss+ ( dice are regulat$4 ,9 ! above case ! appeal to ! process ( production 0 subsidi>y1 b :5 we come to consid] ! nature ( a v small succession or gr\p ?is appeal becomes mu* m important4 ,let u be told ( a c]ta9 succession ( 'heads' & 'tails' to ! numb] ( t54 ,! range "h is f> too small = decision1 & unless we are told :e!r ! ag5t :o obta9$ !m 0 toss+ or design+ we are q unable to say :e!r or n ! designation ( 'r&om' ought to be appli$ to ! result obta9$4 ,! tru? mu/ nev] be =gott5 t ?\gh 'design' is sure to break d[n 9 ! long run if x make ! attempt to produce directly ! semblance ( r&omness1#d yet = a %ort spell x c simulate x p]fectly4 ,any %ort succession1 say ( heads & tails1 may h be5 equally well br\ght ab\t by toss+ or by delib]ate *oice4 #ac4 ,! read] w obs]ve t ?is "q ( r&omness is be+ "h treat$ z simply "o ( ultimate /ati/ical fact4 ,i h fully admitt$ t ?is is n ! primitive conception1 nor is x ! popul> int]pretation1 b to adopt x seems ! only c\rse op5 to u if we are to draw inf]5ces su* z ^? contemplat$ 9 ,probability4 ,:5 we look to ! produc+ ag5cy ( ! ultimate arrangem5t we may f9d ?is v v>i\s4 ,x may prove itself to be 7a few /ages back7 "o ( consci\s delib]ate purpose1 z 9 draw+ a c>d or toss+ a die3 x may be ! outcome ( an extremely complicat$ int]action ( _m natural causes1 z 9 ! arrangem5t ( ! fl[]s scatt]$ ov] a lawn or mead[3 x may be ( a k9d ( :i* we "k lit]ally no?+ :atev]1 z 9 ! case ( ! actual arrangem5t ( ! />s relatively to ea* o!r4 ,?is 0 ! /ate ( ?+s _h 9 view :5 x 0 said a few pages back t r&omness & design w\ld result 9 some?+ ( a cross-division4 ,pl5ty ( arrangem5ts 9 :i* design _h a h&1 a /age or two back1 c be m5tion$1 :i* w\ld be q indi/+ui%able 9 _! results f ^? 9 :i* no design :atev] c\ld be trac$4 ,p]haps ! mo/ /rik+ case 9 po9t "h is to be f\nd 9 ! arrangem5t ( ! digits 9 "o ( ! natural ari?metical con/ants1 su* z or e1 or 9 a table ( log>i?ms4 ,if we look to ! process ( production ( ^! digits1 no extrem] in/ance c be f\nd ( :at we mean by ! anti!sis ( r&omness3 e figure has its necess>ily pre-orda9$ position1 & a mom5t's flagg+ ( int5tion w\ld defeat ! :ole purpose ( ! calculator4 ,& yet1 if we look to results only1 no bett] in/ance c be f\nd ?an "o ( ^! r[s ( digits if x 7 int5d$ to illu/rate :at we practically und]/& by a *ance arrangem5t ( a numb] ( objects4 ,ea* digit occurs approximately equally (t51 & ?is t5d5cy develops z we advance fur!r3 ! mutual juxtaposition ( ! digits also %[s ! same t5d5cy1 t is1 any digit 7say #e7 is j z (t5 foll[$ by #f or #g z by any ( ! o!rs4 ,9 fact1 if we 7 to take ! :ole r[ ( hi!rto calculat$ figures1 cut (f ! fir/ five z famili> to u all1 & contemplate ! re/1 no "o w\ld h ! slighte/ reason to suppose t ^! _h n come out z ! results ( a die ) t5 equal faces4 #ad4 ,if x be ask$ :y ?is is s1 a r puzzl+ "q is rais$4 ,:]ev] physical causation is involv$ we are g5]ally und]/ood to h satisfi$ ! dem& impli$ 9 ?is "q if we assign antec$5ts :i* w be foll[$ regul>ly by ! ev5t be=e u2 b 9 geometry & ari?metic !re is no op5+ = antec$5ts4 ,:at we !n commonly look = is a demon/ration1 i4e4 ! resolution ( ! obs]v$ fact into axioms if possible1 or at any rate into admitt$ tru?s ( wid] g5]ality4 ,i d n "k t a demon/ration c be giv5 z to ! exi/5ce ( ?is *>act]i/ic ( /ati/ical r&omness 9 su* successions ( digits z ^? "u consid]ation4 ,b ! foll[+ rem>ks may s]ve to %ift ! onus ( unlikelihood by sugge/+ t ! prepond]ance ( analogy is r 9 fav\r ( ! exi/5ce4 ,take ! well-kn[n con/ant = consid]ation4 ,?is /&s = a quantity :i* pres5ts itself 9 a va/ numb] ( ari?metical & geometrical relations2 let u take = exam9ation ! be/ kn[n ( ^!1 by reg>d+ x z /&+ = ! ratio ( ! circumf]5ce to ! diamet] ( a circle4 ,s reg>d$1 x is no?+ m ?an a simple case ( ! measurem5t ( a magnitude by an arbitr>ily select$ unit4 ,conceive !n t we _h be=e u a rod or l9e & t we wi%$ to measure x ) absolute accuracy4 ,we mu/ suppose--if we are to h a suitable analogue to ! det]m9ation ( to sev]al hundr$ figures1--t by ! application ( cont9u$ high] magnify+ p[] we c detect ev] f9] subdivisions 9 ! graduation4 ,we lay our rod aga9/ ! scale & f9d x1 say1 fall betwe5 #ca & #cb in*es2 we !n look at ! next division ( ! scale1 viz4 t into t5?s ( an in*4 ,c we see ! slighte/ reason :y ! numb] ( ^! t5?s %\ld be o!r ?an indep5d5t ( ! numb] ( :ole in*es8 ,! piece ov] :i* we are measur+ may 9 fact be reg>d$ z an entirely new piece1 :i* _h fall5 into our h&s aft] t ( #ca in*es _h be5 measur$ & done )2 & simil>ly ) e successive piece ov]1 z we proce$ to ! ev] f9] & f9] divisions4 ,simil> rem>ks may be made ab\t mo/ o!r incomm5surable quantities1 su* z irr$ucible roots4 ,conceive two /raight l9es at "r angles1 & t we lay (f a c]ta9 numb] ( in*es along ea* ( ^! f ! po9t ( int]section2 say two & five in*es1 & jo9 ! extremities ( ^! s z to =m ! diagonal ( a "r-angl$ triangle4 ,if we proce$ to measure ?is diagonal 9 t]ms ( ei!r ( ! o!r l9es we are to all int5ts & purposes extract+ a squ>e root4 ,we %\ld expect1 r ?an o!rwise1 to f9d "h1 z 9 ! case ( 1 t incomm5surability & resultant r&omness ( ord] 9 ! digits 0 ! rule1 & comm5surability 0 ! exception4 ,n[ & !n1 z :5 ! two sides 7 ?ree & f\r1 we %\ld f9d ! diagonal comm5surable ) !m2 b ^! w\ld be ! occasional exceptions1 or r !y w\ld be ! comp>atively f9ite exceptions amid/ ! indef9itely num]\s cases :i* furni%$ ! rule4 #ae4 ,! be/ way p]haps ( illu/rat+ ! truly r&om "* ( su* a r[ ( figures is by appeal+ to graphical aid4 ,x is n easy "h1 any m ?an 9 ord9>y /ati/ics1 to grasp ! import ( m]e figures2 :]eas ! arrangem5t ( gr\ps ( po9ts or l9es is mu* m readily seiz$4 ,! eye is v quick 9 detect+ any symptoms ( regul>ity 9 ! arrangem5t1 or any t5d5cy to d5s] aggregation 9 "o direction ?an 9 ano!r4 ,h[ !n are we to dispose our figures s z to =ce !m to display _! true "*8 ,i %\ld sugge/ t we set ab\t draw+ a l9e at r&om2 &1 s9ce we _c tru/ our own unaid$ ef=ts to d ?is1 t we rely ^u ! help ( su* a table ( figures to d x = u1 & !n exam9e ) :at sort ( effici5cy !y c p]=m ! task4 ,! problem ( draw+ /raight l9es at r&om1 "u v>i\s limitations ( direction or int]section1 is famili> en\gh1 b ,i d n "k t any "o has sugge/$ ! draw+ ( a l9e ^: %ape z well z position %all be ( a purely r&om "*4 ,= simplicity we suppose ! l9e to be conf9$ to a plane4 ,! def9ition ( su* a l9e does n seem to involve any p>ticul> difficulty4 ,phras$ 9 accordance ) ! ord9>y language we %\ld describe x z ! pa? 7i4e4 any pa?7 trac$ out by a po9t :i* at e mom5t is z likely to move 9 any "o direction z 9 any o!r4 ,t we c\ld n ourselves draw su* a l9e1 & t we c\ld n get x trac$ by any physical ag5cy1 is c]ta94 ,! m]e in]tia ( any mov+ body w always give x a t5d5cy1 h[ev] slight1 to g on 9 a /raight l9e at ea* mom5t1 in/ead ( be+ in/antly responsive to in/antane\sly v>y+ dictates z to its direction ( motion4 ,nor c we conceive or picture su* a l9e 9 its ultimate or ideal condition4 ,b x is easy to give a graphical approximation to x1 & x is easy also to %[ h[ ?is approximation may be c>ri$ on z f> z we please t[>ds ! ideal 9 "q4 ,we may proce$ z foll[s4 ,take a %eet ( ! ord9>y rul$ pap] prep>$ = ! graphical exposition ( curves4 ,select z our />t+ po9t ! int]section ( two ( ^! l9es1 & consid] ! eight 'po9ts ( ! compass' indicat$ by ^! l9es & ! bisections ( ! conta9$ "r angles4#e ,= sugge/+ ! r&om selection among/ ^! directions let !m be numb]$ f #j to #g1 & let u say t a l9e measur$ due 'nor?' %all be designat$ by ! figure #j1 'nor?-ea/' by #a1 & s on4 ,! selection among/ ^! numb]s1 & !re=e directions1 at e corn]1 might be h&$ ov] to a die ) eight faces2 b = ! purpose ( ! illu/ration 9 view we select ! digits #j to #g z !y pres5t !mselves 9 ! calculat$ value ( 4 ,! sort ( pa? along :i* we %\ld travel by a s]ies ( su* /eps ?us tak5 at r&om may be readily conceiv$2 x is giv5 at ! end ( ?is *apt]4 ,= ! purpose ) :i* ?is illu/ration 0 propos$1 viz4 ! graphical display ( ! succession ( digits 9 any "o ( ! incomm5surable con/ants ( ari?metic or geometry1 ! above may suffice4 ,aft] actually te/+ "s ( !m 9 ?is way !y seem to me1 s f> z ! eye1 or ! !oretical pr9ciples to be pres5tly m5tion$1 are any guide1 to answ] q fairly to ! description ( r&omness4 #af4 ,z we are on ! subject1 h[ev]1 x seems wor? go+ f>!r by enquir+ h[ ne> we c\ld get to ! ideal ( r&omness ( direction4 ,to c>ry ?is out completely two improvem5ts mu/ be made4 ,= "o ?+1 in/ead ( conf9+ ourselves to eight directions we mu/ admit an inf9ite numb]4 ,?is w\ld (f] no great difficulty2 = in/ead ( employ+ a small numb] ( digits we %\ld m]ely h to use "s k9d ( circul> teetotum :i* w\ld re/ indiff]5tly 9 any direction4 ,b 9 ! next place in/ead ( %ort f9ite /eps we mu/ suppose !m indef9itely %ort4 ,x is "h t ! actual unatta9ability makes itself felt4 ,we are famili> en\gh ) ! device1 employ$ by ,newton1 ( pass+ f ! discont9u\s polygon to ! cont9u\s curve4 ,b we c resort to ?is device because ! ideal1 viz4 ! curve1 is z easily drawn 7&1 ,i %\ld say1 z easily conceiv$ or pictur$7 z any ( ! /eps :i* lead u t[>ds x4 ,b 9 ! case be=e u x is o!rwise4 ,! l9e 9 "q w rema9 discont9u\s1 or r angul>1 to ! la/3 = its angles d n t5d ev5 to lose _! %>pness1 ?\gh ! fragm5ts :i* compose !m increase 9 numb] & dim9i% 9 magnitude )\t any limit4 ,& su* an ideal is n conceivable z an ideal4 ,x is z if we _h a r\gh body "u ! microscope1 & f\nd t z we subject$ x to high] & high] p[]s !re 0 no t5d5cy = ! angles to r\nd !mselves (f4 ,our 'r&om l9e' mu/ rema9 z 'spiky' z ev]1 ?\gh ! size ( its spikes ( c\rse dim9i%es )\t any limit4 ,! case !re=e seems to be ?is4 ,x is easy1 9 words1 to indicate ! conception by speak+ ( a l9e :i* at e in/ant is z likely to take "o direction z ano!r4 ,x is easy moreov] to draw su* a l9e ) any degree ( m9ut5ess :i* we *oose to dem&4 ,b x is n possible to conceive or picture ! l9e 9 its ultimate =m4#f ,!re is 9 fact no 'limit' "h1 intelligible to ! und]/&+ or picturable by ! imag9ation 7correspond+ to ! asymptote ( a curve1 or ! cont9u\s curve to ! incessantly develop+ polygon71 t[>ds :i* we f9d ourselves cont9ually approa*+1 & :i* !re=e we are apt to conceive ourselves z ultimately atta9+4 ,! usual assumption !re=e :i* und]lies ! ,newtonian inf9itesimal geometry & ! ,diff]5tial ,calculus1 ceases to apply "h4 #ag4 ,if we l to consid] su* a l9e 9 "o ( its approximate /ages1 z above indicat$1 x seems to me t "s ( ! usual !orems ( ,probability1 :]e l>ge numb]s are conc]n$1 may safely be appli$4 ,if x be ask$1 = in/ance1 :e!r su* a l9e w ultimately t5d to /ray indef9itely f> f its />t+ po9t1 ,b]n\lli's ',law ( ,l>ge ,numb]s' may be appeal$ to1 9 virtue ( :i* we %\ld say t x 0 excessively unlikely t its div]g5ce %\ld be relatively great4 ,recur to our graphical illu/ration1 & consid] fir/ ! resultant deviation ( ! po9t 7aft] a great _m /eps7 "r or left ( ! v]tical l9e ?r\gh ! />t+ po9t4 ,( ! eight admissible motions at ea* /age two w n affect ?is relative position1 :il/ ! o!r six are equally likely to move u a /ep to ! "r or to ! left4 ,our resultant 'drift' !re=e to ! "r or left w be analog\s to ! resultant diff]5ce betwe5 ! numb] ( heads & tails aft] a great _m tosses ( a p5ny4 ,n[ ! well-kn[n outcome ( su* a numb] ( tosses is t ultimately ! proportional approximation to ! priori probability1 i4e4 to equality ( heads & tails1 is m & m ne>ly c>ri$ out1 b t ! absolute deflection is m & m widely display$4 ,apply+ ?is to ! case 9 po9t1 & rememb]+ t ! results apply equally to ! horizontal & v]tical directions1 we %\ld say t aft] any v great numb] ( su* '/eps' z ^? contemplat$1 ! ratio ( our di/ance f ! />t+ po9t to ! :ole di/ance travell$ w pretty c]ta9ly be small1 :]eas ! actual di/ance f x w\ld be l>ge4 ,we %\ld also say t ! long] we cont9u$ to produce su* a l9e ! m pron\nc$ w\ld ^! t5d5cies become4 ,s f> z conc]ns ?is te/1 & t af=d$ by ! g5]al appe>ance ( ! l9es drawn1--?is la/1 z above rem>k$1 be+ tol]ably tru/wor?y1--,i feel no d\bt z to ! g5]ally 'r&om' "* ( ! r[s ( figures display$ by ! incomm5surable or irrational ratios 9 "q4 ,z x may int]e/ ! read] to see an actual specim5 ( su* a pa? ,i app5d "o repres5t+ ! arrangem5t ( ! eight digits f #j to #g 9 ! value ( 4 ,! data are tak5 f ,mr ,%anks' a/oni%+ p]=mance 9 ! calculation ( ?is con/ant to #gjg places ( figures 7,proc4 ( ,r4 ,s41 ,,xxi4 p4 #cai74 ,( ^!1 aft] omitt+ #h & #i1 !re rema9 #efh2 ! diagram repres5ts ! c\rse trac$ out by foll[+ ! direction ( ^! z ! clue to our pa?4 ,_m ( ! /eps h ( c\rse be5 tak5 9 opposite directions twice or (t5]4 ,! result seems to me to furni% a v fair graphical indication ( r&omness4 ,i h comp>$ x ) correspond+ pa?s furni%$ by r[s ( figures tak5 f log>i?mic tables1 & 9 o!r ways1 & f9d ! results to be mu* ! same4 ,figure3 ,digits ( z a pa?4 #a4 ,accord+ to ,pr(4 ,skeat 7,etymological ,diction>y7 ! e>lie/ kn[n mean+ is t ( furi\s action1 z 9 a *>ge ( cavalry4 ,! etymology1 he consid]s1 is connect$ ) ! ,teutonic ^w r& 7brim71 & implies ! furi\s & irregul> action ( a riv] full to ! brim4 #b4 ,see ! problem pap] ( ,jan4 #ah1 #ahed1 9 ! ,cambridge ,ma!matical ,tripos4 #c4 ,z1 accord+ to ,mr ,h4 ,godfray1 ! majority ( ! c&idates did assume :5 ! problem 0 once propos$ 9 an exam9ation4 ,see ! ,educational ,times 7,repr9t1 ,vol4 ,,vii4 p4 #ii47 #d4 ,vide p4 #fh4 #e4 ,x w\ld ( c\rse be m complete to take t5 alt]natives ( direction1 & ?us to omit none ( ! digits2 b ?is is mu* m tr\blesome 9 practice ?an to conf9e ourselves to eight4 #f4 ,any m ?an we picture ! %ape ( an equiangul> spiral at ! c5tre4 ,,*apt] ,,vi4#a ,,! ,,subjective ,,side ,,( ,,probability4 ,,measurem5t ,,( ,,belief4 #a4 ,orig9ally writt5 9 some:at ( a _s ( prote/ aga9/ :at seem$ to me ! preval5t disposition to foll[ ,de ,morgan 9 tak+ too subjective a view ( ! sci5ce4 ,9 read+ x ?r\gh n[ ,i _c f9d any s+le s5t5ce to :i* ,i c\ld take di/9ct objection1 ?\gh ,i mu/ admit t if ,i 7 writ+ x entirely afre% ,i %\ld endeav\r to express myself ) less emphasis1 & ,i h made alt]ations 9 t direction4 ,! read] :o wi%es to see a view n sub/antially v diff]5t f m9e1 b express$ ) a some:at opposite emphasis1 c ref] to ,mr ,f4 ,y4 ,edgewor?'s article on ,! ,philosophy ( ,*ance 7,m9d1 ,vol4 ,,ix47 #a4 ,hav+ n[ obta9$ a cle> conception ( a c]ta9 k9d ( s]ies1 ! next enquiry is1 ,:at is to be done ) ?is s]ies8 ,h[ is x to be employ$ z a means ( mak+ inf]5ces8 ,! g5]al /ep t we are n[ ab\t to take might be describ$ z "o f ! objective to ! subjective1 f ! ?+s !mselves to ! /ate ( our m9ds 9 contemplat+ !m4 ,! read] %\ld obs]ve t a sub/itution has1 9 a great numb] ( cases1 already be5 made z a fir/ /age t[>ds br++ ! ?+s into a %ape fit = calculation4 ,?is sub/itution1 z describ$ 9 =m] *apt]s1 is1 9 a measure1 a process ( idealization4 ,! s]ies we actually meet ) are apt to %[ a *angeable type1 & ! individuals ( !m w sometimes transgress _! lic5s$ irregul>ity4 ,h5ce !y h to be prun$ a little into %ape1 z natural objects almo/ always h be=e !y are capable ( be+ accurately reason$ ab\t4 ,! =m 9 :i* ! s]ies em]ges is t ( a s]ies ) a fix$ type4 ,?is imag9>y or ideal s]ies is ! basis ( our calculation4 #b4 ,x mu/ n be suppos$ t ?is is at all at v>iance ) ! ass]tion previ\sly made1 t ,probability is a sci5ce ( inf]5ce ab\t real ?+s2 x is only by a sub/itution ( ! above k9d t we are enabl$ to reason ab\t ! ?+s4 ,9 nature ne>ly all ph5om5a pres5t !mselves 9 a =m :i* dep>ts f t rigor\sly accurate "o :i* sci5tific purposes mo/ly dem&1 s we h to introduce an imag9>y s]ies1 :i* %all be free f any su* defects4 ,! only condition to be fulfill$ is1 t ! sub/itution is to be z little arbitr>y1 t is1 to v>y f ! tru? z slightly1 z possible4 ,?is k9d ( sub/itution g5]ally passes )\t notice :5 natural objects ( any k9d are made subjects ( exact sci5ce4 ,i direct di/9ct att5tion to x "h simply f ! appreh5sion t want ( famili>ity ) ! subject-matt] might lead "s read]s to suppose t x involves1 9 ?is case1 an exceptional deflection f accuracy 9 ! =mal process ( inf]5ce4 ,x may be rem>k$ also t ! adoption ( ?is imag9>y s]ies (f]s no c\nt5ance :atev] to ! doctr9e criticis$ 9 ! la/ *apt]1 9 accordance ) :i* x 0 suppos$ t our s]ies possess$ a fix$ un*angeable type :i* 0 m]ely ! developm5t ( ! probabilities ( ?+s1 to use ,laplace's expression4 ,x diff]s f any?+ contemplat$ on t hypo!sis by ! fact t x is to be recogniz$ z a necess>y sub/itution ( our own = ! actual s]ies1 & to be kept 9 z close con=mity ) facts z possible4 ,x is a m]e fiction or artifice necess>ily resort$ to = ! purpose ( calculation1 & = ?is purpose only4 ,?is caution is ! m necess>y1 because 9 ! example t ,i %all select1 & :i* belongs to ! mo/ fav\rite class ( examples 9 ?is subject1 ! sub/itution becomes accid5tally unnecess>y4 ,! ?+s1 z has be5 repeat$ly po9t$ out1 may sometimes ne$ no trimm+1 because 9 ! =m 9 :i* !y actually pres5t !mselves !y are almo/ idealiz$4 ,9 mo/ cases a good deal ( alt]ation is necess>y to br+ ! s]ies into %ape1 b 9 "s--prom95tly 9 ! case ( games ( *ance--we f9d ! alt]ations1 = all practical purposes1 ne$less4 #c4 ,we />t !n1 f su* a s]ies z ?is1 ^u ! enquiry1 ,:at k9d ( inf]5ce c be made ab\t x8 ,x may assi/ ! logical read] to in=m him t our fir/ /ep w be analog\s to "o class ( :at are commonly kn[n z imm$iate inf]5ces1--inf]5ces1 t is1 ( ! type1--',all m5 are mortal1 !re=e any p>ticul> man or m5 are mortal4' ,?is case1 simple & obvi\s z x is 9 ,logic1 requires v c>eful consid]ation 9 ,probability4 ,x is obvi\s t we mu/ be prep>$ to =m an op9ion ^u ! propriety ( tak+ ! /ep involv$ 9 mak+ su* an inf]5ce4 ,hi!rto we h _h z little to d z possible ) ! irregul> individuals2 we h reg>d$ !m simply z fragm5ts ( a regul> s]ies4 ,b we _c long cont9ue to neglect all consid]ation ( !m4 ,ev5 if ^! ev5ts 9 ! gross be tol]ably c]ta91 x is n only 9 ! gross t we h to deal ) !m2 !y con/antly come be=e u a few at a "t1 or ev5 z individuals1 & we h to =m "s op9ion ab\t !m 9 ?is /ate4 ,an insurance (fice1 = in/ance1 deals ) numb]s l>ge en\gh to obviate mo/ ( ! unc]ta9ty1 b ea* ( _! transactions has ano!r p>ty int]e/$ 9 x--,:at has ! man :o insures to say to _! proce$+s8 = to him ?is "q becomes an individual "o4 ,& ev5 ! (fice itself receives its cases s+ly1 & w\ld !re=e l to h z cle> views z possible ab\t ^! s+le cases4 ,n[1 ! rem>ks made 9 ! prec$+ *apt]s ab\t ! subjects :i* ,probability discusses might seem to preclude all enquiries ( ?is k9d1 = 0 n ignorance ( ! individual presuppos$ to su* an ext5t t ev5 7z w be se5 h]eaft]7 causation might be d5i$1 )9 consid]able limits1 )\t affect+ our conclusions8 ,! answ] to ?is enquiry w require u to turn n[ to ! consid]ation ( a totally di/9ct side ( ! "q1 & "o :i* has n yet come be=e u4 ,our be/ introduction to x w be by ! discussion ( a special example4 #d4 ,let a p5ny be toss$ up a v great _m times2 we may !n be suppos$ to "k = c]ta9 ?is fact 7among/ _m o!rs7 t 9 ! long run head & tail w occur ab\t equally (t54 ,b suppose we consid] only a mod]ate numb] ( ?r[s1 or few] /ill1 & s cont9ue limit+ ! numb] until we come d[n to ?ree or two1 or ev5 "o8 ,we h1 z ! extreme cases1 c]ta9ty or some?+ undi/+ui%ably ne> x1 & utt] unc]ta9ty4 ,h we n1 betwe5 ^! extremes1 all gradations ( belief8 ,!re is a l>ge body ( writ]s1 includ+ "s ( ! mo/ em95t au?orities ^u ?is subject1 :o /ate or imply t we are di/9ctly consci\s ( su* a v>iation ( ! am\nt ( our belief1 & t ?is /ate ( our m9ds c be measur$ & det]m9$ ) almo/ ! same accuracy z ! ext]nal ev5ts to :i* !y ref]4 ,! pr9cipal ma!matical support] ( ?is view is ,de ,morgan1 :o has insi/$ /rongly ^u x 9 all 8 works on ! subject4 ,! cle>e/ exposition ( 8 op9ions w be f\nd 9 8 ,=mal ,logic1 9 :i* "w he has made ! view :i* we are n[ discuss+ ! basis ( 8 sy/em4 ,he holds t we h a c]ta9 am\nt ( belief ( e proposition :i* may be set be=e u1 an am\nt :i* 9 its nature admits ( det]m9ation1 ?\gh we may practically f9d x difficult 9 any p>ticul> case to det]m9e x4 ,he consid]s1 9 fact1 t ,probability is a sort ( si/] sci5ce to ,=mal ,logic1#a speak+ ( x 9 ! foll[+ words3 ,i _c und]/& :y ! /udy ( ! effect1 :i* p>tial belief ( ! premises produces ) respect to ! conclusion1 %\ld be sep>at$ f t ( ! consequ5ces ( suppos+ ! =m] to be absolutely true4#b ,9 o!r words1 !re is a sci5ce--,=mal ,logic--:i* inve/igates ! rules accord+ to :i* "o proposition c be necess>ily inf]r$ f ano!r2 9 close correspond5ce ) ?is !re is a sci5ce :i* inve/igates ! rules accord+ to :i* ! am\nt ( our belief ( "o proposition v>ies ) ! am\nt ( our belief ( o!r propositions ) :i* x is connect$4 ,! same view is also support$ by ano!r high au?ority1 ! late ,pr(4 ,donk91 :o says 7,phil4 ,mag4 ,may1 #ahea71 ,x w1 ,i suppose1 be g5]ally admitt$1 & has (t5 be5 m or less explicitly /at$1 t ! subject-matt] ( calculation 9 ! ma!matical !ory ( ,probabilities is quantity ( belief4 #e4 ,be=e proce$+ to criticise ?is op9ion1 "o rem>k may be made ^u x :i* has be5 too frequ5tly ov]look$4 ,x %\ld be borne 9 m9d t1 ev5 7 ?is view ( ! subject n actually incorrect1 x might be object$ to z insuffici5t = ! purpose ( a def9ition1 on ! gr\nd t v>iation ( belief is n conf9$ to ,probability4 ,x is a prop]ty ) :i* t sci5ce is conc]n$1 no d\bt1 b x is a prop]ty :i* meets u 9 o!r directions z well4 ,9 e case 9 :i* we ext5d our inf]5ces by ,induction or ,analogy1 or dep5d ^u ! witness ( o!rs1 or tru/ to our own memory ( ! pa/1 or come to a conclusion ?r\gh conflict+ argum5ts1 or ev5 make a long & complicat$ d$uction by ma!matics or logic1 we h a result ( :i* we c sc>cely feel z c]ta9 z ( ! premises f :i* x 0 obta9$4 ,9 all ^! cases !n we are consci\s ( v>y+ quantities ( belief1 b are ! laws accord+ to :i* ! belief is produc$ & v>i$ ! same8 ,if !y _c be r$uc$ to "o h>moni\s s*eme1 if 9 fact !y c at be/ be br\ght to no?+ b a numb] ( diff]5t s*emes1 ea* ) its own body ( laws & rules1 !n x is va9 to endeav\r to =ce !m into "o sci5ce4 ,?is op9ion is /r5g!n$ by obs]v+ t mo/ ( ! writ]s :o adopt ! def9ition 9 "q d practically dismiss f consid]ation mo/ ( ! above-m5tion$ examples ( dim9ution ( belief1 & conf9e _! att5tion to classes ( ev5ts :i* h ! prop]ty discuss$ 9 ,*ap ,i41 viz4 'ignorance ( ! few1 k ( ! _m4' ,x is q true t consid]able viol5ce has to be done to "s ( ^! examples1 by introduc+ exce$+ly arbitr>y suppositions into !m1 be=e !y c be =c$ to assume a suitable =m4 ,b /ill !re is little d\bt t1 if we c>efully exam9e ! language employ$1 we %all f9d t 9 almo/ e case assumptions are made :i* virtually imply t our k ( ! individual is d]iv$ f propositions giv5 9 ! typical =m describ$ 9 ,*ap ,i4 ,?is w be m fully prov$ :5 we come to consid] "s common misapplications ( ! sci5ce4 #f4 ,ev5 !n1 if ! above-m5tion$ view ( ! subject 7 correct1 x w\ld yet1 ,i consid]1 be insuffici5t = ! purpose ( a def9ition2 b x is at lea/ v d\btful :e!r x is correct4 ,be=e we c\ld prop]ly assign to ! belief side ( ! "q ! prom95ce giv5 to x by ,de ,morgan & o!rs1 c]ta9ly be=e ! sci5ce c\ld be def9$ f t side1 x w\ld be necess>y1 x appe>s1 to e/abli% ! two foll[+ positions1 aga9/ bo? ( :i* /rong objections c be br\ght4 7#a7 ,t our belief ( e proposition is a ?+ :i* we c1 /rictly speak+1 be said to measure2 t !re mu/ be a c]ta9 am\nt ( x 9 e case1 :i* we c realize someh[ 9 consci\sness & ref] to "s /&>d s z to pron\nce ^u its value4 7#b7 ,t ! value ?us appreh5d$ is ! correct "o accord+ to ! !ory1 viz4 t x is ! exact fraction ( full conviction t x %\ld be4 ,?is /atem5t w p]haps seem some:at obscure at fir/2 x w be expla9$ pres5tly4 #g4 7,i47 ,n[1 9 ! fir/ place1 z reg>ds ! difficulty ( obta9+ any measure ( ! am\nt ( our belief4 ,"o s\rce ( ?is difficulty is too obvi\s to h escap$ notice2 ?is is ! di/urb+ influ5ce produc$ on ! quantity ( belief by any /rong emotion or passion4 ,a deep int]e/ 9 ! matt] at /ake1 :e!r x excite hope or fe>1 plays great havoc ) ! belief-met]1 s t we mu/ assume ! m9d to be q unimpassion$ 9 weigh+ ! evid5ce4 ,?is is notic$ & ackn[l$g$ by ,laplace & o!rs2 b ^! writ]s seem to me to assume x to be ! only s\rce ( error1 & also to be ( comp>ative unimportance4 ,ev5 if x 7 ! only s\rce ( error ,i _c see t x w\ld be unimportant4 ,we exp]i5ce hope or fe> 9 s v _m in/ances1 t to omit su* influ5ces f consid]ation w\ld be almo/ equival5t to say+ t :il/ we pr(ess to consid] ! :ole quantity ( our belief we w 9 reality consid] only a portion ( x4 ,v /rong feel+s are1 ( c\rse1 exceptional1 b we %\ld nev]!less f9d t ! emotional elem5t1 9 "s =m or o!r1 makes itself felt on almo/ e occasion4 ,x is v seldom t we _c speak ( our surprise or expectation 9 ref]5ce to any p>ticul> ev5t4 ,bo? ( ^! expressions1 b especially ! =m]1 seem to po9t to some?+ m ?an m]e belief4 ,x is true t ! ^w 'expectation' is g5]ally def9$ 9 treatises on ,probability z equival5t to belief2 b x seems d\btful :e!r any "o :o att5ds to ! popul> use ( ! t]ms w\ld admit t !y 7 exactly synonym\s4 ,be ?is h[ev] z x may1 ! emotional elem5t is pres5t ^u almo/ e occasion1 & its di/urb+ influ5ce !re=e is con/antly at "w4 #h4 ,ano!r cause1 :i* co-op]ates ) ! =m]1 is to be f\nd 9 ! extreme complexity & v>iety ( ! evid5ce on :i* our belief ( any proposition dep5ds4 ,h5ce x results t our actual belief at any giv5 mom5t is "o ( ! mo/ fugitive & v>iable ?+s possible1 s t we c sc>cely ev] get suffici5tly cle> hold ( x to measure x4 ,?is is n conf9$ to ! times :5 our m9ds are 9 a turmoil ( excitem5t ?r\gh hope or fe>4 ,9 our calme/ mom5ts we %all f9d x no easy ?+ to give a precise answ] to ! "q1 ,h[ firmly d ,i hold ?is or t belief8 ,!re may be "o or two prom95t argum5ts 9 its fav\r1 & "o or two correspond+ objections aga9/ x1 b ?is is f> f compris+ all ! causes by :i* our /ate ( belief is produc$4 ,because su* reasons z ^! are all t c be practically introduc$ into oral or writt5 controv]sies1 we mu/ n conclude t x is by ^! only t our conviction is influ5c$4 ,on ! contr>y1 our conviction g5]ally re/s ^u a sort ( *aotic basis compos$ ( an inf9ite numb] ( inf]5ces & analogies ( e description1 & ^! moreov] di/ort$ by our /ate ( feel+ at ! "t1 dimm$ by ! degree ( our recollection ( !m aft]w>ds1 & probably receiv$ f "t to "t ) v>y+ =ce accord+ to ! way 9 :i* !y happ5 to comb9e 9 our consci\sness at ! mom5t4 ,to borr[ a /rik+ illu/ration f ,abraham ,tuck]1 ! sub/ructure ( our convictions is n s mu* to be comp>$ to ! solid f\ndations ( an ord9>y build+1 z to ! piles ( ! h\ses ( ,rott]dam :i* re/ someh[ 9 a deep b$ ( s(t mud4 ,!y be> _! weight securely en\gh1 b x w\ld n be easy to po9t out accurately ! dep5d5ce ( ! diff]5t p>ts ^u "o ano!r4 ,directly we beg9 to ?9k ( ! am\nt ( our belief1 we h to ?9k ( ! argum5ts by :i* x is produc$--9 fact1 ^! argum5ts w intrude !mselves )\t our *oice4 ,z ea* 9 turn fla%es ?r\gh ! m9d1 x modifies ! /r5g? ( our conviction2 we are l a p]son li/5+ to ! confus$ hubbub ( a cr[d1 :]e !re is always some?+ arbitr>y 9 ! p>ticul> s\nd we *oose to li/5 to4 ,!re may be reasons en\gh to suffice abundantly = our ultimate *oice1 b on exam9ation we %all f9d t !y are by no means appreh5d$ ) ! same =ce at diff]5t times4 ,! belief produc$ by "s /rong argum5t may be v decisive at ! mom5t1 b x w (t5 beg9 to dim9i% :5 ! argum5t is n actually be=e ! m9d4 ,x is l be+ dazzl$ by a /rong light2 ! impression /ill rema9s1 b beg9s almo/ imm$iately to fade away4 ,i ?9k t ?is is ! case1 h[ev] we try to limit ! s\rces ( our conviction4 #i4 7,,ii47 ,b suppos+ t x 7 possible to /rike a sort ( av]age ( ?is fluctuat+ /ate1 %\ld we f9d ?is av]age to be ( ! am\nt assign$ by !ory8 ,9 o!r words1 is our natural belief 9 ! happ5+ ( two diff]5t ev5ts 9 direct proportion to ! frequ5cy ) :i* ^? ev5ts happ5 9 ! long run8 ,!re is a lott]y ) #ajj tickets & t5 prizes2 is a man's belief t he w get a prize fairly repres5t$ by "o-t5? ( c]ta9ty8 ,! m]e ref]5ce to a lott]y %\ld be suffici5t to disprove ?is4 ,lott]ies h fl\ri%$ at all times1 & h nev] fail$ to be abundantly support$1 9 spite ( ! mo/ p]fect conviction1 on ! "p ( _m1 if n ( mo/1 ( ^? :o put into !m1 t 9 ! long run all w lose4 ,d$uctions %\ld und\bt$ly be made = ^? :o act f sup]/iti\s motives1 f belief 9 om5s1 dreams1 & s on4 ,b ap>t f ^!1 & suppos+ any "o to come =tifi$ by all t ma!matics c d = him1 x is difficult to believe t 8 natural impressions ab\t s+le ev5ts w\ld be always :at !y %\ld be accord+ to !ory4 ,are !re _m :o c hone/ly decl>e t !y w\ld h no desire to buy a s+le ticket8 ,!y w\ld probably say to !mselves t ! sum !y paid away 0 no?+ wor? m5tion+ to lose1 & t !re 0 a *ance ( ga9+ a great deal2 9 o!r words1 !y are n apportion+ _! belief 9 ! way t !ory assigns4 ,:at be>s out ?is view is1 t ! same p]sons :o w\ld act 9 ?is way 9 s+le in/ances w\ld (t5 n ?9k ( do+ s 9 any b s+le in/ances4 ,9 o!r words1 ! natural t5d5cy "h is to attribute too great an am\nt ( belief :]e x is or %\ld be small2 i4e4 to depreciate ! risk 9 proportion to ! cont+5t advantage4 ,!y w\ld v likely1 :5 argu$ )1 atta* disp>ag+ epi!ts to ?is /ate ( feel+1 by call+ x an unacc\ntable fasc9ation1 or some?+ ( t k9d1 b ( its exi/5ce !re c be little d\bt4 ,we are speak+ n[ ( :at is ! natural t5d5cy ( our m9ds1 n ( t into :i* !y may at l5g? be discipl9$ by education & ?\ght4 ,if1 h[ev]1 educat$ p]sons h succe$$ = ! mo/ "p 9 controll+ ?is t5d5cy 9 games ( *ance1 ! _s ( reckless speculation has sc>cely yet be5 bani%$ f comm]ce4 ,on exam9ation1 ?is t5d5cy w be f\nd s preval5t 9 all ages1 ranks1 & dispositions1 t x w\ld be inadmissible to neglect x 9 ord] to br+ our suppos$ in/9cts m closely into accordance ) ! commonly receiv$ !ories ( ,probability4 #aj4 ,!re is ano!r aspect ( ?is "q :i* has be5 (t5 ov]look$1 b :i* seems to des]ve "s att5tion4 ,grant$ t we h an in/9ct ( cr$5ce1 :y %\ld x be assum$ t ?is mu/ be j ( t int5sity :i* subsequ5t exp]i5ce w ju/ify8 ,our in/9cts are implant$ 9 u = good purposes1 & are int5d$ to act imm$iately & unconsci\sly4 ,!y are1 h[ev]1 subject to control1 & h to be br\ght into accordance ) :at we believe to be true & "r4 ,9 o!r dep>tm5ts ( psy*ology we d n assume t e spontane\s prompt+ ( nature is to be left j z we f9d x1 or ev5 t on ! av]age1 omitt+ individual v>iations1 x is set at t pit* t w be f\nd 9 ! end to be ! be/ :5 we come to ?9k ab\t x & assign its rules4 ,take1 = example1 ! case ( res5tm5t4 ,"h we h an in/9ctive t5d5cy1 & "o t on ! :ole is good 9 its results4 ,b morali/s are agre$ t almo/ all our ef=ts at self-control are to be direct$ t[>ds subdu+ x & keep+ x 9 its "r direction4 ,x is assum$ to be giv5 z a sort ( r\gh protection1 & to be set1 if "o might s express oneself1 at too high a pit* to be delib]ately & consci\sly act$ on 9 society4 ,may n some?+ ( ?is k9d be ! case also ) our belief8 ,i only make a pass+ ref]5ce to ?is po9t "h1 z on ! !ory ( ,probability adopt$ 9 ?is "w x does n appe> to be at all mat]ial to ! sci5ce4 ,b x seems a /rong argum5t aga9/ ! exp$i5cy ( comm5c+ ! /udy ( ! sci5ce f ! subjective side1 or ev5 ( assign+ any great degree ( prom95ce to ?is side4 ,t m5 d n believe 9 exact accordance ) ?is !ory mu/ h /ruck almo/ e "o1 b ?is has probably be5 consid]$ z m]e exception & irregul>ity2 ! assumption be+ made t on ! av]age1 & 9 f> ! majority ( cases1 !y d s believe4 ,z /at$ above1 x is v d\btful :e!r ! t5d5cy :i* has j be5 discuss$ is n s widely preval5t t x might ) f> m propriety be call$ ! rule ?an ! exception4 ,& x may be bett] t ?is %\ld be s3 _m good results may foll[ f t *e]ful disposition :i* induces a man sometimes to g on try+ aft] "s great good1 ! *ance ( :i* he ov]values4 ,he w keep on ?r\gh tr\ble & disappo9tm5t1 )\t s]i\s h>m p]haps1 :5 ! cool & calculat+ by/&] sees pla9ly t 8 'measure ( belief' is mu* high] ?an x %\ld be4 ,s1 too1 ! t5d5cy also s common1 ( und]rat+ ! *ance ( a great evil may also "w = good4 ,by _m m5 dea? might be look$ ^u z an almo/ inf9ite evil1 at lea/ !y w\ld s reg>d x !mselves2 suppose !y kept ?is cont+5cy con/antly be=e !m at its "r value1 h[ w\ld x be possible to get ?r\gh ! practical "w ( life8 ,m5 w\ld be /opp+ indoors because if !y w5t out !y might be murd]$ or bitt5 by a mad dog4 ,to say ?is is n to advocate a return to our in/9cts2 inde$ :5 we h once rea*$ ! critical & consci\s /ate1 x is h>dly possible to d s2 b x %\ld be notic$ t ! advantage ga9$ by correct+ !m is at be/ b a balanc$ "o4#c ,:at is mo/ to our pres5t purpose1 x sugge/s ! inexp$i5cy ( attempt+ to f\nd an exact !ory on :at may aft]w>ds prove to be a m]e in/9ct1 unau?oriz$ 9 its full ext5t by exp]i5ce4 #aa4 ,x may be repli$1 t ?\gh p1 z a matt] ( fact1 d n apportion belief 9 ?is exact way1 yet !y ought to d s4 ,! purport ( ?is rem>k w be exam9$ pres5tly2 x ne$ only be said "h t x grants all t is n[ cont5d$ =4 ,= x admits t ! degree ( our belief is capable ( modification1 & may ne$ x4 ,b 9 accordance ) :at is ! belief to be modifi$8 obvi\sly 9 accordance ) exp]i5ce2 x _c be tru/$ to by itself1 b ! fraction at :i* x is to be rat$ mu/ be det]m9$ by ! comp>ative frequ5cy ( ! ev5ts to :i* x ref]s4 ,exp]i5ce !n furni%+ ! /&>d1 x is surely mo/ reasonable to />t f ?is exp]i5ce1 & to f\nd ! !ory ( our processes ^u x4 ,if we d n d ?is1 x %\ld be obs]v$ t we are deta*+ ,probability altoge!r f ! /udy ( ?+s ext]nal to u1 & mak+ x no?+ else 9 effect ?an a portion ( ,psy*ology4 ,if we refuse to be controll$ by exp]i5ce1 b conf9e our att5tion to ! laws accord+ to :i* belief is naturally or in/9ctively comp\nd$ & di/ribut$ 9 our m9ds1 we h no "r !n to appeal to exp]i5ce aft]w>ds ev5 = illu/rations1 unless "u ! express und]/&+ t we d n gu>antee its accuracy4 ,our belief 9 "s s+le ev5ts1 = example1 might be correct1 & yet t 9 a comp\nd ( sev]al 7if d]iv$ m]ely f our in/9ctive laws ( belief7 v possibly might n be correct1 b might lead u into practical mi/akes if we det]m9$ to act ^u x4 ,ev5 if ! two 7 9 accordance1 ?is accordance w\ld h to be prov$1 :i* w\ld lead u r\nd1 by :at ,i _c b ?9k a circuit\s process1 to ! po9t :i* has be5 already *os5 = comm5c+ )4 #ab4 ,de ,morgan seems to imply t ! doctr9e criticis$ above f9ds a ju/ification f ! analogy ( ,=mal ,logic4 ,if ! laws ( necess>y inf]5ce c be /udi$ ap>t f all ref]5ce to ext]nal facts 7except by way ( illu/ration71 :y n ^? ( probable inf]5ce8 ,!re does n1 h[ev]1 seem to be mu* =ce 9 any su* analogy4 ,=mal ,logic1 at any rate "u its mod]n or ,kantian mode ( treatm5t1 is bas$ ^u ! assumption t !re are laws ( ?\ght z di/+ui%$ f laws ( ?+s1 & t ^! laws ( ?\ght c be asc]ta9$ & /udi$ )\t tak+ into acc\nt _! ref]5ce to any p>ticul> object4 ,n[ s long z we are conf9$ to necess>y or irrev]sible laws1 z is ( c\rse ! case 9 ord9>y ,=mal ,logic1 ?is assumption leads to no special difficulties4 ,we mean by ?is1 t no conflict arises betwe5 ^! subjective & objective necessities4 ,! two exi/ 9 p]fect h>mony side by side1 ! "o be+ ! accurate c\nt]p>t ( ! o!r4 ,s precise is ! correspond5ce betwe5 !m1 t few p]sons w\ld notice1 until /udy ( metaphysics _h call$ _! att5tion to su* po9ts1 t !re 7 ^! two sides to ! "q4 ,!y w\ld make _! appeal to ei!r ) equal confid5ce1 say+ indiff]5tly1 '! ?+ mu/ be s1' or1 'we _c conceive its be+ o!rwise4' ,9 fact x is only s9ce ! "t ( ,kant t ?is m5tal analysis has be5 to any ext5t appreciat$ & accept$4 ,& ev5 n[ ! dom9ant exp]i5ce s*ool ( philosophy w\ld n admit t !re are "h two really di/9ct sides to ! ph5om5on2 !y ma9ta9 ei!r t ! subjective necessity is no?+ m ?an ! consequ5ce by invet]ate association ( ! objective uni=mity1 or else t ?is s-call$ necessity 7say 9 ! ,law ( ,contradiction7 is aft] all m]ely v]bal1 m]ely a diff]5t way ( say+ ! same ?+ ov] aga9 9 o!r words4 ,:atev] ! explanation adopt$1 ! g5]al result is t fallacies1 z real acts ( ?\ght1 are impossible )9 ! doma9 ( pure logic2 error )9 t prov9ce is only possibly by a mom5t>y lapse ( att5tion1 t is ( consci\sness4 #ac4 ,b ?\gh ?is p]fect h>mony betwe5 subjective & objective uni=mities or laws may exi/ )9 ! doma9 ( pure logic1 x is f> f exi/+ )9 t ( probability4 ,! mom5t we make ! quantity ( our belief an integral "p ( ! subject to be /udi$1 any su* inv>iable correspond5ce ceases to exi/4 ,9 ! =m] case1 we c\ld n consci\sly ?9k errone\sly ev5 ?\gh we might try to d s2 9 ! latt]1 we n only c believe errone\sly b con/antly d s4 ,f> f ! quantity ( our belief be+ s exactly adju/$ 9 con=mity ) ! facts to :i* x ref]s t we _c ev5 9 imag9ation g a/ray1 we f9d t x frequ5tly exi/s 9 excess or defect ( t :i* subsequ5t judgm5t w approve4 ,our in/9cts ( cr$5ce are unque/ionably 9 frequ5t ho/ility ) exp]i5ce2 & :at d we d !n8 ,we simply modify ! in/9cts into accordance ) ! ?+s4 ,we are con/antly p]=m+ ?is practice1 & no cultivat$ m9d w\ld f9d x possible to d any?+ else4 ,no man w\ld ?9k ( divorc+ 8 belief f ! ?+s on :i* x 0 ex]cis$1 or w\ld suppose t ! =m] _h any?+ else to d ?an to foll[ ! lead ( ! latt]4 ,h5ce x results t t sep>ation ( ! subjective necessity f ! objective1 & t det]m9ation to treat ! =m] z a sci5ce ap>t by itself1 = :i* a plausible def5ce c\ld be made 9 ! case ( pure logic1 is entirely inadmissible 9 ! case ( probability4 ,h[ev] we might contrive to '?9k' aright )\t appeal to facts1 we _c believe aright )\t incessantly *eck+ our proce$+s by su* appeals4 ,:atev] !n may be ! claims ( ,=mal ,logic to rank z a sep>ate sci5ce1 x does n appe> t x c furni% any support to ! !ory ( ,probability at pres5t "u exam9ation4 #ad4 ,! po9t 9 "q is sometimes urg$ z foll[s4 ,suppose a man ) two1 & only two1 alt]natives be=e him1 "o ( :i* he kn[s mu/ involve success & ! o!r failure4 ,he kn[s no?+ m ab\t !m ?an ?is1 & he is =c$ to act4 ,w\ld he n reg>d !m ) absolutely simil> & equal feel+s ( confid5ce1 )\t ! necessity ( ref]r+ !m to any real or imag9>y s]ies8 ,if s1 is n ?is equival5t to say+ t 8 belief ( ei!r1 s9ce "o ( !m mu/ come to pass1 is equal to t ( ! o!r1 & !re=e t 8 belief ( ea* is "o-half ( full confid5ce8 ,simil>ly if !re are m ?an two alt]natives3 let x be suppos$ t !re are any numb] ( !m1 among/ :i* no di/9ctions :atev] c be disc]n$ except 9 su* p>ticul>s z we "k = c]ta9 w n affect ! result2 %\ld we n feel equally confid5t 9 respect ( ea* ( !m8 & s "h aga9 %\ld we riot h a fractional e/imate ( our absolute am\nt ( belief8 ,x is ?us attempt$ to lay ! basis ( a pure sci5ce ( ,probability1 det]m9+ ! di/ribution & comb9ation ( our belief hypo!tically2 viz4 if ! cont+5cies are exactly alike1 !n our belief is s apportion$1 ! "q :e!r ! cont+5cies are equal be+ ( c\rse decid$ z ! objective data ( ,logic or ,ma!matics are decid$4 ,to discuss ?is "q fully w\ld require a /atem5t at "s l5g? ( ! reasons 9 fav\r ( ! objective or mat]ial view ( ,logic1 z oppos$ to ! ,=mal or ,conceptuali/4 ,i %all h to speak on ?is subject 9 ano!r *apt]1 & w n !re=e ent] ^u x "h4 ,b "o conclusive objection :i* is applicable m peculi>ly to ,probability may be (f]$ at once4 ,to pursue ! l9e ( enquiry j indicat$1 is1 z already rem>k$1 to des]t ! /rictly logical gr\nd1 & to take up t appropriate to psy*ology2 ! prop] "q1 9 all ^! cases1 be+ n :at d m5 believe1 b :at ought !y to believe8 ,admitt+1 z 0 done above1 t 9 ! case ( ,=mal ,logic ^! two enquiries1 or r ^? correspond+ to !m1 practically run into "o1 ow+ to ! fact t m5 _c consci\sly '?9k' wrongly2 x _c be too /rongly insi/$ on t 9 ,probability ! two are p]fectly sep>able & di/9ct4 ,x is ( no use say+ :at m5 d or w believe1 we want to "k :at !y w be "r 9 believ+2 & ?is c nev] be settl$ )\t an appeal to ! ph5om5a !mselves4 #ae4 ,b ap>t f ! above consid]ations1 ?is way ( putt+ ! case does n seem to me at all conclusive4 ,take ! foll[+ example4 ,a man#d f9ds himself on ! s&s ( ! ,wa% or ,morecambe ,bay1 9 a d5se mi/1 :5 ! spr+-tide is com+ 92 & kn[s !re=e t to be once caught by ! tide w\ld be fatal4 ,he he>s a *ur*-bell at a di/ance1 b has no means ( kn[+ :e!r x is on ! same side ( ! wat] ) himself or on ! opposite side4 ,he _c tell !re=e :e!r by foll[+ its s\nd he w be l$ out into ! mid-/ream & be lo/1 or l$ back to dry l& & safety4 ,"h !re c be no repetition ( ! ev5t1 & ! cases are indi/+ui%ably alike1 to him1 9 ! only circum/ances :i* c affect ! issue3 is n !n 8 prospect ( dea?1 x w be said1 necess>ily equal to "o-half8 ,a prop] analysis ( 8 /ate ( m9d w\ld be a psy*ological r ?an a logical enquiry1 & 9 any case1 z above rem>k$1 ! decision ( ?is "q does n t\* our logical position4 ,b accord+ to ! be/ introspection ,i c give ,i %\ld say t :at really passes ?r\gh ! m9d 9 su* a case is some?+ ( ?is k9d3 ,9 mo/ d\btful positions & circum/ances we are accu/om$ to decide our conduct by a consid]ation ( ! relative advantages & disadvantages ( ea* side1 t is by ! obs]v$ or inf]r$ frequ5cy ) :i* "o or ! o!r alt]native has succe$$4 ,9 proportion z ^! become m ne>ly balanc$1 we are m frequ5tly mi/ak5 9 ! individual cases2 t is1 x becomes m & m ne>ly :at w\ld be call$ 'a m]e toss up' :e!r we are "r or wrong4 ,! case 9 "q seems m]ely ! limit+ case1 9 :i* x has be5 contriv$ t !re %all be no appreciable diff]5ce betwe5 ! alt]natives1 by :i* to decide 9 fav\r ( "o or o!r1 & we accord+ly feel no confid5ce 9 ! p>ticul> result4 ,hav+ to decide1 h[ev]1 we decide accord+ to ! prec$5t ( simil> cases :i* h occurr$ be=e4 ,to /& /ill & wait = bett] in=mation is c]ta9 dea?1 & we !re=e appeal to & employ ! only rule we "k (2 or r we feel1 or endeav\r to feel1 z we h felt be=e :5 act+ 9 ! pres5ce ( alt]natives z ne>ly balanc$ z possible4 ,b ,i c nei!r p]ceive 9 my own case1 nor feel conv9c$ 9 t ( o!rs1 t ?is appeal1 9 a case :i* _c be repeat$1#e to a rule act$ on & ju/ifi$ 9 cases :i* c be & are repeat$1 at all =ces u to admit t our /ate ( m9d is ! same 9 ea* case4 #af4 ,?is example s]ves to br+ out v cle>ly a po9t :i* has be5 already m5tion$1 & :i* w h to be insi/$ ^u aga91 viz4 t all :i* ,probability discusses is ! /ati/ical frequ5cy ( ev5ts1 or1 if we pref] s to put x1 ! quantity ( belief ) :i* any "o ( ^! ev5ts %\ld be individually reg>d$1 b leaves all ! subsequ5t conduct dep5d5t ^u t frequ5cy1 or t belief1 to ! *oice ( ! ag5ts4 ,suppose !re are two travell]s 9 ! pr$icam5t 9 "q3 %all !y keep toge!r1 or sep>ate 9 opposite directions8 ,9 ei!r case alike ! *ance ( safety to ea* is ! same1 viz4 "o-half1 b cle>ly _! circum/ances mu/ decide :i* c\rse x is pref]able to adopt4 ,if !y are husb& & wife1 !y w probably pref] to rema9 toge!r2 if !y are sole deposit>ies ( an important /ate secret1 !y may decide to "p4 ,9 o!r words1 we h to select "h betwe5 ! two alt]natives ( ! c]ta9ty ( a s+le loss1 & ! ev5 *ance ( a d\ble loss2 alt]natives :i* ! common ma!matical /atem5t ( _! *ances has a decid$ t5d5cy to make u reg>d z indi/+ui%able f "o ano!r4 ,b cle>ly ! decision mu/ be gr\nd$ on ! desires1 feel+s1 & consci5ce ( ! ag5ts4 ,probability _c say a ^w ^u ?is "q4 ,z ,i h po9t$ out else:]e1 !re has be5 mu* confusion on ?is matt] 9 applications ( ! sci5ce to bett+1 & 9 ! discussion ( ! ,pet]sburg problem4 ,we h ?us exam9$ ! doctr9e 9 "q ) a m9ut5ess :i* may seem t$i\s1 b 9 consequ5ce ( ! em95ce ( its support]s x w\ld h be5 presumptu\s to h reject$ x )\t ! /ronge/ gr\nds4 ,! objections :i* h be5 urg$ might be summ>is$ z foll[s3--! am\nt ( our belief ( any giv5 proposition1 suppos+ x to be 9 its nature capable ( accurate det]m9ation 7:i* does n seem to be ! case71 dep5ds ^u a great v>iety ( causes1 ( :i* /ati/ical frequ5cy--! subject ( ,probability--is b "o4 ,t ev5 if we conf9e our att5tion to ?is "o cause1 ! natural am\nt ( our belief is n necess>ily :at !ory w\ld assign1 b has to be *eck$ by appeal to exp]i5ce4 ,! subjective side ( ,probability !re=e1 ?\gh v int]e/+ & well des]v+ ( exam9ation1 seems a m]e app5dage ( ! objective1 & af=ds 9 itself no safe gr\nd = a sci5ce ( inf]5ce4 #ag4 ,! conception !n ( ! sci5ce ( ,probability z a sci5ce ( ! laws ( belief seems to break d[n at e po9t4 ,we mu/ n h[ev] re/ cont5t ) su* m]ely negative criticism4 ,! degree ( belief we ent]ta9 ( a proposition may be h>d to get at accurately1 & :5 obta9$ may be (t5 wrong1 & may ne$ !re=e to be *eck$ by an appeal to ! objects ( belief4 ,/ill 9 popul> e/imation we d seem to be able ) m or less accuracy to =m a graduat$ scale ( int5sity ( belief4 ,:at we h to exam9e n[ is :e!r ?is be possible1 &1 if s1 :at is ! explanation ( ! fact8 ,t x is g5]ally believ$ t we c =m su* a scale sc>cely admits ( d\bt4 ,!re is a :ole vocabul>y ( common expressions su* z1 ',i feel almo/ sure1' ',i d n feel q c]ta91' ',i am less confid5t ( ?is ?an ( t1' & s on4 ,:5 we make use ( any "o ( ^! phrases we seldom d\bt t we h a di/9ct mean+ to convey by means ( x4 ,nor d we feel mu* at a loss1 "u any giv5 circum/ances1 z to :i* ( ^! expressions we %\ld employ 9 pref]5ce to ! o!rs4 ,if we 7 ask$ to arrange 9 ord]1 accord+ to ! int5sity ( ! belief ) :i* we respectively hold !m1 ?+s broadly m>k$ (f f "o ano!r1 we c\ld d x f our consci\sness ( belief alone1 )\t a fre% appeal to ! evid5ce ^u :i* ! belief dep5d$4 ,pass+ ov] ! loos] propositions :i* are us$ 9 common conv]sation1 let u take b "o simple example f among/ ^? :i* furni% num]ical data4 ,d ,i n feel m c]ta9 t "s "o w die ?is week 9 ! :ole t[n1 ?an 9 ! p>ticul> /reet 9 :i* ,i live8 & if ! t[n is kn[n to conta9 a population "o hundr$ times great] ?an t 9 ! /reet1 w\ld n almo/ any "o be prep>$ to ass]t on reflection t he felt a hundr$ times m sure ( ! fir/ proposition ?an ( ! second8 ,or to take a non-num]ical example1 are we n (t5 able to say unhesitat+ly :i* ( two propositions we believe ! mo/1 & to "s r\gh degree h[ mu* m we believe "o ?an ! o!r1 at a "t :5 all ! evid5ce ^u :i* ea* re/s has fad$ f ! m9d1 s t ea* has to be judg$1 z we may say1 solely on its own m]its8 ,"h !n a problem proposes itself4 ,if popul> op9ion1 z illu/rat$ 9 common language1 be correct1--& v consid]able weight mu/ ( c\rse be attribut$ to x1--!re does exi/ some?+ :i* we call p>tial belief 9 ref]5ce to any proposition ( ! num]ical k9d describ$ above4 ,n[ :at we want to d is to f9d "s te/ or ju/ification ( ?is belief1 to obta9 9 fact "s intelligible answ] to ! "q1 ,is x correct8 ,we %all f9d incid5tally t ! answ] to ?is "q w ?r[ a good deal ( light ^u ano!r "q ne>ly z important & f> m intricate1 viz4 ,:at is ! mean+ ( ?is p>tial belief8 #ah4 ,we %all f9d x advisable to comm5ce by asc]ta9+ h[ su* enquiries z ! above w\ld be answ]$ 9 ! case ( ord9>y full belief4 ,su* a /ep w\ld n (f] ! slighte/ difficulty4 ,suppose1 to take a simple example1 t we h obta9$ ! foll[+ proposition1--:e!r by induction1 or by ! rules ( ord9>y d$uctive logic1 does n matt] = our pres5t purpose1--t a c]ta9 mixture ( oxyg5 & hydrog5 is explosive4 ,"h we h an inf]5ce1 & consequ5t belief ( a proposition4 ,n[ suppose !re 7 any enquiry z to :e!r our belief 7 correct1 :at %\ld we d8 ,! simple/ way ( settl+ ! matt] w\ld be to f9d out by a di/9ct appeal to exp]i5ce :e!r ! proposition 0 true4 ,s9ce we are reason+ ab\t ?+s1 ! ju/ification ( ! belief1 t is1 ! te/ ( its correctness1 w\ld be mo/ readily f\nd 9 ! tru? ( ! proposition4 ,if by any process ( inf]5ce ,i h come to believe t a c]ta9 mixture w explode1 ,i consid] my belief to be ju/ifi$1 t is to be correct1 if "u prop] circum/ances ! explosion always does occur2 if x does n occur ! belief 0 wrong4 ,su* an answ]1 no d\bt1 goes b a little way1 or r no way at all1 t[>ds expla9+ :at is ! nature ( belief 9 itself2 b x is suffici5t = our pres5t purpose1 :i* is m]ely t ( det]m9+ :at is meant by ! correctness ( our belief1 & by ! te/ ( its correctness4 ,9 all inf]5ces ab\t ?+s1 9 :i* ! am\nt ( our belief is n tak5 into acc\nt1 su* an explanation z ! above is q suffici5t2 x w\ld be ! ord9>y "o 9 any "q ( sci5ce4 ,x is moreov] p]fectly intelligible1 :e!r ! conclusion is p>ticul> or univ]sal4 ,:e!r we believe t '"s m5 die'1 or t 'all m5 die'1 our belief may ) equal ease be te/$ by ! appropriate tra9 ( exp]i5ce4 #ai4 ,b :5 we attempt to apply ! same te/ to p>tial belief1 we %all f9d ourselves r$uc$ to an awkw>d p]plexity4 ,a difficulty n[ em]ges :i* has be5 s+ul>ly ov]look$ by ^? :o h treat$ ( ! subject4 ,z a simple example w s]ve our purpose1 we w take ! case ( a p5ny4 ,i am ab\t to toss "o up1 & ,i !re=e half believe1 to adopt ! curr5t language1 t x w give head4 ,n[ x seems to be ov]look$ t if we appeal to ! ev5t1 z we did 9 ! case la/ exam9$1 our belief mu/ inevitably be wrong1 & !re=e ! te/ above m5tion$ w fail4 ,= ! ?+ mu/ ei!r happ5 or n happ53 i4e4 9 ?is case ! p5ny mu/ ei!r give head1 or n give x2 !re is no ?ird alt]native4 ,b :i*ev] way x occurs1 our half-belief1 s f> z su* a /ate ( m9d admits ( int]pretation1 mu/ be wrong4 ,if head does come1 ,i am wrong 9 n hav+ expect$ x en\gh2 = ,i only half believ$ 9 its occurr5ce4 ,if x does n happ51 ,i am equally wrong 9 hav+ expect$ x too mu*2 = ,i half believ$ 9 its occurr5ce1 :5 9 fact x did n occur at all4 ,! same difficulty w occur 9 e case 9 :i* we attempt to ju/ify our /ate ( p>tial belief 9 a s+le cont+5t ev5t4 ,let u take ano!r example1 slightly diff]+ f ! la/4 ,a man is to receive #a if a die gives six1 to pay #as4 if x gives any o!r numb]4 ,x w g5]ally be admitt$ t he ought to give #bs4 #f;d4 = ! *ance1 & t if he does s he w be pay+ a fair sum4 ,?is example only diff]s f ! la/ 9 ! fact t in/ead ( simple belief 9 a proposition1 we h tak5 :at ma!maticians call '! value ( ! expectation'4 ,9 o!r words1 we h br\ght into a great] prom95ce1 n m]ely ! belief1 b ! conduct :i* is f\nd$ ^u ! belief4 ,b precisely ! same difficulty recurs "h4 ,= appeal+ to ! ev5t1--! s+le ev5t1 t is1--we see t "o or o!r p>ty mu/ lose 8 money )\t comp5sation4 ,9 :at s5se !n c su* an expectation be said to be a fair "o8 #bj4 ,a possible answ] to ?is1 & s f> z appe>s ! only possible answ]1 w be1 t :at we really mean by say+ t we half believe 9 ! occurr5ce ( head is to express our conviction t head w c]ta9ly happ5 on ! av]age e o!r "t4 ,& simil>ly1 9 ! second example1 by call+ ! sum a fair "o x is meant t 9 ! long run nei!r p>ty w ga9 or lose4 ,z we %all recur pres5tly to ! po9t rais$ 9 ?is =m ( answ]1 ! only notice t ne$ be tak5 ( x at ?is po9t is to call att5tion to ! fact t x entirely ab&ons ! :ole "q 9 dispute1 = x admits t ?is p>tial belief does n 9 any /rict s5se apply to ! individual ev5t1 s9ce x cle>ly _c be ju/ifi$ !re4 ,at su* a result inde$ we _c be surpris$2 at lea/ we _c on ! !ory adopt$ ?r\gh\t ?is ,essay4 ,= be>+ 9 m9d t ! employm5t ( ,probability po/ulates ignorance ( ! s+le ev5t1 x is n easy to see h[ we are to ju/ify any o!r op9ion or /atem5t ab\t ! s+le ev5t ?an a confession ( su* ignorance4 #ba4 ,s f> !n we d n seem to h made ! slighte/ approximation to a solution ( ! p>ticul> "q n[ "u exam9ation4 ,! m closely we h analys$ special examples1 ! m unmi/akeably are we br\ght to ! conclusion t 9 ! individual in/ance no ju/ification ( any?+ l quantitative belief is to be f\nd2 at lea/ none is to be f\nd 9 ! same s5se 9 :i* we expect x 9 ord9>y sci5tific conclusions1 :e!r ,inductive or ,d$uctive4 ,& yet we h to face & acc\nt = ! fact t common impressions1 z atte/$ by a :ole vocabul>y ( common phrases1 are 9 fav\r ( ! exi/5ce ( ?is quantitative belief4 ,h[ are we to acc\nt = ?is8 ,if we appeal to an example aga91 & analyse x some:at m closely1 we may yet f9d our way to "s satisfactory explanation4 ,9 our previ\s analysis 7#ah7 we f\nd x suffici5t to /op at an e>ly /age1 & to give z ! ju/ification ( our belief ! fact ( ! proposition be+ true4 ,/opp+ h[ev] at t /age1 we h f\nd ?is explanation fail altoge!r to give a ju/ification ( p>tial belief2 fail1 t is1 :5 appli$ to ! individual in/ance4 ,! two /ates ( belief & disbelief correspond admirably to ! two results ( ! ev5t happ5+ & n happ5+ respectively1 & unless = psy*ological purposes we saw no reason to analyse fur!r2 b to p>tial belief !re is no?+ correspond+ 9 ! result1 = ! ev5t _c p>tially happ5 9 su* cases z we are conc]n$ )4 ,suppose !n we advance a /ep fur!r 9 ! analysis1 & ask aga9 :at is meant by ! proposition be+ true8 ,?is introduces u1 ( c\rse1 to a v long & intricate pa?2 b 9 ! %ort di/ance along x :i* we %all advance1 we %all n1 x is to be hop$1 f9d any v s]i\s difficulty4 ,z be=e1 we w illu/rate ! analysis by fir/ apply+ x to ! case ( ord9>y full belief4 #bb4 ,:atev] op9ion !n may be held ab\t ! ess5tial nature ( belief1 x w probably be admitt$ t a read9ess to act ^u ! proposition believ$ is an insep>able accompanim5t ( t /ate ( m9d4 ,!re c be no alt]ation 9 our belief 7at any rate 9 ! case ( sane p]sons7 )\t a possible alt]ation 9 our conduct1 nor any?+ 9 our conduct :i* is n connect$ ) some?+ 9 our belief4 ,we w fir/ take an example 9 connection ) ! p5ny1 9 :i* !re is full belief2 we w analyse x a /ep fur!r ?an we did be=e1 & !n attempt to apply ! same analysis to an example ( a simil> k9d1 b "o 9 :i* ! belief is p>tial in/ead ( full4 ,suppose t ,i am ab\t to ?r[ a p5ny up1 & contemplate ! prospect ( its fall+ ^u "o ( its sides & n ^u its edge4 ,we feel p]fectly confid5t t x w d s4 ,n[ :atev] else may be impli$ 9 our belief1 we c]ta9ly mean ?is2 t we are ready to /ake our conduct ^u its fall+ ?us4 ,all our bett+1 & ev]y?+ else t we d1 is c>ri$ on ^u ?is supposition4 ,any risk :atev] t might ensue ^u its fall+ o!rwise w be incurr$ )\t fe>4 ,?is1 x mu/ be obs]v$1 is equally ! case :e!r we are speak+ ( a s+le ?r[ or ( a long succession ( ?r[s4 ,b n[ let u take ! case ( a p5ny fall+1 n ^u "o side or ! o!r1 b ^u a giv5 side1 head4 ,to a c]ta9 ext5t ?is example resembles ! la/4 ,we are p]fectly ready to /ake our conduct ^u :at comes to pass 9 ! long run4 ,:5 we are consid]+ ! result ( a l>ge numb] ( ?r[s1 we are ready to act ^u ! supposition t head comes e o!r "t4 ,if e4g4 we are bett+ ^u x1 we %all n object to pay+ #a e "t t head comes1 on condition ( receiv+ #a e "t t head does n come4 ,?is is no?+ else ?an ! translation1 z we may call x1 into practice1 ( our belief t head & tail occur equally (t54 ,n[ x w be obvi\s1 on a mom5t's consid]ation1 t our conduct is capable ( be+ slightly v>i$3 ( be+ v>i$1 t is1 9 =m1 :il/ x rema9s id5tical 9 respect ( its results4 ,x is cle> t to pay #a e "t we lose1 & to get #a e "t we ga91 comes to precisely ! same ?+1 9 ! case "u consid]ation1 z to pay t5 %ill+s e "t )\t exception1 & to receive #a e "t t head occurs4 ,x is s1 because heads occur1 on ! av]age1 e o!r "t4 ,9 ! long run ! two results co9cide2 b !re is a m>k$ diff]5ce betwe5 ! two cases1 consid]$ individually4 ,! diff]5ce is two-fold4 ,9 ! fir/ place we dep>t f ! notion ( a paym5t e o!r "t1 & come to t ( "o made e "t4 ,9 ! second place1 :at we pay e "t is half ( :at we get 9 ! cases 9 :i* we d get any?+4 ,! diff]5ce may seem slight2 b m>k ! effect :5 our conduct is translat$ back aga9 into ! subjective condition ^u :i* x dep5ds1 viz4 into our belief4 ,x is 9 consequ5ce ( su* a translation1 z x appe>s to me1 t ! notion has be5 acquir$ t we h an accurately det]m9able am\nt ( belief z to e su* proposition4 ,to h losses & ga9s ( equal am\nt1 & to incur !m equally (t51 0 ! exp]i5ce connect$ ) our belief t ! two ev5ts1 head & tail1 w\ld occur equally (t54 ,?is 0 q intelligible1 = x ref]r$ to ! long run4 ,to f9d t ?is c\ld be commut$ = a paym5t made e "t )\t exception1 a paym5t1 obs]ve1 ( half ! am\nt ( :at we occasionally receive1 has v naturally be5 int]pret$ to mean t !re mu/ be a /ate ( half-belief :i* ref]s to ea* individual ?r[4 #bc4 ,"o su* example1 ( c\rse1 does n g f> t[>ds e/abli%+ a !ory4 ,b ! read] w be> 9 m9d t almo/ all our conduct t5ds t[>ds ! same result2 t x is n 9 bett+ only1 b 9 e c\rse ( action 9 :i* we h to c\nt ! ev5ts1 t su* a num]ical apportionm5t ( our conduct is possible4 ,h5ce1 by ! ord9>y pr9ciples ( association1 x w\ld appe> exce$+ly likely t1 n exactly a num]ical condition ( m9d1 b r num]ical associations1 become insep>ably connect$ ) ea* p>ticul> ev5t :i* we "k to occur 9 a c]ta9 proportion ( times4 ,once 9 six times a die gives ace2 a k ( ?is fact1 tak5 9 comb9ation ) all ! practical results to :i* x leads1 produces1 "o _c d\bt1 an insep>able notion ( "o-six? connect$ ) ea* s+le ?r[4 ,b x surely _c be call$ belief to ! am\nt ( "o-six?2 at lea/ x admits nei!r ( ju/ification nor explanation 9 ^! s+le cases1 to :i* alone ! fractional belief1 if su* exi/$1 ought to apply4 ,x is 9 consequ5ce1 ,i appreh5d1 ( su* association t we act 9 su* an unhesitat+ mann] 9 ref]5ce to any s+le cont+5t ev5t1 ev5 :5 we h no expectation ( its be+ repeat$4 ,a die is go+ to be ?r[n up once1 & once only4 ,i bet #e to #a aga9/ ace1 n1 z is commonly ass]t$1 because ,i feel "o-six? "p ( c]ta9ty 9 ! occurr5ce ( ace2 b because ,i "k t su* conduct w\ld be ju/ifi$ 9 ! long run ( su* cases1 & ,i apply to ! solit>y individual ! same rule t ,i %\ld apply to x if ,i knew x 7 "o ( a long s]ies4 ,?is acc\nts = my conduct be+ ! same 9 ! two cases2 by association1 moreov]1 we probably exp]i5ce v simil> feel+s 9 reg>d to !m bo?4 #bd4 ,& "h1 on ! view ( ! subject adopt$ 9 ?is ,essay1 we might /op4 ,we are b\nd to expla9 ! 'measure ( our belief' 9 ! occurr5ce ( a s+le ev5t :5 we judge solely f ! /ati/ical frequ5cy ) :i* su* ev5ts occur1 = su* a s]ies ( ev5ts 0 our />t+-po9t2 b we are n b\nd to inquire :e!r 9 e case 9 :i* p]sons h1 or claim to h1 a c]ta9 measure ( belief !re mu/ be su* a s]ies to :i* to ref] x1 & by :i* to ju/ify x4 ,^? :o />t f ! subjective side1 & reg>d ,probability z ! sci5ce ( quantitative belief1 are oblig$ to d ?is1 b we are free f ! obligation4 ,/ill ! "q is "o :i* is s naturally rais$ 9 connection ) ?is subject1 t x _c be altoge!r pass$ by4 ,i ?9k t to a consid]able ext5t su* a ju/ification z t m5tion$ above w be f\nd applicable 9 o!r cases4 ,! fact is t we are v seldom call$ ^u to decide & act ^u a s+le cont+5cy :i* _c be view$ z be+ "o ( a s]ies4 ,exp]i5ce introduces u1 x mu/ be rememb]$1 n m]ely to a succession ( ev5ts neatly arrang$ 9 a s+le s]ies 7z we h hi!rto assum$ !m to be = ! purpose ( illu/ration71 b to an inf9ite numb] belong+ to a va/ v>iety ( diff]5t s]ies4 ,a man is oblig$ to be act+1 & !re=e ex]cis+ 8 belief ab\t "o ?+ or ano!r1 almo/ ! :ole ( e day ( 8 life4 ,any "o p]son w h to decide 9 8 "t ab\t a multitude ( ev5ts1 ea* "o ( :i* may nev] recur aga9 )9 8 own exp]i5ce4 ,b by ! v fact ( !re be+ a multitude1 ?\gh !y are all ( diff]5t k9ds1 we %all /ill f9d t ord] is ma9ta9$1 & s a c\rse ( conduct c be ju/ifi$4 ,9 a plantation ( trees we %\ld f9d t !re is ord] ( a c]ta9 k9d if we measure !m 9 any "o direction1 ! trees be+ on an av]age ab\t ! same di/ance f ea* o!r4 ,b a some:at simil> ord] w\ld be f\nd if we 7 to exam9e !m 9 any o!r direction :atsoev]4 ,s 9 nature g5]ally2 !re is regul>ity 9 a succession ( ev5ts ( ! same k9d4 ,b !re may also be regul>ity if we =m a s]ies by tak+ successively a numb] out ( totally di/9ct k9ds4 ,x is 9 ?is circum/ance t we f9d an ext5sion ( ! practical ju/ification ( ! measure ( our belief4 ,a man1 say1 buys a life annuity1 insures 8 life on a railway j\rney1 puts into a lott]y1 & s on4 ,n[ we may make a s]ies out ( ^! acts ( 81 ?\gh ea* is 9 itself a s+le ev5t :i* he may nev] int5d to repeat4 ,8 conduct1 & !re=e 8 belief1 measur$ by ! result 9 ea* individual in/ance1 w n be ju/ifi$1 b ! rev]se1 z %[n 9 #ai4 ,c\ld he inde$ repeat ea* k9d ( action (t5 en\gh x w\ld be ju/ifi$2 b f ?is1 by ! conditions ( life1 he is deb>r$4 ,n[ x is p]fectly conceivable t 9 ! new s]ies1 =m$ by 8 successive acts ( diff]5t k9ds1 !re %\ld be no regul>ity4 ,z a matt] ( fact1 h[ev]1 x is f\nd t !re is regul>ity4 ,9 ?is way ! equalization ( 8 ga9s & losses1 = :i* he _c hope 9 annuities1 insurances1 & lott]ies tak5 sep>ately1 may yet be secur$ to him out ( ^! ev5ts tak5 collectively4 ,if 9 ea* case he values 8 *ance at its "r proportion 7& acts accord+ly7 he w 9 ! c\rse ( 8 life nei!r ga9 nor lose4 ,& 9 ! same way if1 :5ev] he has ! alt]native ( diff]5t c\rses ( conduct1 he acts 9 accordance ) ! e/imate ( 8 belief describ$ above1 i4e4 *ooses ! ev5t ^: *ance is ! be/1 he w 9 ! end ga9 m 9 ?is way ?an by any o!r c\rse4 ,by ! exi/5ce1 !re=e1 ( ^! cross-s]ies1 z we may t]m !m1 !re is an imm5se addition to ! numb] ( actions :i* may be fairly consid]$ to belong to ^? c\rses ( conduct :i* (f] _m successive opportunities ( equaliz+ ga9s & losses4 ,all ^! cases !n may be reg>d$ z admitt+ ( ju/ification 9 ! way n[ "u discussion4 #be4 ,9 ! above rem>ks x w be obs]v$ t we h be5 giv+ :at is to be reg>d$ z a ju/ification ( 8 belief f ! po9t ( view ( ! individual ag5t himself4 ,if we suppose ! exi/5ce ( an enl>g$ fell[-feel+1 ! applicability ( su* a ju/ification becomes /ill m ext5sive4 ,we c assign a v intelligible s5se to ! ass]tion t x is #iii to #a t ,i %all n get a prize 9 a lott]y1 ev5 if ?is be /at$ 9 ! =m t my belief 9 my s do+ is repres5t$ by ! fraction #a_/ajjj? ( c]ta9ty4 ,prop]ly x means t 9 a v l>ge numb] ( ?r[s ,i %\ld ga9 once 9 #ajjj times4 ,if we include o!r cont+5cies ( ! same k9d1 z describ$ 9 ! la/ section1 ea* individual may be suppos$ to rea* to some?+ l ?is exp]i5ce )9 ! limits ( 8 own life4 ,he c\ld n d x 9 ?is p>ticul> l9e ( conduct alone1 b he c\ld d x 9 ?is l9e comb9$ ) o!rs4 ,n[ introduce ! possibility ( ea* man feel+ t ! ga9 ( o!rs (f]s "s analogy to 8 own ga9s1 :i* we may conceive 8 do+ except 9 ! case ( ! ga9s ( ^? aga9/ :om he is directly compet+1 & ! above ju/ification becomes /ill m ext5sively applicable4 ,! foll[+ w\ld be a fair illu/ration to te/ ?is view4 ,i "k t ,i mu/ die on "s day ( ! week1 & !re are b sev5 days4 ,my belief1 !re=e1 t ,i %all die on a ,sunday is "o-sev5?4 ,"h ! cont+5t ev5t is cle>ly "o t does n admit ( repetition2 & yet w\ld n ! belief ( e man h ! value assign$ x by ! =mula8 ,x w\ld appe> t ! same pr9ciple w be f\nd to be at "w "h z 9 ! =m] examples4 ,x is q true t ,i h only ! opportunity ( dy+ once myself1 b ,i am a memb] ( a class 9 :i* dea?s occur ) frequ5cy1 & ,i =m my op9ion ^u evid5ce drawn f t class4 ,if1 = example1 ,i _h insur$ my life = #ajjj1 ,i %\ld feel a c]ta9 propriety 9 dem&+ #gjjj 9 case ! (fice decl>$ t x w\ld only pay 9 ! ev5t ( my dy+ on a ,sunday4 ,i1 inde$1 = my own private "p1 might n f9d ! arrangem5t an equitable "o2 b mank9d at l>ge1 9 case !y act$ on su* a pr9ciple1 might fairly commute _! aggregate ga9s 9 su* a way1 :il/ to ! ,insurance ,(fice x w\ld n make any diff]5ce at all4 #bf4 ,! results ( ! la/ few sections might be summ>is$ z foll[s3--! diff]5t am\nts ( belief :i* we ent]ta9 ^u diff]5t ev5ts1 & :i* are recogniz$ by v>i\s phrases 9 common use1 h und\bt$ly "s mean+4 ,b ! great] "p ( _! mean+1 & c]ta9ly _! only ju/ification1 are to be s\ght 9 ! s]ies ( correspond+ ev5ts to :i* !y belong2 9 reg>d to :i* x may be %[n t f> m ev5ts are capable ( be+ ref]r$ to a s]ies ?an might be suppos$ at fir/ sight4 ,! te/ & ju/ification ( belief are to be f\nd 9 conduct2 9 ?is te/ appli$ to ! s]ies z a :ole1 !re is no?+ peculi>1 x diff]s 9 no way f ! simil> te/ :5 we are act+ on our belief ab\t any s+le ev5t4 ,b s appli$1 f ! nature ( ! case x is appli$ successively to ea* ( ! individuals ( ! s]ies2 "h our conduct g5]ally admits ( be+ sep>ately consid]$ 9 ref]5ce to ea* p>ticul> ev5t2 & ?is has be5 und]/ood to d5ote a c]ta9 am\nt ( belief :i* %\ld be a fraction ( c]ta9ty4 ,probably on ! pr9ciples ( association1 a peculi> condition ( m9d is produc$ 9 ref]5ce to ea* s+le ev5t4 ,& ^! associations are n unnaturally reta9$ ev5 :5 we contemplate any "o ( ^! s+le ev5ts isolat$ f any s]ies to :i* x belongs4 ,:5 x is f\nd alone we treat x1 & feel t[>ds x1 z we d :5 x is 9 company ) ! re/ ( ! s]ies4 #bg4 ,we may n[ see1 m cle>ly ?an we c\ld be=e1 :y x is t we are free f any necessity ( assum+ ! exi/5ce ( causation1 9 ! s5se ( necess>y inv>iable sequ5ce1 9 ! case ( ! ev5ts :i* compose our s]ies4 ,aga9/ su* a view x might v plausibly be urg$1 t we con/antly talk ( ! probability ( a s+le ev5t2 b h[ c ?is be done1 x may reasonably be said1 if we once admit ! possibility ( t ev5t occurr+ =tuit\sly8 ,take an in/ance f human life2 ! av]age duration ( ! lives ( a bat* ( m5 ag$ ?irty w be ab\t ?irty-f\r ye>s4 ,we say !re=e to any individual ( !m1 ,y\r expectation ( life is ?irty-f\r ye>s4 ,b h[ c ?is be said if we admit t ! tra9 ( ev5ts compos+ 8 life is liable to be de/itute ( all regul> sequ5ce ( cause & effect8 ,to ?is x may be repli$ t ! d5ial ( causation enables u to say nei!r m nor less ?an its ass]tion1 9 ref]5ce to ! l5g? ( ! individual life1 = ( ?is we are ignorant 9 ea* case alike4 ,by assign+1 z above1 an expectation 9 ref]5ce to ! individual1 we mean no?+ m ?an to make a /atem5t ab\t ! av]age ( 8 class4 ,:e!r !re be causation or n 9 ^! individual cases does n affect our k ( ! av]age1 = ?is by supposition re/s on indep5d5t exp]i5ce4 ,! legitimate inf]5ces are ! same on ei!r hypo!sis1 & ( equal value4 ,! only diff]5ce is t on ! hypo!sis ( non-causation we h =c$ ^u our att5tion ! impropriety ( talk+ ( ! 'prop]' expectation ( ! individual1 ow+ to ! fact t all k ( its am\nt is =mally impossible2 on ! o!r hypo!sis ! impropriety is ov]look$ f ! fact ( su* k be+ only practically unatta9able4 ,z a matt] ( fact ! am\nt ( our k is ! same 9 ea* case2 x is a k ( ! av]age1 & ( t only4#f #bh4 ,we may conclude1 !n1 t ! limits )9 :i* we are ?us able to ju/ify ! am\nt ( our belief are f> m ext5sive ?an might appe> at fir/ sight4 ,:e!r e case 9 :i* p]sons feel an am\nt ( belief %ort ( p]fect confid5ce c\ld be =c$ into ! prov9ce ( ,probability is a wid] "q4 ,ev51 h[ev]1 if ! belief c\ld be suppos$ capable ( ju/ification on its pr9ciples1 its rules c\ld nev] 9 su* cases be made use (4 ,suppose1 = example1 t a fa!r 7 9 d\bt :e!r to give a c]ta9 m$ic9e to 8 sick *ild4 ,on ! "o h&1 ! doctor decl>$ t ! *ild w\ld die unless ! m$ic9e 7 giv52 on ! o!r1 ?r\gh a mi/ake1 ! fa!r _c feel q sure t ! m$ic9e he has is ! "r "o4 ,x is conceivable t "s ma!maticians1 9 _! conviction t ev]y?+ has its def9ite num]ical probability1 w\ld decl>e t ! man's belief _h "s 'value' 7if !y c\ld only f9d out :at x is71 say n9e-t5?s2 by :i* !y w\ld mean t 9 n9e cases out ( t5 9 :i* he ent]ta9$ a belief ( t p>ticul> value he prov$ to be "r4 ,s ) 8 belief & d\bt on ! o!r side ( ! "q4 ,putt+ ! two toge!r1 !re is b "o c\rse :i*1 z a prud5t man & a good fa!r1 he c possibly foll[4 ,x may be s1 b :5 7z "h7 ! id5tification ( an ev5t 9 a s]ies dep5ds on purely subjective conditions1 z 9 ?is case ^u ! degree ( vividness ( 8 conviction1 ( :i* no "o else c judge1 no te/ is possible1 & !re=e no pro( c be f\nd4 #bi4 ,s mu* !n = ! attempts1 s frequ5tly made1 to f\nd ! sci5ce on a subjective basis2 !y c lead1 z x has "h be5 endeav\r$ to %[1 to no satisfactory result4 ,/ill our belief is s insep>ably connect$ ) our action1 t some?+ ( a def5ce c be made = ! attempts describ$ above2 b :5 x is attempt$1 z is (t5 ! case1 to import o!r s5tim5ts besides pure belief1 & to f9d a ju/ification = !m also 9 ! results ( our sci5ce1 ! confusion becomes f> worse4 ,! foll[+ extract f ,ar*bi%op ,?omson's ,laws ( ,?\ght 7#abb1 ,ed4 ,,ii47 w %[ :at k9d ( applications ( ! sci5ce are contemplat$ "h3 ,9 apply+ ! doctr9e ( *ances to t subject 9 connexion ) :i* x 0 inv5t$--games ( *ance1--! pr9ciples ( :at has be5 happily t]m$ 'moral ari?metic' mu/ n be =gott54 ,n only w\ld x be difficult = a game/] to f9d an antagoni/ on t]ms1 z to =tune & ne$s1 precisely equal1 b also x is impossible t ) su* an equality ! advantage ( a consid]able ga9 %\ld balance ! h>m ( a s]i\s loss4 ',if two m51' says ,buffon1 '7 to det]m9e to play = _! :ole prop]ty1 :at w\ld be ! effect ( ?is agreem5t8 ,! "o w\ld only d\ble 8 =tune1 & ! o!r r$uce 8 to naught4 ,:at proportion is !re betwe5 ! loss & ! ga98 ,! same t !re is betwe5 all & no?+4 ,! ga9 ( ! "o is b a mod]ate sum1--! loss ( ! o!r is num]ically inf9ite1 & morally s great t ! lab\r ( 8 :ole life may n p]haps suffice to re/ore 8 prop]ty4' ,z moral advice ?is is all v true & good4 ,b if x be reg>d$ z a contribution to ! sci5ce ( ! subject x is q inappropriate1 & seems calculat$ to cause confusion4 ,! doctr9e ( *ances pron\nces ^u c]ta9 k9ds ( ev5ts 9 respect ( numb] & magnitude2 x has absolutely no?+ to d ) any p>ticul> p]son's feel+s ab\t ^! relations4 ,we might z well app5d a coroll>y to ! rules ( ari?metic1 to po9t out t al?\gh x is v true t twice two are f\r x does n foll[ t f\r1 horses w give twice z mu* pleasure to ! own] z two w4 ,if two m5 play on equal t]ms _! *ances are equal2 9 o!r words1 if !y 7 (t5 to play 9 ?is mann] ea* w\ld lose z frequ5tly z he w\ld ga94 ,t is all t ,probability c say2 :at "u ! circum/ances may be ! det]m9ation & op9ions ( ! m5 9 "q1 x is = !m & !m alone to decide4 ,!re are _m p]sons :o _c be> m$iocrity ( any k9d1 & to :om ! prospect ( d\bl+ _! =tune w\ld outweigh a great] *ance ( los+ x altoge!r4 ,!y alone are ! judges4 ,if we w introduce su* a balance ( pleasure & pa9 ! individual mu/ make ! calculation = himself4 ,! supposition is t total ru9 is v pa9ful1 p>tial loss pa9ful 9 a less proportion ?an t assign$ by ! ratio ( ! losses !mselves2 ! inf]5ce is !re=e drawn t on ! av]age m pa9 is caus$ by occasional great losses ?an by frequ5t small ones1 ?\gh ! money value ( ! losses 9 ! long run may be ! same 9 ea* case4 ,b if we suppose a c\ntry :]e ! desire ( sp5d+ l>gely is v /rong1 & :]e ow+ to abundant production loss is easily replac$1 ! calculation might incl9e ! o!r way4 ,"u su* circum/ances x is q possible t m happ9ess might result f play+ = high ?an = l[ /akes4 ,! fact is t all emotional consid]ations ( ?is k9d are irrelevant2 !y are1 at mo/1 m]e applications ( ! !ory1 & su* z ea* individual is alone compet5t to make = himself4 ,"s m rem>ks w be made ^u ?is subject 9 ! *apt] ^u ,insurance & ,gambl+4 #cj4 ,x is by ! introduction ( su* consid]ations z ^! t ! ,pet]sburg ,problem has be5 s p]plex$4 ,hav+ already giv5 "s description ( ?is problem we w ref] to x v briefly "h4 ,x pres5ts u ) a sequ5ce ( sets ( ?r[s = ea* ( :i* sets ,i am to receive some?+1 say a %ill+1 z ! m9imum receipt4 ,my receipts increase 9 proportion to ! r>ity ( ea* p>ticul> k9d ( set1 & ea* k9d is obs]v$ or inf]r$ to gr[ m r>e 9 a c]ta9 def9ite b unlimit$ ord]4 ,by ! word+ ( ! problem1 prop]ly int]pret$1 ,i am suppos$ nev] to /op4 ,cle>ly !re=e1 h[ev] l>ge a fee ,i pay = ea* ( ^! sets1 ,i %all be sure to make x up 9 "t4 ,! ma!matical expression ( ?is is1 t ,i ought always to pay an inf9ite sum4 ,to ?is ! objection is oppos$1 t no s5sible man w\ld ?9k ( advanc+ ev5 a l>ge f9ite sum1 say #ej4 ,c]ta9ly he w\ld n2 b :y8 ,because nei!r he nor ^? :o are to pay him w\ld be likely to live long en\gh = him to obta9 ?r[s good en\gh to remun]ate him = "o-t5? ( 8 outlay2 to say no?+ ( 8 tr\ble & loss ( "t4 ,we mu/ n suppose t ! problem1 z /at$ 9 ! ideal =m1 w co9cide ) ! practical =m 9 :i* x pres5ts itself 9 life4 ,a c>p5t] might z well object to ,euclid's second po/ulate1 because 8 plane came to a /op 9 six feet on ! plank on :i* he 0 at "w4 ,_m p]sons h fail$ to p]ceive ?is1 & h assum$ t1 besides enabl+ u to draw num]ical inf]5ces ab\t ! memb]s ( a s]ies1 ! !ory ought also to be call$ ^u to ju/ify all ! op9ions :i* av]age respectable m5 might be incl9$ to =m ab\t !m1 z well z ! conduct !y might *oose to pursue 9 consequ5ce4 ,x is obvi\s t to ent] ^u su* consid]ations z ^! is to div]ge f our prop] gr\nd4 ,we are conc]n$1 9 ^! cases1 ) ! actions ( m5 only1 z giv5 9 /ati/ics2 ) ! emotions !y exp]i5ce 9 ! p]=mance ( ^! actions we h no direct conc]n :atev]4 ,! error is ! same z if any "o 7 to conf\nd1 9 political economy1 value 9 use ) value 9 ex*ange1 & object to measur+ ! value ( a loaf by its co/ ( production1 because bread is wor? m to a man :5 he is hungry ?an x is j aft] 8 d9n]4 #ca4 ,"o class ( emotions inde$ ought to be except$1 :i*1 f ! app>5t uni=mity & consi/5cy ) :i* !y %[ !mselves 9 diff]5t p]sons & at diff]5t times1 d really pres5t "s bett] claim to consid]ation4 ,9 connection ) a sci5ce ( inf]5ce !y c nev] inde$ be reg>d$ z m ?an an accid5t ( :at is ess5tial to ! subject1 b comp>$ ) o!r emotions !y seem to be insep>able accid5ts4 ,! read] w rememb] t att5tion 0 drawn 9 ! e>li] "p ( ?is *apt] to ! comp\nd nature ( ! /ate ( m9d :i* we t]m belief4 ,x is p>tly intellectual1 p>tly also emotional2 x pr(esses to re/ ^u exp]i5ce1 b 9 reality ! exp]i5ce acts ?r\gh ! di/ort+ m$ia ( hopes & fe>s & o!r di/urb+ ag5cies4 ,s long z we conf9e our att5tion to ! /ate ( m9d ( ! p]son :o believes1 x appe>s to me t ^! two p>ts ( belief are q insep>able4 ,inde$1 to speak ( !m z two p>ts may convey a wrong impression2 = ?\gh !y spr+ f diff]5t s\rces1 !y s entirely m]ge 9 "o result z to produce :at might be call$ an indi/+ui%able comp\nd4 ,e k9d ( inf]5ce1 :e!r 9 probability or n1 is liable to be di/urb$ 9 ?is way4 ,a timid man may hone/ly believe t he w be w\nd$ 9 a com+ battle1 :5 o!rs1 ) ! same exp]i5ce b calm] judgm5ts1 see t ! *ance is too small to des]ve consid]ation4 ,b su* a man's belief1 if we look only to t1 w n diff] 9 its nature f s\nd belief4 ,8 conduct also 9 consequ5ce ( 8 belief w by itself af=d no gr\nd ( discrim9ation2 he w make 8 w z s9c]ely z a man :o is unmi/akeably on 8 dea?-b$4 ,! only res\rce is to *eck & correct 8 belief by appeal+ to pa/ & curr5t exp]i5ce4#g ,?is 0 advanc$ z an objection to ! !ory on :i* probability is reg>d$ z conc]n$ prim>ily ) laws ( belief4 ,b on ! view tak5 9 ?is ,essay 9 :i* we are suppos$ to be conc]n$ ) laws ( inf]5ce ab\t ?+s1 error & difficulty f ?is s\rce vani%4 ,let u be> cle>ly 9 m9d t we are conc]n$ ) inf]5ces ab\t ?+s1 & :atev] !re may be 9 belief :i* does n dep5d on exp]i5ce w disappe> f notice4 #cb4 ,^! emotions !n c claim no notice z an integral portion ( any sci5ce ( inf]5ce1 & %\ld 9 /rictness be rigidly exclud$ f x4 ,b if any ( !m are uni=m & regul> 9 _! production & magnitude1 !y may be fairly admitt$ z accid5tal & extrane\s accompanim5ts4 ,?is is really ! case to "s ext5t ) our surprise4 ,?is emotion does %[ a consid]able degree ( uni=mity4 ,! r>] any ev5t is ! m am ,i1 9 common ) mo/ o!r m51 surpris$ at x :5 x does happ54 ,?is surprise may range ?r\gh all degrees1 f ! mo/ languid =m ( int]e/ up to ! condition :i* we t]m 'be+ />tl$'4 ,& s9ce ! surprise seems to be pretty mu* ! same1 "u simil> circum/ances1 at diff]5t times1 & 9 ! case ( diff]5t p]sons1 x is free f t extreme irregul>ity :i* is f\nd 9 mo/ ( ! o!r m5tal conditions :i* accompany ! contemplation ( unexpect$ ev5ts4 ,h5ce our surprise1 ?\gh1 z /at$ above1 hav+ no prop] claim to admission into ! sci5ce ( ,probability1 is su* a con/ant & regul> accompanim5t ( t :i* ,probability is conc]n$ )1 t notice mu/ (t5 be tak5 ( x4 ,ref]5ces w occasionally be f\nd to ?is aspect ( ! "q 9 ! foll[+ *apt]s4 ,x may be rem>k$ 9 pass+1 = ! sake ( fur!r illu/ration ( ! subject1 t ?is emotional accompanim5t ( surprise1 to :i* we are ?us able to assign some?+ l a fractional value1 diff]s 9 two important respects f ! commonly accept$ fraction ( belief4 ,9 ! fir/ place1 x has :at may be t]m$ an indep5d5t exi/5ce2 x is intelligible by itself4 ,! belief1 z we endeav\r$ to %[1 ne$s explanation & f9ds x 9 our consequ5t conduct4 ,n s ) ! emotion2 ?is /&s ^u its own foot+1 & may be exam9$ 9 & by itself4 ,h5ce1 9 ! second place1 x is z applicable1 & z capable ( any k9d ( ju/ification1 9 relation to ! s+le ev5t1 z to a s]ies ( ev5ts4 ,9 ?is respect1 z w be rememb]$1 x (f]s a complete contra/ to our /ate ( belief ab\t any "o cont+5t ev5t4 ,may n ^! consid]ations help to acc\nt = ! g5]al acceptance ( ! doctr9e1 t we h a c]ta9 def9ite & measurable am\nt ( belief ab\t ^! ev5ts8 ,i _c help ?9k+ t :at is s obvi\sly true ( ! emotional portion ( ! belief1 has be5 unconsci\sly transf]r$ to ! o!r or intellectual portion ( ! comp\nd condition1 to :i* x is n applicable1 & :]e x _c f9d a ju/ification4 #cc4 ,a fur!r illu/ration may n[ be giv5 ( ! subjective view ( ,probability at pres5t "u discussion4 ,an appeal to common language is always ( s]vice1 z ! employm5t ( any di/9ct ^w is g5]ally a pro( t mank9d h obs]v$ "s di/9ct prop]ties 9 ! ?+s1 :i* h caus$ !m to be s+l$ out & h t "n appropriat$ to !m4 ,!re is su* a class ( words assign$ by popul> usage to ! k9d ( ev5ts ( :i* ,probability takes acc\nt4 ,if we exam9e !m we %all f9d1 ,i ?9k1 t !y direct u unmi/akeably to ! two-fold aspect ( ! "q1--! objective & ! subjective1 ! quality 9 ! ev5ts & ! /ate ( our m9ds 9 consid]+ !m1--t h occupi$ our att5tion dur+ ! =m] *apt]s4 ,! ^w 'extraord9>y'1 = in/ance1 seems to po9t to ! obs]v$ fact1 t ev5ts are arrang$ 9 a sort ( ordo or rank4 ,no "o ( !m might be s exactly plac$ t we c\ld h inf]r$ its position1 b :5 we take a great _m into acc\nt toge!r1 runn+ our eye1 z x 71 along ! l9e1 we beg9 to see t !y really d = ! mo/ "p /& 9 ord]4 ,^? :i* /& away f ! l9e h ?is div]g5ce obs]v$1 & are call$ extraord9>y1 ! re/ ord9>y1 or 9 ! l9e4 ,s too 'irregul>' & 'abnormal' are d\btless us$ f ! appe>ance ( ?+s1 :5 exam9$ 9 l>ge numb]s1 be+ t ( an arrangem5t by rule or measure4 ,?is only holds :5 !re are a good _m2 we c\ld n speak ( ! s+le ev5ts be+ s arrang$4 ,aga9 ! ^w 'law'1 9 its philosophical s5se1 has n[ become q popul>is$4 ,h[ ! t]m became introduc$ is n c]ta91 b !re c be little d\bt t x 0 some:at 9 ?is way3--,! effect ( a law1 9 its usual application to human conduct1 is to produce regul>ity :]e x did n previ\sly exi/2 :5 !n a regul>ity began to be p]ceiv$ 9 nature1 ! same ^w 0 us$1 :e!r ! cause 0 suppos$ to be ! same or n4 ,9 ea* case !re 0 ! same g5]ality ( agreem5t1 subject to occasional deflection4#h ,on ! o!r h&1 obs]ve ! words 'wond]ful'1 'unexpect$'1 'incr$ible'4 ,_! connotation describes /ates ( m9d simply2 !y are ( c\rse n conf9$ to ,probability1 9 ! s5se ( /ati/ical frequ5cy1 b imply simply t ! ev5ts !y d5ote are su* z f "s cause we did n expect w\ld happ51 & at :i* !re=e1 :5 !y d happ51 we are surpris$4 ,n[ :5 we be> 9 m9d t ^! two classes ( words are 9 _! orig9 p]fectly di/9ct2--! "o d5ot+ simply ev5ts ( a c]ta9 "*2 ! o!r1 ?\gh also d5ot+ ev5ts1 connot+ simply /ates ( m9d2--& yet t !y are univ]sally appli$ to ! same ev5ts1 s z to be us$ z p]fectly synonym\s1 we h 9 ?is a /rik+ illu/ration ( ! two sides "u :i* ,probability may be view$1 & ( ! univ]sal recognition ( a close connection betwe5 !m4 ,! words are popul>ly us$ z synonym\s1 & we mu/ n press _! mean+ too f>2 b if x 7 to be obs]v$1 z ,i am r incl9$ to ?9k x c\ld1 t ! application ( ! words :i* d5ote m5tal /ates is wid] ?an t ( ! o!rs1 we %\ld h an illu/ration ( :at has be5 already obs]v$1 viz4 t ! prov9ce ( ,probability is n s ext5sive z t ov] :i* v>iation ( belief might be obs]v$4 ,probability only consid]s ! case 9 :i* ?is v>iation is br\ght ab\t 9 a c]ta9 def9ite /ati/ical way4 #cd4 ,x w be f\nd 9 ! end bo? int]e/+ & important to h devot$ "s att5tion to ?is subjective side ( ! "q4 ,9 ! fir/ place1 z a m]e speculative inquiry ! quantity ( our belief ( any proposition des]ves notice4 ,to /udy x at all deeply w\ld be to trespass into ! prov9ce ( ,psy*ology1 b x is s intimately connect$ ) our own subject t we _c avoid all ref]5ce to x4 ,we !re=e discuss ! laws "u :i* our expectation & surprise at isolat$ ev5ts increases or dim9i%es1 s z to acc\nt = ^! /ates ( m9d 9 any individual in/ance1 &1 if necess>y1 to correct !m :5 !y v>y f _! prop] am\nt4 ,b !re is ano!r m important reason ?an ?is4 ,x is q true t :5 ! subjects ( our discussion 9 any p>ticul> in/ance lie entirely )9 ! prov9ce ( ,probability1 !y may be treat$ )\t any ref]5ce to our belief4 ,we may or we may n employ ?is side ( ! "q accord+ to our pleasure4 ,if1 = example1 ,i am ask$ :e!r x is m likely t ,a4 ,b4 w die ?is ye>1 ?an t x w ra9 to-morr[1 ,i may calculate ! *ance 7:i* really is at bottom ! same ?+ z my belief7 ( ea*1 f9d !m respectively1 "o-six? & "o-sev5?1 say1 & !re=e decide t my 'expectation' ( ! =m] is ! great]1 viz4 t ?is is ! m likely ev5t4 ,9 ?is case ! process is precisely ! same :e!r we suppose our belief to be introduc$ or n2 our m5tal /ate is1 9 fact1 q immat]ial to ! "q4 ,b1 9 o!r cases1 x may be diff]5t4 ,suppose t we are comp>+ two ?+s1 ( :i* "o is :olly ali5 to ,probability1 9 ! s5se t x is hopeless to attempt to assign any degree ( num]ical frequ5cy to x1 ! only gr\nd !y h 9 common may be ! am\nt ( belief to :i* !y are respectively entitl$4 ,we _c comp>e ! frequ5cy ( _! occurr5ce1 = "o may occur too seldom to judge by1 p]haps x may be unique4 ,x has be5 already said1 t our belief ( _m ev5ts re/s ^u a v complicat$ & ext5sive basis4 ,my belief may be ! product ( _m conflict+ argum5ts1 & _m analogies m or less remote2 ^! pro(s !mselves may h mo/ly fad$ f my m9d1 b !y w leave _! effect beh9d !m 9 a weak or /rong conviction4 ,at ! "t1 !re=e1 ,i may /ill be able to say1 ) "s degree ( accuracy1 ?\gh a v slight degree1 :at am\nt ( belief ,i ent]ta9 ^u ! subject4 ,n[ we _c comp>e ?+s t are het]og5e\s3 if1 !re=e1 we are to decide betwe5 ?is & an ev5t det]m9$ naturally & prop]ly by ,probability1 x is impossible to appeal to *ances or frequ5cy ( occurr5ce4 ,! measure ( belief is ! only common gr\nd1 & we mu/ !re=e comp>e ?is quantity 9 ea* case4 ,! te/ af=d$ w be an exce$+ly r\gh "o1 = ! reasons m5tion$ above1 b x w be bett] ?an none2 9 "s cases x w be f\nd to furni% all we want4 ,suppose1 = example1 t "o lett] 9 a million is lo/ 9 ! ,po/ ,(fice1 & t 9 any giv5 in/ance ,i wi% to "k :i* is m likely1 t a lett] has be5 s lo/1 or t my s]vant has /ol5 x8 ,if ! latt] alt]native c\ld1 l ! =m]1 be /at$ 9 a num]ical =m1 ! comp>ison w\ld be simple4 ,b x _c be r$uc$ to ?is =m1 at lea/ n consci\sly & directly4 ,/ill1 if we c\ld feel t our belief 9 ! man's di%one/y 0 great] ?an "o-million?1 we %\ld !n h homog5e\s ?+s be=e u1 & !re=e comp>ison w\ld be possible4 #ce4 ,we are n[ 9 a position to give a tol]ably accurate def9ition ( a phrase :i* we h frequ5tly be5 oblig$ to employ1 or incid5tally to sugge/1 & ( :i* ! read] may h look$ = a def9ition already1 viz4 ! probability ( an ev5t1 or :at is equival5t to ?is1 ! *ance ( any giv5 ev5t happ5+4 ,i consid] t ^! t]ms presuppose a s]ies2 )9 ! indef9itely num]\s class :i* composes ?is s]ies a small] class is di/+ui%$ by ! pres5ce or abs5ce ( "s attribute or attributes1 z 0 fully illu/rat$ & expla9$ 9 a previ\s *apt]4 ,^! l>g] & small] classes respectively are commonly spok5 ( z in/ances ( ! 'ev5t1' & ( 'its happ5+ 9 a giv5 p>ticul> way4' ,adopt+ ?is phraseology1 :i* ) prop] explanations is suitable en\gh1 we may def9e ! probability or *ance 7! t]ms are "h reg>d$ z synonym\s7 ( ! ev5t happ5+ 9 t p>ticul> way z ! num]ical fraction :i* repres5ts ! proportion betwe5 ! two diff]5t classes 9 ! long run4 ,?us1 = example1 let ! probability be t ( a giv5 infant liv+ to be eighty ye>s ( age4 ,! l>g] s]ies w comprise all infants1 ! small] all :o live to eighty4 ,let ! proportion ( ! =m] to ! latt] be #i to #a2 9 o!r words1 suppose t "o infant 9 t5 lives to eighty4 ,!n ! *ance or probability t any giv5 infant w live to eighty is ! num]ical fraction #a_/aj4 ,?is assumes t ! s]ies are ( indef9ite ext5t1 & ( ! k9d :i* we h describ$ z possess+ a fix$ type4 ,if ?is be n ! case1 b ! s]ies be suppos$ t]m9able1 or regul>ly or irregul>ly fluctuat+1 z might be ! case1 = in/ance1 9 a society :]e ow+ to sanit>y or o!r causes ! av]age longevity 0 /eadily und]go+ a *ange1 !n 9 s f> z ?is is ! case ! s]ies ceases to be a subject ( sci5ce4 ,:at we h to d "u ^! circum/ances1 is to sub/itute a s]ies ( ! "r k9d = ! inappropriate "o pres5t$ by nature1 *oos+ x1 ( c\rse1 ) z little deflection z possible f ! obs]v$ facts4 ,?is is no?+ m ?an has to be done1 & inv>iably is done1 :5ev] natural objects are made subjects ( /rict sci5ce4 #cf4 ,a ^w or two ( explanation may be add$ ab\t ! expression employ$ above1 '! proportion 9 ! long run4' ,! run mu/ be suppos$ to be v long inde$1 9 fact nev] to /op4 ,z we keep on tak+ m t]ms ( ! s]ies we %all f9d ! proportion /ill fluctuat+ a little1 b its fluctuations w gr[ less4 ,! proportion1 9 fact1 w gradually approa* t[>ds "s fix$ num]ical value1 :at ma!maticians t]m its limit4 ,?is fractional value is ! "o spok5 ( above4 ,9 ! cases 9 :i* d$uctive reason+ is possible1 ?is fraction may be obta9$ )\t direct appeal to /ati/ics1 f reason+ ab\t ! conditions "u :i* ! ev5ts occur1 z 0 expla9$ 9 ! f\r? *apt]4 ,"h becomes app>5t ! full importance ( ! di/9ction s frequ5tly insi/$ on1 betwe5 ! actual irregul> s]ies be=e u & ! sub/itut$ "o ( calculation1 & ! mean+ ( ! ass]tion 7,*4 ,i4 #ac71 t x 0 9 ! case ( ! latt] only t /rict sci5tific inf]5ces c\ld be made4 ,= h[ c we h a 'limit' 9 ! case ( ^? s]ies :i* ultimately exhibit irregul> fluctuations8 ,:5 we say1 = in/ance1 t x is an ev5 *ance t a giv5 p]son recov]s f ! *ol]a1 ! mean+ ( ?is ass]tion is t 9 ! long run "o half ( ! p]sons attack$ by t disease d recov]4 ,b if we exam9$ a suffici5tly ext5sive range ( /ati/ics1 we might f9d t ! mann]s & cu/oms ( society _h produc$ su* a *ange 9 ! type ( ! disease or its treatm5t1 t we 7 no ne>] approa*+ t[>ds a fix$ limit ?an we 7 at fir/4 ,! conception ( an ultimate limit 9 ! ratio betwe5 ! numb]s ( ! two classes 9 ! s]ies necess>ily involves an absolute fixity ( ! type4 ,:5 !re=e nature does n pres5t u ) ?is absolute fixity1 z %e seldom or nev] does except 9 games ( *ance 7& n demon/rably !re71 our only res\rce is to introduce su* a s]ies1 9 o!r words1 z has s (t5 be5 said1 to sub/itute a s]ies ( ! "r k9d4 #cg4 ,! above1 :i* may be consid]$ tol]ably complete z a def9ition1 might equally well h be5 giv5 9 ! la/ *apt]4 ,x has be5 def]r$ h[ev] to ! pres5t place1 9 ord] to connect ) x at once a proposition involv+ ! conceptions introduc$ 9 ?is *apt]2 viz4 ! /ate ( our own m9ds1 9 ref]5ce to ! am\nt ( belief we ent]ta9 9 contemplat+ any "o ( ! ev5ts ^: probability has j be5 describ$4 ,reasons 7 giv5 aga9/ ! op9ion t our belief admitt$ ( any exact apportionm5t l ! num]ical "o j m5tion$4 ,/ill1 x 0 %[n t a reasonable explanation c\ld be giv5 ( su* an expression z1 'my belief is #a_/aj? ( c]ta9ty'1 ?\gh x 0 an explanation :i* po9t$ unmi/akeably to a s]ies ( ev5ts1 & ceas$ to be intelligible1 or at any rate ju/ifiable1 :5 x 0 n view$ 9 su* a relation to a s]ies4 ,9 s f>1 !n1 z ?is explanation is adopt$1 we may say t our belief is 9 proportion to ! above fraction4 ,?is ref]r$ to ! purely intellectual "p ( belief :i* _c be conceiv$ to be sep>able1 ev5 9 ?\ght1 f ! ?+s ^u :i* x is ex]cis$4 ,) ?is intellectual "p !re are commonly associat$ v>i\s emotions4 ,^! we c to a c]ta9 ext5t sep>ate1 &1 :5 sep>at$1 c measure ) t degree ( accuracy :i* is possible 9 ! case ( o!r emotions4 ,!y are moreov] intelligible 9 ref]5ce to ! individual ev5ts4 ,!y w be f\nd to increase & dim9i% 9 accordance1 to "s ext5t1 ) ! fraction :i* repres5ts ! sc>city ( ! ev5t4 ,! emotion ( surprise does s ) "s degree ( accuracy4 ,! above inve/igation describes1 ?\gh 9 a v brief =m1 ! am\nt ( tru? :i* appe>s to me to be conta9$ 9 ! ass]tion frequ5tly made1 t ! fraction expressive ( ! probability repres5ts also ! fractional "p ( full c]ta9ty to :i* our belief ( ! individual ev5t am\nts4 ,any fur!r analysis ( ! matt] w\ld seem to belong to ,psy*ology r ?an to ,probability4 #a4 ,9 ! ord9>y signification ( ?is t]m4 ,z ,de ,morgan uses x he makes ,=mal ,logic include ,probability1 z "o ( its bran*es1 z indicat$ 9 8 title ,=mal ,logic1 or ! ,calculus ( ,inf]5ce1 necess>y & probable4 #b4 ,=mal ,logic4 ,preface1 page v4 #c4 ,an illu/ration ( ! po9ts "h insi/$ on has rec5tly #ahgf be5 giv5 9 a qu>t] :]e few w\ld h expect$ x2 ,i allude1 z _m read]s w readily inf]1 to ,j4 ,s4 ,mill's exce$+ly int]e/+ ,essays on ,!ism4 ,x is n )9 our prov9ce "h to criticise any ( _! conclusions1 b !y h express$ 9 a v significant way ! conviction ent]ta9$ by him t beliefs :i* are n ju/ifi$ by evid5ce1 & possibly may n be capable ( ju/ification 7^? = in/ance ( immortality & ! exi/5ce ( ! ,deity71 may nev]!less n only cont9ue to exi/ 9 cultivat$ m9ds1 b may also be pr(itably enc\rag$ !re1 at any rate 9 ! %ape ( hopes1 = c]ta9 suppos$ advantages att5dant on _! ret5tion1 irrespective ev5 ( _! tru?4 #d4 ,x is necess>y to take an example 9 :i* ! man is =c$ to act1 or we %\ld n be able to %ew t he has any belief on ! subject at all4 ,he may decl>e t he nei!r kn[s nor c>es any?+ ab\t ! matt]1 & t !re=e !re is no?+ ( ! nature ( belief to be extract$ out ( 8 m5tal condition4 ,he v likely w\ld take ?is gr\nd if we ask$ him1 z ,de ,morgan does1 ) a slightly diff]5t ref]5ce 7,=mal ,logic1 p4 #ahc71 :e!r he consid]s t !re are volcanoes on ! unse5 side ( ! moon l>g] ?an ^? on ! side turn$ t[>ds u2 or1 ) ,jevons 7,pr9ciples ( ,sci5ce1 ,ed4 ,,ii4 p4 #bab7 :e!r he consid]s t a ,platy?liptic ,coeffici5t is positive4 ,^! d n !re=e seem good in/ances to illu/rate ! position t we always ent]ta9 a c]ta9 degree ( belief on e "q :i* c be /at$1 & t utt] inability to give a reason 9 fav\r ( ei!r alt]native corresponds to half belief4 #e4 ,except inde$ on ! pr9ciples indicat$ fur!r on 9 #bd1 #be4 #f4 ,= a full] discussion ( ?is1 see ! ,*apt] on ,causation4 #g4 ,! be/ example ,i c recall ( ! di/9ction betwe5 judg+ f ! subjective & ! objective side1 9 su* cases z ^!1 occurr$ once 9 a railway tra94 ,i met a timid old lady :o 0 9 mu* fe> ( accid5ts4 ,i endeav\r$ to soo! h] on ! usual /ati/ical gr\nd ( ! extreme r>ity ( su* ev5ts4 ,%e li/5$ pati5tly1 & !n repli$1 ,yes1 ,sir1 t is all v well2 b ,i don't see h[ ! real dang] w be a bit ! less because ,i don't believe 9 x4 #h4 ,?is w\ld /ill hold ( empirical laws :i* may be capable ( be+ brok53 we n[ h v mu* %ift$ ! ^w1 to d5ote an ultimate law :i* x is suppos$ _c be brok54 ,,*apt] ,,vii4 ,,! ,,rules ,,( ,,inf]5ce ,,9 ,,probability4 #a4 ,9 ! previ\s *apt]1 an inve/igation 0 made into :at may be call$1 f ! analogy ( ,logic1 ,imm$iate ,inf]5ces4 ,giv5 t n9e m5 out ( t51 ( any assign$ age1 live to =ty1 :at c\ld be inf]r$ ab\t ! prospect ( life ( any p>ticul> man8 ,x 0 %[n t1 al?\gh ?is /ep 0 v f> f be+ s simple z x is frequ5tly suppos$ to be1 & z ! correspond+ /ep really is 9 ,logic1 !re 0 nev]!less an intelligible s5se 9 :i* we might speak ( ! am\nt ( our belief 9 any "o ( ^! 'proportional propositions1' z !y may succ9ctly be t]m$1 & ju/ify t am\nt4 ,we mu/ n[ proce$ to ! consid]ation ( inf]5ces m prop]ly s call$1 ,i mean inf]5ces ( ! k9d analog\s to ^? :i* =m ! /aple ( ord9>y logical treatises4 ,9 o!r words1 hav+ asc]ta9$ 9 :at mann] p>ticul> propositions c\ld be inf]r$ f ! g5]al propositions :i* includ$ !m1 we mu/ n[ exam9e 9 :at cases "o g5]al proposition c be inf]r$ f ano!r4 ,by a g5]al proposition "h is meant1 ( c\rse1 a g5]al proposition ( ! /ati/ical k9d contemplat$ 9 ,probability4 ,! rules ( su* inf]5ce be+ v few & simple1 _! consid]ation w n deta9 u long4 ,f ! data n[ 9 our possession we are able to d$uce ! rules ( probability giv5 9 ord9>y treatises ^u ! sci5ce4 ,x w\ld be m correct to say t we are able to d$uce "s ( ^! rules1 =1 z w appe> on exam9ation1 !y are ( two v diff]5t k9ds1 re/+ on entirely di/9ct gr\nds4 ,!y might be divid$ into ^? :i* are =mal1 & ^? :i* are m or less exp]im5tal4 ,?is may be o!rwise express$ by say+ t1 f ! k9d ( s]ies describ$ 9 ! fir/ *apt]s1 "s rules w foll[ necess>ily by ! m]e application ( ari?metic2 :il/ o!rs ei!r dep5d ^u peculi> hypo!ses1 or dem& = _! e/abli%m5t cont9ually r5ew$ appeals to exp]i5ce1 & ext5sion by ! aid ( ! v>i\s res\rces ( ,induction4 ,we %all conf9e our att5tion at pres5t pr9cipally to ! =m] class2 ! latt] c only be fully und]/ood :5 we h consid]$ ! connection ( our sci5ce ) ,induction4 #b4 ,! fundam5tal rules ( ,probability /rictly s call$1 t is ! =mal rules1 may be divid$ into two classes1--^? obta9$ by addition or subtraction on ! "o h&1 correspond+ to :at are g5]ally t]m$ ! connection ( exclusive or incompatible ev5ts2#a & ^? obta9$ by multiplication or division1 on ! o!r h&1 correspond+ to :at are commonly t]m$ dep5d5t ev5ts4 ,we w exam9e ^! 9 ord]4 7#a7 ,we c make inf]5ces by simple addition4 ,if1 = in/ance1 !re are two di/9ct prop]ties obs]vable 9 v>i\s memb]s ( ! s]ies1 :i* prop]ties d n occur 9 ! same individual2 x is pla9 t 9 any bat* ! numb] t are ( "o k9d or ! o!r w be equal to ! sum ( ^? ( ! two k9ds sep>ately4 ,?us #cf4d infants 9 #ajj live to ov] sixty1 #ce4d 9 #ajj die be=e !y are t52#b take a l>ge numb]1 say #aj1jjj1 !n !re w be ab\t #cfdj :o live to ov] sixty1 & ab\t #cedj :o d n rea* t52 h5ce ! total numb] :o d n die )9 ! assign$ limits w be ab\t #bhbj altoge!r4 ,( c\rse if ^! proportions 7 accurately assign$1 ! resultant sum w\ld be equally accurate3 b1 z ! read] kn[s1 9 ,probability ?is proportion is m]ely ! limit t[>ds :i* ! numb]s t5d 9 ! long run1 n ! precise result assign$ 9 any p>ticul> case4 ,h5ce we c only v5ture to say t ?is is ! limit t[>ds :i* we t5d z ! numb]s become great] & great]4 ,?is rule1 9 its g5]al algebraic =m1 w\ld be express$ 9 ! language ( ,probability z foll[s3--,if ! *ances ( two exclusive or incompatible ev5ts be respectively #a_/m & #a_/n ! *ance ( "o or o!r ( !m happ5+ w be #a_/m #a_/n or 7m n7_/mn4 ,simil>ly if !re 7 m ?an two ev5ts ( ! k9d 9 "q4 ,on ! pr9ciples adopt$ 9 ?is "w1 ! rule1 :5 ?us algebraically express$1 means precisely ! same ?+ z :5 x is express$ 9 ! /ati/ical =m4 ,x 0 %[n at ! conclusion ( ! la/ *apt] t to say1 = example1 t ! *ance ( a giv5 ev5t happ5+ 9 a c]ta9 way is #a_/f1 is only ano!r way ( say+ t 9 ! long run x does t5d to happ5 9 t way once 9 six times4 ,x is pla9 t a sort ( coroll>y to ?is rule might be obta9$1 9 precisely ! same way1 by subtraction in/ead ( addition4 ,/at$ g5]ally x w\ld be z foll[s3--,if ! *ance ( "o or o!r ( two incompatible ev5ts be #a_/m & ! *ance ( "o alone be #a_/n1 ! *ance ( ! rema9+ "o w be #a_/m - #a_/n or 7n - m7_/nm4 ,= example1 if ! *ance ( any "o dy+ 9 a ye> is #a_/aj1 & 8 *ance ( dy+ ( "s p>ticul> disease is #a_/ajj1 8 *ance ( dy+ ( any o!r disease is #i_/ajj4 ,! read] w rem>k "h t !re are two app>5tly diff]5t modes ( /at+ ?is rule1 accord+ z we speak ( '"o or o!r ( two or m ev5ts happ5+1' or ( '! same ev5t happ5+ 9 "o or o!r ( two or m ways4' ,b no confusion ne$ arise on ?is gr\nd2 ei!r way ( speak+ is legitimate1 ! diff]5ce be+ m]ely v]bal1 & dep5d+ 7z 0 %[n 9 ! fir/ *apt]1 #h7 ^u :e!r ! di/9ctions betwe5 ! 'ways' are or are n too deep & num]\s to entitle ! ev5t to be conv5tionally reg>d$ z ! same4 ,we may also "h po9t out ! ju/ification = ! common doctr9e t c]ta9ty is repres5t$ by unity1 j z any giv5 degree ( probability is repres5t$ by its appropriate fraction4 ,if ! /atem5t t an ev5t happ5s once 9 m times1 is equival5tly express$ by say+ t its *ance is #a_/m1 x foll[s t to say t x happ5s m times 9 m times1 or e "t )\t exception1 is equival5t to say+ t its *ance is m_/m or #a4 ,n[ an ev5t t happ5s e "t is ( c\rse "o ( ^: occurr5ce we are c]ta92 h5ce ! fraction :i* repres5ts ! '*ance' ( an ev5t :i* is c]ta9 becomes unity4 ,x w be equally obvi\s t giv5 t ! *ance t an ev5t w happ5 is #a_/m1 ! *ance t x w n happ5 is #a - #a_/m or 7m - #a7_/m4 #c4 7#b7 ,we c also make inf]5ces by multiplication or division4 ,suppose t two ev5ts in/ead ( be+ incompatible1 are connect$ toge!r 9 ! s5se t "o is cont+5t ^u ! occurr5ce ( ! o!r4 ,let u be told t a giv5 proportion ( ! memb]s ( ! s]ies possess a c]ta9 prop]ty1 & a giv5 proportion aga9 ( ^! possess ano!r prop]ty1 !n ! proportion ( ! :ole :i* possess bo? prop]ties w be f\nd by multiply+ toge!r ! two fractions :i* repres5t ! above two proportions4 ,( ! inhabitants ( ,london1 tw5ty-five 9 a ?\s&1 say1 w die 9 ! c\rse ( ! ye>2 we suppose x to be kn[n also t "o dea? 9 five is due to fev]2 we %\ld !n inf] t "o 9 #bjj ( ! inhabitants w die ( fev] 9 ! c\rse ( ! ye>4 ,x w\ld ( c\rse be equally simple1 by division1 to make a sort ( conv]se inf]5ce4 ,giv5 ! total mortality p] c5t4 ( ! population f fev]1 & ! proportion ( fev] cases to ! aggregate ( o!r cases ( mortality1 we might h inf]r$1 by divid+ "o fraction by ! o!r1 :at 0 ! total mortality p] c5t4 f all causes4 ,! rule z giv5 above is v>i\sly express$ 9 ! language ( ,probability4 ,p]haps ! simple/ & be/ /atem5t is t x gives u ! rule ( dep5d5t ev5ts4 ,t is2 if ! *ance ( "o ev5t is #a_/m1 & ! *ance t if x happ5s ano!r w also happ5 #a_/n1 !n ! *ance ( ! latt] is #a_/mn4 ,9 ?is case x is assum$ t ! latt] is s entirely dep5d5t ^u ! =m] t ?\gh x does n always happ5 ) x1 x c]ta9ly w n happ5 )\t x2 ! necessity ( ?is assumption h[ev] may be obviat$ by say+ t :at we are speak+ ( 9 ! latt] case is ! jo9t ev5t1 viz4 bo? toge!r if !y are simultane\s ev5ts1 or ! latt] 9 consequ5ce ( ! =m]1 if !y are successive4 #d4 ,! above inf]5ces are necess>y1 9 ! s5se 9 :i* ari?metical inf]5ces are necess>y1 & !y d n dem& = _! e/abli%m5t any arbitr>y hypo!sis4 ,we assume 9 !m no m ?an is w>rant$1 & 9 fact necessitat$ by ! data actually giv5 to u1 & make our inf]5ces f ^! data by ! help ( ari?metic4 ,9 ! simple examples giv5 above no?+ is requir$ beyond ari?metic 9 its mo/ famili> =m1 b x ne$ h>dly be add$ t 9 practice examples may (t5 pres5t !mselves :i* w require mu* pr(\nd] me?ods ?an ^!4 ,x may task all ! res\rces ( t high] & m ab/ract ari?metic kn[n z algebra to extract a solution4 ,b z ! necessity ( appeal to su* me?ods z ^! does n t\* ! pr9ciples ( ?is "p ( ! subject we ne$ n ent] ^u !m "h4 #e4 ,! =mula next to be discuss$ /&s ^u a some:at diff]5t foot+ f ! above 9 respect ( its cog5cy & fre$om f appeal to exp]i5ce1 or to hypo!sis4 ,9 ! two =m] in/ances we consid]$ cases 9 :i* ! data 7 suppos$ to be giv5 "u ! conditions t ! prop]ties :i* di/+ui%$ ! diff]5t k9ds ( ev5ts ^: frequ5cy 0 discuss$1 7 respectively kn[n to be disconnect$ & kn[n to be connect$4 ,let u n[ suppose t no su* conditions are giv5 to u4 ,"o man 9 t51 say1 has black hair1 & "o 9 twelve is %ort-sight$2 :at conclusions c\ld we !n draw z to ! *ance ( any giv5 man hav+ "o only ( ^! two attributes1 or nei!r1 or bo?8 ,x is cle>ly possible t ! prop]ties 9 "q might be inconsi/5t ) "o ano!r1 s z nev] to be f\nd comb9$ 9 ! same p]son2 or all ! %ort-sight$ might h black hair2 or ! prop]ties might be allott$#c 9 almo/ any o!r proportion :atev]4 ,if we are p]fectly ignorant ^u ^! po9ts1 x w\ld seem t no inf]5ces :atev] c\ld be drawn ab\t ! requir$ *ances4 ,inf]5ces h[ev] are drawn1 & practically1 9 mo/ cases1 q ju/ly drawn4 ,an escape f ! app>5t indet]m9at5ess ( ! problem1 z above describ$1 is f\nd by assum+ t1 n m]ely w "o-t5? ( ! :ole numb] ( m5 h black hair 7= ?is 0 giv5 z "o ( ! data71 b also t "o-t5? alike ( ^? :o are & :o are n %ort-sight$ h black hair4 ,let u take a bat* ( #abjj1 z a sample ( ! :ole4 ,n[1 f ! data :i* 7 orig9ally giv5 to u1 x w easily be se5 t 9 e su* bat* !re w be on ! av]age #abj :o h black hair1 & !re=e #ajhj :o h n4 ,& "h 9 /rict "r we ought to /op1 at lea/ until we h appeal$ aga9 to exp]i5ce2 b we d n /op "h4 ,f data :i* we assume1 we g on to inf] t ( ! #abj1 #aj 7i4e4 "o-twelf? ( #abj7 w be %ort-sight$1 & #aaj 7! rema9d]7 w n4 ,simil>ly we inf] t ( ! #ajhj1 #ij are %ort-sight$1 & #iij are n4 ,on ! :ole1 !n1 ! #abjj are ?us divid$3--black-hair$ %ort-sight$1 #aj2 %ort-sight$ )\t black hair1 #ij2 black-hair$ m5 :o are n %ort-sight$1 #aaj2 m5 :o are nei!r %ort-sight$ nor h black hair1 #iij4 ,?is rule1 express$ 9 its mo/ g5]al =m1 9 ! language ( ,probability1 w\ld be z foll[s3--,if ! *ances ( a ?+ be+ p & q are respectively #a_/m & #a_/n1 !n ! *ance ( its be+ bo? p & q is #a_/mn1 p & n q is 7n - #a7_/mn1 q & n p is 7m - #a7_/mn1 n p & n q is 77m - #a77n - #a77_/mn1 :]e p & q are indep5d5t4 ,! sum ( ^! *ances is obvi\sly unity2 z x ought to be1 s9ce "o or o!r ( ! f\r alt]natives mu/ necess>ily exi/4 #f4 ,i h purposely emphasiz$ ! di/9ction betwe5 ! inf]5ce 9 ?is case1 & t 9 ! two prec$+1 to an ext5t :i* to _m read]s may seem unw>rant$4 ,b x appe>s to me t :]e a sci5ce makes use1 z ,probability does1 ( two su* v di/9ct s\rces ( conviction z ! necess>y rules ( ari?metic & ! m]ely m or less cog5t ones ( ,induction1 x is h>dly possible to lay too mu* /ress ^u ! di/9ction4 ,few w be prep>$ to d5y t v arbitr>y assumptions h be5 made by _m writ]s on ! subject1 & none w d5y t 9 ! case ( :at are call$ 'inv]se probabilities' assumptions are sometimes made :i* are at lea/ decid$ly op5 to "q4 ,! be/ c\rse !re=e is to make a pause & /r+5t enquiry at ! po9t at :i* ! possibility ( su* error & d\btfulness fir/ exhibits itself4 ,^! rem>ks apply to "s ( ! be/ writ]s on ! subject2 9 ! case ( inf]ior writ]s1 or ^? :o appeal to ,probability )\t hav+ prop]ly ma/]$ its pr9ciples1 we may g fur!r4 ,x w\ld really n be ass]t+ too mu* to say t !y seem to ?9k !mselves ju/ifi$ 9 assum+ t :]e we "k no?+ ab\t ! di/ribution ( ! prop]ties allud$ to we mu/ assume !m to be di/ribut$ z above describ$1 & !re=e apportion our belief 9 ! same ratio4 ,?is is call$ 'assum+ ! ev5ts to be indep5d5t1' ! supposition be+ made t ! rule w c]ta9ly foll[ f ?is indep5d5ce1 & t we h a "r1 if we "k no?+ to ! contr>y1 to assume t ! ev5ts are indep5d5t4 ,! validity ( ?is la/ claim has already be5 discuss$ 9 ! fir/ *apt]2 x is only ano!r ( ! attempts to con/ruct priori ! s]ies :i* exp]i5ce w pres5t to u1 & "o = :i* no su* /rong def5ce c be made z = ! equality ( heads & tails 9 ! ?r[s ( a p5ny4 ,b ! mean+ to be assign$ to ! 'indep5d5ce' ( ! ev5ts 9 "q dem&s a mom5t's consid]ation4 ,! circum/ances ( ! problem are ^!4 ,!re are two diff]5t qualities1 by ! pres5ce & abs5ce respectively ( ea* ( :i*1 among/ ! individuals ( a s]ies1 two di/9ct pairs ( classes ( ^! individuals are produc$4 ,= ! e/abli%m5t ( ! rule "u discussion x 0 f\nd t "o supposition 0 bo? necess>y & suffici5t1 namely1 t ! division into classes caus$ by ea* ( ! above di/9ctions %\ld subdivide ea* ( ! classes creat$ by ! o!r di/9ction 9 ! same ratio 9 :i* x subdivides ! :ole4 ,if ! indep5d5ce be grant$ & s def9$ z to mean ?is1 ! rule ( c\rse w /&1 b1 )\t especial att5tion be+ drawn to ! po9t1 x does n seem t ! ^w w\ld naturally be s und]/ood4 #g4 ,! above1 !n1 be+ ! fundam5tal rules ( inf]5ce 9 probability1 ! "q at once arises1 ,:at is _! relation to ! great body ( =mul :i* are made use ( 9 treatises ^u ! sci5ce1 & 9 practical applications ( x8 ,! reply w\ld be t ^! =mul1 9 s f> z !y prop]ly belong to ! sci5ce1 are no?+ else 9 reality ?an applications ( ! above fundam5tal rules4 ,su* applications may assume any degree ( complexity1 = ow+ to ! difficulty ( p>ticul> examples1 9 ! =m 9 :i* !y actually pres5t !mselves1 rec\rse mu/ sometimes be made to ! pr(\nde/ !orems ( ma!matics4 ,/ill we ought n to reg>d ^! !orems z be+ any?+ else ?an conv5i5t & necess>y abbreviations ( ari?metical processes1 :i* 9 practice h become too cumb]some to be o!rwise p]=m$4 ,?is explanation w acc\nt = "s ( ! rules z !y are ord9>ily giv51 b by no means = all ( !m4 ,x w acc\nt = ^? :i* are demon/rable by ! c]ta9 laws ( ari?metic1 b n = ^? :i* 9 reality re/ only ^u inductive g5]alizations4 ,& x c h>dly be d\bt$ t _m rules ( ! latt] description h become associat$ ) ^? ( ! =m]1 s t 9 popul> e/imation !y h be5 bl5d$ into "o sy/em1 ( :i* all ! sep>ate rules are suppos$ to possess a simil> orig9 & equal c]ta9ty4 ,h9ts h already be5 frequ5tly giv5 ( ?is t5d5cy1 b ! subject is "o ( su* extreme importance t a sep>ate *apt] 7t on ,induction7 mu/ be devot$ to its consid]ation4 #h4 ,9 e/abli%+ ! validity ( ! above rules1 we h tak5 z ! basis ( our inve/igations1 9 accordance ) ! g5]al s*eme ( ?is "w1 ! /ati/ical frequ5cy ( ! ev5ts ref]r$ to2 b x 0 also %[n t ea* =mula1 :5 e/abli%$1 might ) equal propriety be express$ 9 ! m famili> =m ( a fraction repres5t+ ! '*ance' ( ! occurr5ce ( ! p>ticul> ev5t4 ,! "q may !re=e n[ be rais$1 ,c ^? writ]s :o 7z describ$ 9 ! la/ *apt]7 take z ! prim>y subject ( ! sci5ce n ! degree ( /ati/ical frequ5cy1 b ! quantity ( belief1 ) equal consi/5cy make ?is ! basis ( _! rules1 & s also reg>d ! fraction expressive ( ! *ance z a m]ely synonym\s expression8 ,de ,morgan ma9ta9s t :]eas 9 ord9>y logic we suppose ! premises to be absolutely true1 ! prov9ce ( ,probability is to /udy '! effect :i* p>tial belief ( ! premises produces ) respect to ! conclusion4' ,x w\ld appe> !re=e z if 9 /rictness we ought on ?is view to be able to det]m9e ?is consequ5t dim9ution at fir/ h&1 f introspection ( ! m9d1 t is ( ! conceptions & beliefs :i* x ent]ta9s2 in/ead ( mak+ any rec\rse to /ati/ics to tell u h[ mu* we ought to believe ! conclusion4 ,any read]s :o h concurr$ ) me 9 ! g5]al results ( ! la/ *apt]1 w naturally agree 9 ! conclusion t no?+ des]v+ ! "n ( logical sci5ce c be extract$ f any results ( appeal to our consci\sness z to ! quantity ( belief we ent]ta9 ( ?is or t proposition4 ,suppose1 = example1 t "o p]son 9 #ajj dies on ! sea passage out to ,india1 & t "o 9 #i dies dur+ a #e ye>s resid5ce !re4 ,x w\ld commonly be said t ! *ance t any "o1 :o is n[ go+ out1 has ( liv+ to />t homew>ds #e ye>s h5ce1 is #hh_/ajj2 = 8 *ance ( gett+ !re is #ii_/ajj2 & ( 8 surviv+1 if he gets !re1 #h_/i2 h5ce ! result or dep5d5t ev5t is got by multiply+ ^! fractions toge!r1 :i* gives #hh_/ajj4 ,"h ! real basis ( ! reason+ is /ati/ical1 & ! processes or results are m]ely translat$ aft]w>ds into fractions4 ,b c we say ! same :5 we look at ! belief side ( ! "q8 ,i q admit ! psy*ological fact t we h degrees ( belief1 m or less correspond+ to ! frequ5cy ( ! ev5ts to :i* !y ref]4 ,9 ! above example1 = in/ance1 we %\ld und\bt$ly admit on enquiry t our belief 9 ! man's return 0 affect$ by ea* ( ! risks 9 "q1 s t we _h less expectation ( x ?an if he 7 subject to ei!r risk sep>ately2 t is1 we %\ld 9 "s way comp\nd ! risks4 ,b :at ,i _c recognise is t we %\ld be able to p]=m ! process ) any approa* to accuracy )\t appeal to ! /ati/ics1 or t1 ev5 suppos+ we c\ld d s1 we %\ld h any gu>antee ( ! correctness ( ! result )\t simil> appeal4 ,x appe>s to me 9 fact t b little mean+1 & c]ta9ly no security1 c be atta9$ by s reg>d+ ! process ( inf]5ce4 ,! probabilities express$ z degrees ( belief1 j z ^? :i* are express$ z fractions1 mu/1 :5 we are put ^u our ju/ification1 fir/ be translat$ into _! correspond+ facts ( /ati/ical frequ5cy ( occurr5ce ( ! ev5ts1 & !n ! inf]5ces mu/ be drawn & ju/ifi$ !re4 ,?is "p ( ! op]ation1 z we h already %[n1 is mo/ly c>ri$ on by ! ord9>y rules ( ari?metic4 ,:5 we h obta9$ our conclusion we may1 if we please1 translate x back aga9 into ! subjective =m1 j z we c & d = conv5i5ce into ! fractional1 b ,i d n see h[ ! process ( inf]5ce c be conceiv$ z tak+ place 9 t =m1 & /ill less h[ any pro( ( x c ?us be giv54 ,if !re=e ! process ( inf]5ce be s express$ x mu/ be reg>d$ z a symbolical process1 symbolical ( su* an inf]5ce ab\t ?+s z has be5 describ$ above1 & x !re=e seems to me m advisable to /ate & exp\nd x 9 ?is latt] =m4 ,on ,inv]se ,probability & ! ,rules requir$ = x4 #i4 ,x has be5 already /at$ t ! only fundam5tal rules ( inf]5ce 9 ,probability are ! two describ$ 9 #b1 #c1 b !re are ( c\rse abundance ( d]ivative rules1 ! nature & use ( :i* are be/ obta9$ f ! /udy ( any manual ^u ! subject4 ,"o class ( ^! d]ivative rules1 h[ev]1 is suffici5tly di/9ct 9 respect ( ! que/ions to :i* x may give rise1 to des]ve special exam9ation4 ,x involves ! di/9ction commonly recognis$ z t betwe5 ,direct & ,inv]se ,probability4 ,x is ?us introduc$ by ,de ,morgan3-- ,9 ! prec$+ *apt] we h calculat$ ! *ances ( an ev5t1 kn[+ ! circum/ances "u :i* x is to happ5 or fail4 ,we are n[ to place ourselves 9 an inv]t$ position3 we "k ! ev5t1 & ask :at is ! probability :i* results f ! ev5t 9 fav\r ( any set ( circum/ances "u :i* ! same might h happ5$4#d ,! di/9ction might !re=e be summ>ily describ$ z t betwe5 f9d+ an effect :5 we are giv5 ! causes1 & f9d+ a cause :5 we are giv5 effects4 ,on ! pr9ciples ( ! sci5ce involv$ 9 ! def9ition :i* 0 discuss$ & adopt$ 9 ! e>li] *apt]s ( ?is "w1 ! read] w easily inf] t no su* di/9ction z ?is c be reg>d$ z fundam5tal4 ,"o common feature 0 trac$ 9 all ! objects :i* 7 to be ref]r$ to ,probability1 & f ?is feature ! possible rules ( inf]5ce c be imm$iately d]iv$4 ,all o!r di/9ctions are m]ely ^? ( arrangem5t or managem5t4 ,b al?\gh ! di/9ction is n by any means fundam5tal1 x is nev]!less true t ! practical treatm5t ( su* problems z ^? pr9cipally occurr+ 9 ,inv]se ,probability1 does correspond to a v s]i\s s\rce ( ambiguity & p]plexity4 ,! arbitr>y assumptions :i* appe> 9 ,direct ,probability are n by any means s]i\s1 b ^? :i* invade u 9 a l>ge proportion ( ! problems (f]$ by ,inv]se ,probability are bo? s]i\s & inevitable4 #aj4 ,?is w be be/ se5 by ! exam9ation ( special examples2 z any1 h[ev] simple1 w s]ve our purpose1 let u take ! two foll[+3-- 7#a7 ,a ball is drawn f a bag conta9+ n9e black balls & "o :ite3 :at is ! *ance ( its be+ ! :ite ball8 7#b7 ,a ball is drawn f a bag conta9+ t5 balls1 & is f\nd to be :ite2 :at is ! *ance ( !re hav+ be5 b t "o :ite ball 9 ! bag8 ,! class ( :i* ! fir/ example is a simple in/ance has be5 already abundantly discuss$4 ,! int]pretation ( x is z foll[s3 ,if balls be cont9ually drawn & replac$1 ! proportion ( :ite ones to ! :ole numb] drawn w t5d t[>ds ! fraction #a_/aj4 ,! contemplat$ action is a s+le "o1 b we view x z "o ( ! above s]ies2 at lea/ our op9ion is =m$ ^u t assumption4 ,we conclude t we are go+ to take "o ( a s]ies ( ev5ts :i* may appe> individually =tuit\s1 b 9 :i*1 9 ! long run1 ^? ( a giv5 k9d are "o-t5? ( ! :ole2 ?is k9d 7:ite7 is !n s+l$ out by anticipation4 ,by /at+ t its *ance is #a_/aj1 we m]ely mean to ass]t ?is physical fact1 toge!r ) su* o!r m5tal facts1 emotions1 inf]5ces1 c41 z may be prop]ly associat$ ) x4 #aa4 ,h we to int]pret ! second example 9 a diff]5t way8 ,"h also we h a s+le in/ance1 b ! nature ( ! "q w\ld seem to decide t ! only s]ies to :i* x c prop]ly be ref]r$ is ! foll[+3--,balls are cont9ually drawn f diff]5t bags ea* conta9+ t51 & are always f\nd to be :ite2 :at is ultimately ! proportion ( cases 9 :i* !y w be f\nd to h be5 tak5 f bags ) only "o :ite ball 9 !m8 ,n[ x may be readily %[n#e t "t has no?+ to d ) ! "q2 omitt+ !re=e ! consid]ation ( ?is elem5t1 we h = ! two s]ies f :i* our op9ions 9 ^! two examples respectively are to be =m$3--7#a7 balls ( diff]5t col\rs pres5t$ to u 9 a giv5 ultimate ratio2 7#b7 bags ) diff]5t cont5ts simil>ly pres5t$4 ,f ^! data respectively we h to assign _! due weight to our anticipations ( 7#a7 a :ite ball2 7#b7 a bag conta9+ b "o :ite ball4 ,s /at$ ! problems w\ld appe> to be =mally id5tical4 ,:51 h[ev]1 we beg9 ! practical "w ( solv+ !m we p]ceive a mo/ important di/9ction4 ,9 ! fir/ example !re is n mu* t is arbitr>y2 balls w\ld "u su* circum/ance really come out m or less accurately 9 ! proportion expect$4 ,moreov]1 9 case x %\ld be object$ t x is difficult to prove t !y w d s1 x does n seem an unfair dem& to say t ! balls are to be 'well-mix$' or 'fairly di/ribut$1' or to introduce any ( ! o!r conditions by :i*1 "u ! semblance ( judg+ priori1 we take c>e to secure our prospect ( a s]ies ( ! desir$ k9d4 ,b we _c say ! same 9 ! case ( ! second example4 #ab4 ,! l9e ( pro( by :i* x is g5]ally attempt$ to solve ! second example is ( ?is k9d2--,x is %[n t !re be+ "o :ite ball = c]ta9 9 ! bag1 ! only possible antec$5ts are ( t5 k9ds1 viz4 bags1 ea* ( :i* conta9s t5 balls1 b 9 :i* ! :ite balls range respectively f "o to t5 9 numb]4 ,?is ( c\rse imposes limits ^u ! k9d ( t]ms to be f\nd 9 our s]ies4 ,b we want m ?an su* limitations1 we mu/ "k ! proportions 9 :i* ^! t]ms are ultimately f\nd to arrange !mselves 9 ! s]ies4 ,n[ ?is requires an exp]i5ce ab\t bags :i* may n1 & inde$ 9 a l>ge proportion ( simil> cases1 _c1 be giv5 to u4 ,if !re=e we are to solve ! "q at all we mu/ make an assumption2 let u make ! foll[+2--t ea* ( ! bags describ$ above occurs equally (t51--& see :at foll[s4 ,! bags be+ drawn f equally (t51 x does n foll[ t !y w ea* yield equal numb]s ( :ite balls4 ,on ! contr>y !y w1 z 9 ! la/ example1 yield !m 9 direct proportion to ! numb] ( su* balls :i* !y conta94 ,! bag ) "o :ite & n9e black w yield a :ite ball once 9 t5 times2 t ) two :ite1 twice2 & s on4 ,! result ( ?is1 x w be easily se51 is t 9 #ajj draw+s !re w be obta9$ on ! av]age #ee :ite balls & #de black4 ,n[ ) ^? draw+s t d n yield :ite balls we h1 by ! "q1 no?+ to d1 = t "q po/ulat$ ! draw+ ( a :ite ball z an accompli%$ fact4 ,! s]ies we want is !re=e compos$ ( ^? :i* d yield :ite4 ,n[ :at is ! additional attribute :i* is f\nd 9 "s memb]s1 & 9 "s memb]s only1 ( ?is s]ies1 & :i* we m5tally anticipate8 ,cle>ly x is ! attribute ( hav+ be5 drawn f a bag :i* only conta9$ "o ( ^! :ite balls4 ,( ^! !re is1 out ( ! #ee draw+s1 b "o4 ,accord+ly ! requir$ *ance is #a_/ee4 ,t is to say1 ! :ite ball w h be5 drawn f ! bag conta9+ only t "o :ite1 once 9 #ee times4 #ac4 ,n[1 ) ! exception ( ! passage 9 italics1 ! process "h is precisely ! same z 9 ! o!r example2 x is some:at long] only because we are n able to appeal imm$iately to exp]i5ce1 b are =c$ to try to d$uce :at ! result w be1 ?\gh ! validity ( ?is d$uction itself re/s1 ( c\rse1 ultimately ^u exp]i5ce4 ,b ! above passage is a v important "o4 ,x is sc>cely necess>y to po9t out h[ arbitr>y x is4 ,= is ! supposition1 t ! diff]5t specifi$ k9ds ( bags are equally likely1 ! mo/ reasonable supposition "u ! circum/ances 9 "q8 ,"o man may ?9k x is1 ano!r may take a contr>y view4 ,9 fact 9 an excell5t manual#f ^u ! subject a totally diff]5t supposition is made1 at any rate 9 "o example2 x is tak5 = grant$ 9 t in/ance1 n t e possible numb] ( black & :ite balls respectively is equally likely1 b t e possible way ( gett+ ea* numb] is equally likely1 :5ce x foll[s t bags ) an int]m$iate numb] ( black & :ite balls are f> m likely ?an ^? ) an extreme numb] ( ei!r4 ,on ?is supposition five black & five :ite be+ obta9able 9 #beb ways aga9/ ! t5 ways ( obta9+ "o :ite & n9e black1 x foll[s t ! *ance t we h drawn f a bag ( ! latt] description is mu* less ?an on ! hypo!sis fir/ made4 ,! *ance1 9 fact1 becomes n[ #a_/eab in/ead ( #a_/ee4 ,9 ! "o case ea* di/9ct result is consid]$ equally likely1 9 ! o!r e di/9ct way ( gett+ ea* result4 #ad4 ,unc]ta9ties ( ?is k9d are peculi>ly likely to arise 9 ^! inv]se probabilities1 because :5 we are m]ely giv5 an effect & told to look out = ! *ance ( "s assign$ cause1 we are (t5 giv5 no clue z to ! relative preval5ce ( ^! causes1 b are left to det]m9e !m on g5]al pr9ciples4 ,give u ei!r _! actual preval5ce 9 /ati/ics1 or ! conditions by :i* su* preval5ce is br\ght ab\t1 & we "k :at to d2 b )\t ! help ( su* data we are r$uc$ to guess+4 ,9 ! above example1 if we _h be5 told h[ ! bag _h be5 orig9ally fill$1 t is by :at process1 or "u :at circum/ances1 we %\ld h kn[n :at to d4 ,if x _h be5 fill$ at r&om f a box conta9+ equal numb]s ( black & :ite balls1 ! supposition 9 ,mr ,:itwor?'s example is ! mo/ reasonable2 b 9 ! abs5ce ( any su* in=mation z ?is we are entirely 9 ! d>k1 & ! supposition made 9 #ab is nei!r m nor less tru/wor?y & reasonable ?an _m o!rs1 ?\gh x d\btless possesses ! m]it ( sup]ior simplicity4#g ,if ! read] w recur to ,*4 ,v4 #d1 #e1 he w f9d ?is p>ticul> difficulty fully expla9$4 ,ev]ybody practically admits t a c]ta9 *>act]i/ic arrangem5t or di/ribution has to be introduc$ at "s prior /age2 & t1 z soon z ?is /age has be5 select$1 !re are no fur!r !oretic difficulties to be enc\nt]$4 ,b :5 we come to decide1 9 examples ( ! class 9 "q1 at :at /age x is mo/ reasonable to make our po/ulate1 we are (t5 left )\t any v def9ite or rational guidance4 #ae4 ,:51 h[ev]1 we take :at may be call$1 by comp>ison ) ! above purely artificial examples1 in/ances pres5t$ by nature1 mu* ( ?is unc]ta9ty w disappe>1 & !n all real di/9ction betwe5 direct & inv]se probability w (t5 vani%4 ,9 su* cases ! causes are mo/ly det]m9$ by tol]ably def9ite rules1 in/ead ( be+ a m]e cl\d-l& ( caprici\s guesses4 ,we may ei!r f9d _! relative frequ5cy ( occurr5ce by ref]5ce to tables1 or may be able to inf] x by exam9ation ( ! circum/ances "u :i* !y are br\ght ab\t4 ,almo/ any simple example w\ld !n s]ve to illu/rate ! fact t "u su* circum/ances ! di/9ction betwe5 direct & inv]se probability disappe>s altoge!r1 or m]ely resolves itself into "o ( "t1 :i*1 z w be m fully %[n 9 a future *apt]1 is entirely =eign to our subject4 ,x is n ( c\rse int5d$ to imply t difficulties simil> to ^? m5tion$ above d n occasionally invade u "h also4 ,z already m5tion$1 !y are1 if n inh]5t 9 ! subject1 at any rate almo/ unavoidable 9 comp>ison ) ! simpl] & m direct proc$ure ( det]m9+ :at is likely to foll[ f assign$ conditions4 ,:at is meant is t s long z we conf9e ourselves )9 ! comp>atively regul> & uni=m field ( natural sequ5ces & co-exi/5ces1 /ati/ics ( causes may be j z readily available z ^? ( effects4 ,!re w n be mu* m t is arbitr>y 9 ! "o ?an 9 ! o!r4 ,b ( c\rse ?is security is lo/ :51 z w be almo/ imm$iately notic$1 :at may be call$ metaphysical r ?an natural causes are introduc$ into ! enquiry4 ,= in/ance1 x is kn[n t 9 ,london ab\t #bj p die p] ?\s& ea* ye>4 ,suppose x also kn[n t ( e #ajj dea?s !re are ab\t #d attributable to bron*itis4 ,! odds !re=e aga9/ any unkn[n p]son dy+ ( bron*itis 9 a giv5 ye> are #abdi to #a4 ,exactly ! same /ati/ics are available to solve ! inv]se problem3--,a man is dead1 :at is ! *ance t he di$ ( bron*itis8 ,"h1 s9ce ! man's dea? is tak5 = grant$1 we d n require to "k ! g5]al av]age mortality4 ,all t we want is ! proportional mortality f ! disease 9 "q z giv5 above4 ,if ,probability dealt only ) inf]5ces f\nd$ 9 ?is way ^u actual /ati/ics1 & ^! tol]ably ext5sive1 x is sc>cely likely t any di/9ction su* z ?is betwe5 direct & inv]se problems w\ld ev] h be5 drawn4 #af4 ,consid]$ !re=e z a contribution to ! !ory ( ! subject1 ! di/9ction betwe5 ,direct & ,inv]se ,probability mu/ be ab&on$4 ,:5 ! appropriate /ati/ics are at h& ! two classes ( problems become id5tical 9 me?od ( treatm5t1 & :5 !y are n we h no m "r to extract a solution 9 "o case ?an 9 ! o!r4 ,! discussion h[ev] may s]ve to direct r5ew$ att5tion to ano!r & f> m important di/9ction4 ,x w rem9d u t !re is "o class ( examples to :i* ! calculus ( ,probability is rightfully appli$1 because /ati/ical data are all we h to judge by2 :]eas !re are o!r examples 9 reg>d to :i*1 if we w insi/ ^u mak+ use ( ^! rules1 we may ei!r be delib]ately ab&on+ ! opportunity ( gett+ f> m tru/wor?y in=mation by o!r means1 or we may be obta9+ solutions ab\t matt]s on :i* ! human intellect has no "r to any def9ite quantitative op9ion4 #ag4 ,! ne>e/ approa* to any practical ju/ification ( su* judgm5ts t ,i rememb] to h se5 is af=d$ by cases ( :i* ! foll[+ example is a specim53-- ,( #aj cases treat$ by ,li/]'s me?od1 #g did well & #c suff]$ f blood-poison+3 ( #ad treat$ ) ord9>y dress+s1 #i did well & #e _h blood-poison+2 :at are ! odds t ! success ( ,li/]'s me?od 0 due to *ance84#h ,or1 to put x into o!r words1 a %ort exp]i5ce has %[n an actual sup]iority 9 "o me?od ov] ! o!r3 :at are ! *ances t an indef9itely long exp]i5ce1 "u simil> conditions1 w confirm ?is sup]iority8 ,! propos] treat$ ?is z a 'bag & balls' problem1 analog\s to ! foll[+3 #aj balls f "o bag gave #g :ite & #c black1 #ad f ano!r bag gave #i :ite & #e black3 :at is ! *ance t ! actual ratio ( :ite to black balls 0 great] 9 ! =m] ?an 9 ! latt]8--?is actual ratio be+ ( c\rse consid]$ a true indication ( :at w\ld be ! ultimate proportions ( :ite & black draw+s4 ,?is seems to me to be ! only reasonable way ( treat+ ! problem1 if x is to be consid]$ capable ( num]ical solution at all4 ,( c\rse ! inevitable assumption has to be made "h ab\t ! equal preval5ce ( ! diff]5t possible k9ds ( bag1--or1 z ! support]s ( ! ju/ice ( ! calculation w\ld put x1 ( ! obligation to assume ! equal priori likelihood ( ea* k9d1--b ,i ?9k t 9 ?is p>ticul> example ! arbitr>9ess ( ! assumption is less ?an usual4 ,?is is because ! problem discusses simply a balance betwe5 two extremely simil> cases1 & !re is a c]ta9 set-(f aga9/ ea* o!r ( ! objectionable assumptions on ea* side4 ,_h "o set ( exp]im5ts only be5 propos$1 & _h we be5 ask$ to evaluate ! probability ( cont9u$ repetition ( !m confirm+ _! v]dict1 ,i %\ld h felt all ! scruples ,i h already m5tion$4 ,b "h we h got two sets ( exp]im5ts c>ri$ on "u almo/ exactly simil> circum/ances1 & !re is !re=e less arbitr>9ess 9 assum+ t _! unkn[n conditions are tol]ably equally preval5t4 #ah4 ,examples ( ! description commonly introduc$ seem objectionable en\gh1 b if we wi% to realize to its full ext5t ! vagu5ess ( "s ( ! problems submitt$ to ?is ,inv]se ,probability1 we h n f> to seek4 ,9 natural z 9 artificial examples1 :]e /ati/ics are unatta9able ! enquiry becomes utt]ly hopeless1 & all attempts at lay+ d[n rules = calculation mu/ be ab&on$4 ,take1 = in/ance1 ! "q :i* has giv5 rise to "s discussion1#i :e!r su* & su* gr\ps ( />s are or are n to be reg>d$ z ! results ( an accid5tal di/ribution2 or ! /ill wid] & vagu] "q1 :e!r su* & su* ?+s1 or say ! _w itself1 h be5 produc$ by *ance8 ,9 cases ( ?is k9d ! insup]able difficulty is 9 det]m9+ :at s5se exactly is to be atta*$ to ! words 'accid5tal' & 'r&om' :i* ent] into ! discussion4 ,"s acc\nt 0 giv51 9 ! f\r? *apt]1 ( _! sci5tific & conv5tional mean+ 9 ,probability4 ,!re seem to be ! same objections to g5]aliz+ !m out ( su* relation1 z !re is 9 metaphysics to talk+ ( ! ,inf9ite or ! ,absolute4 ,inf9ite magnitude1 or inf9ite p[]1 "o c to "s ext5t compreh5d1 or at lea/ "o may und]/& :at is be+ talk$ ab\t1 b '! inf9ite' seems to me a t]m devoid ( mean+4 ,s ( any?+ suppos$ to h be5 produc$ at r&om3 tell u ! nature ( ! ag5cy1 ! limits ( its r&omness & s on1 & we c v5ture ^u ! problem1 b )\t su* data we "k n :at to d4 ,! fur!r consid]ation ( su* a problem might1 ,i ?9k1 )\t arrogance be relegat$ to ! ,*apt] on ,fallacies4 ,accord+ly any fur!r rem>ks :i* ,i h to make ^u ! subject w be f\nd !re1 & at ! conclusion ( ! *apt] on ,causation & ,design4 #a4 ,x might be m accurate to speak ( 'incompatible hypo!ses ) respect to any individual case'1 or 'mutually exclusive classes ( ev5ts'4 #b4 ,! examples1 ( ?is k9d1 ref]r+ to human mortality are tak5 f ! ,c>lisle tables4 ,^! diff] consid]ably1 z is well kn[n1 f o!r tables1 b we h ! high au?ority ( ,de ,morgan = reg>d+ !m z ! be/ repres5tative ( ! av]age mortality ( ! ,engli% middle classes at ! pres5t day4 #c4 ,i say1 almo/ any proportion1 because1 z may easily be se51 ari?metic imposes c]ta9 re/rictions ^u ! assumptions t c be made4 ,we c\ld n1 = in/ance1 suppose t all ! black-hair$ m5 are %ort-sight$1 = 9 any giv5 bat* ( m5 ! =m] are m num]\s4 ,b ! range ( ^! re/rictions is limit$1 & _! exi/5ce is n ( importance 9 ! above discussion4 #d4 ,essay on ,probabilities1 p4 #ec4 ,i h be5 rem9d$ t 9 8 article on ,probability 9 ! ,encyclopdia ,metropolitana he has /at$ t su* rules involve no new pr9ciple4 #e4 ,?is po9t w be fully discuss$ 9 a future *apt]1 aft] ! g5]al /&-po9t ( an objective sy/em ( logic has be5 expla9$ & illu/rat$4 #f4 ,:itwor?'s ,*oice & ,*ance1 ,ed4 ,,ii41 p4 #abc4 ,see also ,boole's ,laws ( ,?\ght1 p4 #cgj4 #g4 ,op9ions diff] ab\t ! def5ce ( su* suppositions1 z !y d ab\t ! nature ( !m4 ,"s writ]s1 admitt+ ! above assumption to be d\btful1 call x ! mo/ imp>tial hypo!sis4 ,o!rs reg>d x z a sort ( mean hypo!sis4 #h4 ,educational ,times2 ,repr9t1 ,vol4 xxxvii4 p4 #dj4 ,! "q 0 propos$ by ,dr4 ,macali/] & gave rise to consid]able controv]sy4 ,z usual ) problems ( ?is inv]se k9d h>dly any two ( ! writ]s 7 9 agreem5t z to ! assumptions to be made1 or !re=e z to ! num]ical e/imate ( ! odds4 #i4 ,see ,todhunt]'s ,hi/ory1 pp4 #ccc1 #d4 ,!re is an int]e/+ discussion ^u ?is "q by ! late ,j4 ,d4 ,=bes 9 a pap] 9 ! ,philosophical ,magaz9e = ,dec4 #ahej4 ,x 0 repli$ to 9 a subsequ5t numb] by ,pr(4 ,donk94 ,,*apt] ,,viii4 ,,! ,,rule ,,( ,,succession4#a #a4 ,a ^w ( apology may be (f]$ "h = ! introduction ( a new "n4 ,! only o!r alt]native w\ld h be5 to entitle ! rule "o ( ,induction4 ,b su* a title ,i _c admit1 = reasons :i* w be almo/ imm$iately expla9$4 #a4 ,9 ! la/ *apt] we discuss$ at "s l5g? ! nature ( ! k9ds ( inf]5ce 9 ,probability :i* correspond to ^? t]m$1 9 ,logic1 imm$iate & m$iate inf]5ces4 ,we asc]ta9$ :at 0 ! mean+ ( say+1 = example1 t ! *ance ( any giv5 man ,a4 ,b4 dy+ 9 a ye> is #a_/c1 :5 conclud$ f ! g5]al proposition t "o man out ( ?ree 9 8 circum/ances dies4 ,we also discuss$ ! nature & evid5ce ( rules ( a m completely inf]5tial "*4 ,b to /op at ?is po9t w\ld be to take a v imp]fect view ( ! subject4 ,if ,probability is a sci5ce ( real inf]5ce ab\t ?+s1 x mu/ surely lead up to some?+ m ?an su* m]ely =mal conclusions2 we mu/ be able1 if n by means ( x1 at any rate by "s means1 to /ep beyond ! limits ( :at has be5 actually obs]v$1 & to draw conclusions ab\t :at is z yet unobs]v$4 ,?is leads at once to ! "q1 ,:at is ! connection ( ,probability ) ,induction8 ,?is is a "q into :i* x w be necess>y to ent] n[ ) "s m9ut5ess4 ,t !re is a close connection betwe5 ,probability & ,induction1 mu/ h be5 obs]v$ by almo/ e "o :o has treat$ ( ei!r subject2 ,i h n h[ev] se5 any acc\nt ( ?is connection t seem$ to me to be satisfactory4 ,an explicit description ( x %\ld r be s\ght 9 treatises ^u ! n>r[] subject1 ,probability2 b x is precisely "h t ! mo/ confusion is to be f\nd4 ,! prov9ce ( ,probability be+ some:at n>r[1 incursions h be5 con/antly made f x into ! adjac5t t]ritory ( ,induction4 ,9 ?is way1 among/ ! ari?metical rules discuss$ 9 ! la/ *apt]1 o!rs h be5 frequ5tly introduc$ :i* ought n 9 /rictness to be class$ ) !m1 z !y re/ on an entirely diff]5t basis4 #b4 ,! orig9 ( su* confusion is easy ( explanation2 x arises1 d\btless1 f ! habit ( lay+ undue /ress ^u ! subjective side ( ,probability1 ^u t :i* treats ( ! quantity ( our belief ^u diff]5t subjects & ! v>iations ( :i* t quantity is susceptible4 ,x has be5 already urg$ t ?is v>iation ( belief is at mo/ b a con/ant accompanim5t ( :at is really ess5tial to ,probability1 & is moreov] common to o!r subjects z well4 ,by def9+ ! sci5ce !re=e f ?is side ^! o!r subjects w\ld claim admittance into x2 "s ( ^!1 z ,induction1 h be5 accept$1 b o!rs h be5 some:at arbitr>ily reject$4 ,our belief 9 a wid] proposition ga9$ by ,induction is1 prior to v]ification1 n s /rong z t ( ! n>r[] g5]alization f :i* x is inf]r$4 ,?is be+ obs]v$1 a s-call$ rule ( probability has be5 giv5 by :i* x is suppos$ t ?is dim9ution ( ass5t c\ld 9 _m in/ances be calculat$4 ,b "t also works *anges 9 our conviction2 our belief 9 ! happ5+ ( almo/ e ev5t1 if we recur to x long aft]w>ds1 :5 ! evid5ce has fad$ f ! m9d1 is less /rong ?an x 0 at ! "t4 ,:y are n rules ( oblivion ins]t$ 9 treatises ^u ,probability8 ,if a man is told h[ firmly he ought to expect ! tide to rise aga91 because x has already ris5 t5 times1 might he n also ask = a rule :i* %\ld tell him h[ firm %\ld be 8 belief ( an ev5t :i* re/s ^u a t5 ye>s' recollection8#a ,! infractions ( a rule ( ?is latt] k9d c\ld sc>cely be m num]\s & ext5sive1 z we %all see pres5tly1 ?an ^? ( ! =m] confess$ly are4 ,! fact is t ! ag5cies1 by :i* ! /r5g? ( our conviction is modifi$1 are s indef9itely num]\s t !y _c all be assembl$ into "o sci5ce2 = purposes ( def9ition !re=e ! quantity ( belief _h bett] be omitt$ f consid]ation1 or at any rate reg>d$ z a m]e app5dage1 & ! sci5ce1 def9$ f ! o!r or /ati/ical side ( ! subject1 9 :i*1 z has be5 %[n1 a tol]ably cle> b\nd>y-l9e c be trac$4 #c4 ,induction1 h[ev]1 f its importance does m]it a sep>ate discussion2 a s+le example w %[ its be>+ ^u ?is "p ( our subject4 ,we are consid]+ ! prospect ( a giv5 man1 ,a4 ,b4 liv+ ano!r ye>1 & we f9d t n9e out ( t5 m5 ( 8 age d survive4 ,9 =m+ an op9ion ab\t 8 surviv+1 h[ev]1 we %all f9d t !re are 9 reality two v di/9ct causes :i* aid 9 det]m9+ ! /r5g? ( our conviction2 di/9ct1 b 9 practice s intimately connect$ t we are v apt to ov]look "o1 & attribute ! effect entirely to ! o!r4 7,i47 ,!re is t :i* /rictly belongs to ,probability2 t :i* 7z 0 expla9$ 9 ,*ap ,,vi47 measures our belief ( ! individual case z d$uc$ f ! g5]al proposition4 ,grant$ t n9e m5 out ( t5 ( ! k9d to :i* ,a4 ,b4 belongs d live ano!r ye>1 x obvi\sly does n foll[ at all necess>ily t he w4 ,we describe ?is /ate ( ?+s by say+1 t our belief ( 8 surviv+ is dim9i%$ f c]ta9ty 9 ! ratio ( #aj to #i1 or1 9 o!r words1 is measur$ by ! fraction #i_/aj4 7,,ii47 ,b are we c]ta9 t n9e m5 out ( t5 l him w live ano!r ye>8 we "k t !y h s surviv$ 9 "t pa/1 b w !y cont9ue to d s8 ,s9ce ,a4 ,b4 is /ill alive x is pla9 t ?is proposition is to a c]ta9 ext5t assum$1 or r obta9$ by ,induction4 ,we _c h[ev] be z c]ta9 ( ! inductive inf]5ce z we are ( ! data f :i* x 0 inf]r$4 ,"h1 !re=e1 is a second cause :i* t5ds to dim9i% our belief2 9 practice ^! two causes always accompany ea* o!r1 b 9 ?\ght !y c be sep>at$4 ,! two di/9ct causes describ$ above are v liable to be confus$ toge!r1 & ! class ( cases f :i* examples are necess>ily = ! mo/ "p drawn increases ?is liability4 ,! /ep f ! /atem5t 'all m5 h di$ 9 a c]ta9 proportion' to ! inf]5ce '!y w cont9ue to die 9 t proportion' is s slight a /ep t x is unnotic$1 & ! dim9ution ( conviction t %\ld accompany x is unsuspect$4 ,9 :at are call$ priori examples ! /ep is /ill slight]4 ,we feel s c]ta9 ab\t ! p]man5ce ( ! laws ( me*anics1 t few p w\ld ?9k ( reg>d+ x z an inf]5ce :5 !y believe t a die w 9 ! long run turn up all its faces equally (t51 because o!r dice h done s 9 "t pa/4 #d4 ,x has be5 already po9t$ out 79 ,*apt] ,,vi47 t1 s f> z conc]ns t def9ition ( ,probability :i* reg>ds x z ! sci5ce :i* discusses ! degree & modifications ( our belief1 ! "q at issue seems to be simply ?is3--,are ! causes allud$ to above 9 7,,ii47 capable ( be+ r$uc$ to "o simple coh]5t s*eme1 s t any univ]sal rules = ! modification ( ass5t c be obta9$ f !m8 ,if !y are1 /rong gr\nds w h be5 %[n = class+ !m ) 7,i471 9 o!r words1 = consid]+ !m z rules ( probability4 ,ev5 !n !y w\ld be rules practically ( a v diff]5t k9d1 cont+5t in/ead ( necess>y 7if "o may use ^! t]ms )\t committ+ oneself to any philosophical sy/em71 b ?is objection might p]haps be ov]rul$ by ! great] simplicity secur$ by class+ !m toge!r4 ,?is view is1 ) v>i\s modifications1 g5]ally adopt$ by writ]s on ,probability1 or at lea/1 z ,i und]/& ! matt]1 impli$ by _! me?ods ( def9ition & treatm5t4 ,or1 on ! o!r h&1 mu/ ^! causes be reg>d$ z a va/ sy/em1 "o might almo/ say a *aos1 ( p]fectly di/9ct ag5cies2 :i* may inde$ be classifi$ & arrang$ to "s ext5t1 b f :i* we c nev] hope to obta9 any rules ( p]fect g5]ality :i* %all n be subject to con/ant exception8 ,if s1 b "o c\rse is left2 to exclude !m all alike f ,probability4 ,9 o!r words1 we mu/ assume ! g5]al proposition1 viz4 t :i* has be5 describ$ ?r\gh\t z our />t+-po9t1 to be giv5 to u2 x may be obta9$ by any ( ! num]\s rules furni%$ by ,induction1 or x may be inf]r$ d$uctively1 or giv5 by our own obs]vation2 its value may be dim9i%$ by its dep5d+ ^u ! te/imony ( witnesses1 or its be+ recall$ by our own memory4 ,its real value may be influ5c$ by ^! causes or any comb9ations ( !m2 b all ^! are prelim9>y que/ions ) :i* we h no?+ directly to d4 ,we assume our /ati/ical proposition to be true1 neglect+ ! dim9ution ( its value by ! process ( atta9m5t2 we take x up fir/ at ?is po9t & !n apply our rules to x4 ,we receive x 9 fact1 if "o may use ! expression1 ready-made1 & ask no que/ions ab\t ! process or complet5ess ( its manufacture4 #e4 ,x is n to be suppos$1 ( c\rse1 t any writ]s h s]i\sly attempt$ to r$uce to "o sy/em ( calculation all ! causes m5tion$ above1 & to embrace 9 "o =mula ! dim9ution ( c]ta9ty to :i* ! inclusion ( !m subjects u4 ,b on ! o!r h&1 !y h be5 unwill+ to re/ra9 !mselves f all appeal to !m4 ,f an e>ly p]iod 9 ! /udy ( ! sci5ce attempts h be5 made to proce$1 by ! ,calculus ( ,probability1 f ! obs]v$ cases to adjac5t & simil> cases4 ,9 practice1 z has be5 already said1 x is n possible to avoid "s ext5sion ( ?is k9d4 ,b x %\ld be obs]v$1 t 9 ^! in/ances ! div]g5ce f ! /rict gr\nd ( exp]i5ce is n 9 reality recogniz$1 at lea/ n z a "p ( our logical proc$ure4 ,we h1 x is true1 w&]$ some:at beyond x1 & s obta9$ a wid] proposition ?an our data /rictly necessitat$1 & !re=e "o ( less c]ta9ty4 ,/ill we assume ! conclusion giv5 by induction to be equally c]ta9 ) ! data1 or r omit all notice ( ! div]g5ce f consid]ation4 ,x is assum$ t ! unexam9$ in/ances w resemble ! exam9$1 an assumption = :i* abundant w>rant may exi/2 ! !ory ( ! calculation re/s ^u ! supposition t !re w be no diff]5ce betwe5 !m1 & ! practical error is insignificant simply because ?is diff]5ce is small4 #f4 ,b ! rule we are n[ ab\t to discuss1 & :i* may be call$ ! ,rule ( ,succession1 is ( a v diff]5t k9d4 ,x n only recognizes ! fact t we are leav+ ! gr\nd ( pa/ exp]i5ce1 b takes ! consequ5ces ( ?is div]g5ce z ! express subject ( its calculation4 ,x pr(esses to give a g5]al rule = ! measure ( expectation t we %\ld h ( ! reappe>ance ( a ph5om5on t has be5 already obs]v$ any numb] ( times4 ,?is rule is g5]ally /at$ some:at z foll[s3 ,to f9d ! *ance ( ! recurr5ce ( an ev5t already obs]v$1 divide ! numb] ( times ! ev5t has be5 obs]v$1 increas$ by "o1 by ! same numb] increas$ by two4 #g4 ,x w be in/ructive to po9t out ! orig9 ( ?is rule2 if only to rem9d ! read] ( ! necessity ( keep+ ma!matical =mul to _! prop] prov9ce1 & to %[ :at a/oni%+ conclusions are apt to be accept$ on ! suppos$ w>rant ( ma!matics4 ,rev]t !n to ! example ( ,inv]se ,probability on p4 #ahb4 ,we saw t "u c]ta9 assumptions1 x w\ld foll[ t :5 a s+le :ite ball _h be5 drawn f a bag kn[n to conta9 #aj balls :i* 7 :ite or black1 ! *ance c\ld be det]m9$ t !re 0 only "o :ite ball 9 x4 ,hav+ done ?is we readily calculate 'directly' ! *ance t ?is :ite ball w be drawn next "t4 ,simil>ly we c reckon ! *ances ( !re be+ two1 ?ree1 c4 up to t5 :ite balls 9 x1 & det]m9e on ea* ( ^! suppositions ! *ance ( a :ite ball be+ drawn next "t4 ,add+ ^! toge!r we h ! answ] to ! "q3--a :ite ball has be5 drawn once f a bag kn[n to conta9 t5 balls1 :ite or black2 :at is ! *ance ( a second "t draw+ a :ite ball8 ,s f> only ari?metic is requir$4 ,= ! next /ep we ne$ high] ma!matics1 & by its aid we solve ?is problem3--,a :ite ball has be5 drawn m times f a bag :i* conta9s any numb]1 we "k n :at1 ( balls ea* ( :i* is :ite or black1 f9d ! *ance ( ! next draw+ also yield+ a :ite ball4 ,! answ] is 7m #a7_/7m #b74 ,?us f> ma!matics4 ,!n comes 9 ! physical assumption t ! univ]se may be lik5$ to su* a bag z ! above1 9 ! s5se t ! above rule may be appli$ to solve ?is "q3--an ev5t has be5 obs]v$ to happ5 m times 9 a c]ta9 way1 f9d ! *ance t x w happ5 9 t way next "t4 ,laplace1 = in/ance1 has po9t$ out t at ! date ( ! writ+ ( 8 ,essai ,philosophique1 ! odds 9 fav\r ( ! sun's ris+ aga9 7on ! old assumption z to ! age ( ! _w7 7 #a1hbf1bad to #a4 ,de ,morgan says t a man :o /&+ on ! bank ( a riv] has se5 t5 %ips pass by ) flags %\ld judge x to be #aa to #a t ! next %ip w also c>ry a flag4 #h4 ,x is h>d to take su* a rule z ?is s]i\sly1 = !re does n seem to be ev5 t mod]ate confirmation ( x :i* we %all f9d to hold good 9 ! case ( ! application ( ab/ract =mul to ! e/imation ( ! evid5ce ( witnesses4 ,if h[ev] its validity is to be discuss$ !re appe> to be two v di/9ct l9es ( enquiry along :i* we may be l$4 7#a7 ,9 ! fir/ place we may take x = :at x pr(esses to be1 & = :at x is commonly und]/ood to be1 viz4 a rule :i* assigns ! measure ( expectation we ought to ent]ta9 ( ! recurr5ce ( ! ev5t "u ! circum/ances 9 "q4 ,( c\rse1 on ! view adopt$ 9 ?is "w1 we insi/ on enquir+ :e!r x is really true t on ! av]age ev5ts d ?us repeat _! p]=mance 9 accordance ) ?is law4 ,?us te/$1 no "o surely w\ld attempt to def5d su* a =mula4 ,s f> f pa/ occurr5ce be+ a gr\nd = belief 9 future recurr5ce1 !re are 7z w be m fully po9t$ out 9 ! ,*apt] on ,fallacies7 pl5ty ( cases 9 :i* ! direct contr>y holds good4 ,!n aga9 a rule ( ?is k9d is subject to ! v s]i\s p]plexity to be expla9$ 9 our next *apt]1 aris+ out ( ! necess>y arbitr>9ess ( su* inv]se ref]5ce4 ,t is1 :5 an ev5t has happ5$ b a few times1 we h no c]ta9 guide2 & :5 x has happ5$ b once1#b we h no guide :atev]1 z to ! class ( cases to :i* x is to be ref]r$4 ,9 ! example above1 ab\t ! flags1 :y did we /op %ort at ?is notion simply1 in/ead ( specify+ ! size1 %ape1 c4 ( ! flags8 ,de ,morgan1 x mu/ be rememb]$1 only accepts ?is rule 9 a qualifi$ s5se4 ,he reg>ds x z furni%+ a m9imum value = ! am\nt ( our expectation4 ,he t]ms x ! rule ( probability ( a pure induction1 & says ( x1 ,! probabilities %[n by ! above rules are m]ely m9ima :i* may be augm5t$ by o!r s\rces ( k4 ,t is1 he recognizes only ^? in/ances 9 :i* our belief 9 ! ,uni=mity ( ,nature & 9 ! exi/5ce ( special laws ( causation comes 9 to supplem5t t :i* arises f ! m]e frequ5cy ( pa/ occurr5ce4 ,?is h[ev] does n meet ^? cases 9 :i* pa/ occurr5ce is a positive gr\nd ( disbelief 9 future recurr5ce4 #i4 7#b7 ,!re is h[ev] ano!r & v diff]5t view :i* might be tak5 ( su* a rule4 ,x is "o1 an obscure recognition ( :i* has v likely _h mu* to d ) ! acceptance :i* ! rule has receiv$4 ,:at we might suppose ourselves to be ?us express+ is1--n ! measure ( rational expectation :i* might be held by m9ds suffici5tly advanc$ to be able to classify & to draw consci\s inf]5ces1 b1--! law accord+ to :i* ! primitive elem5ts ( belief 7 />t$ & develop$4 ,( c\rse su* an int]pretation z ?is w\ld be equival5t to quitt+ ! prov9ce ( ,logic altoge!r & cross+ ov] into t ( ,psy*ology2 b x w\ld be a p]fectly valid l9e ( enquiry4 ,we %\ld be attempt+ no?+ m ?an a developm5t ( ! rese>*es ( ,fe*n] & 8 foll[]s 9 psy*ophysical measurem5t4 ,only !n we ought1 l !m1 n to />t ) any analogy ( a ballot box & its cont5ts1 b to base our enquiry on c>eful det]m9ation ( ! actual m5tal ph5om5a exp]i5c$4 ,we "k h[ ! law has be5 det]m9$ 9 accordance ) :i* ! int5sity ( ! feel+ ( light v>ies ) t ( its objective s\rce4 ,we see h[ x is possible to measure ! gr[? ( memory accord+ to ! numb] ( repetitions ( a s5t5ce or a succession ( m]e syllables4 ,9 ?is latt] case1 = in/ance1 we j try exp]im5ts1 & det]m9e h[ mu* bett] a man c rememb] any utt]ances aft] eight he>+s ?an aft] sev54#c ,n[ ?is case furni%es a v close p>allel to our suppos$ attempt to measure ! increase ( int5sity ( belief aft] repeat$ recurr5ce4 ,t is1 if x 7 possible to exp]im5t 9 ?is ord] ( m5tal ph5om5a1 we ought simply to repeat a ph5om5on a c]ta9 numb] ( times & !n asc]ta9 by actual introspection or by "s simple te/1 h[ fa/ ! belief 0 increas+4 ,?us view$ ! problem seems to me a hopeless "o4 ,! difficulties are s]i\s en\gh1 :5 we are try+ to measure our simple s5sations1 ( lay+ aside ! effects ( pa/ tra9+1 & ( attempt+1 z x 71 to leave ! m9d op5 & passive to m]e reception ( /imuli4 ,b if we 7 to attempt 9 ?is way to measure our belief ^! difficulties w\ld become q insup]able4 ,we c no m dive/ ourselves ( pa/ tra9+ "h ?an we c ( intellig5ce or ?\ght4 ,i d n see h[ any "o c\ld possibly avoid class+ ! obs]v$ recurr5ces ) o!rs :i* he _h exp]i5c$1 & ( be+ ?us guid$ by special analogies & inductions in/ead ( tru/+ solely to ,de ,morgan's 'pure induction'4 ,! same consid]ations t5d to rebut ano!r =m ( def5ce = ! rule 9 "q4 ,x is urg$1 = in/ance1 t we may at lea/ resort to x 9 ^? cases 9 :i* we are 9 entire ignorance z to ! numb] & nature ( ! antec$5ts4 ,?is is a position to :i* ,i c h>dly conceive x possible t we %\ld ev] be r$uc$4 ,h[ev] remote or exceptional may be ! ph5om5on select$ we may yet br+ x into relation ) "s accept$ g5]alizations & ?us draw our conclusions f ^! r ?an f purely priori consid]ations4 #aj4 ,s9ce !n pa/ acquisitions _c be laid aside or all[$ =1 ! only rema9+ res\rce w\ld be to exp]im5t ^u ! infant m9d4 ,"o w\ld n l to pron\nce t any l9e ( enquiry is impossible2 b ! difficulties w\ld c]ta9ly be enorm\s4 ,& int]e/+ z ! facts w\ld be1 suppos+ t we _h succe$$ 9 secur+ !m1 !y w\ld n be ( ! slighte/ importance 9 ,logic4 ,h[ev] ! "q 7 settl$3--:e!r1 = in/ance1 we prov$ t ! s5tim5t or emotion ( belief grew up sl[ly & gradually f a sort ( z]o po9t "u ! impress ( repetition ( exp]i5ce2 or :e!r we prov$ t a s+le occurr5ce produc$ complete belief 9 ! repetition ( ! ev5t1 s t exp]i5ce gradually untaught u & weak5$ our convictions2--9 no case w\ld ! mature m9d ga9 any aid z to :at x ought to believe4 ,i _c b ?9k t "s su* view z ?is mu/ occasionally und]lie ! acceptance :i* ?is rule has receiv$4 ,= in/ance1 ,laplace1 ?\gh unhesitat+ly adopt+ x z a real1 t is1 objective rule ( inf]5ce1 has gone into s mu* physiological & psy*ological matt] t[>ds ! end ( 8 discussion 7,essai philosophique7 z to sugge/ t :at he _h 9 view 0 ! natural hi/ory ( belief r ?an its subsequ5t ju/ification4 ,aga91 ! curi\s doctr9e adopt$ by ,jevons1 t ! pr9ciples ( ,induction re/ entirely ^u ! !ory ( ,probability1--a v diff]5t doctr9e f t :i* is convey$ by say+ t all k ( facts is probable only1 i4e4 n necess>y1--seems un9telligible except on "s su* int]pretation4 ,we %all h m to say on ?is subject 9 our next *apt]4 ,x w be en\gh "h to rem>k t 9 our pres5t reflective & rational /age we f9d t e inf]5ce 9 ,probability involves "s appeal to1 or support f1 ,induction1 b t x is impossible to base ei!r ^u ! o!r4 ,h[ev] f> back we try to pu% our way1 & h[ev] dispos$ we might be to acc\nt = our ultimate beliefs by ,association1 x seems to me t s long z we consid] ourselves to be deal+ ) rules ( inf]5ce we mu/ /ill di/+ui% betwe5 ,induction & ,probability4 #a4 ,john ,craig1 9 8 (t5 nam$ "w1 ,!ologi ,*ri/ian ,pr9cipia ,ma!matica 7,lond4 #afii7 attempt$ some?+ 9 ?is direction :5 he propos$ to solve su* problems z3--,qu&o evanescet probabilitas cujusvis ,hi/ori1 cujus subjectum e/ transi5s1 viv tantum voce transmiss1 det]m9>e4 #b4 ,:5 m #a ! fraction becomes #b_/c2 i4e4 ! odds are #b to #a 9 fav\r ( recurr5ce4 ,& !re are writ]s :o accept ?is result4 ,= in/ance1 ,jevons 7,pr9ciples ( ,sci5ce p4 #beh7 says ,?us on ! fir/ occasion on :i* a p]son sees a %>k1 & notices t x is accompani$ by a little pilot fi%1 ! odds are #b to #a t ! next %>k w be s accompani$4 ,to say no?+ ( ! fact t recogniz+ & nam+ ! fi% implies t !y h (t5 be5 se5 be=e1 h[ _m ( ! obs]v$ *>act]i/ics ( t s+le 'ev5t' are to be consid]$ ess5tial8 ,mu/ ! pilot prec$e2 & at ! same di/ance8 ,mu/ we consid] ! latitude1 ! ocean1 ! season1 ! species ( %>k1 z matt] also ( repetition on ! next occasion8 & s on4 ,i _c see h[ ! ,inductive problem c be ev5 intelligibly /at$1 = quantitative purposes1 on ! fir/ occurr5ce ( any ev5t4 #c4 ,see 9 ,m9d 7x4 #ded7 ,mr ,jacob's acc\nt ( ! rese>*es ( ,h]r ,ebb+haus z describ$ 9 8 "w ,ueb] das ,g$*tniss4 ,,*apt] ,,ix4 ,,induction ,,& ,,its ,,connection ,,) ,,probability4 #a4 ,we 7 occupi$1 dur+ ! la/ *apt]1 ) ! exam9ation ( a rule1 ! object ( :i* 0 to enable u to make inf]5ces ab\t in/ances z yet unexam9$4 ,x 0 pr(ess$ly1 !re=e1 a rule ( an inductive "*4 ,b1 9 ! =m 9 :i* x is commonly express$1 x 0 f\nd to fail utt]ly4 ,x is reasonable !re=e to enquire at ?is po9t :e!r ,probability is entirely a =mal or d$uctive sci5ce1 or :e!r1 on ! o!r h&1 we are able1 by means ( x1 to make valid inf]5ces ab\t in/ances z yet unexam9$4 ,?is "q has be5 already 9 "p answ]$ by implication 9 ! c\rse ( ! la/ two *apt]s4 ,x is propos$ 9 ! pres5t *apt] to devote a full] inve/igation to ?is subject1 & to describe1 z m9utely z limits w all[1 ! nature ( ! connection betwe5 ,probability & ,induction4 ,we %all f9d x advisable = cle>ness ( conception to comm5ce our enquiry at a some:at e>ly /age4 ,we w travel ov] ! gr\nd1 h[ev]1 z rapidly z possible1 until we approa* ! b\nd>y ( :at c prop]ly be t]m$ ,probability4 #b4 ,let u !n conceive "s "o sett+ to "w to inve/igate nature1 "u its broade/ aspect1 ) ! view ( sy/ematiz+ ! facts ( exp]i5ce t are kn[n1 & !nce 79 case he %\ld f9d t ?is is possible7 discov]+ o!rs :i* are at pres5t unkn[n4 ,he obs]ves a multitude ( ph5om5a1 physical & m5tal1 contempor>y & successive4 ,he enquires :at connections are !re betwe5 !m8 :at rules c be f\nd1 s t "s ( ^! ?+s be+ obs]v$ ,i c inf] o!rs f !m8 ,we suppose him1 let x be obs]v$1 delib]ately resolv+ to inve/igate ! ?+s !mselves1 & n to be turn$ aside by any prior enquiry z to !re be+ laws "u :i* ! m9d is compell$ to judge ( ! ?+s4 ,?is may arise ei!r f a disbelief 9 ! exi/5ce ( any indep5d5t & necess>y m5tal laws1 & a consequ5t conviction t ! m9d is p]fectly compet5t to obs]ve & believe any?+ t exp]i5ce (f]s1 & %\ld believe no?+ else1 or simply f a pref]5ce = inve/igations ( ! latt] k9d4 ,9 o!r words1 we suppose him to reject ,=mal ,logic1 & to apply himself to a /udy ( objective exi/5ces4 ,x mu/ n = a mom5t be suppos$ t we are "h do+ m ?an conceiv+ a fictiti\s case = ! purpose ( m vividly sett+ be=e ! read] ! nature ( ! inductive process1 ! assumptions x has to make1 & ! "* ( ! mat]ials to :i* x is appli$4 ,x is n psy*ologically possible t any "o %\ld come to ! /udy ( nature ) all 8 m5tal faculties 9 full p]fection1 b void ( all mat]ials ( k1 & free f any bias z to ! uni=mities :i* might be f\nd to prevail ar\nd him4 ,9 practice1 ( c\rse1 ! =m & ! matt]--! laws ( belief or association1 & ! objects to :i* !y are appli$--act & react ^u "o ano!r1 & nei!r c exi/ 9 any b a l[ degree )\t presuppos+ ! exi/5ce ( ! o!r4 ,b ! supposition is p]fectly legitimate = ! purpose ( call+ att5tion to ! requirem5ts ( su* a sy/em ( ,logic1 & is inde$ no?+ m ?an :at has to be done at almo/ e /ep 9 psy*ological enquiry4#a #c4 ,8 task at fir/ might be conceiv$ to be a sl[ & t$i\s "o4 ,x w\ld consi/ ( a gradual accumulation ( individual in/ances1 z m>k$ out f "o ano!r by v>i\s po9ts ( di/9ction1 & connect$ ) "o ano!r by po9ts ( resemblance4 ,^! w\ld h to be respectively di/+ui%$ & associat$ 9 ! m9d1 & ! consequ5t results w\ld !n be summ$ up 9 g5]al propositions1 f :i* inf]5ces c\ld aft]w>ds be drawn4 ,^! inf]5ces c\ld1 ( c\rse1 conta9 no new facts1 !y w\ld only be repetitions ( :at he or o!rs _h previ\sly obs]v$4 ,all t we %\ld h s f> done w\ld h be5 to make our classifications ( ?+s & !n to appeal to !m aga94 ,we %\ld !re=e be keep+ well )9 ! prov9ce ( ord9>y logic1 ! processes ( :i* 7:atev] _! ultimate explanation7 may ( c\rse always be express$1 9 accordance ) ,ari/otle's ,dictum1 z ways ( det]m9+ :e!r or n we c %[ t "o giv5 class is includ$ :olly or p>tly )9 ano!r1 or exclud$ f x1 z ! case may be4 #d4 ,b a v %ort c\rse ( obs]vation w\ld sugge/ ! possibility ( a wide ext5sion ( 8 in=mation4 ,exp]i5ce itself w\ld soon detect t ev5ts 7 connect$ toge!r 9 a regul> way2 he w\ld asc]ta9 t !re are 'laws ( nature4' ,com+ ) no priori necessity ( believ+ 9 !m1 he w\ld soon f9d t z a matt] ( fact !y d exi/1 ?\gh he c\ld n feel any c]ta9ty z to ! ext5t ( _! preval5ce4 ,! discov]y ( ?is arrangem5t 9 nature w\ld at once alt] ! plan ( 8 proce$+s1 & set ! tone to ! :ole range ( 8 me?ods ( inve/igation4 ,8 ma9 "w n[ w\ld be to f9d out by :at means he c\ld be/ discov] ^! laws ( nature4 ,an illu/ration may assi/4 ,suppose ,i 7 engag$ 9 break+ up a va/ piece ( rock1 say slate1 into small pieces4 ,i %\ld beg9 by we>ily work+ ?r\gh x in* by in*4 ,b ,i %\ld soon f9d ! process completely *ang$ ow+ to ! exi/5ce ( cleavage4 ,by ?is arrangem5t ( ?+s a v few bl[s w\ld d ! "w--n1 z ,i might possibly h at fir/ suppos$1 to ! ext5t ( a few in*es--b "r ?r\gh ! :ole mass4 ,9 o!r words1 by ! process itself ( cutt+1 z %[n 9 exp]i5ce1 & by no?+ else1 a con/itution w\ld be detect$ 9 ! ?+s t w\ld make t process va/ly m easy & ext5sive4 ,su* a discov]y w\ld ( c\rse *ange our tactics4 ,our pr9cipal object w\ld !nce=? be to asc]ta9 ! ext5t & direction ( ?is cleavage4 ,some?+ resembl+ ?is is f\nd 9 ,induction4 ,! discov]y ( laws ( nature enables ! m9d to d>t ) its inf]5ces f a few facts completely ?r\gh a :ole class ( objects1 & ?us to acquire results ! successive individual atta9m5t ( :i* w\ld h involv$ long & we>isome inve/igation1 & w\ld inde$ 9 multitudes ( in/ances h be5 out ( ! "q4 ,we h no demon/rative pro( t ?is /ate ( ?+s is univ]sal2 b hav+ f\nd x prevail ext5sively1 we g on ) ! resolution at lea/ to try = x ev]y:]e else1 & we are n disappo9t$4 ,f propositions obta9$ 9 ?is way1 or r f ! orig9al facts on :i* ^! propositions re/1 we c make new inf]5ces1 n inde$ ) absolute c]ta9ty1 b ) a degree ( conviction t is ( ! utmo/ practical use4 ,we h ga9$ ! great /ep ( be+ able to make tru/wor?y g5]alizations4 ,we conclude1 = in/ance1 n m]ely t ,john & ,h5ry die1 b t all m5 die4 #e4 ,! above brief inve/igation conta9s1 x is hop$1 a tol]ably correct outl9e ( ! nature ( ! ,inductive inf]5ce1 z x pres5ts itself 9 ,mat]ial or ,sci5tific ,logic4 ,x involves ! di/9ction drawn by ,mill1 & ) :i* ! read] ( 8 ,sy/em ( ,logic w be famili>1 betwe5 an inf]5ce drawn accord+ to a =mula & "o drawn f a =mula4 ,we d 9 reality make our inf]5ce f ! data af=d$ by exp]i5ce directly to ! conclusion2 x is a m]e arrangem5t ( conv5i5ce to d s by pass+ ?r\gh ! g5]alization4 ,b x is "o ( su* extreme conv5i5ce1 & "o s necess>ily =c$ ^u u :5 we are appeal+ to our own pa/ exp]i5ce or to t ( o!rs = ! gr\nds ( our conclusion1 t practically we f9d x ! be/ plan to divide ! process ( inf]5ce into two p>ts4 ,! fir/ "p is conc]n$ ) e/abli%+ ! g5]alization2 ! second 7:i* conta9s ! rules ( ord9>y logic7 det]m9es :at conclusions c be drawn f ?is g5]alization4 #f4 ,we may n[ see our way to asc]ta9+ ! prov9ce ( ,probability & its relation to k9dr$ sci5ces4 ,inductive ,logic gives rules = discov]+ su* g5]alizations z ^? spok5 ( above1 & = te/+ _! correctness4 ,if !y are express$ 9 univ]sal propositions x is ! "p ( ord9>y logic to det]m9e :at inf]5ces c be made f & by !m2 if1 on ! o!r h&1 !y are express$ 9 proportional propositions1 t is1 propositions ( ! k9d describ$ 9 our fir/ *apt]1 !y are h&$ ov] to ,probability4 ,we f9d1 = example1 t ?ree infants out ( t5 die 9 _! fir/ f\r ye>s4 ,x belongs to ,induction to say :e!r we are ju/ifi$ 9 g5]aliz+ our obs]vation into ! ass]tion1 ,all infants die 9 t proportion4 ,:5 su* a proposition is obta9$1 :atev] may be ! value to be assign$ to x1 we recognize 9 x a s]ies ( a famili> k9d1 & x is at once claim$ by ,probability4 ,9 ?is latt] case ! division into two p>ts1 ! inductive & ! ratioc9ative1 seems decid$ly m ?an "o ( conv5i5ce2 x is inde$ imp]atively necess>y = cle>ness ( ?\ght & cog5cy ( treatm5t4 ,x is true t 9 almo/ e example t c be select$ we %all f9d bo? ( ! above elem5ts exi/+ toge!r & comb9+ to det]m9e ! degree ( our conviction1 b :5 we come to exam9e !m closely x appe>s to me t ! gr\nds ( _! cog5cy1 ! k9d ( conviction !y produce1 & consequ5tly ! rules :i* !y give rise to1 are s entirely di/9ct t !y _c possibly be h>moniz$ into a s+le consi/5t sy/em4 ,! op9ion !re=e accord+ to :i* c]ta9 ,inductive =mul are reg>d$ z compos+ a portion ( ,probability1 & :i* f9ds utt]ance 9 ! ,rule ( ,succession criticis$ 9 our la/ *apt]1 _c1 ,i ?9k1 be ma9ta9$4 ,x w\ld be m correct to say1 z /at$ above1 t ,induction is q di/9ct f ,probability1 yet co-op]ates 9 almo/ all its inf]5ces4 ,by ,induction we det]m9e1 = example1 :e!r1 & h[ f>1 we c safely g5]alize ! proposition t f\r m5 9 t5 live to be fifty-six2 suppos+ su* a proposition to be safely g5]aliz$1 we h& x ov] to ,probability to say :at sort ( inf]5ces c be d$uc$ f x4 #g4 ,s mu* !n = ! op9ion :i* t5ds to reg>d pure ,induction z a subdivision ( ,probability4 ,by ! majority ( philosophical & logical writ]s a widely diff]5t view has ( c\rse be5 ent]ta9$4 ,!y are mo/ly dispos$ to di/+ui% ^! sci5ces v %>ply f1 n to say to contra/ !m )1 "o ano!r2 ! "o be+ accept$ z philosophical or logical1 & ! o!r reject$ z ma!matical4 ,?is may )\t (f5ce be t]m$ ! popul> prejudice aga9/ ,probability4 ,a some:at diff]5t view1 h[ev]1 mu/ be notic$ "h1 :i*1 by a sort ( reaction aga9/ ! latt]1 seems ev5 to g beyond ! =m]2 & :i* occasionally f9ds expression 9 ! /atem5t t all inductive reason+ ( e k9d is m]ely a matt] ( ,probability4 ,two examples ( ?is may be giv54 ,beg9n+ ) ! old] au?ority1 !re is an (t5 quot$ say+ by ,butl] at ! comm5cem5t ( 8 ,analogy1 t 'probability is ! v guide ( life'2 a say+ :i* seems frequ5tly to be und]/ood to signify t ! rules or pr9ciples ( ,probability are ?us all-preval5t :5 we are draw+ conclusions 9 practical life4 ,judg+ by ! drift ( ! context1 inde$1 ?is seems a fair int]pretation ( 8 mean+1 9 s f> ( c\rse z !re c\ld be said to be any su* ?+ z a sci5ce ( ,probability 9 ^? days4 ,pr(4 ,jevons1 9 8 ,pr9ciples ( ,sci5ce 7p4 #aig71 has express$ a some:at simil> view1 ( c\rse 9 a way m consi/5t ) ! pr9ciples ( mod]n sci5ce1 physical & ma!matical4 ,he says1 ,i am conv9c$ t x is impossible to exp\nd ! me?ods ( induction 9 a s\nd mann]1 )\t re/+ !m on ! !ory ( ,probability4 ,p]fect k alone c give c]ta9ty1 & 9 nature p]fect k w\ld be inf9ite k1 :i* is cle>ly beyond our capacities4 ,we h1 !re=e1 to cont5t ourselves ) p>tial k1--k m+l$ ) ignorance1 produc+ d\bt4#b #h4 ,!re are two s5ses 9 :i* ?is disposition to m]ge ! two sci5ces into "o may be und]/ood4 ,us+ ! ^w ,probability 9 its vague popul> signification1 no?+ m may be int5d$ ?an to call att5tion to ! fact1 t 9 e case alike our conclusions are no?+ m ?an 'probable1' t is1 t !y are n1 & _c be1 absolutely c]ta94 ,?is mu/ be fully admitt$1 = ( c\rse no "o acqua9t$ ) ! complexity ( physical & o!r evid5ce w\ld s]i\sly ma9ta9 t absolute ideal c]ta9ty c be atta9$ 9 any bran* ( appli$ logic4 ,hypo!tical c]ta9ty1 9 ab/ract sci5ce1 may be possible1 b n absolute c]ta9ty 9 ! doma9 ( ! concrete4 ,?is has be5 already notic$ 9 a =m] *apt]1 :]e1 h[ev]1 x 0 po9t$ out t :atev] ju/ification may exi/1 on ! subjective view ( logic1 = reg>d+ ?is common preval5ce ( abs5ce ( c]ta9ty z w>rant+ u 9 fus+ ! sci5ces into "o1 no su* ju/ification is admitt$ :5 we take ! objective view4 #i4 ,:at may be meant1 h[ev]1 is t ! gr\nds ( ?is abs5ce ( c]ta9ty are always ( ! same g5]al "*4 ,?is argum5t1 if admitt$1 w\ld h real =ce1 & mu/ !re=e be briefly notic$4 ,we h se5 abundantly t :5 we say ( a conclusion )9 ! /rict prov9ce ( ,probability1 t x is n c]ta91 all t we mean is t 9 "s proportion ( cases only w su* conclusion be "r1 9 ! o!r cases x w be wrong4 ,n[ :5 we say1 9 ref]5ce to any inductive conclusion1 t we feel unc]ta9 ab\t its absolute cog5cy1 are we consci\s ( ! same int]pretation8 ,x seems to me t we are n4 ,x is inde$ q possible t on ultimate analysis x might be prov$ t exp]i5ce ( failure 9 ! pa/ employm5t ( our me?ods ( inve/igation 0 ! ma9 cause ( our pres5t want ( p]fect confid5ce 9 !m4 ,b ?is1 z we h repeat$ly insi/$1 does n belong to ! prov9ce ( logical1 b to t ( ,psy*ological enquiry4 ,x is surely n ! case t we are1 z a rule1 consci\sly guid$ by su* occasional or repeat$ in/ances ( pa/ failure4 ,9 s f> z !y are at all influ5tial1 !y seem to d _! "w by infus+ a vague want ( confid5ce :i* _c be ref]r$ to any /ati/ical gr\nds = its ju/ification1 at lea/ n 9 a quantitative way4 ,"p ( our want ( confid5ce is d]iv$ sympa!tically f ^? :o h inve/igat$ ! matt] m ne>ly at fir/ h&4 ,"h aga91 analysis might detect t a giv5 proportion ( pa/ failures lay at ! root ( ! di/ru/1 b x does n %[ at ! surface4 ,moreov]1 "o reason :y we _c feel p]fectly c]ta9 ab\t our inductions is1 t ! memory has to be appeal$ to = "s ( our data2 & w any "o ass]t t ! only reason :y we d n place absolute reliance on our memory ( ev5ts long pa/ is t we h be5 deceiv$ 9 t way be=e8 ,9 any o!r s5se1 !re=e1 ?an z a ne$ful prote/ aga9/ atta*+ too great demon/rative =ce to ! conclusions ( ,inductive ,logic1 x seems decid$ly mislead+ to speak ( its reason+s z re/+ ^u ,probability4 #aj4 ,we may n[ see cle>ly ! reasons = ! limits )9 :i* causation#c is necess>ily requir$1 b beyond :i* x is n ne$$4 ,to be able to g5]alize a =mula s z to ext5d x f ! obs]v$ to ! unobs]v$1 x is cle>ly ess5tial t !re %\ld be a c]ta9 p]man5ce 9 ! ord] ( nature2 ?is p]man5ce is "o =m ( :at is impli$ 9 ! t]m causation4 ,if ! circum/ances "u :i* m5 live & die rema9+ ! same1 we did n feel w>rant$ 9 inf]r+ t f\r m5 out ( t5 w\ld cont9ue to live to fifty1 because 9 ! case ( ^? :om we _h obs]v$ ?is proportion _h hi!rto done s1 x is cle> t we %\ld be admitt+ t ! same antec$5ts ne$ n be foll[$ by ! same consequ5ts4 ,?is uni=mity be+ :at ! ,law ( ,causation ass]ts1 ! tru? ( ! law is cle>ly necess>y to enable u to obta9 our g5]alizations3 9 o!r words1 x is necess>y = ! ,inductive "p ( ! process4 ,b x seems to be equally cle> t causation is n necess>y = t "p ( ! process :i* belongs to ,probability4 ,provid$ only t ! tru? ( our g5]alizations is secur$ to u1 9 ! way j m5tion$1 :at does x matt] to u :e!r or n ! individual memb]s are subject to causation8 ,= x is n 9 reality ab\t ^! individuals t we make inf]5ces4 ,z ?is la/ po9t has be5 already fully treat$ 9 ,*apt] ,,vi41 any fur!r allusion to x ne$ n be made "h4 #aa4 ,! above description1 or r indication1 ( ! process ( obta9+ ^! g5]alizations mu/ suffice = ! pres5t4 ,let u n[ turn & consid] ! means by :i* we are practically to make use ( !m :5 !y are obta9$4 ,! po9t :i* we _h rea*$ 9 ! c\rse ( ! inve/igations ent]$ into 9 ! six? & sev5? *apt]s 0 ?is3--,giv5 a s]ies ( a c]ta9 k9d1 we c\ld draw inf]5ces ab\t ! memb]s :i* compos$ x2 inf]5ces1 t is1 ( a peculi> k9d1 ! value & mean+ ( :i* 7 fully discuss$ 9 _! prop] place4 ,we mu/ n[ %ift our po9t ( view a little2 in/ead ( />t+1 z 9 ! =m] *apt]s1 ) a det]m9ate s]ies suppos$ to be giv5 to u1 let u assume t ! individual only is giv51 & t ! "w is impos$ ^u u ( f9d+ out ! appropriate s]ies4 ,h[ are we to set ab\t ! task8 ,9 ! =m] case our data 7 ( ?is k9d3--,eight out ( t5 m51 ag$ fifty1 w live elev5 ye>s m1 & we asc]ta9$ 9 :at s5se1 & ) :at c]ta9ty1 we c\ld inf] t1 say1 ,john ,smi?1 ag$ fifty1 w\ld live to sixty-"o4 #ab4 ,let u !n suppose1 in/ead1 t ,john ,smi? pres5ts himself1 h[ %\ld we 9 ?is case set ab\t obta9+ a s]ies = him8 ,9 o!r words1 h[ %\ld we collect ! appropriate /ati/ics8 ,x %\ld be borne 9 m9d t :5 we are attempt+ to make real inf]5ces ab\t ?+s z yet unkn[n1 x is 9 ?is =m t ! problem w practically pres5t itself4 ,at fir/ sight ! answ] to ?is "q may seem to be obta9$ by a v simple process1 viz4 by c\nt+ h[ _m m5 ( ! age ( ,john ,smi?1 respectively d & d n live = elev5 ye>s4 ,9 reality h[ev] ! process is f> f be+ s simple z x appe>s4 ,= x mu/ be rememb]$ t ea* individual ?+ has n "o di/9ct & appropriate class or gr\p1 to :i*1 & to :i* alone1 x prop]ly belongs4 ,we may inde$ be practically 9 ! habit ( consid]+ x "u su* a s+le aspect1 & x may !re=e seem to u m famili> :5 x occupies a place 9 "o s]ies r ?an 9 ano!r2 b su* a practice is m]ely cu/om>y on our "p1 n obligatory4 ,x is obvi\s t e individual ?+ or ev5t has an indef9ite numb] ( prop]ties or attributes obs]vable 9 x1 & might !re=e be consid]$ z belong+ to an indef9ite numb] ( diff]5t classes ( ?+s4 ,by belong+ to any "o class x ( c\rse becomes at ! same "t a memb] ( all ! high] classes1 ! g5]a1 ( :i* t class 0 a species4 ,b1 moreov]1 by virtue ( ea* accid5tal attribute :i* x possesses1 x becomes a memb] ( a class int]sect+1 s to say1 "s ( ! o!r classes4 ,john ,smi? is a consumptive man say1 & a native ( a nor!rn climate4 ,be+ a man he is ( c\rse includ$ 9 ! class ( v]tebrates1 also 9 t ( animals1 z well z 9 any high] su* classes t !re may be4 ,! prop]ty ( be+ consumptive ref]s him to ano!r class1 n>r[] ?an any ( ! above2 :il/ t ( be+ born 9 a nor!rn climate ref]s him to a new & di/9ct class1 n cont]m9\s ) any ( ! re/1 = !re are ?+s born 9 ! nor? :i* are n m54 #ac4 ,:5 !re=e ,john ,smi? pres5ts himself to our notice )\t1 s to say1 any p>ticul> label atta*$ to him in=m+ u "u :i* ( 8 v>i\s aspects he is to be view$1 ! process ( ?us ref]r+ him to a class becomes to a great ext5t arbitr>y4 ,if he _h be5 indicat$ to u by a g5]al "n1 t1 ( c\rse1 w\ld h be5 "s clue2 = ! "n hav+ a det]m9ate connotation w\ld specify at any rate a fix$ gr\p ( attributes )9 :i* our selection 0 to be conf9$4 ,b names & attributes be+ connect$ toge!r1 we are "h suppos$ to be j z mu* 9 ignorance :at "n he is to be call$ by1 z :at gr\p out ( all 8 innum]able attributes is to be tak5 acc\nt (2 = to tell u "o ( ^! ?+s w\ld be precisely ! same 9 effect z to tell u ! o!r4 ,9 say+ t x is ?us arbitr>y "u :i* class he is plac$1 we mean1 ( c\rse1 t !re are no logical gr\nds ( decision2 ! selection mu/ be det]m9$ by "s extrane\s consid]ations4 ,m]e inspection ( ! individual w\ld simply %[ u t he c\ld equally be ref]r$ to an indef9ite numb] ( classes1 b w\ld 9 itself give no inducem5t to pref]1 = our special purpose1 "o ( ^! classes to ano!r4 ,?is v>iety ( classes to :i* ! individual may be ref]r$ ow+ to 8 possession ( a multiplicity ( attributes1 has an important be>+ on ! process ( inf]5ce :i* 0 indicat$ 9 ! e>li] sections ( ?is *apt]1 & :i* we mu/ n[ exam9e 9 m special ref]5ce to our p>ticul> subject4 #ad4 ,x w s]ve to br+ out m cle>ly ! nature ( "s ( ^? peculi>ities ( ! /ep :i* we are n[ ab\t to take 9 ! case ( ,probability1 if we fir/ exam9e ! =m :i* ! correspond+ /ep assumes 9 ! case ( ord9>y ,logic4 ,suppose !n t we wi%$ to asc]ta9 :e!r a c]ta9 ,john ,smi?1 a man ( ?irty1 :o is among/ o!r ?+s a resid5t 9 ,india1 & di/9ctly affect$ ) canc]1 w cont9ue to survive !re = tw5ty ye>s long]4 ,! t]ms 9 :i* ! man is ?us introduc$ to u ref] him to diff]5t classes 9 ! way already indicat$4 ,correspond+ to ^! classes !re w be a numb] ( propositions :i* h be5 obta9$ by previ\s obs]vations & inductions1 & :i* we may !re=e assume to be available & ready at h& :5 we want to make use ( !m4 ,let u conceive !m to be su* z ^! foll[+3--,"s m5 live to fifty2 "s ,indian resid5ts live to fifty2 no man suff]+ ?us f canc] lives = five ye>s4 ,f ! fir/ & second ( ^! premises no?+ :atev] c be inf]r$1 = !y are bo?#d p>ticul> propositions1 & !re=e lead to no conclusion 9 ?is case4 ,! ?ird answ]s our enquiry decisively4 ,to ! logical read] x w h>dly be necess>y to po9t out t ! process "h "u consid]ation is t ( f9d+ middle t]ms :i* %all s]ve to connect ! subject & pr$icate ( our conclusion4 ,?is subject & pr$icate 9 ! case 9 "q1 are ! individual be=e u & 8 dea? )9 ! /at$ p]iod4 ,reg>d$ by !mselves !re is no?+ 9 common betwe5 !m1 & !re=e no l9k by :i* !y may be connect$ or disconnect$ ) ea* o!r4 ,! v>i\s classes above ref]r$ to are a set ( su* middle t]ms1 & ! propositions belong+ to !m are a correspond+ set ( major premises4 ,by ! help ( any "o ( !m we are enabl$1 "u suitable circum/ances1 to connect toge!r ! subject & pr$icate ( ! conclusion1 t is1 to inf] :e!r ! man w or w n live tw5ty ye>s4 #ae4 ,n[ 9 ! p]=mance ( su* a logical process !re are two consid]ations to :i* ! read]'s att5tion mu/ = a mom5t be direct$4 ,!y are simple en\gh 9 ?is case1 b w ne$ c>eful explanation 9 ! correspond+ case 9 ,probability4 ,9 ! fir/ place1 x is cle> t :5ev] we c make any inf]5ce at all1 we c d s ) absolute c]ta9ty4 ,logic1 )9 its own doma91 kn[s no?+ ( hesitation or d\bt4 ,if ! middle t]m is appropriate x s]ves to connect ! extremes 9 su* a way z to preclude all unc]ta9ty ab\t ! conclusion2 if x is n1 !re is s f> an end ( ! matt]3 no conclusion c be drawn1 & we are !re=e left :]e we 74 ,assum+ our premises to be correct1 we ei!r "k our conclusion = c]ta91 or we "k no?+ :atev] ab\t x4 ,9 ! second place1 x %\ld be notic$ t none ( ! possible alt]natives 9 ! %ape ( su* major premises z ^? giv5 above c ev] contradict any ( ! o!rs1 or be at all inconsi/5t ) !m4 ,reg>d$ z isolat$ propositions1 !re is ( c\rse no?+ to secure su* h>mony2 !y h v diff]5t pr$icates1 & may seem q out ( ea* o!r's rea* = ei!r support or opposition4 ,b by means ( ! o!r premise !y are 9 ea* case br\ght into relation ) "o ano!r1 & ! g5]al int]e/s ( tru? & consi/5cy prev5t !m !re=e f contradict+ "o ano!r4 ,z isolat$ propositions x might h be5 ! case t all m5 live to fifty1 & t no ,indian resid5ts d s1 b hav+ recognis$ t "s m5 are resid5ts 9 ,india1 we see at once t ^! premises are inconsi/5t1 & !re=e t "o or o!r ( !m mu/ be reject$4 ,9 all appli$ logic ?is necessity ( avoid+ self-contradiction is s obvi\s & imp]i\s t no "o w\ld ?9k x necess>y to lay d[n ! =mal po/ulate t all su* possible major premises are to be mutually consi/5t4 ,to suppose t ?is po/ulate is n compli$ )1 w\ld be 9 effect to make two or m contradictory assumptions ab\t matt]s ( fact4 #af4 ,b n[ obs]ve ! diff]5ce :5 we attempt to take ! correspond+ /ep 9 ,probability4 ,= ord9>y propositions1 univ]sal or p>ticul>1 sub/itute /ati/ical propositions ( :at we h be5 9 ! habit ( call+ ! 'proportional' k9d4 ,9 o!r words1 in/ead ( ask+ :e!r ! man w live = tw5ty ye>s1 let u ask :e!r he w live = "o ye>8 ,we %all be unable to f9d any univ]sal propositions :i* w cov] ! case1 b we may )\t difficulty obta9 an abundance ( appropriate proportional ones4 ,!y w be ( ! foll[+ description3--,( m5 ag$ #cj1 #ih 9 #ajj live ano!r ye>2 ( resid5ts 9 ,india a small] proportion survive1 let u = example say #ij 9 #ajj2 ( m5 suff]+ f canc] a small] proportion /ill1 let u say #bj 9 #ajj4 ,n[ 9 bo? ( ! respects to :i* att5tion has j be5 drawn1 propositions ( ?is k9d (f] a m>k$ contra/ ) ^? la/ consid]$4 ,9 ! fir/ place1 !y d n1 l ord9>y propositions1 ei!r ass]t unequivocally yes or no1 or else refuse to op5 _! lips2 b !y give in/ead a sort ( qualifi$ or hesitat+ answ] conc]n+ ! individuals includ$ 9 !m4 ,?is is ( c\rse no?+ m ?an ! famili> *>act]i/ic ( :at may be call$ 'probability propositions4' ,b x leads up to1 & inde$ r5d]s possible1 ! second & m important po9t2 viz4 t ^! v>i\s answ]s1 ?\gh !y _c directly & =mally contradict ea* o!r 7?is _! nature z proportional propositions1 w n z a rule p]mit71 may yet1 9 a way :i* w n[ h to be po9t$ out1 be f\nd to be m or less 9 conflict ) ea* o!r4 ,h5ce x foll[s t 9 ! attempt to draw a conclusion f premises ( ! k9d 9 "q1 we may be plac$ 9 a position ( "s p]plexity2 b x is a p]plexity :i* may pres5t itself 9 two =ms1 a mild & an aggravat$ =m4 ,we w notice !m 9 turn4 #ag4 ,! mild =m occurs :5 ! diff]5t classes to :i* ! individual case may be appropriately ref]r$ are successively includ$ "o )9 ano!r2 = "h our sets ( /ati/ics1 ?\gh lead+ to diff]5t results1 w n (t5 be f\nd to be v s]i\sly at v>iance ) "o ano!r4 ,all t comes ( x is t z we asc5d 9 ! scale by appeal+ to high] & high] g5]a1 ! /ati/ics gr[ cont9ually less appropriate to ! p>ticul> case 9 po9t1 & su* in=mation !re=e z !y af=d becomes gradually less explicit & accurate4 ,! "q t we orig9ally want$ to det]m9e1 be x rememb]$1 is :e!r ,john ,smi? w die )9 "o ye>4 ,b all k ( ?is fact be+ unatta9able1 ow+ to ! abs5ce ( suitable inductions1 we felt ju/ifi$ 7) ! explanation1 & "u ! re/rictions m5tion$ 9 ,*ap ,,vi471 9 sub/itut+1 z ! only available equival5t = su* individual k1 ! answ] to ! foll[+ /ati/ical enquiry1 ,:at proportion ( m5 9 8 circum/ances die8 #ah4 ,b !n at once !re beg9s to arise "s d\bt & ambiguity z to :at exactly is to be und]/ood by 8 circum/ances4 ,we may "k v well :at ^! circum/ances are 9 !mselves1 & yet be 9 p]plexity z to h[ _m ( !m we ought to take into acc\nt :5 endeav\r+ to e/imate 8 fate4 ,we might conceivably1 = a beg9n+1 *oose to conf9e our att5tion to ^? prop]ties only :i* he has 9 common ) all animals4 ,if s1 & /ati/ics on ! subject 7 atta9able1 !y w\ld presumably be ( "s su* "* z ?is1 ,n9ety-n9e animals out ( a hundr$ die )9 a ye>4 ,unusual z su* a ref]5ce w\ld be1 we %\ld1 logically speak+1 be do+ no?+ m ?an tak+ a wid] class ?an ! "o we 7 accu/om$ to4 ,simil>ly we might1 if we pleas$1 take our /& at ! class ( v]tebrates1 or at t ( mammalia1 if zoologi/s 7 able to give u ! requisite in=mation4 ,( c\rse we reject ^! wide classes & pref] a n>r[] "o4 ,if ask$ :y we reject !m1 ! natural answ] is t !y are s g5]al1 & resemble ! p>ticul> case be=e u 9 s few po9ts1 t we %\ld be exce$+ly likely to g a/ray 9 tru/+ to !m4 ,?\gh accuracy _c be insur$1 we may at lea/ avoid any ne$less exagg]ation ( ! relative numb] & magnitude ( our errors4 #ai4 ,! above answ] is q valid2 b :il/ caution+ u aga9/ appeal+ to too wide a class1 x seems to sugge/ t we _c g wrong 9 ! opposite direction1 t is 9 tak+ too n>r[ a class4 ,& yet we d avoid any su* extremes4 ,john ,smi? is n only an ,engli%man2 he may also be a native ( su* a "p ( ,engl&1 be liv+ 9 su* a ,presid5cy1 & s on4 ,an indef9ite numb] ( su* additional *>act]i/ics might be br\ght out into notice1 _m ( :i* at any rate h "s be>+ ^u ! "q ( vitality4 ,:y d we reject any consid]ation ( ^! n>r[] classes8 ,we d reject !m1 b x is = :at may be t]m$ a practical r ?an a !oretical reason4 ,z 0 expla9$ 9 ! fir/ *apt]s1 x is ess5tial t our s]ies %\ld conta9 a consid]able numb] ( t]ms if !y are to be ( any s]vice to u4 ,n[ _m ( ! attributes ( any individual are s r>e t to take !m into acc\nt w\ld be at v>iance ) ! fundam5tal assumption ( our sci5ce1 viz4 t we are prop]ly conc]n$ only ) ! av]ages ( l>ge numb]s4 ,! m special & m9ute our /ati/ics ! bett]1 provid$ only t we c get en\gh ( !m1 & s make up ! requisite l>ge numb] ( in/ances4 ,?is is1 h[ev]1 impossible 9 _m cases4 ,we are !re=e oblig$ to neglect "o attribute aft] ano!r1 & s to enl>ge ! cont5ts ( our class2 at ! av[$ risk ( some:at increas$ v>iety & unsuitability 9 ! memb]s ( x1 = at ea* /ep ( ?is k9d we div]ge m & m f ! sort ( in/ances t we really want4 ,we cont9ue to d s1 until we no long] ga9 m 9 quantity ?an we lose 9 quality4 ,we f9ally take our /& at ! po9t :]e we fir/ obta9 /ati/ics drawn f a suffici5tly l>ge range ( obs]vation to secure ! requisite degree ( /ability & uni=mity4 #bj4 ,9 su* an example z ! "o j m5tion$1 :]e "o ( ! successive classes--man--is a well-def9$ natural k9d or species1 !re is su* a complete break 9 ea* direction at ?is po9t1 t e "o is prompt$ to take 8 /& "h4 ,on ! "o h&1 no enquir] w\ld ev] ?9k ( introduc+ any ref]5ce to ! high] classes ) few] attributes1 su* z animal or organiz$ be+3 & on ! o!r h&1 ! inf]ior classes1 creat$ by our tak+ notice ( 8 employm5t or place ( resid5ce1 c41 d n z a rule diff] suffici5tly 9 _! *>act]i/ics f ! class man to make x wor? our :ile to att5d to !m4 ,n[ & !n inde$ ^! *>act]i/ics d rise into importance1 & :5ev] ?is is ! case we conc5trate our att5tion ^u ! class to :i* !y correspond1 t is1 ! class :i* is m>k$ (f by _! pres5ce4 ,?us1 = in/ance1 ! quality ( consumptiv5ess sep>ates any "o (f s widely f ! majority ( 8 fell[-m5 9 all que/ions p]ta9+ to mortality1 t /ati/ics ab\t ! lives ( consumptive m5 diff] mat]ially f ^? :i* ref] to m5 9 g5]al4 ,& we see ! result2 if a consumptive man c effect an insurance at all1 he mu/ d x = a mu* high] premium1 calculat$ ^u 8 special circum/ances4 ,9 o!r words1 ! attribute is suffici5tly important to m>k (f a fre% class or s]ies4 ,s ) insurance aga9/ accid5t4 ,x is n inde$ attempt$ to make a special rate ( insurance = ! memb]s ( ea* sep>ate trade1 b ! diff]5ces ( risk to :i* !y are liable oblige u to take su* facts to "s degree into acc\nt4 ,h5ce1 trades are r\ghly divid$ into two or ?ree classes1 su* z ! ord9>y1 ! haz>d\s1 & ! extra-haz>d\s1 ea* hav+ to pay its own rate ( premium4 #ba4 ,:]e "o or o!r ( ! classes ?us corresponds to natural k9ds1 or involves di/9ctions ( co-ord9ate importance ) ^? ( natural k9ds1 ! process is n difficult2 !re is almo/ always "s "o ( ^! classes :i* is s univ]sally recognis$ to be ! appropriate "o1 t mo/ p]sons are q unaw>e ( !re be+ any necessity = a process ( selection4 ,except 9 ! cases :]e a man has a sickly con/itution1 or foll[s a dang]\s employm5t1 we seldom h occasion to collect /ati/ics = him f any class b t ( m5 9 g5]al ( 8 age 9 ! c\ntry4 ,:51 h[ev]1 ^! successive classes are n ready m>k$ out = u by nature1 & !nce arrang$ 9 easily di/+ui%able gr\ps1 ! process is m obvi\sly arbitr>y4 ,suppose we 7 consid]+ ! *ance ( a man's h\se be+ burnt d[n1 ) :at collection ( attributes %\ld we re/ cont5t 9 ?is in/ance8 ,%\ld we include all k9ds ( build+s1 or only dwell+-h\ses1 or conf9e ourselves to ^? :]e !re is mu* wood1 or ^? :i* h /oves8 ,all ^! attributes1 & a multitude ( o!rs may be pres5t1 &1 if s1 !y are all circum/ances :i* help to modify our judgm5t4 ,we mu/ be guid$ "h by ! /ati/ics :i* we happ5 to be able to obta9 9 suffici5t numb]s4 ,"h aga91 r\gh di/9ctions ( ?is k9d are practically drawn 9 ,insurance ,(fices1 by divid+ risks into ord9>y1 haz>d\s1 & extra-haz>d\s4 ,we exam9e our case1 ref] x to "o or o!r ( ^! classes1 & !n =m our judgm5t ^u its prospects by ! /ati/ics appropriate to its class4 #bb4 ,s mu* = :at may be call$ ! mild =m 9 :i* ! ambiguity occurs2 b !re is an aggravat$ =m 9 :i* x may %[ itself1 & :i* at fir/ sight seems to place u 9 f> great] p]plexity4 ,suppose t ! diff]5t classes m5tion$ above are n includ$ successively "o )9 ! o!r4 ,we may !n be q at a loss :i* ( ! /ati/ical tables to employ4 ,let u assume1 = example1 t n9e out ( t5 ,engli%m5 are injur$ by resid5ce 9 ,madeira1 b t n9e out ( t5 consumptive p]sons are b5efit$ by su* a resid5ce4 ,^! /ati/ics1 ?\gh fanciful1 are conceivable & p]fectly compatible4 ,john ,smi? is a consumptive ,engli%man2 are we to recomm5d a visit to ,madeira 9 8 case or n8 ,9 o!r words1 :at inf]5ces are we to draw ab\t ! probability ( 8 dea?8 ,bo? ( ! /ati/ical tables apply to 8 case1 b !y w\ld lead u to directly contradictory conclusions4 ,?is does n mean1 ( c\rse1 contradictory precisely 9 ! logical s5se ( t ^w1 = "o ( ^! propositions does n ass]t t an ev5t mu/ happ5 & ! o!r d5y t x mu/2 b contradictory 9 ! s5se t "o w\ld cause u 9 "s consid]able degree to believe :at ! o!r w\ld cause u 9 "s consid]able degree to disbelieve4 ,?is ref]s1 ( c\rse1 to ! individual ev5ts2 ! /ati/ics are by supposition 9 no degree contradictory4 ,)\t fur!r data1 !re=e1 we c come to no decision4 #bc4 ,practically1 ( c\rse1 if we 7 =c$ to a decision ) only ^! data be=e u1 we %\ld make our *oice by ! consid]ation t ! /ate ( a man's lungs has probably m to d ) 8 heal? ?an ! place ( 8 bir? has2 t is1 we %\ld conclude t ! duration ( life ( consumptive ,engli%m5 corresponds mu* m closely ) t ( consumptive p]sons 9 g5]al ?an ) t ( _! heal?y c\ntrym54 ,b ?is is1 ( c\rse1 to import empirical consid]ations into ! "q4 ,! data1 z !y are giv5 to u1 & if we conf9e ourselves to !m1 leave u 9 absolute unc]ta9ty ^u ! po9t4 ,x may be t ! consumptive ,engli%m5 almo/ all die :5 transport$ into ! o!r climate2 x may be t !y almo/ all recov]4 ,if !y die1 ?is is 9 obvi\s accordance ) ! fir/ set ( /ati/ics2 x w be f\nd 9 accordance ) ! second set ?r\gh ! fact ( ! =eign consumptives pr(it+ by ! *ange ( climate 9 m ?an :at might be t]m$ _! due proportion4 ,a simil> explanation w apply to ! o!r alt]native1 viz4 to ! supposition t ! consumptive ,engli%m5 mo/ly recov]4 ,! problem is1 !re=e1 left absolutely indet]m9ate1 = we _c "h appeal to any g5]al rule s simple & s obvi\sly applicable z t :i*1 9 a =m] case1 recomm5d$ u always to pref] ! m special /ati/ics1 :5 suffici5tly ext5sive1 to ^? :i* are wid] & m g5]al4 ,we h no means "h ( kn[+ :e!r "o set is m special ?an ! o!r4 ,& 9 ?is no difficulty c be f\nd1 s long z we conf9e ourselves to a j view ( ! subject4 ,let me aga9 recall to ! read]'s m9d :at our pres5t position is2 we h sub/itut$ = k ( ! individual 7f9d+ t unatta9able7 a k ( :at occurs 9 ! av]age ( simil> cases4 ,?is /ep _h to be tak5 ! mom5t ! problem 0 h&$ ov] to ,probability4 ,b ! conception ( simil>ity 9 ! cases introduces u to a p]plexity2 we manage inde$ to evade x 9 _m in/ances1 b "h x is inevitably =c$ ^u our notice4 ,!re are "h two aspects ( ?is simil>ity1 & !y introduce u to two di/9ct av]ages4 ,two ass]tions are made z to :at happ5s 9 ! long run1 & bo? ( ^! ass]tions1 by supposition1 are v]ifi$4 ,( _! tru? !re ne$ be no d\bt1 = bo? 7 suppos$ to be obta9$ f exp]i5ce4 #bd4 ,x may p]haps be suppos$ t su* an example z ?is is a r$uctio ad absurdum ( ! pr9ciple ^u :i* ,life & o!r ,insurances are f\nd$4 ,b a mom5t's consid]ation w %[ t ?is is q a mi/ake1 & t ! pr9ciple ( insurance is j z applicable to examples ( ?is k9d z to any o!r4 ,an (fice ne$ f9d no difficulty 9 ! case suppos$4 ,!y might 7= a reason to be m5tion$ pres5tly1 !y probably w\ld n7 insure ! individual )\t inconsi/5cy at a rate det]m9$ by ei!r av]age4 ,!y might say to him1 ,y are an ,engli%man4 ,out ( ! multitude ( ,engli% :o come to u n9e 9 t5 die if !y g to ,madeira4 ,we w insure y at a rate assign$ by ^! /ati/ics1 kn[+ t 9 ! long run all w come "r s f> z we are conc]n$4 ,y are also consumptive1 x is true1 & we d n "k :at proportion ( ! ,engli% are consumptive1 nor :at proportion ( ,engli% consumptives die 9 ,madeira4 ,b ?is does n really matt] = our purpose4 ,! =mula1 n9e 9 t5 die1 is 9 reality calculat$ by tak+ into acc\nt ^! unkn[n proportions2 =1 ?\gh we d n "k !m 9 !mselves1 /ati/ics tell u all t we c>e to "k ab\t _! results4 ,9 o!r words1 :atev] unkn[n elem5ts may exi/1 mu/1 9 reg>d to all ! effects :i* !y c produce1 h be5 already tak5 into acc\nt1 s t our ignorance ab\t !m _c 9 ! lea/ degree invalidate su* conclusions z we are able to draw4 ,& ?is is suffici5t = our purpose4 ,b precisely ! same language might be held to him if he pres5t$ himself z a consumptive man2 t is to say1 ! (fice c\ld safely c>ry on its proce$+s ^u ei!r alt]native4 ,?is w\ld1 ( c\rse1 be a v imp]fect /ate = ! matt] to be left 94 ,! only rational plan w\ld be to isolate ! case ( consumptive ,engli%m51 s z to make a sep>ate calculation = _! circum/ances4 ,?is calculation w\ld !n at once sup]s$e all o!r tables s f> z !y 7 conc]n$2 = ?\gh1 9 ! end1 x c\ld n arrogate to itself any sup]iority ov] ! o!rs1 x w\ld 9 ! mean "t be m>k$ by few] & slight] ab]rations f ! tru?4 #be4 ,! real reason :y ! ,insurance (fice c\ld n long "w on ! above t]ms is ( a v diff]5t k9d f t :i* "s read]s might contemplate1 & belongs to a class ( consid]ations :i* h be5 mu* neglect$ 9 ! attempts to con/ruct sci5ces ( ! diff]5t bran*es ( human conduct4 ,x is no?+ else ?an t annoy+ cont+5cy to :i* prophets s9ce ! "t ( ,jonah h be5 subject1 ( utt]+ suicidal prophecies2 ( publi%+ conclusions :i* are p]fectly c]ta9 :5 e condition & cause b "o h be5 tak5 into acc\nt1 t "o be+ ! effect ( ! prophecy itself ^u ^? to :om x ref]s4 ,9 our example above1 ! (fice 79 s f> z ! p>ticul> cases 9 ,madeira are conc]n$7 w\ld get on v well until ! consumptive ,engli%m5 9 "q f\nd out :at mu* bett] t]ms !y c\ld make by ann\nc+ !mselves z consumptives1 & pay+ ! premium appropriate to t class1 in/ead ( ann\nc+ !mselves z ,engli%m54 ,b if !y did ?is !y w\ld ( c\rse be di/urb+ ! /ati/ics4 ,! tables 7 bas$ ^u ! assumption t a c]ta9 fix$ proportion 7x does n matt] :at proportion7 ( ! ,engli% lives w\ld cont9ue to be consumptive lives1 :i*1 "u ! suppos$ circum/ances1 w\ld probably soon cease to be true4 ,:5 x is said t n9e ,engli%m5 out ( t5 die 9 ,madeira1 x is meant t ( ^? :o come to ! (fice1 z ! phrase is1 at r&om1 or 9 _! fair proportions1 n9e-t5?s die4 ,! consumptives are suppos$ to g !re j l r$-hair$ m51 or poets1 or any o!r special class4 ,or !y might g 9 any proportions great] or less ?an ^? ( o!r classes1 s long z !y adh]$ to ! same proportion ?r\gh\t4 ,! tables are !n calculat$ on ! cont9uance ( ?is /ate ( ?+s2 ! practical contradiction is 9 suppos+ su* a /ate ( ?+s to cont9ue aft] ! p _h once _h a look at ! tables4 ,if we m]ely make ! assumption t ! publication ( ^! tables made no su* alt]ation 9 ! conduct ( ^? to :om x ref]r$1 no hit* ( ?is k9d ne$ occur4 #bf4 ,! assumptions "h made1 z has be5 said1 are n 9 any way contradictory1 b !y ne$ "s explanation4 ,x w readily be se5 t1 tak5 toge!r1 !y are inconsi/5t ) ! supposition t ea* ( ^! classes is homog5e\s1 t is1 t ! /ati/ical proportions :i* hold ( ! :ole ( ei!r ( !m w also hold ( any portion ( !m :i* we may take4 ,!re are c]ta9 individuals 7viz4 ! consumptive ,engli%m57 :o belong to ea* class1 & ( c\rse ! two diff]5t sets ( /ati/ics _c bo? be true ( !m tak5 by !mselves4 ,!y might co9cide 9 _! *>act]i/ics ) ei!r class1 b n ) bo?2 probably 9 mo/ practical cases !y w co9cide ) nei!r1 b be ( a some:at int]m$iate "*4 ,n[ :5 x is said ( any su* het]og5e\s body t1 say1 n9e-t5?s die1 :at is meant 7or r impli$7 is t ! class might be brok5 up into small] subdivisions ( a m homog5e\s "*1 9 "s ( :i*1 ( c\rse1 m ?an n9e-t5?s die1 :il/ 9 o!rs less1 ! diff]5ces dep5d+ ^u _! "*1 con/itution1 pr(ession1 c42 ! numb] ( su* divisions & ! am\nt ( _! div]g5ce f "o ano!r be+ p]haps v consid]able4 ,n[ :5 we speak ( ei!r class z a :ole & say t n9e-t5?s die1 ! mo/ natural & s\nde/ mean+ is t t w\ld be ! proportion if all )\t exception w5t abroad1 or 7:at comes to ! same ?+7 if ea* ( ^! v>i\s subdivisions 0 repres5t$ 9 fair proportion to its numb]s4 ,or x might only be meant t !y g 9 "s o!r proportion1 dep5d+ ^u _! ta/es1 pursuits1 & s on4 ,b :atev] mean+ be adopt$ "o condition is necess>y1 viz4 t ! proportion ( ea* class t w5t at ! "t ! /ati/ics 7 drawn up mu/ be adh]$ to ?r\gh\t4 ,:5 ! class is homog5e\s ?is is n ne$$1 b :5 x is het]og5e\s ! /ati/ics w\ld be int]f]$ ) unless ?is condition 7 secur$4 ,we are "h suppos$ to h two sets ( /ati/ics1 "o = ! ,engli% & "o = ! consumptives1 s t ! consumptive ,engli% are 9 a s5se c\nt$ twice ov]4 ,if _! mortality is ( an int]m$iate am\nt1 !re=e1 !y s]ve to keep d[n ! mortality ( "o class & to keep up t ( ! o!r4 ,if ! /ati/ics are suppos$ to be exhau/ive1 by ref]r+ to ! :ole ( ea* class1 x foll[s t actually ! same individuals mu/ be c\nt$ ea* "t2 b if repres5tatives only ( ea* class are tak51 ! same individuals ne$ n be ins]t$ 9 ea* set ( tables4 #bg4 ,:5 !re=e !y come to insure 7our rem>ks are /ill conf9$ to our suppos$ ,madeira case71 we h "s ,engli% consumptives c\nt$ z ,engli%1 & pay+ ! high rate2 & o!rs c\nt$ z consumptives & pay+ ! l[ rate4 ,logically inde$ we may suppose !m all ent]$ 9 ea* class1 & pay+ !re=e ea* rate4 ,:at we h said above is t any individual may be conceiv$ to pres5t himself = ei!r ( ^! classes4 ,conceive t "s "o else pays 8 premium = him1 s t x is a matt] ( indiff]5ce to him p]sonally at :i* rate he insures1 & !re is no?+ to prev5t "s ( ! class 7or = t matt] all7 go+ to "o class1 & o!rs 7or all aga97 go+ to ! o!r class4 ,s long !re=e z we make ! logically possible ?\gh practically absurd supposition t "s m5 w cont9ue to pay a high] rate ?an !y ne$1 !re is no?+ to prev5t ! ,engli% consumptives 7"s or all7 f insur+ 9 ea* category & pay+ its appropriate premium4 ,z soon z !y gave any ?\ght to ! matt]1 ( c\rse !y w\ld1 9 ! case suppos$1 all pref] to insure z consumptives4 ,b _! do+ ?is w\ld di/urb ea* set ( /ati/ics4 ,! ,engli% mortality 9 ,madeira w\ld in/antly become heavi]1 s f> z ! ,insurance company 0 conc]n$1 by ! loss ( all _! be/ lives2 :il/ ! consumptive /ati/ics 7unless all ! ,engli% consumptives _h already be5 tak5 = insurance7 w\ld be 9 ! same way det]iorat$4#e ,a slight readju/m5t !re=e ( ea* scale ( insurance w\ld !n be ne$$2 ?is is ! di/urbance m5tion$ j above4 ,x mu/ be cle>ly und]/ood1 h[ev]1 t x is n our orig9al /ati/ics :i* h prov$ to be inconsi/5t1 b simply t !re 7 practical ob/acles to c>ry+ out a sy/em ( insurance ^u !m4 #bh4 ,examples subject to ! difficulty n[ "u consid]ation w d\btless seem p]plex+ to ! /ud5t unacqua9t$ ) ! subject4 ,!y are difficult to reconcile ) any o!r view ( ! sci5ce ?an t insi/$ on ?r\gh\t ?is ,essay1 viz4 t we are only conc]n$ ) av]ages4 ,x w p]haps be urg$ t !re are two diff]5t values ( ! man's life 9 ^! cases1 & t !y _c bo? be true4 ,:y n8 ,! 'value' ( 8 life is simply ! numb] ( ye>s to :i* m5 9 8 circum/ances d1 on ! av]age1 atta92 we h ! man set be=e u "u two diff]5t circum/ances2 :at wond]1 !re=e1 t ^! %\ld (f] diff]5t av]ages8 ,9 su* an objection x is =gott5 t we h _h to sub/itute = ! unatta9able result ab\t ! individual1 ! really atta9able result ab\t a set ( m5 z mu* l him z possible4 ,! difficulty & app>5t contradiction only arise :5 p w try to f9d "s ju/ification = _! belief 9 ! individual case4 ,:at c we possibly conclude1 x may be ask$1 ab\t ?is p>ticul> man ,john ,smi?'s prospects :5 we are ?us (f]$ two diff]5t values = 8 life8 ,no?+ :atev]1 x mu/ be repli$2 nor c\ld we 9 reality draw a conclusion1 be x rememb]$1 9 ! =m] case1 :5 we 7 practically conf9$ to "o set ( /ati/ics4 ,!re also we _h :at we call$ ! 'value' ( 8 life1 & s9ce we only knew ( "o su* value1 we came to reg>d x z 9 "s s5se appropriate to him z an individual4 ,"h1 on ! o!r h&1 we h two values1 belong+ to diff]5t s]ies1 & z ^! values are really diff]5t x may be compla9$ t !y are discordant1 b su* a compla9t c only be made :5 we d :at we h no "r to d1 viz4 assign a value to ! individual :i* %all admit ( individual ju/ification4 #bi4 ,is x !n p]fectly arbitr>y :at s]ies or class ( in/ances we select by :i* to judge8 ,by no means2 x has be5 /at$ repeat$ly t 9 *oos+ a s]ies1 we mu/ seek = "o ! memb]s ( :i* %all resemble our individual 9 z _m ( 8 attributes z possible1 subject only to ! re/riction t x mu/ be a suffici5tly ext5sive s]ies4 ,:at is meant is1 t 9 ! above case1 :]e we h two s]ies1 we _c fairly call !m contradictory2 ! only valid *>ge is "o ( incomplet5ess or insuffici5cy = _! purpose1 a *>ge :i* applies 9 exactly ! same s5se1 be x rememb]$1 to all /ati/ics :i* comprise g5]a unnecess>ily wid] ?an ! species ) :i* we are conc]n$4 ,! only diff]5ce betwe5 ! two diff]5t classes ( cases is1 t 9 ! "o in/ance we are on a pa? :i* we "k w lead at ! la/1 ?r\gh _m errors1 t[>ds ! tru? 79 ! s5se 9 :i* tru? c be atta9$ "h71 & we took x = want ( a bett]4 ,9 ! o!r in/ance we h two su* pa?s1 p]fectly diff]5t pa?s1 ei!r ( :i* h[ev] w lead u t[>ds ! tru? z be=e4 ,contradiction c only seem to arise :5 x is attempt$ to ju/ify ea* sep>ate /ep on our pa?s1 z well z _! ultimate t5d5cy4 ,/ill x _c be d5i$ t ^! objections are a s]i\s drawback to ! complet5ess & validity ( any anticipations :i* are m]ely f\nd$ ^u /ati/ical frequ5cy1 at any rate 9 an e>ly /age ( exp]i5ce1 :5 b few /ati/ics h be5 collect$4 ,su* k z ,probability c give is n 9 any individual case ( a high ord]1 be+ subject to ! *>act]i/ic infirmity ( repeat$ error2 b ev5 :5 measur$ by its own /&>d x comm5ces at a v l[ /age ( pr(ici5cy4 ,! errors are !n relatively v num]\s & l>ge comp>$ ) :at !y may ultimately be r$uc$ to4 #cj4 ,"h z else:]e !re is a cont9u\s process ( specialization go+ on4 ,! ne$s ( a gradually wid5+ exp]i5ce are p]petually call+ ^u u to subdivide classes :i* are f\nd to be too het]og5e\s4 ,sometimes ! only compla9t t has to be made is t ! class to :i* we are oblig$ to ref] is f\nd to be some:at too broad to suit our purpose1 & t x might be subdivid$ ) conv5i5ce4 ,?is is ! case1 z has be5 %[n above1 :5 an ,insurance (fice f9ds t its increas+ bus9ess makes x possible & desirable to sep>ate (f ! m5 :o foll[ "s p>ticul> trades f ! re/ ( _! fell[-c\ntrym54 ,simil>ly 9 e o!r dep>tm5t 9 :i* /ati/ics are made use (4 ,?is increas$ dem& = specificness leads1 9 fact1 z naturally 9 ?is direction1 z does ! progress ( civilization to ! subdivision ( trades 9 any t[n or c\ntry4 ,s 9 ref]5ce to ! o!r k9d ( p]plexity m5tion$ above4 ,no?+ is m common 9 ^? sci5ces or practical arts1 9 :i* d$uction is b little available1 & :]e 9 consequ5ce our k is = ! mo/ "p ( ! empirical k9d1 ?an to meet ) sugge/ions :i* po9t m or less directly 9 contr>y directions4 ,:5ev] "s new sub/ance is discov]$ or br\ght into m g5]al use1 ^? :o h to deal ) x mu/ be famili> ) su* a /ate ( ?+s4 ,! m$ical man :o has to employ a new drug may (t5 f9d himself confront$ by ! two di/9ct recomm5dations1 t on ! "o h& x %\ld be employ$ = c]ta9 diseases1 & t on ! o!r h& x %\ld n be tri$ on c]ta9 con/itutions4 ,a man ) su* a con/itution1 b suff]+ f su* a disease1 pres5ts himself2 :i* recomm5dation is ! doctor to foll[8 ,he feels at once oblig$ to set to "w to collect n>r[] & m special /ati/ics1 9 ord] to escape f su* an ambiguity4 #ca4 ,9 ?is & a multitude ( analog\s cases af=d$ by ! m practical arts x is n ( c\rse necess>y t num]ical data %\ld be quot$ & appeal$ to2 x is suffici5t t ! judgm5t is m or less consci\sly det]m9$ by !m4 ,all t is necess>y to make ! examples appropriate is t we %\ld admit t 9 _! case /ati/ical data are our ultimate appeal 9 ! pres5t /ate ( k4 ,( c\rse if ! empirical laws c be resolv$ into _! compon5t causes we may appeal to direct d$uction1 & 9 ?is case ! employm5t ( /ati/ics1 & consequ5tly ! use ( ! !ory ( ,probability1 may be sup]s$$4 ,9 ?is direction !re=e1 z "t proce$s1 ! advance ( /ati/ical ref9em5t by ! incessant subdivision ( classes to meet ! develop+ wants ( man is pla9 en\gh4 ,b if we glance backw>ds to a m primitive /age1 we %all soon see 9 :at a v imp]fect /ate ! op]ation comm5ces4 ,at ?is e>ly /age1 h[ev]1 ,probability & ,induction are s closely connect$ toge!r z to be v apt to be m]g$ into "o1 or at any rate to h _! functions conf\nd$4 #cb4 ,s9ce ! g5]alization ( our /ati/ics is f\nd to belong to ,induction1 ?is process ( g5]alization may be reg>d$ z prior to1 or at lea/ indep5d5t (1 ,probability4 ,we h1 moreov]1 already discuss$ 79 ,*apt] ,,vi47 ! /ep correspond+ to :at are t]m$ imm$iate inf]5ces1 & 79 ,*apt] ,,vii47 t correspond+ to syllogi/ic inf]5ces4 ,our pres5t position !re=e is t 9 :i* we may consid] ourselves 9 possession ( any numb] ( g5]alizations1 b wi% to employ !m s z to make inf]5ces ab\t a giv5 individual2 j z 9 "o dep>tm5t ( common logic we are engag$ 9 f9d+ middle t]ms to e/abli% ! desir$ conclusion4 ,9 ?is latt] case ! process is f\nd to be extremely simple1 no accumulation ( diff]5t middle t]ms be+ able to lead to any real ambiguity or contradiction4 ,9 ,probability1 h[ev]1 ! case is diff]5t4 ,"h1 if we attempt to draw inf]5ces ab\t ! individual case be=e u1 z (t5 is attempt$--9 ! ,rule ( ,succession = example--we %all enc\nt] ! full =ce ( ?is ambiguity & contradiction4 ,treat ! "q1 h[ev]1 fairly1 & all difficulty disappe>s4 ,our inf]5ce really is n ab\t ! individuals z individuals1 b ab\t s]ies or successions ( !m4 ,we wi%$ to "k :e!r ,john ,smi? w die )9 ! ye>2 ?is1 h[ev]1 _c be kn[n4 ,b ,john ,smi?1 by ! possession ( _m attributes1 belongs to _m diff]5t s]ies4 ,! multiplicity ( middle t]ms1 !re=e1 is :at ought to be expect$4 ,we c "k :e!r a succession ( m51 resid5ts 9 ,india1 consumptives1 c4 die )9 a ye>4 ,we may make our selection1 !re=e1 among/ ^!1 & 9 ! long run ! belief & consequ5t conduct ( ourselves & o!r p]sons 7z describ$ 9 ,*apt] ,,vi47 w become capable ( ju/ification4 ,) reg>d to *oos+ "o ( ^! s]ies r ?an ano!r1 we h two oppos+ pr9ciples ( guidance4 ,on ! "o h&1 ! m special ! s]ies ! bett]2 =1 ?\gh n m "r 9 ! end1 we %all ?us be m ne>ly "r all along4 ,b1 on ! o!r h&1 if we try to make ! s]ies too special1 we %all g5]ally meet ! practical objection aris+ f insuffici5t /ati/ics4 #a4 ,"s ( my read]s may be famili> ) a v /rik+ digression 9 ,buffon's ,natural ,hi/ory 7,natural ,hi/4 ( ,man1 ,,viii471 9 :i* he supposes ! fir/ man 9 full possession ( 8 faculties1 b ) all 8 exp]i5ce to ga91 & speculates on ! gradual acquisition ( 8 k4 ,:atev] may be ?\ght ( 8 p>ticul> conclusions ! passage is v int]e/+ & sugge/ive to any /ud5t ( ,psy*ology4 #b4 ,see also ,dugald ,/ew>t 7,ed4 by ,hamilton2 ,,vii4 pp4 #aae-aai74 #c4 ,requir$ t is = purposes ( logical inf]5ce )9 ! limits ( ,probability2 x is n int5d$ to imply any d\bts z to its actual univ]sal preval5ce1 or its all-importance = sci5tific purposes4 ,! subject is m fully discuss$ 9 a future *apt]4 #d4 ,z p>ticul> propositions !y are bo? ( c\rse id5tical 9 =m4 ,! fact t ! '"s' 9 ! =m] corresponds to a l>g] proportion ?an 9 ! latt]1 is a di/9ction ali5 to pure ,logic4 #e4 ,! reason is obvi\s4 ,! heal?ie/ ,engli% lives 9 ,madeira 7viz4 ! consumptive ones7 h n[ ceas$ to be reckon$ z ,engli%2 :]eas ! wor/ consumptive lives !re 7viz4 ! ,engli%7 are n[ increas$ 9 relative numb]s4 ,,*apt] ,x4 ,,*ance ,,z ,,oppos$ ,,to ,,causation ,,& ,,design4 #a4 ,! rem>ks 9 ! previ\s *apt] w h s]v$ to cle> ! way = an enquiry :i* probably excites m popul> int]e/ ?an any o!r )9 ! range ( our subject1 viz4 ! det]m9ation :e!r su* & su* ev5ts are to be attribut$ to ,*ance on ! "o h&1 or to ,causation or ,design on ! o!r4 ,z ! pr9cipal difficulty seems to arise f ! ambiguity ) :i* ! problem is g5]ally conceiv$ & /at$1 ow+ to ! extreme g5]ality ( ! conceptions involv$1 x becomes necess>y to di/+ui% cle>ly betwe5 ! sev]al di/9ct issues :i* are apt to be involv$4 ,i4 ,!re is1 to beg9 )1 a v old objection1 f\nd$ on ! assumption :i* our sci5ce is suppos$ to make ( ! exi/5ce ( ,*ance4 ,! objection aga9/ *ance is ( c\rse _m c5turies old] ?an ! ,!ory ( ,probability2 & z x seems a ne>ly obsolete objection at ! pres5t day we ne$ n pause long = its consid]ation4 ,if we spelt ! ^w ) a capital ,c1 & ma9ta9$ t x 0 repres5tative ( "s di/9ct creative or adm9i/rative ag5cy1 we %\ld presumably be guilty ( "s =m ( ,mani*eism4 ,b ! only rational mean+ ( ! objection w\ld appe> to be t ! pr9ciples ( ! sci5ce compel u to assume t ev5ts 7"s ev5ts1 only1 t is7 happ5 )\t causes1 & are !reby remov$ f ! cu/om>y control ( ! ,deity4 ,z repeat$ly po9t$ out already ?is is altoge!r a mi/ake4 ,! sci5ce ( ,probability makes no assumption :atev] ab\t ! way 9 :i* ev5ts are br\ght ab\t1 :e!r by causation or )\t x4 ,all t we und]take to d is to e/abli% & expla9 a body ( rules :i* are applicable to classes ( cases 9 :i* we d n or _c make inf]5ces ab\t ! individuals4 ,! objection !re=e mu/ be some:at diff]5tly /at$1 & appe>s f9ally to r$uce itself to ?is3--t ! assumptions ^u :i* ! sci5ce ( ,probability re/s1 are n inconsi/5t ) a disbelief 9 causation )9 c]ta9 limits2 causation be+ ( c\rse und]/ood simply 9 ! s5se ( regul> sequ5ce4 ,s /at$ ! objection seems p]fectly valid1 or r ! facts on :i* x is bas$ mu/ be admitt$2 ?\gh :at connection !re w\ld be betwe5 su* lack ( causation & abs5ce ( ,div9e sup]9t5d5ce ,i q fail to see4 ,z ?is ,!ological objection di$ away ! m5 ( physical sci5ce1 & ^? :o sympa?iz$ ) !m1 began to en=ce ! same prote/2 & simil> cautions are /ill to be f\nd f "t to "t 9 mod]n treatises4 ,hume1 = in/ance1 9 8 %ort essay on ,probability1 comm5ces ) ! rem>k1 ?\gh !re be no su* ?+ z *ance 9 ! _w1 our ignorance ( ! real cause ( any ev5t has ! same influ5ce on ! und]/&+1 c4 ,de ,morgan inde$ goes s f> z to decl>e t ! f\ndations ( ! !ory ( ,probability h ceas$ to exi/ 9 ! m9d t has =m$ ! conception1 t any?+ ev] did happ5 or w happ5 )\t "s p>ticul> reason :y x %\ld h be5 precisely :at x 0 & n any?+ else4#a ,simil> rem>ks might be quot$ f ,laplace & o!rs4 #b4 ,9 ! p>ticul> =m ( ! controv]sy above ref]r$ to1 & :i* is mo/ly f\nd 9 ! region ( ! natural & physical sci5ces1 ! cont5tion t *ance & causation are irreconcileable occupies r a def5sive position2 ! ma9 fact insi/$ on be+ t1 :5ev] 9 ^! subjects we may happ5 to be ignorant ( ! details we h no w>rant = assum+ z a consequ5ce t ! details are uncaus$4 ,b ?is suppos$ irreconcileability is sometimes urg$ 9 a mu* m aggressive _s 9 ref]5ce to social enquiries4 ,"h ! attempt is (t5 made to prove causation 9 ! details1 f ! kn[n & admitt$ regul>ity 9 ! av]ages4 ,a consid]able am\nt ( controv]sy 0 excit$ "s ye>s ago ^u ?is topic1 9 great "p orig9at$ by ! vigor\s & outspok5 support ( ! necessit>ian side by ,buckle 9 8 ,hi/ory ( ,civilization4 ,x %\ld be rem>k$ t 9 ^! cases ! attempt is sometimes made z x 7 to />tle ! read] into acquiesc5ce by ! s+ul>ity ( ! examples *os54 ,in/ances are select$ :i*1 ?\gh !y possess no great] logical value1 are1 if "o may s express x1 emotionally m effective4 ,e read] ( ,buckle's ,hi/ory1 = in/ance1 w rememb] ! /ress :i* he laid ^u ! obs]v$ fact1 t ! numb] ( suicides 9 ,london rema9s ab\t ! same1 ye> by ye>2 & he may rememb] also ! sort ( panic ) :i* ! promulgation ( ?is fact 0 accompani$ 9 _m qu>t]s4 ,s too ! way 9 :i* ,laplace notices t ! numb] ( undirect$ lett]s annually s5t to ! ,po/ ,(fice rema9s ab\t ! same1 & ! comm5ts ( ,dugald ,/ew>t ^u ?is p>ticul> uni=mity1 seem to imply t !y reg>d$ ?is in/ance z m rem>kable ?an _m analog\s ones tak5 f o!r qu>t]s4 ,t !re is a c]ta9 f\ndation ( tru? 9 ! reason+s 9 support ( :i* ! above examples are advanc$1 _c be d5i$1 b _! au?ors appe> to me v mu* to ov]rate ! sort ( opposition t exi/s betwe5 ! !ory ( ,*ances & ! doctr9e ( ,causation4 ,z reg>ds fir/ t wid] conception ( ord] or regul>ity :i* we h t]m$ uni=mity1 any?+ :i* might be call$ objective *ance w\ld c]ta9ly be at v>iance ) ?is 9 "o respect4 ,9 ,probability ultimate regul>ity is always po/ulat$2 9 toss+ a die1 if n m]ely ! individual ?r[s 7 unc]ta9 9 _! results1 b ev5 ! av]age also1 ow+ to ! nature ( ! die1 or ! numb] ( ! m>ks ^u x1 be+ arbitr>ily int]f]$ )1 ( c\rse no k9d ( sci5ce w\ld attempt to take any acc\nt ( x4 #c4 ,s mu* mu/ und\bt$ly be grant$2 b mu/ ! same admission be made z reg>ds ! succession ( ! individual ev5ts8 ,c causation1 9 ! s5se ( inv>iable succession 7= we are "h %ift+ on to ?is n>r[] gr\nd71 be d5i$1 n inde$ )\t suspicion ( sci5tific het]odoxy1 b at any rate )\t ?r[+ unc]ta9ty ^u ! f\ndations ( ,probability8 ,de ,morgan1 z we h se51 /rongly ma9ta9s t ?is _c be s4 ,i f9d myself unable to agree ) him "h1 b ?is disagreem5t spr+s n s mu* f diff]5ces ( detail1 z f ^? ( ! po9t ( view 9 :i* we reg>d ! sci5ce4 ,he always appe>s to incl9e to ! op9ion t ! individual judgm5t 9 probability is to admit ( ju/ification2 t :5 we say1 = in/ance1 t ! odds 9 fav\r ( "s ev5t are ?ree to two1 t we c expla9 & ju/ify our /atem5t )\t any necess>y ref]5ce to a s]ies or class ( su* ev5ts4 ,x is n easy to see h[ ?is c be done 9 any case1 b ! ob/acles w\ld d\btless be great] ev5 ?an !y are1 if k ( ! individual ev5t 7 n m]ely unatta9$1 b1 ow+ to ! abs5ce ( any causal connection1 ess5tially unatta9able4 ,on ! !ory adopt$ 9 ?is "w we simply po/ulate ignorance ( ! details1 b x is n reg>d$ z ( any importance on :at sort ( gr\nds ?is ignorance is bas$4 ,x may be t k is out ( ! "q f ! nature ( ! case1 ! causative l9k1 s to say1 be+ miss+4 ,x may be t su* l9ks are kn[n to exi/1 b t ei!r we _c asc]ta9 !m1 or %\ld f9d x tr\blesome to d s4 ,x is ! fact ( ?is ignorance t makes u appeal to ! !ory ( ,probability1 ! gr\nds ( x are ( no importance4 #d4 ,on ! view "h adopt$ we are conc]n$ only ) av]ages1 or ) ! s+le ev5t z d$uc$ f an av]age & conceiv$ to =m "o ( a s]ies4 ,we />t ) ! assumption1 gr\nd$ on exp]i5ce1 t !re is uni=mity 9 ?is av]age1 &1 s long z ?is is secur$ to u1 we c af=d to be p]fectly indiff]5t to ! fate1 z reg>ds causation1 ( ! individuals :i* compose ! av]age4 ,! "q !n assumes ! foll[+ =m3--,is ?is assumption1 ( av]age regul>ity 9 ! aggregate1 inconsi/5t ) ! admission ( :at may be t]m$ causeless irregul>ity 9 ! details8 ,x does n seem to me t x w\ld be at all easy to prove t ?is is s4 ,z a matt] ( fact ! two beliefs h con/antly co-exi/$ 9 ! same m9ds4 ,?is may n c\nt = mu*1 b x sugge/s t if !re be a contradiction betwe5 !m x is by no means palpable & obvi\s4 ,millions1 = in/ance1 h believ$ 9 ! g5]al uni=mity ( ! seasons tak5 "o ) ano!r1 :o c]ta9ly did n believe 91 & w\ld v likely h be5 ready di/9ctly to d5y1 ! exi/5ce ( necess>y sequ5ces 9 ! v>i\s ph5om5a :i* compose :at we call a season4 ,s ) c>ds & dice2 almo/ e gambl] mu/ h recogniz$ t judgm5t & =esight are ( use 9 ! long run1 b writ]s on *ance seem to ?9k t gambl]s ne$ a good deal ( reason+ to conv9ce !m t ea* sep>ate ?r[ is 9 its nature ess5tially pr$ictable4 #e4 ,9 its application to moral & social subjects1 :at gives ?is controv]sy its ma9 int]e/ is its real or suppos$ be>+ ^u ! vex$ "q ( ! fre$om ( ! w2 = 9 ?is region ,causation1 & ,fatalism or ,necessit>ianism1 are reg>d$ z "o & ! same ?+4 ,"h1 z 9 ! la/ case1 t wide & some:at vague k9d ( regul>ity t we h call$ ,uni=mity1 mu/ be admitt$ z a notori\s fact4 ,/ati/ics h put x out ( ! p[] ( any reasonably in=m$ p]son to feel any hesitation ^u ?is po9t4 ,"s idea has already be5 ga9$1 9 ! e>li] *apt]s1 ( ! nature & am\nt ( ! evid5ce :i* might be furni%$ ( ?is fact1 & any quantity m might be suppli$ f ! works ( pr(ess$ writ]s ^u ! subject4 ,if1 !re=e1 ,free-w be s int]pret$ z to imply su* ess5tial irregul>ity z defies pr$iction bo? 9 ! av]age1 & also 9 ! s+le case1 !n ! negation ( free-w foll[s1 n z a remote logical consequ5ce1 b z an obvi\s inf]5ce f indisputable facts ( exp]i5ce4 ,few p]sons1 h[ev]1 w\ld g s f> z to int]pret x 9 ?is s5se4 ,all t tr\bles !m is ! fe> t someh[ ?is g5]al regul>ity may be f\nd to c>ry ) x causation1 c]ta9ly 9 ! s5se ( regul> inv>iable sequ5ce1 & probably also ) ! fur!r association ( compulsion4 ,reject+ ! latt] association z utt]ly unphilosophical1 ,i _c ev5 see t ! =m] consequ5ce c be admitt$ z really prov$1 ?\gh x d\btless ga9s "s confirmation f ?is s\rce4 #f4 ,! nature ( ! argum5t aga9/ free-w1 drawn f /ati/ics1 at lea/ 9 ! =m 9 :i* x is v commonly express$1 seems to me exce$+ly defective4 ,! antec$5ts & consequ5ts1 9 ! case ( our volitions1 mu/ cle>ly be suppos$ to be v ne>ly imm$iately 9 succession1 if any?+ approa*+ to causation is to be e/abli%$3 :]eas 9 /ati/ical enquiries ! data are (t5 widely sep>ate1 if inde$ !y d n apply m]ely to s+le gr\ps ( actions or results4 ,= in/ance1 9 ! case ( ! misdirect$ lett]s1 :at x is attempt$ to prove is t ea* writ] 0 s mu* ! 'victim ( circum/ances' 7to use a common b mislead+ expression7 t he c\ld n h done o!rwise ?an he did "u 8 circum/ances4 ,b really no accumulation ( figures to prove t ! numb] ( su* lett]s rema9s ! same ye> by ye>1 c h mu* be>+ ^u ?is doctr9e1 ev5 ?\gh !y 7 accompani$ by correspond+ figures :i* %\ld connect ! =getfulness ?us indicat$ ) "s o!r *>act]i/ics 9 ! writ]s4 ,s ) ! numb] ( suicides4 ,if #bej p d1 or lately did1 annually put an end to !mselves 9 ,london1 ! fact1 z x ?us /&s by itself1 may be "o ( importance to ! philan?ropi/ & /atesman1 b x ne$s br++ into mu* clos] relation ) psy*ological elem5ts if x is to conv9ce u t ! actions ( m5 are always in/ances ( inflexible ord]4 ,9 fact1 in/ead ( hav+ secur$ our ,a & ,b "h 9 close/ intimacy ( succession to "o ano!r1--to employ ! symbolic notation commonly us$ 9 works on ,inductive ,logic to illu/rate ! causal connection1--we f9d !m sep>at$ by a consid]able int]val2 (t5 inde$ we m]ely h an ,a or a ,b by itself4 #g4 ,aga91 ano!r defici5cy 9 su* reason+ seems to be ! lay+ undue weight ^u ! m]e regul>ity or p]si/5cy ( ! /ati/ics4 ,^! may lead to v important results1 b !y are n exactly :at is want$ = ! purpose ( prov+ any?+ aga9/ ! fre$om ( ! w2 x is n inde$ easy to see :at connection ?is has ) su* facts z t ! annual numb] ( !fts or ( suicides rema9s at pretty ne>ly ! same figure4 ,/ati/ical uni=mity seems to me to e/abli% no?+ else1 at lea/ directly1 9 ! case ( human actions1 ?an x does 9 t ( physical *>act]i/ics4 ,take b "o in/ance1 t ( ! misdirect$ lett]s4 ,we 7 already aw>e t ! height1 weight1 *e/ measurem5t1 & s on1 ( a l>ge numb] ( p]sons pres]v$ a tol]ably regul> av]age amid/ innum]able deflections1 & we 7 prep>$ by analogy to anticipate ! same regul>ity 9 _! m5tal *>act]i/ics4 ,all t we ga91 by c\nt+ ! numb]s ( lett]s :i* are po/$ )\t addresses1 is a c]ta9 am\nt ( direct evid5ce t ?is is ! case4 ,j z obs]vations ( ! =m] k9d _h already %[n t /ati/ics ( ! /r5g? & /ature ( ! human body gr\p$ !mselves ab\t a mean1 s d ^? ( ! latt] t a simil> /ate ( ?+s prevails 9 respect ( ! read9ess & g5]al tru/wor?9ess ( ! memory4 ,! evid5ce is n s direct & conclusive 9 ! latt] case1 = ! memory is n s+l$ out & subject$ to measurem5t by itself1 b is tak5 9 comb9ation ) innum]able o!r influ5c+ circum/ances4 ,/ill !re c be little d\bt t ! /ati/ics tell on ! :ole 9 ?is direction1 & t by duly v>y+ & ext5d+ !m !y may obta9 consid]able probative =ce4 ,! fact is t ,probability has no?+ m to d ) ,natural ,!ology1 ei!r 9 its fav\r or aga9/ x1 ?an ! g5]al pr9ciples ( ,logic or ,induction h4 ,x is simply a body ( rules = draw+ inf]5ces ab\t classes ( ev5ts :i* are di/+ui%$ by a c]ta9 quality4 ,! believ] 9 a ,deity w1 by ! /udy ( nature1 be l$ to =m an op9ion ab\t ,8 works1 & s to a c]ta9 ext5t ab\t ,8 attributes4 ,b x is surely unreasonable to propose t he %\ld ab&on 8 belief because ! sequ5ce ( ev5ts1--n1 obs]ve1 _! g5]al t5d5cy t[>ds happ9ess or mis]y1 good or evil1--is br\ght ab\t 9 a way diff]5t f :at he _h expect$2 :e!r x be by display+ ord] :]e he _h expect$ irregul>ity1 or by involv+ ! ma*9]y ( second>y causes :]e he _h expect$ imm$iate ag5cy4 #h4 ,x is bo? amus+ & in/ructive to consid] :at v diff]5t feel+s might h be5 excit$ 9 our m9ds by ?is co-exi/5ce (1 :at may be call$1 ignorance ( individuals & k ( aggregates1 if !y _h pres5t$ !mselves to our obs]vation 9 a rev]se ord]4 ,be+ utt]ly unable to make assur$ pr$ictions ab\t a s+le life1 or ! conduct ( individuals1 p are sometimes />tl$1 & occasionally ev5 dismay$1 at ! unexpect$ discov]y t su* pr$ictions c be confid5tly made :5 we are speak+ ( l>ge numb]s4 ,& s "s are prompt$ to exclaim1 ,?is is d5y+ ,provid5ce6 x is utt] ,fatalism6 ,b let u assume1 = a mom5t1 t our famili>ity ) ! subject _h be5 exp]i5c$1 9 ! fir/ in/ance1 9 ref]5ce to ! aggregates in/ead ( ! individual lives4 ,x is difficult1 p]haps1 to c>ry out su* a supposition completely2 ?\gh we may readily conceive some?+ approa*+ to x 9 ! case ( an ignorant cl]k 9 a ,life ,assurance ,(fice1 :o _h nev] ?\ght ( life1 except z hav+ su* a 'value' at su* an age1 & :o _h h>dly e/imat$ x except 9 ! =m ( av]ages4 ,might we n suppose him1 9 "s mom5t ( reflectiv5ess1 be+ a/oni%$ & dismay$ at ! sudd5 realization ( ! utt] unc]ta9ty 9 :i* ! s+le life is involv$8 ,& might n 8 exclamation 9 turn be1 ,:y ?is is d5y+ ,provid5ce6 ,x is utt] *aos & *ance6 ,a belief 9 a ,creator & ,adm9i/rator ( ! _w is n conf9$ to any p>ticul> assumption ab\t ! nature ( ! imm$iate sequ5ce ( ev5ts1 b ^? :o h be5 accu/om$ hi!rto to reg>d ! ev5ts "u "o ( ! aspects above ref]r$ to1 w (t5 = a "t feel at a loss h[ to connect !m ) ! o!r4 #i4 ,s f> we h be5 t\*+ on a v g5]al "q2 viz4 ! relation ( ! fundam5tal po/ulates ( ,probability to ! conception ( ,ord] or ,uni=mity 9 ! _w1 physical or moral4 ,! difficulties :i* !nce arise are ma9ly !ological1 metaphysical or psy*ological4 ,:at we mu/ n[ consid] are problems ( a m detail$ or logical "*4 ,!y are prom95tly ^! two2 7#a7 ! di/9ction betwe5 *ance arrangem5t & causal arrangem5t 9 physical ph5om5a2 & 7#b7 ! di/9ction betwe5 *ance arrangem5t & design$ arrangem5t :]e we are suppos$ to be contemplat+ rational ag5cy z act+ on "o side at lea/4 ,,ii4 ,! fir/ ( ^! que/ions raises ! anti!sis betwe5 *ance & causation1 n z a g5]al *>act]i/ic p]vad+ all ph5om5a1 b 9 ref]5ce to "s specifi$ occurr5ce3--,is ?is a case ( *ance or n8 ,! mo/ /r5u\s support]s ( ! univ]sal preval5ce ( causation & ord] admit t ! "q is a relevant "o1 & !y mu/ !re=e be suppos$ to h "s rule = te/+ ! answ]s to x4 ,suppose1 = in/ance1 a man is seiz$ ) a fit 9 a h\se :]e he has gone to d9e1 & dies !re2 & "s "o rem>ks t t 0 ! v h\se 9 :i* he 0 born4 ,we beg9 to wond] if ?is 0 an odd co9cid5ce & no?+ m4 ,b if our in=mant goes on to tell u t ! h\se 0 an old family "o1 & 0 occupi$ by ! bro!r ( ! deceas$1 we %\ld feel at once t ^! facts put ! matt] 9 a r diff]5t light4 ,or aga91 z ,c\rnot sugge/s1 if we he> t two bro!rs h be5 kill$ 9 battle on ! same day1 x makes a great diff]5ce 9 our e/imation ( ! case :e!r !y 7 kill$ fight+ 9 ! same engagem5t or :e!r "o fell 9 ! nor? ( ,france & ! o!r 9 ! s\?4 ,! latt] we %\ld at once class ) m]e co9cid5ces1 :]eas ! =m] might admit ( explanation4 #aj4 ,! problem1 z ?us conceiv$1 seems to be "o r ( ,inductive ,logic ?an ( ,probability1 because !re is n ! slighte/ attempt to calculate *ances4 ,b x des]ves "s notice "h4 ,( c\rse no accurate ?9k] :o 0 "u ! sway ( mod]n physical notions w\ld = a mom5t d\bt t ea* ( ! two elem5ts 9 "q _h its own 'cause' beh9d x1 f :i* 7assum+ p]fect k7 x might h be5 confid5tly inf]r$4 ,no m w\ld he d\bt1 ,i appreh5d1 t if we c\ld take a suffici5tly m9ute & compreh5sive view1 & p5etrate suffici5tly f> back into ! pa/1 we %\ld rea* a /age at :i* 7aga9 assum+ p]fect k7 ! co-exi/5ce ( ! two ev5ts c\ld equally h be5 =ese54 ,! employm5t ( ! ^w casual !re=e does n imply any rejection ( a cause2 b x does nev]!less correspond to a di/9ction ( "s practical importance4 ,we call a co9cid5ce casual1 ,i appreh5d1 :5 we mean to imply t no k ( "o ( ! two elem5ts1 :i* we c suppose to be practically atta9able1 w\ld enable u to expect ! o!r4 ,we "k ( no g5]alization :i* cov]s !m bo?1 except ( c\rse su* z are tak5 = grant$ to be inop]ative4 ,9 su* an application x seems t ! ^w 'casual' is n us$ 9 anti!sis to 'causal' or to 'design$'1 b r to t broad] conception ( ord] or regul>ity to :i* ,i %\ld apply ! t]m ,uni=mity4 ,! casual co9cid5ce is "o :i* we _c br+ "u any special g5]alization2 c]ta91 probable1 or ev5 plausible4 ,a slightly diff]5t way ( express+ ?is di/9ction is to reg>d ^! 'm]e co9cid5ces' z be+ simply cases 9 po9t ( indep5d5t ev5ts1 9 ! s5se 9 :i* indep5d5ce 0 describ$ 9 a =m] *apt]4 ,we saw t any two ev5ts1 ,a & ,b1 7 s describ$ :5 ea* happ5s ) precisely ! same relative /ati/ical frequ5cy :e!r ! o!r happ5s or n4 ,?is /ate ( ?+s seems to hold good ( ! successions ( heads & tails 9 toss+ co9s1 z 9 t ( male & female bir?s 9 a t[n1 or t ( ! digits 9 _m ma!matical tables4 ,?us we suppose t :5 m5 are pick$ up 9 ! /reet & tak5 into a h\se to die1 !re w n be 9 ! long run any pref]5tial selection = or aga9/ ! h\se 9 :i* !y 7 born4 ,& all t we necess>ily mean to claim :5 we d5y ( su* an occurr5ce1 9 any p>ticul> case1 t x is a m]e co9cid5ce1 is t t p>ticul> case mu/ be tak5 out ( ! common li/ & transf]r$ to "o 9 :i* !re is "s su* pref]5tial selection4 #aa4 ,,iii4 ,! next problem is a some:at m intricate "o1 & w !re=e require r c>eful subdivision4 ,x involves ! anti!sis betwe5 ,*ance & ,design4 ,t is1 we are n n[ 7z 9 ! prec$+ case7 consid]+ objects 9 _! physical aspect alone1 & tak+ acc\nt only ( ! relative frequ5cy ( _! co-exi/5ce or sequ5ce2 b we are consid]+ ! ag5cy by :i* !y are produc$1 & we are enquir+ :e!r t ag5cy tru/$ to :at we call *ance1 or :e!r x employ$ :at we call design4 ,! read] mu/ cle>ly und]/& t we are n n[ discuss+ ! m]e "q ( fact :e!r a c]ta9 assign$ arrangem5t is :at we call a *ance "o4 ,?is1 z 0 fully po9t$ out 9 ! f\r? *apt]1 c be settl$ by m]e inspection1 provid$ ! mat]ials are ext5sive en\gh4 ,:at we are n[ propos+ to d is to c>ry on ! enquiry f ! po9t at :i* we !n _h to leave x (f1 by solv+ ! "q1 ,giv5 a c]ta9 arrangem5t1 is x m likely t ?is 0 produc$ by design1 or by "s ( ! me?ods commonly call$ *ance me?ods8 ,! di/9ction w be obvi\s if we rev]t to ! succession ( figures :i* con/itute ! ratio 4 ,z ,i h said1 ?is arrangem5t1 reg>d$ z a m]e succession ( digits1 appe>s to fulfil p]fectly ! *>act]i/ics ( a *ance arrangem5t4 ,if we 7 to omit ! fir/ f\r or five digits1 :i* are famili> to mo/ ( u1 we might safely defy any "o to :om x 0 %[n to say t x 0 n got at by simply draw+ figures f a bag4 ,he might look at x = 8 :ole life )\t detect+ t x 0 any?+ b ! result ( su* a *ance selection4 ,& rightly s1 because reg>d$ z a m]e arrangem5t x is a *ance "o3 x fulfils all ! requirem5ts ( su* an arrangem5t4#b ,! "q we are n[ proce$+ to discuss is ?is3 ,giv5 any su* arrangem5t h[ are we to det]m9e ! process by :i* x 0 arriv$ at8 ,we are suppos$ to h "s ev5t be=e u :i* might h be5 produc$ 9 ei!r ( two alt]native ways1 i4e4 by *ance or by "s k9d ( delib]ate design2 & we are ask$ to det]m9e ! odds 9 fav\r ( "o or o!r ( ^! alt]natives4 ,x is !re=e a problem 9 ,inv]se ,probability & is liable to all ! difficulties to :i* problems ( ?is class are apt to be expos$4 #ab4 ,= ! !oretic solution ( su* a "q we require ! two foll[+ data3-- 7#a7 ,! relative frequ5cy ( ! two classes ( ag5cies1 viz4 t :i* is to act 9 a *ance way & t :i* is to act design$ly4 7#b7 ,! probability t ea* ( ^! ag5cies1 if x 7 ! really op]ative "o1 w\ld produce ! ev5t 9 "q4 ,! latt] ( ^! data c g5]ally be secur$ )\t any difficulty4 ,! det]m9ation ( ! v>i\s cont+5cies on ! *ance hypo!sis ought n1 if ! example 7 a suitable "o1 to (f] any o!r ?an ari?metical difficulties4 ,& z reg>ds ! design alt]native1 x is g5]ally tak5 = grant$ t if ?is _h be5 op]ative x w\ld c]ta9ly h produc$ ! result aim$ at4 ,= in/ance1 if t5 p5ce are f\nd on a table1 all ) head upp]mo/1 & x be ask$ :e!r *ance or design _h be5 at "w "h2 we feel no difficulty up to a c]ta9 po9t4 ,_h ! p5ce be5 toss$ we %\ld h got t5 heads only once 9 #ajbd ?r[s2 b _h !y be5 plac$ design$ly ! result w\ld h be5 a*iev$ ) c]ta9ty4 ,b ! o!r po/ulate1 viz4 t ( ! relative preval5ce ( ^! two classes ( ag5cies1 op5s up a f> m s]i\s class ( difficulties4 ,cases c be f\nd no d\bt1 ?\gh !y are n v frequ5t1 9 :i* ?is "q c be answ]$ approximately1 & !n !re is no fur!r tr\ble4 ,= in/ance1 if 9 a s*ool class-li/ ,i 7 to see ! f\r names ,br[n1 ,jones1 ,rob9son1 ,smi?1 /&+ 9 ?is ord]1 x might occur to me to enquire :e!r ?is arrangem5t 7 alphabetical or "o ( m]it4 ,9 our enl>g$ s5se ( ! t]ms ?is is equival5t to *ance & design z ! alt]natives2 =1 s9ce ! initial lett] ( a boy's "n has no kn[n connection ) 8 atta9m5ts1 ! successive arrangem5t ( ^! lett]s on any o!r ?an ! alphabetical plan w display ! r&om features1 j z we f\nd to be ! case ) ! digits ( an incomm5surable magnitude4 ,! odds are #bc to #a aga9/ #d names com+ undesign$ly 9 alphabetical ord]2 !y are equival5t to c]ta9ty 9 fav\r ( _! do+ s if ?is ord] _h be5 design$4 ,z reg>ds ! relative frequ5cy ( ! two k9ds ( ord]s 9 s*ool exam9ations ,i d n "k t /ati/ics are at h&1 ?\gh !y c\ld easily be procur$ if necess>y1 b x is pretty c]ta9 t ! majority adopt ! ord] ( m]it4 ,put = hypo!sis ! proportion z high z #i to #a1 & x w\ld /ill be f\nd m likely ?an n t 9 ! case 9 "q ! ord] 0 really an alphabetical "o4 #ac4 ,b 9 ! va/ majority ( cases we h no su* /ati/ics at h&1 & !n we f9d ourselves expos$ to v s]i\s ambiguities4 ,^! may be divid$ into two di/9ct classes1 ! nature ( :i* w be/ be se5 by ! discussion ( examples4 ,9 ! fir/ place we are especially liable to ! drawback already describ$ 9 a =m] *apt] z r5d]+ m]e /ati/ics s untru/wor?y1 :i* consi/s 9 ! fact t ! proportions are s apt to be di/urb$ almo/ f mom5t to mom5t by ! possession ( fre% h9ts or in=mation4 ,we saw = in/ance :y x 0 t /ati/ics ( mortality 7 s v uns]viceable 9 ! mid/ ( a disease or 9 ! crisis ( a battle4 ,suppose n[ t on com+ into a room ,i see on ! table t5 co9s ly+ face upp]mo/1 & am ask$ :at 0 ! likelihood t ! arrangem5t 0 br\ght ab\t by design4 ,ev]y?+ turns ^u special k ( ! circum/ances ( ! case4 ,:o _h be5 9 ! room8 ,7 !y *ildr51 or co9-collectors1 or p]sons :o might h be5 suppos$ to h indulg$ 9 toss+ = sport or = gambl+ purposes8 ,7 ! co9s new or old ones8 a di/9ction ( ?is k9d w\ld be v p]t95t :5 we 7 consid]+ ! exi/5ce ( any motive = arrang+ !m ! same way upp]mo/4 ,& s on2 we feel t our /ati/ics are at ! m]cy ( any mom5t>y fragm5t ( in=mation4 #ad4 ,b !re is ano!r consid]ation besides ?is4 ,n only %\ld we be ?us influ5c$ by :at may be call$ ext]nal circum/ances ( a g5]al k9d1 su* z ! "* & position ( ! ag5ts1 we %\ld also be influ5c$ by :at we suppos$ to be ! conv5tional#c e/imate ) :i* ?is or t p>ticul> *ance arrangem5t 0 !n reg>d$4 ,?us f "t to "t z new games ( c>ds become popul> new comb9ations acquire significance2 & !re=e :5 ! "q ( design takes ! =m ( possible *eat+ a k ( ! curr5t e/imate ( su* comb9ations becomes exce$+ly important4 #ae4 ,! full significance ( ^! difficulties w be/ be appreh5d$ by ! discussion ( a case :i* is n fictiti\s or inv5t$ = ! purpose1 b :i* has actually giv5 rise to s]i\s dispute4 ,"s ye>s ago ,pr(4 ,piazzi ,smy? publi%$ a "w#d ^u ! great pyramid ( ,ghizeh1 ! g5]al object ( :i* 0 to %[ t t build+ conta9$1 9 its magnitude1 proportions & cont5ts1 a numb] ( almo/ imp]i%able natural /&>ds ( l5g?1 volume1 c4 ,among/ o!r ?+s x 0 det]m9$ t ! value ( 0 accurately 7! degree ( accuracy is n1 ,i ?9k1 assign$7 indicat$ by ! ratio ( ! sides to ! height4 ,! cont5tion 0 t ?is result c\ld n be accid5tal b mu/ h be5 design$4 ,z reg>ds ! e/imation ( ! value ( ! *ance hypo!sis ! calculation is n q s cle> z 9 ! case ( dice or c>ds4 ,we _c inde$ suppose t1 = a giv5 l5g? ( base1 any height c be equally possible4 ,we mu/ limit ourselves to a c]ta9 range "h2 = if too high ! build+ w\ld be insecure1 & if too l[ x w\ld be ridicul\s4 ,aga91 we mu/ decide to h[ close an approximation ! measurem5ts are made4 ,if !y are gu>ante$ to ! hundr$? ( an in* ! co9cid5ce w\ld be ( a q diff]5t ord] f "o :]e ! gu>antee ext5d$ only to an in*4 ,suppose t ?is has be5 decid$1 & t we h asc]ta9$ t out ( #aj1jjj possible heights = a pyramid ( giv5 base j t "o has be5 select$ :i* w\ld mo/ ne>ly yield ! ratio ( ! radius to ! circumf]5ce ( a circle4 ,! rema9+ consid]ation w\ld be ! relative frequ5cy ( ! 'design' alt]native1--:at is call$ its priori probability1--t is1 ! relative frequ5cy ) :i* su* build]s c be suppos$ to h aim$ at t ratio2 ) ! obvi\s impli$ assumption t if !y did aim at x !y w\ld c]ta9ly secure x4 ,consid]+ our extreme ignorance ( ! atta9m5ts ( ! build]s x is obvi\s t no attempt at num]ical appreciation is "h possible4 ,if inde$ ! 'design' 0 int]pret$ to mean consci\s resolve to produce t ratio1 in/ead ( m]e resolve to employ "s me?od :i* happ5$ to produce x1 few p]sons w\ld feel mu* hesitation4 ,n only d we feel tol]ably c]ta9 t ! build]s did n "k ! value ( 1 except 9 ! rude way 9 :i* all artific]s mu/ "k x2 b we c see no rational motive1 if !y did "k x1 :i* %\ld induce !m to p]petuate x 9 _! build+4 ,if1 h[ev]1 to adopt an +5i\s sugge/ion1#e we suppose t ! build] may h proce$$ 9 ! foll[+ fa%ion1 ! matt] assumes a diff]5t aspect4 ,suppose t hav+ decid$ on ! height ( 8 pyramid he drew a circle ) t z radius3 t1 lay+ d[n a cord along ! l9e ( ?is circle1 he drew ?is cord out into a squ>e1 :i* squ>e m>k$ ! base ( ! build+4 ,h>dly any simpl] means c\ld be devis$ 9 a comp>atively rude age2 & x is obvi\s t ! circumf]5ce ( ! base1 be+ equal to ! l5g? ( ! cord1 w\ld be> exactly ! admitt$ ratio to ! height4 ,9 o!r words1 ! exact atta9m5t ( a geometric value does n imply a k ( t ratio1 b m]ely ( "s me?od :i* involves & displays x4 ,a t]$o c bore1 z well z any ( u1 a hole :i* displays ! geometric prop]ties ( a circle1 b we d n cr$it x ) correspond+ k4 ,z be=e said1 all num]ical appreciation ( ! likelihood ( ! design alt]native is out ( ! "q4 ,b1 if ! precision is equal to :at ,mr ,smy? claim$1 ,i suppose t mo/ p]sons 7) ! above sugge/ion be=e !m7 w ?9k x some:at m likely t ! co9cid5ce 0 n a *ance "o4 #af4 ,!re /ill rema9s a s]i\s1 & highly int]e/+ speculative consid]ation4 ,9 ! above argum5t we took x = grant$1 9 calculat+ ! *ance alt]native1 t only "o ( ! #aj1jjj possible values 0 fav\rable2 t is1 we took x = grant$ t ! ratio 0 ! only "o ^: claims1 s to say1 7 be=e ! c\rt4 ,b x is cle> t if we _h obta9$ j d\ble ?is ratio ! result w\ld h be5 ( simil> significance1 = x w\ld h be5 simply ! ratio ( ! circumf]5ce to ! diamet]4 ,9 fact1 ,mr ,smy?'s select$ ratio1--! height to twice ! bread? ( ! base z comp>$ ) ! diamet] to ! circumf]5ce1--is obvi\sly only "o ( a plurality ( ratios4 ,aga92 if ! measur$ results _h %[n t ! ratio ( ! height to "o side ( ! base 0 #a 3 sqrt#b 7i4e4 t ( a side to a diagonal ( a squ>e7 or #a 3 sqrt#c 7i4e4 t ( a side to a diagonal ( a cube7 w\ld n su* results equally %[ evid5ce ( design8 ,proce$+ 9 ?is way1 we might sugge/ "o kn[n ma!matical ratio aft] ano!r until mo/ ( ! #aj1jjj suppos$ possible values _h be5 tak5 into acc\nt4 ,we might !n argue ?us3 s9ce almo/ e possible height ( ! pyramid w\ld correspond to "s ma!matical ratio1 a build]1 ignorant ( !m all alike1 w\ld be n at all unlikely to /umble ^u "o or o!r ( !m3 :y !n attribute design to him 9 "o case r ?an ano!r8 #ag4 ,! answ] to ?is objection has be5 already h9t$ at4 ,ev]y?+ turns ^u ! conv5tional e/imate ( "o result z comp>$ ) ano!r4 ,rev]t1 = simplicity to ! co9s4 ,t5 heads is j z likely z alt]nate heads & tails1 or five heads foll[$ by five tails2 or1 9 fact1 z any "o ( ! rema9+ #ajbc possible cases4 ,b univ]sal conv5tion has pick$ out a run ( t5 z be+ rem>kable4 ,"h1 ( c\rse1 ! conv5tion seems a v natural & inde$ inevitable "o1 b 9 o!r cases x is :olly arbitr>y4 ,= in/ance1 9 c>ds1 que5 ( spades & knave ( diamonds is exactly z uncommon z any o!r su* pair3 moreov]1 till bezique 0 introduc$ x (f]$ presumably no sup]ior int]e/ ov] any o!r specifi$ pair4 ,b dur+ ! "t :5 t game 0 v popul> ?is comb9ation 0 br\ght into ! category ( co9cid5ces 9 :i* int]e/ 0 felt2 &1 giv5 di%one/y among/ ! play]s1 its *ance ( be+ design$ /ood at once on a mu* bett] foot+4#f ,return+ !n to ! pyramid1 we see t 9 balanc+ ! claims ( *ance & design we mu/1 9 fairness to ! latt]1 reckon to its acc\nt sev]al o!r values z well z t ( 1 e4g4 sqrt#b & sqrt#c1 & a few m su* simple & famili> ratios1 z well z "s ( _! multiples4 ,b ?\gh ! numb] ( su* values :i* might be reckon$1 on ! gr\nd t !y are actually kn[n to u1 is inf9ite1 yet ! numb] t ought to be reckon$1 on ! gr\nd t !y c\ld h be5 famili> to ! build]s ( a pyramid1 are v few4 ,! ord] ( probability = or aga9/ ! exi/5ce ( design w n !re=e be s]i\sly alt]$ "h by su* consid]ations4#g #ah4 ,up to ?is po9t x w be obs]v$ t :at we h be5 balanc+ aga9/ ea* o!r are two =ms ( ag5cy1--( human ag5cy1 t is1--"o act+ ?r\gh *ance1 & ! o!r by direct design4 ,9 ?is case we "k :]e we are1 = we c ?or\ghly und]/& ag5cy ( ?is k9d4 ,! problem is inde$ b seldom num]ically soluble1 & 9 mo/ cases n soluble at all1 b x is at any rate capable ( be+ cle>ly /at$4 ,we "k ! k9d ( answ] to be expect$ & ! reasons :i* w\ld s]ve to det]m9e x1 if !y 7 atta9able4 ,! next /age 9 ! enquiry w\ld be t ( balanc+ ord9>y human *ance ag5cy aga9/1--,i w n call x direct spirituali/ ag5cy1 = t w\ld be n>r[+ ! hypo!sis unnecess>ily1--b aga9/ all o!r possible causes4 ,"s ( ! inve/igations ( ! ,society = ,psy*ical ,rese>* w furni% an admirable illu/ration ( :at is int5d$ by ?is /atem5t4 ,!re is a full discussion ( ^! applications 9 a rec5t essay by ,mr ,f4 ,y4 ,edgewor?2#h b z 8 acc\nt ( ! matt] is connect$ ) o!r calculations & diagrams ,i c only quote x 9 "p4 ,b ,i am 9 sub/antial agreem5t ) him4 ,x is record$ t #ahcc guesses 7 made by a 'p]cipi5t' z to ! suit ( c>ds :i* ! 'ag5t' _h fix$ ^u4 ,! numb] ( successful guesses 0 #eaj1 consid]ably above #deh1 ! numb] :i*1 z be+ ! qu>t] ( #ahcc1 w\ld1 on ! supposition ( pure *ance1 be m likely ?an any o!r numb]4 ,n[1 by ! ,law ( ,error1 we are able approximately to det]m9e ! probability ( su* an excess occurr+ by *ance4 ,x is equal to ! extremity ( ! tail ( a probability-curve su* z ^? we h already _h occasion to exam9e4444 ,! proportion ( ?is extremity ( ! tail to ! :ole body is #j4jjc to #a4 ,t fraction1 !n1 is ! probability ( a *ance %ot /rik+ t extremity ( ! tail2 ! probability t1 if ! guess+ 7 gov]n$ by pure *ance1 a numb] ( successful guesses equal or great] ?an #eaj w\ld occur3 odds1 t is1 ( ab\t #ccb to #a aga9/ su* occurr5ce4 #ai4 ,mr ,edgewor? holds1 z /rongly z ,i d1 t = purposes ( calculation1 9 any /rict s5se ( ! ^w1 we ought to h "s det]m9ation ( ! data on ! non-*ance side ( ! hypo!sis4 ,we ought to "k its relative frequ5cy ( occurr5ce1 & ! relative frequ5cy ) :i* x atta9s its aims4 ,i am also 9 agreem5t ) him t :at t o!r cause may be1--:e!r "s trick1 or unconsci\s illusion1 or ?\ght-transf]5ce ( ! sort :i* is v9dicat$ by ! inve/igators--x is = common-s5se & ord9>y ,logic to consid]4 ,i am 9 agreem5t !re=e ) ^? :o ?9k t ?\gh we _c =m a quantitative op9ion we c 9 c]ta9 cases =m a tol]ably decisive "o4 ,( c\rse if we all[ ! la/ ^w to ! support]s ( ! *ance hypo!sis we c nev] rea* pro(1 = x w always be op5 to !m to revise & re-fix ! antec$5t probability ( ! c\nt] hypo!sis4 ,:at we may fairly require is t ^? :o d5y ! *ance explanation %\ld assign "s sort ( m9imum value to ! probability ( occurr5ce on ! o!r supposition1 & we c !n try to surm\nt ?is by increas+ ! r>ity ( ! actually produc$ ph5om5on on ! *ance hypo!sis4 ,if1 = in/ance1 !y decl>e t 9 _! e/imation ! odds aga9/ any o!r ?an ! *ance ag5cy be+ at "w are great] ?an #ccb to #a1 we mu/ try to secure a yet uncommon] occurr5ce ?an t 9 "q4 ,if ! support]s ( ?\ght-transf]5ce h ! c\rage ( _! convictions1--z !y mo/ assur$ly h1--!y w\ld n %r9k f accept+ ?is te/4 ,i am incl9$ to ?9k t ev5 at pres5t1 on su* evid5ce z t above1 ! probability t ! results 7 got at by ord9>y guess+ is v small4 #bj4 ,! problems discuss$ 9 ! prec$+ sections are at lea/ intelligible ev5 if !y are n always resolvable4 ,b be=e f9i%+ ?is *apt] we mu/ take notice ( "s speculations ^u ?is "p ( ! subject :i* d n seem to keep q )9 ! limits ( :at is intelligible4 ,take = in/ance ! "q discuss$ by ,arbu?nott 79 a pap] 9 ! ,phil4 ,transactions1 ,vol4 ,,xxvii47 "u ! title ,an ,argum5t = ,div9e ,provid5ce1 tak5 f ! con/ant ,regul>ity obs]v$ 9 ! bir? ( bo? sexes4 ,_h 8 argum5t be5 ( ! ord9>y teleological k9d2 t is1 _h he simply ma9ta9$ t ! exi/5t ratio ( approximate equality1 ) a six p] c5t4 surplusage ( males1 0 a b5efic5t "o1 !re w\ld h be5 no?+ "h to object aga9/4 ,b :at he contemplat$ 0 j su* a balance ( alt]nate hypo!ses betwe5 *ance & design z we are "h consid]+4 ,8 conclusion 9 8 own words is1 x is art1 n *ance1 t gov]ns4 ,x is difficult to r5d] su* an argum5t precise )\t r5d]+ x simply ridicul\s4 ,/rictly und]/ood x c surely be> only "o ( two int]pretations4 ,on ! "o h& we may be p]sonify+ ,*ance3 reg>d+ x z an ag5t :i* mu/ be reckon$ ) z be+ q capable ( hav+ produc$ man1 or at any rate hav+ arrang$ ! proportion ( ! sexes4 ,& !n ! decision mu/ be drawn1 z betwe5 ?is ag5t & ! ,creator1 :i* ( ! two produc$ ! exi/5t arrangem5t4 ,if s1 & ,*ance be def9$ z any ag5t :i* produces a *ance or r&om arrangem5t1 ,i am afraid !re c be little d\bt t x 0 ?is ag5t t 0 at "w 9 ! case 9 "q4 ,! arrangem5t ( male & female bir?s pres5ts1 s f> z we c see1 "o ( ! mo/ p]fect examples ( *ance3 !re is ultimate uni=mity em]g+ out ( individual irregul>ity3 all ! 'runs' or successions ( ea* alt]native are duly repres5t$3 ! fact (1 say1 five sons hav+ be5 already born 9 a family does n seem to h any c]ta9 effect 9 dim9i%+ ! likelihood ( ! next be+ a son1 & s on4 ,su* a ne>ly p]fect in/ance ( 'indep5d5t ev5ts' is comp>atively v r>e 9 physical ph5om5a4 ,x is all t we c claim f a *ance arrangem5t4#i ,! only o!r int]pretation ,i c see is to sugge/ t !re 0 b "o ag5t :o might1 l any "o ( u1 h ei!r toss$ up or design$1 & we h to asc]ta9 :i* c\rse he probably adopt$ 9 ! case 9 "q4 ,"h too1 if we are to judge ( 8 mode ( action by ! te/s we %\ld apply to any "w ( our own1 x w\ld c]ta9ly look v mu* z if he _h adopt$ "s s*eme ( toss+4 #ba4 ,! simple fact is t any rational attempt to decide betwe5 *ance & design z ag5cies mu/ be conf9$ to ! case ( f9ite intellig5ces4 ,"o ( ! important det]m9+ elem5ts "h1 z we h se51 is ! /ate ( k ( ! ag5t1 & ! conv5tional e/imate ent]ta9$ ab\t ?is or t p>ticul> arrangem5t2 & ^! c be appreciat$ only :5 we are deal+ ) be+s l ourselves4 ,= in/ance1 to return to t mu* debat$ "q ab\t ! arrangem5t ( ! />s1 !re c h>dly be any d\bt t :at ,mit*ell1--:o />t$ ! discussion1--_h 9 view 0 ! decision betwe5 ,*ance & ,design4 ,he says 7,trans4 ,roy4 ,soc4 #agfg7 ,! argum5t ,i int5d to make use (444 is ( t k9d :i* inf]s ei!r design or "s g5]al law f a g5]al analogy & f ! greatness ( ! odds aga9/ ?+s hav+ be5 9 ! pres5t situation if x 0 n ow+ to "s su* cause4 ,& he concludes t _h ! />s be5 scatt]$ by m]e *ance z x might happ5 !re w\ld be odds ( ne> #ejj1jjj to #a t no six />s out ( t numb] #aejj1 scatt]$ at r&om 9 ! :ole heav5s1 w\ld be )9 s small a di/ance f ea* o!r z ! ,pleiades are4 ,"u any su* int]pretation ! controv]sy seems to me to be idle4 ,i d n = a mom5t dispute t !re is "s =ce 9 ! ord9>y teleological argum5t :i* seeks to trace signs ( goodness & wisdom 9 ! g5]al t5d5cy ( ?+s4 ,b :at d we possibly und]/& ab\t ! nature ( creation1 or ! designs ( ! ,creator1 :i* %\ld enable u to decide ab\t ! likelihood ( 8 putt+ ! />s 9 "o %ape r ?an 9 ano!r1 or :i* %\ld all[ any significance to m]e *ance z contra/$ ) 8 suppos$ all-p]vad+ ag5cy8 #bb4 ,r$uc$ to intelligible t]ms ! two foll[+ que/ions seem to me to em]ge f ! controv]sy3-- 7,i47 ,! />s be+ di/ribut$ ?r\gh space1 "s ( !m w\ld ( c\rse be ne>ly 9 a /raight l9e beh9d o!rs :5 look$ at f our planet4 ,suppos+ t !y 7 tol]ably uni=mly di/ribut$1 we c\ld calculate ab\t h[ _m ( !m w\ld ?us be se5 9 app>5t close proximity to "o ano!r4 ,! "q is !n put1 ,are !re m ( !m ne> to ea* o!r1 two & two1 ?an su* calculation w\ld acc\nt =8 ,! answ] is t !re are _m m4 ,s f> z ,i c see ! only direct inf]5ce t c be drawn f ?is is t !y are n uni=mly di/ribut$1 b h a t5d5cy to g 9 pairs4 ,?is1 h[ev]1 is a p]fectly s\nd & reasonable application ( ! !ory4 ,any fur!r conclusions1 su* z t ^! pairs ( />s w =m sy/ems1 z x 71 to !mselves1 revolv+ ab\t "o ano!r1 & = all practical purposes unaffect$ by ! re/ ( ! sid]eal sy/em1 are ( c\rse d]iv$ f a/ronomical consid]ations4#aj ,probability conf9es itself to ! simple answ] t ! di/ribution is n uni=m2 x _c pret5d to say :e!r1 & by :at physical process1 ^! b9>y sy/ems ( />s h be5 'caus$'4#aa #bc4 7,,ii47 ,! second "q is ?is1 ,does ! di/ribution ( ! />s1 aft] all[+ = ! case ( ! b9>y />s j m5tion$1 resemble t :i* w\ld be produc$ by human ag5cy spr9kl+ ?+s 'at r&om'8 7,we are speak+1 ( c\rse1 ( _! di/ribution z x appe>s to u1 on ! visible heav5s1 = ?is is ne>ly all t we c obs]ve2 b if !y ext5d beyond ! telescopic range 9 e direction1 ?is w\ld lead to practically mu* ! same discussion z if we consid]$ _! actual arrangem5t 9 space47 ,we h fully discuss$1 9 a =m] *apt]1 ! mean+ ( 'r&omness4' ,apply+ x to ! case be=e u1 ! "q becomes ?is1 ,is ! di/ribution tol]ably uni=m on ! :ole1 b ) innum]able individual deflections8 ,t is1 :5 we comp>e l>ge areas1 are ! ratios ( ! numb] ( />s 9 ea* equal area approximately equal1 :il/1 z we comp>e small] & small] areas1 d ! relative numb]s become m & m irregul>8 ,) c]ta9 exceptions1 su* z t ( ! ,milky ,way & o!r nebul> clu/]s1 ?is seems to be pretty mu* ! case1 at any rate z reg>ds ! bulk ( ! />s4#ab ,all fur!r que/ions3 ! decision1 = in/ance1 = or aga9/ any =m ( ! ,nebul> ,hypo!sis3 or1 admitt+ ?is1 ! decision :e!r su* & su* p>ts ( ! visible heav5s h sprung f ! same nebula1 mu/ be left to ,a/ronomy to adjudicate4 ,,note ,,on ,,! ,,proportions ,,( ,,! ,,sexes4 ,! foll[+ rem>ks 7 r too long = conv5i5t ins]tion on p4 #bei1 & are !re=e app5d$ "h4 ,! 'r&om' "* ( male & female bir?s has g5]ally be5 re/$ almo/ entirely on /ati/ics ( place & "t4 ,b :at is m want$1 surely1 is ! proportion display$ :5 we comp>e a numb] ( families4 ,?is seems s obvi\s t ,i _c b suppose t ! inve/igation mu/ h be5 already made some:]e1 ?\gh ,i h n f\nd any trace ( x 9 ! mo/ likely qu>t]s4 ,?us ,pr(4 ,lexis 7,mass5]s*e9ung57 :5 support+ 8 view t ! proportion betwe5 ! sexes at bir? is almo/ ! only in/ance kn[n to him1 9 natural ph5om5a1 ( true normal disp]sion ab\t a mean1 re/s 8 conclusions on ! ord9>y /ati/ics ( ! regi/]s ( diff]5t c\ntries4 ,x c]ta9ly ne$s pro( t ! same *>act]i/ics w hold good :5 ! family is tak5 z ! unit1 especially z "s !ories 7e4g4 t ( ,sadl]7 w\ld imply t 'runs' ( boys or girls w\ld be proportionally common] ?an pure *ance w\ld assign4 ,lexis has %[n t ?is is mo/ m>k$ly ! case ) tw9s3 i4e41 to use an obvi\sly intelligible notation1 7,m = male1 ,f = female71 t ,m4,m4 & ,f4,f4 are v mu* common] 9 proportion ?an ,m4,f4 ,i h collect$ /ati/ics includ+ ov] #ac1jjj male & female bir?s1 arrang$ 9 families ( f\r & upw>ds4 ,!y 7 tak5 f ! p$igrees 9 ! ,h]ald's ,visitations1 & !re=e repres5t z a rule a some:at select class1 viz4 ! families ( ! elde/ sons ( ,engli% c\ntry g5tlem5 9 ! sixte5? c5tury4 ,!y are n suffici5tly ext5sive yet = publication1 b ,i give a summ>y ( ! results to indicate _! t5d5cy s f>4 ,! upp] l9e ( figures 9 ea* case gives ! obs]v$ results3 i4e4 9 ! case ( a family ( f\r1 ! numb]s :i* _h f\r male1 ?ree male & "o female1 two male & two female1 & s on4 ,! l[] l9e gives ! calculat$ results2 i4e4 ! correspond+ numb]s :i* w\ld h be5 obta9$ _h bat*es ( ,m4s & ,f4s be5 drawn f a bag 9 :i* !y 7 mix$ 9 ! ratio assign$ by ! total obs]v$ numb]s = ^? families4 #eab families ( #d2 m#d m#c f m#b f#b mf#c f#d yield+ #ha #adh #afa #ih #bd 7obs]v$47 #aahh ,m4 3 #hfj ,f4 #eg #afh #ahd #hh #ae 7calculat$47 #eab families ( #e2 m#e m#d f m#c f#b m#b f#c mf#d f#e yield+ #ej #hb #afa #adc #fa #ae 7obs47 #adjb ,m4 3 #aaeh ,f4 #be #ajc #agb #adc #ei #aj 7calc47 #eab families ( #f2 m#f m#e f m#d f#b m#c f#c m#b f#d mf#e f#f yield+ #cj #dh #aae #adf #abf #dj #g 7obs47 #afab ,m4 3 #adfj ,f4 #aj #ef #acc #aei #ajh #da #e 7calc47 ,! numb]s = ! l>g] families are z yet too small to be wor? giv+1 b !y %[ ! same t5d5cy4 ,x w be se5 t 9 e case ! obs]v$ c5tral values are less ?an ! calculat$2 & t ! obs]v$ extreme values are mu* great] ?an ! calculat$4 ,! results seem to sugge/ 7s f>7 t a family _c be lik5$ to a *ance draw+ ( ! requisite numb] f "o bag4 ,a bett] analogy w\ld be to suppose two bags1 "o ) ,m4s 9 excess & ! o!r ) ,f4s 9 less excess1 & t "s p]sons draw f "o & "s f ! o!r4 ,b full] /ati/ics are ne$$4 ,x w be obs]v$ t ! total excess ( male bir?s is l>ge4 ,?is may arise f undue omission ( females2 b ,i h c>efully conf9$ myself to ! two or ?ree la/ g5]ations1 9 ea* p$igree1 = great] security4 #a4 ,essay on ,probabilities1 p4 #aad4 #b4 ,d\bts h be5 express$ ab\t ! truly r&om "* ( ! digits 9 ?is case 7v4 ,de ,morgan1 ,budget ( ,p>adoxes1 p4 #bia71 & ,jevons has gone s f> z to ask 7,pr9ciples ( ,sci5ce1 p4 #ebi71 ,:y %\ld ! value ( 1 :5 express$ to a great numb] ( figures1 conta9 ! digit #g mu* less frequ5tly ?an any o!r digit6 ,i d n q und]/& :at ?is means4 ,if su* a "q 7 ask$ 9 relation to any unusual div]g5ce f ! priori *ance 9 a case ( ?r[+ dice1 say1 we %\ld probably sub/itute = x ! foll[+1 z be+ m appropriate to our sci5ce3--,assign ! degree ( improbability ( ! ev5t 9 "q2 i4e4 its /ati/ical r>ity4 ,& we %\ld !n proce$ to judge1 9 ! way indicat$ 9 ! text1 :e!r ?is improbability gave rise to any gr\nds ( suspicion4 ,! calculation is simple4 ,! actual numb] ( #g's1 9 ! #gjh digits1 is #ec3 :il/ ! fair av]age w\ld be #ga4 ,! "q is1 ,:at is ! *ance ( su* a dep>ture f ! av]age 9 #gjh turns8 ,by ! usual me?ods ( calculation 7v4 ,gall[ay on ,probability7 ! *ances aga9/ an excess or defect ( #ah are ab\t #dd 3 #a1 9 respect ( any specifi$ digit4 ,b ( c\rse :at we want to decide are ! *ances aga9/ "s "o ( ! t5 %[+ ?is div]g5ce4 ,?is ,i e/imate z be+ approximately det]m9$ by ! fraction 7#dd_/de7aj1 viz4 #j4h4 ,?is repres5ts odds ( only ab\t #d 3 #a aga9/ su* an occurr5ce1 :i* is no?+ rem>kable4 ,z a matt] ( fact sev]al digits 9 ! two o!r magnitudes :i* ,mr ,%anks _h calculat$ to ! same l5g?1 viz4 ,tan-#a #a_/e & ,tan-#a #a_/bci1 %[ ! same div]g5cies 7v4 ,proc4 ,roy4 ,soc4 xxi4 #cai74 ,i may call att5tion "h to a po9t :i* %\ld h be5 notic$ 9 ! *apt] on ,r&omness4 ,we mu/ be cauti\s :5 we decide ^u ! r&om "* by m]e inspection4 ,x is v in/ructive "h to comp>e ! digits 9 ) ^? )9 ! 'p]iod' ( a circulat+ decimal ( v long p]iod4 ,t ( #a #gfii1 :i* yields ! full p]iod ( #gfih figures1 0 calculat$ "s ye>s ago by two ,cambridge graduates 7,mr ,lunn & ,mr ,suffield71 & privately pr9t$4 ,if we conf9e our exam9ation to a portion ( ! succession ! r&om "* seems plausible2 i4e4 ! digits1 & _! v>i\s comb9ations1 come out 9 ne>ly1 b n exactly1 equal numb]s4 ,s if we take bat*es ( #aj2 ! av]ages hov] nicely ab\t #de4 ,b if we took ! :ole p]iod :i* 'circulates1' we %\ld f9d ^! *>act]i/ics ov]done1 & ! r&om "* w\ld disappe>4 ,t is1 in/ead ( a m]ely ultimate approximation to equality we %\ld h 7z f> z ?is is possible7 an absolute atta9m5t ( x4 #c4 ,( c\rse ?is conv5tional e/imate is no?+ diff]5t 9 k9d f t :i* may atta* to any ord] or succession4 ,t5 heads 9 succession is intr9sically or objectively indi/+ui%able 9 "* f alt]nate heads & tails1 or sev5 heads & ?ree tails1 c4 ,its di/9ction only consi/s 9 its almo/ univ]sal acceptance z rem>kable4 #d4 ,our ,inh]itance 9 ! ,great ,pyramid1 ,ed4 ,,iii4 #ahgg4 #e4 ,made 9 ,nature 7,jan4 #bd1 #ahgh7 by ,mr ,j4 ,g4 ,jackson4 ,x mu/ be rem>k$ t ,mr ,smy?'s alt]native /atem5t ( 8 case leads up to t explanation3--,! v]tical height ( ! great pyramid is ! radius ( a !oretical circle ! l5g? ( ^: curv$ circumf]5ce is exactly equal to ! sum ( ! l5g?s ( ! f\r /raight sides ( ! actual & practical squ>e base4 ,z reg>ds ! alt]natives ( *ance & design1 "h1 x mu/ be rememb]$ 9 ju/ice to ,mr ,smy?'s argum5t t ! anti!sis he admits to *ance is n human1 b div9e design4 #f4 ,see ,c\rnot1 ,essai sur les fondem5ts de nos connaissances4 ,vol4 ,i4 p4 #ga4 #g4 ,x des]ves notice t consid]ations ( ?is k9d h f\nd _! way into ! ,law ,c\rts ?\gh ( c\rse )\t any attempt at num]ical valuation4 ,?us1 9 ! celebrat$ ,de ,ros trial1 9 s f> z ! evid5ce 0 indirect1 "o ma9 gr\nd ( suspicion seems to h be5 t ,"l ,de ,ros1 :5 deal+ at :i/1 obta9$ f> m c\rt c>ds ?an *ance c\ld be expect$ to assign him2 & t 9 consequ5ce 8 av]age ga9s = sev]al ye>s 9 succession 7 unusually l>ge4 ,! c\nsel = ! def5ce urg$ t /ill l>g] ga9s _h be5 secur$ by o!r play]s )\t suspicion ( unfairness1--7,i _c f9d t x 0 expla9$ ov] h[ l>ge an area ( exp]i5ce ^! in/ances _h be5 s\ght2 nor h[ f> ! magnitude ( ! /akes1 z di/+ui%$ f ! numb] ( successes1 acc\nt$ = t ( ! actual ga9s71--& t l>ge all[ance mu/ be made = skill :]e ! actual ga9s 7 comput$4 7,see ! ,times' report1 ,feb4 #aa1 #ahcg47 #h4 ,metretike4 ,at ! end ( ?is volume w be f\nd a useful li/ ( a numb] ( o!r publications by ! same au?or on alli$ topics4 #i4 ,t is1 if we look simply to /ati/ical results1 z ,arbu?nott did1 & z we %\ld d if we 7 exam9+ ! tosses ( a p5ny4 ,if ! rem>kable !ory ( ,dr ,ds+ 7,die ,reguli]ung des ,ges*le*ts-v]hltnisses444 ,j5a1 #ahhd7 be confirm$1 ! matt] w\ld assume a some:at diff]5t aspect4 ,he attempts to %[1 bo? on physiological gr\nds1 & by analysis ( /ati/ics ref]r+ to m5 & animals1 t !re is a decid$ly comp5satory process at "w4 ,t is1 if = any cause ei!r sex atta9s a prepond]ance1 ag5cies are at once set 9 motion :i* t5d to r$ress ! balance4 ,?is is a modification & improvem5t ( ! old] !ory1 t ! relative age ( ! p>5ts has some?+ to d ) ! sex ( ! (fspr+4 ,quetelet 7,lett]s1 p4 #fa7 has attempt$ to prove a proposition ab\t ! succession ( male & female bir?s by c]ta9 exp]im5ts suppos$ to be tri$ ^u an urn ) black & :ite balls 9 x4 ,b ?is is go+ too f>4 7,see ! note at ! end ( ?is *apt]47 #aj4 ,x is precisely analog\s to ! conclusion t ! fl[]s ( ! daisies 7z di/+ui%$ f ! plants1 v4 p4 #aji7 are n di/ribut$ at r&om1 b h a t5d5cy to g 9 gr\ps ( two or m4 ,m]e obs]vation %[s ?is3 & !n1 f our k ( ! gr[? ( plants we may inf] t ^! little gr\ps spr+ f ! same root4 #aa4 ,9 ?is discussion1 writ]s (t5 speak ( ! probability ( a physical connection betwe5 ^! d\ble />s4 ,! phrase seems mislead+1 = on ! usual hypo!sis ( univ]sal gravitation all />s are physically connect$1 by gravitation4 ,x is !re=e bett]1 z above1 to make x simply a "q ( relative proximity1 & to leave x to a/ronomy to inf] :at foll[s f unusual proximity4 #ab4 ,pr(essor ,=bes 9 ! pap] 9 ! ,philosophical ,magaz9e already ref]r$ to 7,*4 ,,vii4 #ah7 gave sev]al diagrams to %[ :at 7 ! actual arrangem5ts ( a r&om di/ribution4 ,he scatt]$ peas ov] a *ess-bo>d1 & !n c\nt$ ! numb] :i* re/$ on ea* squ>e4 ,8 figures seem to %[ t ! g5]al appe>ance ( ! />s is mu* ! same z t produc$ by su* a plan ( scatt]+4 ,"s rec5t inve/igations by ,mr ,r4 ,a4 ,proctor seem to %[1 h[ev]1 t !re are at lea/ two exceptions to ?is tol]ably uni=m di/ribution4 7#a7 ,he has asc]ta9$ t ! />s are decid$ly m ?ickly aggregat$ 9 ! ,milky ,way ?an else:]e4 ,s f> z ?is is to be reli$ on ! argum5t is ! same z 9 ! case ( ! d\ble />s2 x t5ds to prove t ! proximity ( ! />s 9 ! ,milky ,way is n m]ely app>5t1 b actual4 7#b7 ,he has asc]ta9$ t !re are two l>ge areas1 9 ! ,nor? & ,s\? hemisph]es1 9 :i* ! />s are mu* m ?ickly aggregat$ ?an else:]e4 ,"h1 x seems to me1 ,probability proves no?+3 we are simply d5y+ t ! di/ribution is uni=m4 ,:at may foll[ 9 ! way ( inf]5ces z to ! physical process ( causation by :i* ! />s h be5 dispos$ is a "q = ! ,a/ronom]4 ,see ,mr ,proctor's ,essays on ,a/ronomy1 p4 #big4 ,also a s]ies ( ,essays 9 ,! ,univ]se & ! com+ ,transits4 ,,*apt] ,,xi4 ,,on ,,c]ta9 ,,consequ5ces ,,( ,,! ,,objective ,,treatm5t ,,( ,a ,,sci5ce ,,( ,,inf]5ce4#a #a4 ,9 ! previ\s edition a l>ge "p ( ?is *apt] 0 devot$ to ! g5]al consid]ation ( ! di/9ction betwe5 a ,mat]ial & a ,conceptuali/ view ( ,logic4 ,i h omitt$ mo/ ( ?is "h1 z also a l>ge "p ( a *apt] devot$ to ! detail$ discussion ( ! ,law ( ,causation1 z ,i hope be=e v long to express my op9ions on ^! subjects m fully1 & m appropriately1 9 a treatise on ! g5]al pr9ciples ( ,inductive ,logic4 #a4 ,/ud5ts ( ,logic are famili> ) t broad di/9ction betwe5 ! two me?ods ( treatm5t to :i* ! names ( ,mat]ial & ,conceptuali/ may be appli$4 ,! di/9ction 0 "o :i* _h be5 gradually gr[+ up "u o!r names be=e x 0 emphasiz$1 & treat$ z a di/9ction )9 ! field ( ,logic prop]1 by ! publication ( ,mill's well kn[n "w4 ,no "o1 = in/ance1 c read ,:ewell's treatises on ,induction1 or ,h]s*el's ,disc\rse1 )\t see+ t !y are treat+ ( mu* ! same subject-matt]1 & reg>d+ x 9 mu* ! same way1 z t :i* ,mill discuss$ "u ! "n ( ,logic1 ?\gh !y 7 n dispos$ to give x t "n4 ,t is1 ^! writ]s ?r\gh\t took x = grant$ t :at !y _h to d 0 to sy/ematise ! facts ( nature 9 _! objective =m1 & "u _! wide/ possible treatm5t1 & to exp\nd ! pr9cipal modes ( inf]5ce & ! pr9cipal practical aids 9 ! inve/igation ( ^! modes ( inf]5ce1 :i* reason c\ld sugge/ & :i* exp]i5ce c\ld ju/ify4 ,:at ,mill did 0 to br+ ^! me?ods into close relation ) su* portions ( ! old s*ola/ic ,logic z he felt able to reta91 to "w !m out into mu* full] detail1 to sy/ematize !m by giv+ !m a c]ta9 philosophical & psy*ological f\ndation1--& to entitle ! result ,logic4 ,! practical treatm5t ( a sci5ce w seldom correspond closely to ! ideal :i* its support]s propose to !mselves1 & /ill seldom] to t :i* its antagoni/s insi/ ^u dem&+ f ! support]s4 ,if we 7 to take our acc\nt ( ! di/9ction betwe5 ! two views ( ,logic exp\nd$ respectively by ,hamilton & by ,mill1 f ,mill & ,hamilton respectively1 we %\ld c]ta9ly n f9d x easy to br+ !m "u "o common def9ition4 ,by su* a te/1 ! mat]ial ,logic w\ld be reg>d$ z no?+ m ?an a some:at arbitr>y selection f ! doma9 ( ,physical ,sci5ce 9 g5]al1 & ! conceptuali/ ,logic no?+ m ?an a some:at arbitr>y selection f ! doma9 ( ,psy*ology4 ,! =m] w\ld omit all consid]ation ( ! laws ( ?\ght & ! latt] all consid]ation ( ! tru? or falsehood ( our conclusions4 ,( c\rse1 9 practice1 su* extremes z ^! are soon se5 to be avoidable1 & 9 spite ( all controv]sial exagg]ations ! exp\nd]s ( ! opposite views d contrive to reta9 a l>ge area ( speculation 9 common4 ,i d n propose "h to exam9e 9 detail ! re/rictions by :i* ?is accommodation is br\ght ab\t1 or ! v real & important di/9ctions ( me?od1 aim1 te/s1 & limits :i* 9 spite ( all approa* to agreem5t are /ill f\nd to subsi/4 ,to attempt ?is w\ld be to op5 up r too wide an enquiry to be suitable 9 a treatise on "o subdivision only ( ! g5]al sci5ce ( ,inf]5ce4 #b4 ,"o subdivision ( ?is enquiry is h[ev] really =c$ ^u our notice4 ,x does become important to consid] ! re/rictions to :i* ! ultra-mat]ial acc\nt ( ! prov9ce ( ,logic has to be subject$1 because we %all ?us h our att5tion drawn to an aspect ( ! subject :i*1 slight & fleet+ z x is )9 ! region ( ,induction becomes v prom95t & comp>atively p]man5t 9 t ( ,probability4 ,accord+ to ?is ultra-mat]ial view1 ,inductive ,logic w\ld g5]ally be consid]$ to h no?+ to d ) any?+ b objective facts3 its duty is to />t f facts & to conf9e itself to su* me?ods z w yield no?+ b facts4 ,:at is d\btful x ei!r e/abli%es or x lets alone = ! pres5t1 :at is unatta9able x rejects1 & 9 ?is way x proce$s to build up by sl[ accretion a va/ fabric ( c]ta9 k4 ,b ( c\rse all ?is is suppos$ to be done by human m9ds1 & !re=e if we enquire :e!r notions or concepts1--call !m :at we w1--h no place 9 su* a s*eme x mu/ necess>ily be admitt$ t !y h "s place4 ,! facts :i* =m our />t+ po9t mu/ be grasp$ by an intellig5t be+ be=e inf]5ce c be built ^u !m2 & ! 'facts' :i* =m ! conclusion h (t51 at any rate = "s "t1 no place any:]e else ?an 9 ! m9d ( man4 ,b no "o c read ,mill's treatise1 = in/ance1 )\t notic+ h[ slight is 8 ref]5ce to ?is aspect ( ! "q4 ,he rem>ks1 9 almo/ contemptu\s indiff]5ce1 t ! man :o digs mu/ ( c\rse h a notion ( ! gr\nd he digs & ( ! spade he puts into x1 b he evid5tly consid]s t ^! 'notions' ne$ n mu* m occupy ! att5tion ( ! speculative logician1 9 s f> z 8 m]e inf]5ces are conc]n$1 ?an !y occupy t ( ! husb&man4 #c4 ,x mu/ be admitt$ t !re is "s w>rant = ?is omission ( all ref]5ce to ! subjective side ( inf]5ce s long z we are deal+ ) ,inductive ,logic4 ,! inductive discov]] is ( c\rse 9 a v diff]5t position4 ,if he is wor?y ( ! "n 8 m9d at e mom5t w be teem+ ) notions :i* he w\ld be z f> z any "o f call+ facts3 he is busy mak+ !m su* to ! be/ ( 8 p[]4 ,b ! logician :o foll[s 9 8 /eps1 & ^: bus9ess x is to expla9 & ju/ify :at 8 lead] has discov]$1 is r apt to ov]look ?is m5tal or unc]ta9 /age4 ,:at he mo/ly deals 9 are ! 'complete inductions' & 'well-gr\nd$ g5]alizations' & s =?1 or ! explod$ errors :i* contradict !m3 ! prison]s & ! corpses respectively1 :i* ! real discov]] leaves on ! field beh9d him :il/ he presses on to complete 8 victory4 ,! :ole me?od ( sci5ce1--expository z contra/$ ) militant1--is to emphasize ! di/9ction betwe5 fact & non-fact1 & to treat ( little else b ^! two4 ,9 o!r words a treatise on ,inductive ,logic c be writt5 )\t any occasion be+ f\nd to def9e :at is meant by a notion or concept1 or ev5 to employ su* t]ms4 #d4 ,& yet1 :5 we come to look m closely1 signs may be detect$ ev5 )9 ! field ( ,inductive ,logic1 ( an occasional break+ d[n ( ! %>p di/9ction 9 "q2 we may meet n[ & !n ) entities 7to use ! wide/ t]m atta9able7 9 ref]5ce to :i* x w\ld be h>d to say t !y are ei!r facts or conceptions4 ,= in/ance1 ,inductive ,logic has (t5 occasion to make use ( ,hypo!ses3 to :i* ( ! above two classes are ^! to be ref]r$8 ,!y d n seem 9 /rictness to belong to ei!r2 nor are !y1 z w pres5tly be po9t$ out1 by any means a solit>y in/ance ( ! k9d4 ,x is true t )9 ! prov9ce ( ,inductive ,logic ^! hypo!ses d n give mu* tr\ble on ?is score4 ,h[ev] vague may be ! =m 9 :i* !y fir/ pres5t !mselves to ! philosoph]'s m9d1 !y h n mu* bus9ess to come be=e u 9 our capacity ( logicians until !y are well on _! way1 s to say1 t[>ds becom+ facts3 until !y are beg9n+ to h>d5 into t firm tangible %ape 9 :i* !y w ev5tually appe>4 ,we g5]ally h "s su* recomm5dations giv5 to u z t our hypo!ses %all be well-gr\nd$ & reasonable4 ,?is seems only ano!r way ( tell+ u t h[ev] freely ! philosoph] may make 8 guesses 9 ! privacy ( 8 own /udy1 he _h bett] n br+ !m out into public until !y c ) fair propriety be t]m$ facts1 ev5 ?\gh ! "n be giv5 ) "s qualification1 z by t]m+ !m 'probable facts4' ,! reason1 !re=e1 :y we d n take mu* acc\nt ( ?is int]m$iate /ate 9 ! hypo!sis1 :5 we are deal+ ) ! inductive processes1 is t "h at any rate x plays only a tempor>y "p2 its appe>ance 9 t guise is b v fugitive4 ,if ! hypo!sis be a s\nd "o1 x w soon take its place z an admitt$ fact2 if n1 x w soon be reject$ altoge!r4 ,its /ate z a hypo!sis is n a normal "o1 & !re=e we h n mu* occasion to scrut9ize its *>act]i/ics4 ,9 s say+1 x mu/ ( c\rse be und]/ood t we are speak+ z inductive logicians2 ! philosoph] 9 8 work%op ought1 z already rem>k$1 to be famili> en\gh ) ! hypo!sis 9 e /age ( its exi/5ce f its orig92 b ! logician's duty is diff]5t1 deal+ z he does ) pro( r ?an ) ! processes ( orig9al inve/igation & discov]y4 ,we might inde$ ev5 g fur!r1 & say t 9 _m cases ! hypo!sis does n pres5t itself to ! read]1 t is to ! recipi5t ( ! k1 until x has ceas$ to des]ve t "n at all4 ,x may be fir/ sugge/$ to him along ) ! pro( :i* e/abli%es x1 he n hav+ _h occasion to ?9k ( x be=e4 ,x ?us comes at a s+le /ep out ( ! obscurity ( ! unkn[n into ! full possession ( its rights z a fact1 skipp+ practically ! int]m$iate or hypo!tical /age altoge!r4 ,! orig9al inve/igator himself may h long pond]$ ov] x1 & kept x pres5t to 8 m9d1 9 ?is its dubi\s /age1 b f9ally h giv5 x to ! _w ) t am\nt ( evid5ce :i* raises x at once 9 ! m9ds ( o!rs to ! level ( commonly accept$ facts4 ,/ill ?is d\btful /age exi/s 9 e hypo!sis1 ?\gh = logical purposes1 & to mo/ m9ds1 x exi/s 9 a v fugitive way only4 ,:5 att5tion has be5 direct$ to x1 x may be also detect$ else:]e 9 ,logic4 ,take ! case1 = in/ance1 ( ! ref]5ce ( names4 ,mill gives ! examples ( ! sun1 & a battle1 z di/+ui%$ f ! ideas ( !m :i* we1 or *ildr51 may ent]ta94 ,"h ! di/9ction is pla9 & obvi\s en\gh4 ,b if1 on ! o!r h&1 we take ! case ( ?+s ^: exi/5ce is d\btful or disput$1 ! difficulty above m5tion$ beg9s to %[ itself4 ,! case ( m]ely ext9ct ?+s1 or su* z h n yet come into exi/5ce1 (f]s inde$ no tr\ble1 s9ce ( c\rse actually pres5t exi/5ce is n necess>y to con/itute a fact4 ,! usual di/9ction may ev5 be reta9$ also 9 ! case ( my?ical exi/5ces4 ,c5taur & ,griff9 h z univ]sally recognis$ a significance among/ ! poets1 pa9t]s1 & h]alds z lion & leop>d h4 ,h5ce we may claim1 ev5 "h1 t our conceptions %all be 'tru?ful1' 'consi/5t ) fact1' & s on1 by :i* we mean t !y are to be 9 accordance ) univ]sal conv5tion ^u su* subjects4 ,necess>y & univ]sal accordance is sometimes claim$ to be all t is meant by 'objective1' & s9ce univ]sal accordance is atta9able 9 ! case ( ! notori\sly fictiti\s1 our fundam5tal di/9ction betwe5 fact & conception1 & our det]m9ation t our t]ms %all ref] to :at is objective r ?an to :at is subjective1 may ) "s degree ( /ra9 be /ill conceiv$ to be t5able ev5 "h4 #e4 ,b :5 we come to ! case ( disput$ ph5om5a ! difficulty re-em]ges4 ,a suppos$ planet or new m9]al1 a d\btful fact 9 hi/ory1 a disput$ !ological doctr9e1 are b a few examples out ( _m t might be (f]$4 ,:at "s p]sons /r5u\sly ass]t1 o!rs z /r5u\sly d5y1 & :atev] hope !re may be ( spe$y agreem5t 9 ! case ( physical ph5om5a1 exp]i5ce %[s t !re is n mu* prospect ( ?is 9 ! case ( ^? :i* are moral & hi/orical1 to say no?+ ( !ological4 ,s long z ^? :o are 9 agreem5t conf9e _! int]c\rse to !mselves1 _! 'facts' are accept$ z su*1 b z soon z !y come to communicate ) o!rs all di/9ction betwe5 fact & conception is lo/ at once1 ! 'facts' ( "o p>ty be+ m]e gr\ndless 'conceptions' to _! oppon5ts4 ,!re is !re=e1 ,i ?9k1 9 ^! cases a real difficulty 9 c>ry+ out di/9ctly & consi/5tly ! acc\nt :i* ! ,mat]iali/ logician (f]s z to ! ref]5ce ( names4 ,x ne$ h>dly be po9t$ out t :at ?us applies to names or t]ms applies equally to propositions 9 :i* p>ticul> or g5]al /atem5ts are made involv+ names4 #f4 ,b :5 we /ep into ,probability1 & treat ?is f ! same mat]ial or ,ph5om5al po9t ( view1 we c no long] neglect ! "q :i* is ?us pres5t$ to u4 ,! difficulty _c "h be reject$1 z ref]r+ to :at is m]ely tempor>y or occasional4 ,! int]m$iate condition betwe5 conjecture & fact1 s f> f be+ tempor>y or occasional only1 is "h normal4 ,x is j ! condition :i* is specially *>act]i/ic ( ,probability4 ,h5ce x foll[s t h[ev] decid$ly we may reject ! ,conceptuali/ !ory we _c altoge!r reject ! use ( ,conceptuali/ language4 ,if we c prove t a giv5 man w die next ye>1 or atta9 suffici5tly ne> to pro( to leave u practically c]ta9 on ! po9t1 we may speak ( 8 dea? z a 7future7 fact4 ,b if we m]ely contemplate 8 dea? z probable8 ,?is is ! sort ( inf]5ce1 or sub/itute = inf]5ce1 ) :i* ,probability is specially conc]n$4 ,we may1 if we s please1 speak ( 'probable facts1' b if we exam9e ! mean+ ( ! words we may f9d !m n m]ely obscure1 b self-contradictory4 ,d\btless !re are facts "h1 9 ! fulle/ s5se ( ! t]m1 namely ! /ati/ics ^u :i* our op9ion is ultimately bas$1 = ^! are kn[n & admitt$ by all :o h look$ into ! matt]4 ,! same language may also be appli$ to t ext5sion ( ^! /ati/ics by induction :i* is involv$ 9 ! ass]tion t simil> /ati/ics w be f\nd to prevail else:]e1 = ^! also may rightfully claim univ]sal acceptance4 ,b ^! /atem5ts1 z 0 abundantly %[n 9 ! e>li] *apt]s1 /& on a v diff]5t foot+ f a /atem5t conc]n+ ! individual ev5t2 ! e/abli%m5t & discussion ( ! =m] belong by rights to ,induction1 & only ! latt] to ,probability4 #g4 ,x is true t = want ( appropriate t]ms to express su* ?+s we are (t5 induc$1 inde$ compell$1 to apply ! same "n ( 'facts' to su* individual cont+5cies4 ,we %\ld n1 = in/ance1 hesitate to speak ( ! fact ( ! man dy+ be+ probable1 possible1 unlikely1 or :atev] x might be4 ,b ,i _c help reg>d+ su* expressions z a /rictly incorrect usage aris+ out ( a defici5cy ( appropriate te*nical t]ms4 ,x is d\btless c]ta9 t "o or o!r ( ! two alt]natives mu/ happ51 b ?is alt]native c]ta9ty is n ! subject ( our contemplation2 :at we h be=e u is ! s+le alt]native1 :i* is notori\sly unc]ta94 ,x is ?is1 & ?is only1 :i* is at pres5t "u notice1 & ^: occurr5ce has to be e/imat$4 ,we h surely no "r to dignify ?is ) ! "n ( a fact1 "u any qualifications1 :5 ! opposite alt]native has claims1 n p]haps actually equal to1 b at any rate n mu* inf]ior to its own4 ,su* language1 z already rem>k$1 may be q "r 9 ,inductive logic1 :]e we are only conc]n$ ) conjectures ( su* a high degree ( likelihood t _! non-occurr5ce ne$ n be tak5 into practical acc\nt1 & :i* are moreov] reg>d$ z m]ely tempor>y4 ,b 9 ,probability ! conjecture may h any degree ( likelihood ab\t x2 x may be j z likely z ! o!r alt]native1 nay x may be mu* less likely4 ,9 ^! latt] cases1 = in/ance1 if ! *ances are v mu* aga9/ ! man's dea?1 x is surely an abuse ( language to speak ( ! 'fact' ( 8 dy+1 ev5 ?\gh we qualify x by decl>+ x to be highly improbable4 ,! subject-matt] ess5tial to ,probability be+ ! unc]ta91 we c nev] ) propriety employ ^u x language :i* 9 its orig9al & correct application is only appropriate to :at is actually or approximately c]ta94 #h4 ,x %\ld be rememb]$ also t ?is /ate ( ?+s1 ?us *>act]i/ic ( ,probability1 is p]man5t !re4 ,s long z !y rema9 "u ! treatm5t ( t sci5ce our conjectures1 or :atev] we l to call !m1 nev] develop into facts4 ,i calculate1 = in/ance1 ! *ance t a die w give ace1 or t a man w live beyond a c]ta9 age4 ,su* an approximation to k z is ?us acquir$ is z mu* z we c ev] aft]w>ds hope to get1 unless we resort to o!r me?ods ( enquiry4 ,we d n1 z 9 ,induction1 feel ourselves on ! br9k ( "s exp]im5tal or o!r pro( :i* at any mom5t may raise x into c]ta9ty4 ,x is no?+ b a conjecture ( a c]ta9 degree ( /r5g?1 & su* x w ev] rema91 s long z ,probability is left to deal ) x4 ,if any?+ m is ev] to be made out ( x we mu/ appeal to direct exp]i5ce1 or to "s k9d ( inductive pro(4 ,z we h s (t5 said1 individual facts c nev] be det]m9$ "h1 b m]ely ultimate t5d5cies & av]ages ( _m ev5ts4 ,i may1 inde$1 by a second appeal to ,probability improve ! "* ( my conjecture1 ?r\gh be+ able to ref] x to a n>r[] & bett] class ( /ati/ics2 b its ess5tial nature rema9s ?r\gh\t :at x 04 ,x appe>s to me !re=e t ! acc\nt ( ! ,mat]iali/ view ( logic indicat$ at ! comm5cem5t ( ?is *apt]1 ?\gh sub/antially s\nd1 ne$s "s slight reconsid]ation & re-/atem5t4 ,x answ]s admirably s f> z ord9>y ,induction is conc]n$1 b ne$s "s revision if x is to be equally applicable to t wid] view ( ! nature & processes ( acquir+ k :]e9 ! sci5ce ( logic is consid]$ to involve ,probability also z well z ,induction4 #i4 ,briefly !n x is ?is4 ,we reg>d ! sci5tific ?9k]1 :e!r he be ! orig9al inve/igator :o discov]s1 or ! logician :o analyses & describes ! pro(s t may be (f]$1 z surr\nd$ by a _w ( objective ph5om5a ext5d+ indef9itely bo? ways 9 "t1 & 9 e direction 9 space4 ,mo/ ( !m are1 & always w rema91 unkn[n4 ,if we speak ( !m z facts we mean t !y are pot5tial objects ( human k1 t "u appropriate circum/ances m5 c\ld come to det]m9ate & f9al agreem5t ab\t !m4 ,! sci5tific or mat]ial logician has to sup]9t5d ! process ( conv]t+ z mu* z possible ( ^! unkn[n ph5om5a into :at are kn[n1 ( aggregat+ !m1 z we h said above1 ab\t ! nucleus ( c]ta9 data :i* exp]i5ce & obs]vation _h to />t )4 ,9 s do+ 8 pr9cipal res\rces are ! ,me?ods ( ,induction1 ( :i* some?+ has be5 said 9 a =m] *apt]2 ano!r res\rce is f\nd 9 ! ,!ory ( ,probability1 & ano!r 9 ,d$uction4 ,n[1 h[ev] su* language may be object$ to z sav\r+ ( ,conceptualism1 ,i c see no bett] comp5di\s way ( describ+ ^! processes ?an by say+ t we are engag$ 9 gett+ at conceptions ( ^! ext]nal ph5om5a1 & z f> z possible conv]t+ ^! conceptions into facts4 ,:at is ! natural hi/ory ( 'facts' if we trace !m back to _! orig98 ,!y fir/ come into be+ z m]e guesses or conjectures1 z contemplat$ possibilities ^: correspond5ce ) reality is ei!r altoge!r disbeliev$ or reg>d$ z entirely d\btful4 ,9 ?is /age1 ( c\rse1 _! contra/ ) facts is %>p en\gh4 ,h[ !y arise x does n belong to ,logic b to ,psy*ology to say4 ,logic inde$ has little or no?+ to d ) !m :il/ !y are 9 ?is =m4 ,ev]yone is busy all 8 life 9 ent]ta9+ su* guesses ^u v>i\s subjects1 ! sup]iority ( ! philosoph] ov] ! common man be+ ma9ly f\nd 9 ! quality ( 8 guesses1 & 9 ! skill & p]si/5ce ) :i* he sifts & exam9es !m4 ,9 ! next /age !y mo/ly g by ! "n ( !ories or hypo!ses1 :5 !y are compreh5sive 9 _! scope1 or are 9 any way on a scale ( gr&eur & importance3 :5 h[ev] !y are ( a trivial k9d1 or ref] to details1 we really h no di/9ctive or appropriate "n = !m1 & mu/ be cont5t !re=e to call !m 'conceptions4' ,?r\gh ?is /age !y flit ) great rapidity 9 ,inductive ,logic2 (t5 ! logician keeps !m back until _! evid5ce is s /rong t !y come be=e ! _w at once 9 ! full dignity ( facts4 ,h5ce1 z already rem>k$1 ?is /age ( _! c>e] is n mu* dwelt ^u 9 ,logic4 ,b ! :ole bus9ess ( ,probability is to discuss & e/imate !m at ?is po9t4 ,consequ5tly1 s f> z ?is sci5ce is conc]n$1 ! explanation ( ! ,mat]ial logician z to ! ref]5ce ( names & propositions has to be modifi$4 #aj4 ,! be/ way !re=e ( describ+ our position 9 ,probability is z foll[s3--,we are ent]ta9+ a conception ( "s ev5t1 pa/1 pres5t1 or future4 ,f ! nature ( ! case ?is conception is all t c be actually ent]ta9$ by ! m9d4 ,9 its pres5t condition x w\ld be incorrect to call x a fact1 ?\gh we w\ld will+ly1 if we c\ld1 conv]t x into su* by mak+ c]ta9 ( x "o way or ! o!r4 ,b s long z our conclusions are to be effect$ by consid]ations ( ,probability only1 we _c d ?is4 ,! utmo/ we c d is to e/imate or evaluate x4 ,! :ole function ( ,probability is to give rules = s do+4 ,by means ( ref]5ce to /ati/ics or by direct d$uction1 z ! case may be1 we are enabl$ to say h[ mu* ?is conception is to be believ$1 t is 9 :at proportion out ( ! total numb] ( cases we %all be "r 9 s do+4 ,our position1 !re=e1 9 ^! cases seems di/9ctly t ( ent]ta9+ a conception1 & ! process ( inf]5ce is t ( asc]ta9+ to :at ext5t we are ju/ifi$ 9 add+ ?is conception to ! already receiv$ body ( tru? & fact4 ,s long1 !n1 z we are conf9$ to ,probability ^! conceptions rema9 su*4 ,b if we turn to ,induction we see t !y are meant to g a /ep fur!r4 ,_! f9al /age is n rea*$ until !y h rip5$ into facts1 & s tak5 _! place among/ unconte/$ tru?s4 ,?is is _! f9al de/9ation 9 ,logic1 & our task is n accompli%$ until !y h rea*$ x4 #aa4 ,su* language z ?is 9 :i* we speak ( our position 9 ,probability z be+ t ( ent]ta9+ a conception1 & be+ occupi$ 9 det]m9+ :at degree ( belief is to be assign$ to x1 may sav\r ( ,conceptualism1 b is 9 _s p]fectly diff]5t f x4 ,our ultimate ref]5ce is always to facts4 ,we />t f !m z our data1 & rea* !m aga9 ev5tually 9 our results :5ev] x is possible4 ,9 ,probability1 ( c\rse1 we _c d ?is 9 ! individual result1 b ev5 !n 7z %[n 9 ,*4 ,,vi47 we always ju/ify our conclusions by appeal to facts1 viz4 to :at happ5s 9 ! long run4 ,! discussion :i* has be5 ?us giv5 to ?is "p ( ! subject may seem some:at t$i\s1 b x 0 s obvi\sly =c$ ^u u :5 consid]+ ! di/9ction betwe5 ! two ma9 views ( ,logic1 t x 0 impossible to pass x ov] )\t fe> ( misappreh5sion & confusion4 ,moreov]1 z w be se5 9 ! c\rse ( ! next *apt]1 sev]al important conclusions c\ld n h be5 prop]ly expla9$ & ju/ifi$ )\t fir/ tak+ pa9s to make ?is "p ( our gr\nd p]fectly pla9 & satisfactory4 ,,*apt] ,,xii4 ,,consequ5ces ,,( ,,! ,,=ego+ ,,di/9ctions4 #a4 ,we are n[ 9 a position to expla9 & ju/ify "s important conclusions :i*1 if n direct consequ5ces ( ! di/9ctions laid d[n 9 ! la/ *apt]1 w at any rate be m readily appreciat$ & accept$ aft] t exposition4 ,9 ! fir/ place1 x w be se5 t 9 ,probability "t has no?+ to d ) ! "q2 9 o!r words1 x does n matt] :e!r ! ev5t1 ^: probability we are discuss+1 be pa/1 pres5t1 or future4 ,! problem be=e u1 9 its simple/ =m1 is ?is3--,/ati/ics 7ext5d$ by ,induction1 & practically (t5 ga9$ by ,d$uction7 in=m u t a c]ta9 ev5t has happ5$1 does happ51 or w happ51 9 a c]ta9 way 9 a c]ta9 proportion ( cases4 ,we =m a conception ( t ev5t1 & reg>d x z possible2 b we want to d m2 we want to "k h[ mu* we ought to expect x 7"u ! explanations giv5 9 a =m] *apt] ab\t quantity ( belief74 ,!re is !re=e a sort ( relative futurity ab\t ! ev5t1 inasmu* z our k ( ! fact1 & !re=e our ju/ification or o!rwise ( ! correctness ( our surmise1 almo/ necess>ily comes aft] ! surmise 0 =m$2 b ! futurity is only relative4 ,! evid5ce by :i* ! "q is to be settl$ may n be =?com+ yet1 or we may h x by u b only consult x aft]w>ds4 ,x is f ! fact ( ! futurity be+1 z above describ$1 only relative1 t ,i h pref]r$ to speak ( ! conception ( ! ev5t r ?an ( ! anticipation ( x4 ,! latt] t]m1 :i* 9 "s respects w\ld h seem$ m intelligible & appropriate1 is op5 to ! objection1 t x does r1 9 popul> e/imation1 convey ! notion ( an absolute z oppos$ to a relative futurity4 #b4 ,= example2 a die is ?r[n4 ,once 9 six times x gives ace2 if !re=e we assume1 )\t exam9ation1 t ! ?r[ is ace1 we %all be "r once 9 six times4 ,9 s do+ we may1 accord+ to ! usual plan1 g =w>ds 9 "t2 t is1 =m our op9ion ab\t ! ?r[ be=eh&1 :5 no "o c tell :at x w be4 ,or we might g backw>ds2 t is1 =m an op9ion ab\t dice t _h be5 ca/ on "s occasion 9 "t pa/1 & !n correct our op9ion by ! te/imony ( "s "o :o _h be5 a witness ( ! ?r[s4 ,9 ei!r case ! m5tal op]ation is precisely ! same2 an op9ion =m$ m]ely on /ati/ical gr\nds is aft]w>ds correct$ by specific evid5ce4 ,! op9ion may h be5 =m$ ^u a pa/1 pres5t1 or future ev5t2 ! evid5ce :i* corrects x aft]w>ds may be our own eyesight1 or ! te/imony ( o!rs1 or any k9d ( inf]5ce2 by ! evid5ce is m]ely meant su* subsequ5t exam9ation ( ! case z is assum$ to set ! matt] at re/4 ,x is q possible1 ( c\rse1 t ?is specific evid5ce %\ld nev] be =?com+2 ! conception 9 t case rema9s z a conception1 & nev] obta9s t degree ( conviction :i* qualifies x to be reg>d$ z a 'fact4' ,?is is cle>ly ! case ) all pa/ ?r[s ( dice ! results ( :i* d n happ5 to h be5 record$4 ,9 discuss+ games ( *ance !re are obvi\s advantages 9 conf9+ ourselves to :at is really1 z well z relatively1 future1 = 9 t case direct in=mation conc]n+ ! contemplat$ result be+ impossible1 all p]sons are on precisely ! same foot+ ( comp>ative ignorance1 & mu/ =m _! op9ion entirely f ! kn[n or inf]r$ frequ5cy ( occurr5ce ( ! ev5t 9 "q4 ,on ! o!r h&1 if ! ev5t be pass$1 !re is almo/ always evid5ce ( "s k9d & ( "s value1 h[ev] slight1 to in=m u :at ! ev5t really 02 if ?is evid5ce is n actually at h&1 we c g5]ally1 by wait+ a little1 obta9 some?+ t %all be at lea/ ( "s use to u 9 =m+ our op9ion4 ,practically !re=e we g5]ally conf9e ourselves1 9 anticipations ( ?is k9d1 to :at is really future1 & s 9 popul> e/imation futurity becomes indissolubly associat$ ) probability4 #c4 ,!re is h[ev] an error closely connect$ ) ! above view ( ! subject1 or at lea/ an inaccuracy ( expression :i* is con/antly liable to lead to error1 :i* has f\nd wide acceptance1 & has be5 sanction$ by writ]s ( ! greate/ au?ority4 ,= in/ance1 bo? ,butl]1 9 8 ,analogy1 & ,mill1 h drawn att5tion1 "u "o =m ( expression or ano!r1 to ! di/9ction betwe5 improbability be=e ! ev5t & improbability aft] ! ev5t1 :i* !y consid] to be p]fectly diff]5t ?+s4 ,t ?is phraseology indicates a di/9ction ( importance _c be d5i$1 b x seems to me t ! language 9 :i* x is (t5 express$ requires to be am5d$4 ,butl]'s rem>ks on ?is subject occur 9 8 ,analogy1 9 ! *apt] on miracles4 ,admitt+ t !re is a /rong presumption aga9/ miracles 78 equival5t = ! ord9>y expression1 an 'improbability be=e ! ev5t'7 he /rives to obta9 ass5t = !m by %[+ t o!r ev5ts1 :i* also h a /rong presumption aga9/ !m1 are receiv$ on :at is 9 reality v slight evid5ce4 ,he says1 ,!re is a v /rong presumption aga9/ common speculative tru?s1 & aga9/ ! mo/ ord9>y facts1 be=e ! pro( ( !m2 :i* yet is ov]come by almo/ any pro(4 ,!re is a presumption ( millions to "o aga9/ ! /ory ( ,cs>1 or ( any o!r man4 ,=1 suppose a numb] ( common facts s & s circum/anc$1 ( :i* "o _h no k9d ( pro(1 %\ld happ5 to come into "o's ?\ghts1 e "o w\ld )\t any possible d\bt conclude !m to be false4 ,& ! l may be said ( a s+le common fact4 #d4 ,^! rem>ks h be5 a good deal criticiz$1 & !y c]ta9ly seem to me mislead+ & obscure 9 _! ref]5ce4 ,if "o may judge by ! context1 & by ano!r passage 9 :i* ! same argum5t is aft]w>ds ref]r$ to1#a x w\ld c]ta9ly appe> t ,butl] drew no di/9ction betwe5 miracul\s acc\nts1 & o!r acc\nts :i*1 to use any ( ! v>i\s expressions 9 common use1 are unlikely or improbable or h a presumption aga9/ !m2 & conclud$ t s9ce "s ( ! latt] 7 in/antly accept$ ^u some:at m$iocre te/imony1 x 0 altoge!r irrational to reject ! =m] :5 simil>ly or bett] support$4#b ,?is subject w come aga9 "u our notice1 & dem& full] discussion1 9 ! *apt] on ! ,cr$ibility ( extraord9>y /ories4 ,x w suffice "h to rem>k t1 h[ev] satisfactory su* a view ( ! matt] might be to "s !ologians1 no antagoni/ ( miracles w\ld = a mom5t accept x4 ,he w\ld naturally object t1 in/ead ( ! miracul\s elem5t be+ 7z ,butl] consid]s7 a small additional presumption aga9/ ! n>rative1 x involv$ ! ev5ts 9 a totally di/9ct class ( incr$ibility2 t x multipli$1 r ?an m]ely add$ to1 ! difficulties & objections 9 ! way ( accept+ ! acc\nt4 ,mill's rem>ks 7,logic1 ,bk4 ,,iii4 *4 ,,xxv4 #d7 are ( a diff]5t "*4 ,discuss+ ! gr\nds ( disbelief he speaks ( p mak+ ! mi/ake ( ov]look+ ! di/9ction betwe5 7:at may be call$7 improbability be=e ! fact1 & improbability aft] x1 two diff]5t prop]ties1 ! latt] ( :i* is always a gr\nd ( disbelief1 ! =m] n always4 ,he in/ances ! ?r[+ ( a die4 ,x is improbable be=eh& t x %\ld turn up ace1 & yet aft]w>ds1 !re is no reason = disbeliev+ x if any cr$ible witness ass]ts x4 ,s aga91 ! *ances are greatly aga9/ ,a4 ,b4's dy+1 yet if any "o tells u t he di$ ye/]day we believe x4 #e4 ,t !re is "s difficulty ab\t su* problems z ^! mu/ be admitt$4 ,! fact t s _m p f9d !m a s\rce ( p]plexity1 & t su* v>i\s explanations are (f]$ to solve ! p]plexity1 are a suffici5t pro( ( ?is4#c ,! consid]ations ( ! la/ *apt]1 h[ev]1 ov]-te*nical & ev5 s*ola/ic z "s ( ! language 9 :i* x 0 express$ may h seem$ to ! read]1 w ,i hope guide u to a m satisfactory way ( reg>d+ ! matt]4 ,:5 we speak ( an improbable ev5t1 x mu/ be rememb]$ t1 objectively consid]$1 an ev5t c only be m or less r>e2 ! extreme degree ( r>ity be+ ( c\rse t 9 :i* ! ev5t does n occur at all4 ,n[1 z 0 %[n 9 ! la/ *apt]1 our position1 :5 =m+ judgm5ts ( ! "t 9 "q1 is t ( ent]ta9+ a conception or conjecture 7call x :at we w71 & assign+ a c]ta9 weight ( tru/wor?9ess to x4 ,! real di/9ction1 !re=e1 betwe5 ! two classes ( examples respectively1 :i* are adduc$ bo? by ,butl] & by ,mill1 consi/s 9 ! way 9 :i* ^? conceptions are obta9$2 !y be+ obta9$ 9 "o case by ! process ( guess+1 & 9 ! o!r by t ( giv+ he$ to ! reports ( witnesses4 #f4 ,take ,butl]'s in/ance fir/4 ,9 ! 'presumption be=e ! pro(' we h repres5t$ to u a man ?9k+ ( ! /ory ( ,cs>1 t is1 mak+ a guess ab\t c]ta9 hi/orical ev5ts )\t any def9ite gr\nds = x1 & !n speculat+ z to :at value is to be atta*$ to ! probability ( its tru?4 ,su* a guess is ( c\rse1 z he says1 conclud$ to be false4 ,b :at does he und]/& by ! 'presumption aft] ! pro('8 ,t a /ory n adopt$ at r&om1 b actually sugge/$ & support$ by witnesses1 %\ld be true4 ,! latt] might be accept$1 :il/ ! =m] w\ld und\bt$ly be reject$2 b all t ?is proves1 or r illu/rates1 is t ! te/imony ( almo/ any witness is 9 mo/ cases va/ly bett] ?an a m]e guess4#d ,we may 9 bo? cases alike speak ( '! ev5t' if we w2 9 fact1 z 0 admitt$ 9 ! la/ *apt]1 common language w n readily l5d itself to any o!r way ( speak+4 ,b x %\ld be cle>ly und]/ood t1 phrase x h[ we w1 :at is really pres5t to ! man's m9d1 & :at is to h its probable value assign$ to x1 is ! conception ( an ev5t1 9 ! s5se 9 :i* t expression has already be5 expla9$4 ,& surely no two conceptions c h a mu* m important di/9ction put betwe5 !m ?an t :i* is involv$ 9 suppos+ "o to re/ on a m]e guess1 & ! o!r on ! report ( a witness4 ,precisely ! same rem>ks apply to ! example giv5 by ,mill4 ,be=e ,a4 ,b4's dea? our op9ion ^u ! subject 0 no?+ b a guess ( our own f\nd$ ^u life /ati/ics2 aft] 8 dea? x 0 f\nd$ ^u ! evid5ce ( "s "o :o presumably _h tol]able opportunities ( kn[+ :at ! facts really 74 #g4 ,t ! di/9ction be=e u has no ess5tial connection :atev] ) "t is inde$ obvi\s on a mom5t's consid]ation4 ,conceive = a mom5t t "s "o _h opportunities ( kn[+ :e!r ,a4 ,b4 w\ld die or n4 ,if he told u t ,a4 ,b4 w\ld die to-morr[1 we %\ld 9 t case be j z ready to believe him z :5 he tells u t ,a4 ,b4 has di$4 ,if we cont9u$ to feel any d\bt ab\t ! /atem5t 7suppos+ always t we _h full confid5ce ab\t 8 v]acity 9 matt]s into :i* he _h duly enquir$71 x w\ld be because we ?\ght t 9 8 case1 z 9 ours1 x 0 equival5t to a guess1 & no?+ m4 ,s ) ! ev5t :5 pa/1 ! fact ( its be+ pa/ makes no diff]5ce :atev]2 until ! cr$ible witness in=ms u ( :at he kn[s to h occurr$1 we %\ld d\bt x if x happ5$ to come into our m9ds1 j z mu* z if x 7 future4 ,! di/9ction1 !re=e1 betwe5 probability be=e ! ev5t & probability aft] ! ev5t seems to resolve itself simply into ?is2--be=e ! ev5t we (t5 h no bett] means ( in=mation ?an to appeal to /ati/ics 9 "s =m or o!r1 & s to guess among/ ! v>i\s possible alt]natives2 aft] ! ev5t ! guess may mo/ commonly be improv$ or sup]s$$ by appeal to specific evid5ce1 9 ! %ape ( te/imony or obs]vation4 ,h5ce1 naturally1 our e/imate 9 ! latt] case is commonly ( mu* m value4 ,b if ^! *>act]i/ics 7 anyh[ inv]t$2 if1 t is1 we 7 to conf9e ourselves to guess+ ab\t ! pa/1 & if we c\ld f9d any additional evid5ce ab\t ! future1 ! respective values ( ! diff]5t e/imates w\ld also be inv]t$4 ,! diff]5ce betwe5 ^! values has no necess>y connection ) "t1 b dep5ds entirely ^u ! diff]5t gr\nds ^u :i* our conception or conjecture ab\t ! ev5t 9 "q re/s4 #h4 ,! foll[+ imag9>y example w s]ve to br+ out ! po9t indicat$ above4 ,conceive a p ) v %ort memories1 & :o pres]v$ no k9d ( record to p]petuate _! hold ^u ! ev5ts :i* happ5$ among/ !m4#e ,! :ole region ( ! pa/ w\ld !n be to !m :at mu* ( ! future is to u2 viz4 a region ( guesses & conjectures1 "o 9 ref]5ce to :i* !y c\ld only judge ^u g5]al consid]ations ( probability1 r ?an by direct & specific evid5ce4 ,b conceive also t !y _h among/ !m a race ( prophets :o c\ld succe$ 9 =etell+ ! future ) z ne> an approa* to accuracy & tru/wor?9ess z our v>i\s hi/ories1 & biographies1 & recollections1 c atta9 9 respect to ! pa/4 ,! pres5t & usual functions ( direct evid5ce or te/imony1 & ( probability1 w\ld !n be simply inv]t$2 & s 9 consequ5ce w\ld ! pres5t accid5tal *>act]i/ics ( improbability be=e & aft] ! ev5t4 ,x w\ld !n be ! latt] :i* w\ld by comp>ison be reg>d$ z 'n always a gr\nd ( disbelief1' :]eas 9 ! case ( ! =m] we %\ld !n h x ma9ta9$ t x always 0 s4 #i4 ,! orig9 ( ! mi/ake j discuss$ is wor? enquir+ into4 ,i take x to be z foll[s4 ,x is (t5 ! case1 z above rem>k$1 :5 we are speculat+ ab\t a future ev5t1 & almo/ always ! case :5 t future ev5t is tak5 f a game ( *ance1 t all p]sons are 9 precisely ! same condition ( ignorance 9 respect to x4 ,! limit ( available in=mation is conf9$ to /ati/ics1 & am\nts to ! k t ! unkn[n ev5t mu/ assume "s "o ( v>i\s alt]native =ms4 ,! conjecture1 !re=e1 ( any "o man ab\t x is z valuable z t ( any o!r4 ,b 9 reg>d to ! pa/ ! case is v diff]5t4 ,"h we are n 9 ! habit ( rely+ ^u /ati/ical in=mation4 ,h5ce ! conjectures ( diff]5t m5 are ( extremely diff]5t values2 9 ! case ( _m !y am\nt to :at we call positive k4 ,?is puts a broad di/9ction1 9 popul> e/imation1 betwe5 :at may be call$ ! objective c]ta9ty ( ! pa/ & ( ! future1 a di/9ction1 h[ev]1 :i* f ! /&+-po9t ( a sci5ce ( inf]5ce ought to h no exi/5ce4 ,9 consequ5ce ( ?is1 :5 we apply to ! pa/ & ! future respectively ! some:at ambigu\s expression '! *ance ( ! ev5t1' x commonly comes to be> v diff]5t significations4 ,appli$ to ! future x be>s its prop] mean+1 namely1 ! value to be assign$ to a conjecture ^u /ati/ical gr\nds4 ,x does s1 because 9 ?is case h>dly any "o has m to judge by ?an su* conjectures4 ,b appli$ to ! pa/ x %ifts its mean+1 ow+ to ! fact t :]eas "s m5 h conjectures only1 o!rs h positive k4 ,by ! *ance ( ! ev5t is n[ (t5 meant1 n ! value to be assign$ to a conjecture f\nd$ on /ati/ics1 b to su* a conjecture d]iv$ f & en=c$ by any body else's conjecture1 t is by 8 k & 8 te/imony4 #aj4 ,!re is a class ( cases 9 app>5t opposition to "s ( ! /atem5ts 9 ?is *apt]1 b :i* w be f\nd1 :5 exam9$ closely1 decid$ly to confirm !m4 ,i am walk+1 say1 9 a remote "p ( ! c\ntry1 & sudd5ly meet ) a fri5d4 ,at ?is ,i am naturally surpris$4 ,yet if ! view be correct t we _c prop]ly speak ab\t ev5ts 9 !mselves be+ probable or improbable1 b only say ?is ( our conjectures ab\t !m1 h[ d we expla9 ?is8 ,we _h =m$ no conjecture be=eh&1 = we 7 n ?9k+ ab\t any?+ ( ! k9d1 b yet few w\ld fail to feel surprise at su* an incid5t4 ,! reply might fairly be made t we _h =m$ su* anticipations tacitly4 ,on any su* occasion e "o unconsci\sly divides ?+s into ^? :i* are kn[n to him & ^? :i* are n4 ,dur+ a consid]able previ\s p]iod a c\ntless numb] ( p]sons _h met u1 & all fall5 into ! li/ ( ! unkn[n to u4 ,!re 0 no?+ to rem9d u ( hav+ =m$ ! anticipation or di/9ction at all1 until x 0 sudd5ly call$ out into vivid consci\sness by ! exceptional ev5t4 ,! words :i* we %\ld in/9ctively use 9 our surprise seem to %[ ?is3--',:o w\ld h ?\ght ( see+ y "h8' viz4 ,:o w\ld h giv5 any weight to ! lat5t ?\ght if x _h be5 call$ out into consci\sness be=eh&8 ,we put our words into ! pa/ t5se1 %[+ t we h _h ! di/9ction lurk+ 9 our m9ds all ! "t4 ,we always h a multitude ( su* ready-made classes ( ev5ts 9 our m9ds1 & :5 a ?+ happ5s to fall into "o ( ^? classes :i* are v small we _c help notic+ ! fact4 ,or suppose ,i am "o ( a regim5t into :i* a %ot flies1 & x /rikes me1 & me only4 ,at ?is ,i am surpris$1 & :y8 ,our common language w guide u to ! reason4 ',h[ /range t x %\ld j h hit me ( all m56' ,we are ?9k+ ( ! v natural two-fold division ( mank9d into1 ourselves1 & ev]ybody else2 our surprise is aga91 z x 71 retrospective1 & 9 ref]5ce to ?is division4 ,no anticipation 0 di/9ctly =m$1 because we did n ?9k be=eh& ( ! ev5t1 b ! ev5t1 :5 x has happ5$1 is at once assign$ to its appropriate class4 #aa4 ,?is view is confirm$ by ! foll[+ consid]ations4 ,tell ! /ory to a fri5d1 & he w be a little surpris$1 b less s ?an we 71 8 division 9 ?is p>ticul> case be+1--8 fri5ds 7( :om we are b "o71 & ! re/ ( mank9d4 ,x is n a necess>y division1 b x is ! "o :i* w be mo/ likely sugge/$ to him4 ,tell x aga9 to a p]fect /rang]1 & 8 division be+ diff]5t 7viz4 we fall+ into ! majority7 we %all fail to make him p]ceive t !re is any?+ at all rem>kable 9 ! ev5t4 ,x is n ( c\rse attempt$ 9 ^! rem>ks to ju/ify our surprise 9 e case 9 :i* x exi/s4 ,diff]5t p]sons might be diff]5tly affect$ 9 ! cases suppos$1 & ! examples are !re=e giv5 ma9ly = illu/ration4 ,/ill on pr9ciples already discuss$ 7,*4 ,,vi4 #cb7 we might expect to f9d some?+ l a g5]al ju/ification ( ! am\nt ( surprise4 #ab4 ,! answ] commonly giv5 9 ^! cases is conf9$ to attempt+ to %[ t ! surprise %\ld n arise1 r ?an to expla9+ h[ x does arise4 ,x takes ! foll[+ =m1--',y h no "r to be surpris$1 = no?+ rem>kable has really occurr$4 ,if ?is p>ticul> ?+ _h n happ5$ some?+ equally improbable mu/4 ,if ! %ot _h n hit y or y\r fri5d1 x mu/ h hit "s "o else :o 0 priori z unlikely to be hit4' ,= "o ?+ ?is answ] does n expla9 ! fact t almo/ e "o is surpris$ 9 su* cases1 & surpris$ some:at 9 ! diff]5t proportions m5tion$ above4 ,moreov] x has ! inh]5t unsatisfactor9ess ( admitt+ t some?+ improbable has really happ5$1 b gett+ ov] ! difficulty by say+ t all ! o!r alt]natives 7 equally improbable4 ,a natural inf]5ce f ?is is t !re is a class ( ?+s1 9 !mselves really improbable1 :i* c yet be e/abli%$ ^u v slight evid5ce4 ,butl] accept$ ?is inf]5ce1 & work$ x out to ! /range conclusion giv5 above4 ,mill attempts to avoid x by ! consid]ation ( ! v diff]5t values to be assign$ to improbability be=e & aft] ! ev5t4 ,"s fur!r discussion ( ?is po9t w be f\nd 9 ! *apt] on ,fallacies1 & 9 t on ! ,cr$ibility ( ,extraord9>y ,/ories4 #ac4 ,9 connection ) ! subject at pres5t "u discussion we w n[ take notice ( a di/9ction :i* we %all (t5 f9d insi/$ on 9 works on ,probability1 b to :i* app>5tly ne$less importance has be5 atta*$4 ,x is frequ5tly said t probability is relative1 9 ! s5se t x has a diff]5t value to diff]5t p]sons accord+ to _! respective in=mation ^u ! subject 9 "q4 ,= example1 two p]sons1 ,a & ,b1 are go+ to draw a ball f a bag conta9+ #d balls3 ,a kn[s t ! balls are black & :ite1 b does n "k m2 ,b kn[s t ?ree are black & "o :ite4 ,x w\ld be said t ! probability ( a :ite ball to ,a is #a_/b1 & to ,b #a_/d4 ,:5 h[ev] we reg>d ! subject f ! mat]ial /&+ po9t1 !re really does n seem to me mu* m 9 ?is ?an ! pr9ciple1 equally true 9 e o!r sci5ce1 t our inf]5ces w v>y accord+ to ! data we assume4 ,we might on logical gr\nds ) almo/ equal propriety speak ( ! area ( a field or ! height ( a m\nta9 be+ relative1 & !re=e hav+ "o value to "o p]son & ano!r to ano!r4 ,! real mean+ ( ! example cit$ above is ?is3 ,a supposes t he is *oos+ :ite at r&om out ( a s]ies :i* 9 ! long run w\ld give :ite & black equally (t52 ,b supposes t he is *oos+ :ite out ( a s]ies :i* 9 ! long run w\ld give ?ree black to "o :ite4 ,by ! application1 !re=e1 ( a precisely simil> rule !y draw diff]5t conclusions2 b s !y w\ld "u ! same circum/ances 9 any o!r sci5ce4 ,if two m5 are measur+ ! height ( a m\nta91 & "o supposes 8 base to be #ajjj feet1 :il/ ! o!r takes x to be #ajja1 !y w\ld ( c\rse =m diff]5t op9ions ab\t ! height4 ,! sci5ce ( m5suration is n suppos$ to h any?+ to d ) ! tru? ( ! data1 b assumes !m to h be5 correctly tak52 :y %\ld n ?is be equally ! case ) ,probability1 mak+ ( c\rse due all[ance = ! peculi> "* ( ! data ) :i* x is conc]n$8 #ad4 ,?is view ( ! relativ5ess ( probability is connect$1 z x appe>s to me1 ) ! subjective view ( ! sci5ce1 & is inde$ *>act]i/ic ( x4 ,x seems a fair illu/ration ( ! weak side ( t view1 t x %\ld lead u to lay any /ress on su* an expression4 ,z 0 fully expla9$ 9 ! la/ *apt]1 9 proportion z we "w out ! ,conceptuali/ pr9ciple we are l$ away f ! fundam5tal "q ( ! mat]ial logic1 viz4 ,is our belief actually correct1 or n8 &1 if ! =m]1 to :at ext5t & degree is x correct8 ,we are direct$ r to ask1 ,:at belief does any "o z a matt] ( fact hold8 ,&1 s9ce ! belief ?us ent]ta9$ naturally v>ies accord+ to ! circum/ances & o!r s\rces ( in=mation ( ! p]son 9 "q1 its relativ5ess comes to be admitt$ z inevitable1 or at lea/ x is n to be wond]$ at if su* %\ld be ! case4 ,on our view ( ,probability1 !re=e1 its 'relativ5ess' 9 any giv5 case is a mislead+ expression1 & x w be f\nd mu* pref]able to speak ( ! effect produc$ by v>iations 9 ! nature & am\nt ( ! data :i* we h be=e u4 ,n[ x mu/ be admitt$ t !re are frequ5tly cases 9 our sci5ce 9 :i* su* v>iations are peculi>ly likely to be f\nd4 ,= in/ance1 ,i am expect+ a fri5d :o is a pass5g] 9 an ocean /eam]4 ,!re are a hundr$ pass5g]s on bo>d1 & ! crew also numb]s a hundr$4 ,i read 9 ! pap]s t "o p]son 0 lo/ by fall+ ov]bo>d2 my anticipation t x 0 my fri5d :o 0 lo/ is b small1 ( c\rse4 ,on turn+ to ano!r pap]1 ,i see t ! man :o 0 lo/ 0 a pass5g]1 n "o ( ! crew2 my slight anxiety is at once d\bl$4 ,b ano!r acc\nt adds t x 0 an ,engli%man1 & on t l9e at t season ! ,engli% pass5g]s are kn[n to be few2 ,i at once beg9 to ent]ta9 decid$ fe>s4 ,& s on1 e trifl+ bit ( in=mation in/antly affect+ my expectations4 #ae4 ,n[ s9ce x is peculi>ly *>act]i/ic ( ,probability1 z di/+ui%$ f ,induction1 to be ?us at ! m]cy1 s to say1 ( e little fact t may be float+ ab\t :5 we are 9 ! act ( =m+ our op9ion1 :at c be ! h>m 7x may be urg$7 ( express+ ?is /ate ( ?+s by t]m+ our /ate ( expectation relative8 ,!re seem to me to be two objections4 ,9 ! fir/ place1 z j m5tion$1 we are induc$ to reject su* an expression on gr\nds ( consi/5cy4 ,x is inconsi/5t ) ! g5]al _s & treatm5t ( ! subject hi!rto adopt$1 & t5ds to divorce ,probability f ,inductive logic in/ead ( reg>d+ !m z cognate sci5ces4 ,we are aim+ at tru?1 z f> z t goal c be rea*$ by our road1 & !re=e we dislike to reg>d our conclusions z relative 9 any o!r s5se ?an t 9 :i* tru? itself may be said to be relative4 ,9 ! second place1 ?is condition ( un/able ass5t1 ?is con/ant liability to h our judgm5t affect$1 to any degree & at any mom5t1 by ! accession ( new k1 ?\gh d\btless *>act]i/ic ( ,probability1 does n seem to me *>act]i/ic ( x 9 its s\nd] & m legitimate applications4 ,x seems r appropriate to a precipitate judgm5t =m$ 9 accordance ) ! rules1 ?an a /rict example ( _! natural employm5t4 ,su* precipitate judgm5ts may occur 9 ! case ( ord9>y d$uctive conclusions4 ,9 ! practical exig5cies ( life we are con/antly 9 ! habit ( =m+ a ha/y op9ion ) ne>ly full confid5ce1 at any rate tempor>ily1 ^u ! /r5g? ( evid5ce :i* we mu/ well "k at ! "t _c be f9al4 ,we wait a %ort "t1 & some?+ else turns up :i* induces u to alt] our op9ion1 p]haps to rev]se x4 ,"h our conclusions may h be5 p]fectly s\nd "u ! giv5 circum/ances1 t is1 !y may be su* z e "o else w\ld h drawn :o 0 b\nd to make up 8 m9d ^u ! data be=e u1 & !y are unque/ionably 'relative' judgm5ts 9 ! s5se n[ "u discussion4 ,& yet1 ,i ?9k1 e "o w\ld %r9k f s t]m+ !m :o wi%$ sy/ematically to c>ry out ! view t ,logic 0 to be reg>d$ z an organon ( tru?4 #af4 ,9 ! examples ( ,probability :i* we h hi!rto employ$1 we h = ! mo/ "p assum$ t !re 0 a c]ta9 body ( /ati/ics set be=e u on :i* our conclusion 0 to re/4 ,x 0 assum$1 on ! "o h&1 t no direct specific evid5ce c\ld be got1 s t ! judgm5t 0 really to be "o ( ,probability1 & to re/ on ^! /ati/ics2 9 o!r words1 t no?+ bett] ?an !m 0 available = u4 ,b x 0 equally assum$1 on ! o!r h&1 t ^! /ati/ics 7 op5 to ! obs]vation ( e "o1 s t we ne$ n h to put up ) any?+ inf]ior to !m 9 =m+ our op9ion4 ,9 o!r words1 we h be5 assum+ t "h1 z 9 ! case ( mo/ o!r sci5ces1 ^? :o h to draw a conclusion />t f ! same foot+ ( opportunity & in=mation4 ,?is1 = in/ance1 cle>ly is or ought to be ! case :5 we are conc]n$ ) games ( *ance2 ignorance or misappreh5sion ( ! common data is nev] contemplat$ !re4 ,s ) ! /ati/ics ( life1 or o!r insurance3 s long z our judgm5t is to be accurate 7aft] its fa%ion7 or ju/ifiable1 ! common tables ( mortality are all t any "o has to g by4 #ag4 ,x is true t 9 ! case ( a man's prospect ( dea? we %\ld ea* qualify our judgm5t by :at we knew or reasonably suppos$ z to 8 heal?1 habits1 pr(ession1 & s on1 & %\ld ?us arrive at v>y+ e/imates4 ,b no "o c\ld ju/ify 8 own e/imate )\t appeal+ explicitly or implicitly to ! /ati/ical gr\nds on :i* he _h reli$1 & if ^! 7 n previ\sly available to o!r p]sons1 he mu/ n[ set !m be=e _! notice4 ,9 o!r words1 ! judgm5ts we ent]ta91 "h z else:]e1 are only relative s long z we re/ !m on gr\nds peculi> to ourselves4 ,! process ( ju/ification1 :i* ,i consid] to be ess5tial to logic1 has a t5d5cy to correct su* individualities ( judgm5t1 & to set all obs]v]s on ! same basis z reg>ds _! data4 ,x is bett] !re=e to reg>d ! conclusions ( ,probability z be+ absolute & objective1 9 ! same s5se z1 ?\gh d\btless 9 a f> less degree ?an1 !y are 9 ,induction4 ,fully admitt+ t our conclusions w 9 _m cases v>y exce$+ly f "t to "t by fre% accessions ( k1 x is pref]able to reg>d su* fluctuations ( ass5t z p>tak+ ( ! nature ( precipitate judgm5ts1 f\nd$ on special /ati/ics1 in/ead ( dep5d+ only on ^? :i* are common to all obs]v]s4 ,9 call+ su* judgm5ts precipitate x is n impli$ t !re is any blame 9 ent]ta9+ !m1 b simply t1 = "o reason or ano!r1 we h be5 induc$ to =m !m )\t wait+ = ! possession ( ! full am\nt ( evid5ce1 /ati/ical or o!rwise1 :i* might ultimately be look$ =4 ,?is explanation w suit ! facts equally well1 & is m consi/5t ) ! g5]al philosophical position ma9ta9$ 9 ?is "w4 #a4 ,is x n self-evid5t t int]nal improbabilities ( all k9ds weak5 ext]nal pro(8 ,d\btless1 b to :at practical purpose c ?is be alleg$ "h1 :5 x has be5 prov$ be=e1 t real int]nal improbabilities1 :i* rise ev5 to moral c]ta9ty1 are ov]come by ! mo/ ord9>y te/imony4 ,"p ,,ii4 *4 ,,iii4 #b4 ,miracles mu/ n be comp>$ to common natural ev5ts2 or to ev5ts :i*1 ?\gh uncommon1 are simil> to :at we daily exp]i5ce2 b to ! extraord9>y ph5om5a ( nature4 ,& !n ! comp>ison w be betwe5 ! presumption aga9/ miracles1 & ! presumption aga9/ su* uncommon appe>ances1 suppose z comets14444 ,"p ,,ii4 *4 ,,ii4 #c4 ,= in/ance1 ,sir ,j4 ,f4 ,/eph5 expla9s x by draw+ a di/9ction betwe5 *ances & probabilities1 :i* he says t ,butl] has confus$ toge!r2 ! objection t v ord9>y pro( w ov]come a presumption ( millions to "o is bas$ ^u a confusion betwe5 probabilities & *ances4 ,! probability ( an ev5t is its capability ( be+ prov$4 ,its *ance is ! num]ical proportion betwe5 ! numb] ( possible cases--suppos$ to be equally fav\rable--fav\rable to its occurr5ce2 & ! numb] ( possible cases unfav\rable to its occurr5ce 7,g5]al view ( ! ,crim9al ,law ( ,engl&1 p4 #bee74 ,donk91 aga9 7,phil4 ,magaz9e1 ,june1 #ahea71 employs ! t]ms improbability & incr$ibility to m>k ! same di/9ction4 #d4 ,9 ! extreme case ( ! witness himself m]ely guess+1 or be+ z untru/wor?y z if he m]ely guess$1 ! two /ories w ( c\rse /& on precisely ! same foot+4 ,?is case w be notic$ aga9 9 ,*apt] ,,xvii4 ,x may be rem>k$ t !re are sev]al subtleties "h :i* _c be adequately notic$ )\t "s previ\s inve/igation into ! "q ( ! cr$ibility ( witnesses4 #e4 ,accord+ to ,dante1 some?+ resembl+ ?is prevail$ among/ ! occupants ( ! ,inf]no4 ,! c>d9als & o!rs :om he !re meets are able to give in=mation ab\t _m ev5ts :i* 7 yet to happ5 ^u e>?1 b !y _h to ask x = _m ev5ts :i* actually _h happ5$4 ,,*apt] ,,xiii4 ,,on ,,! ,,conception ,,& ,,treatm5t ,,( ,,modality4 #a4 ,! read] :o kn[s any?+ ( ! s*ola/ic ,logic w h p]ceiv$ be=e n[ t we h be5 t\*+ 9 a v>iety ( places ^u t mo/ ?orny & repulsive ( di/ricts 9 ! logical t]ritory2--modality4 ,x w be advisable1 h[ev]1 to put toge!r1 some:at m def9itely1 :at has to be said ^u ! subject4 ,i propose1 !re=e1 to devote ?is *apt] to a brief acc\nt ( ! pr9cipal v>ieties ( treatm5t :i* ! modals h receiv$ at ! h&s ( pr(ess$ logicians4 ,x mu/ be rem>k$ at ! outset t ! s5se 9 :i* modality & modal propositions h be5 at v>i\s times und]/ood1 is by no means fix$ & inv>iably ! same4 ,?is div]sity ( view has aris5 p>tly f correspond+ diff]5ces 9 ! view tak5 ( ! prov9ce & nature ( logic1 & p>tly f diff]5ces 9 ! philosophical & sci5tific op9ions ent]ta9$ z to ! con/itution & ord] ( nature4 ,9 lat] times1 moreov]1 ano!r v p[]ful ag5t 9 br++ ab\t a *ange 9 ! treatm5t ( ! subject mu/ be recogniz$ 9 ! gradual & /eady gr[? ( ! !ory ( ,probability1 z work$ out by ! ma!maticians f _! own po9t ( view4 #b4 ,9 spite1 h[ev]1 ( ^! diff]5ces ( treatm5t1 !re has always be5 "s community ( subject-matt] 9 ! discussions ^u ?is topic4 ,!re has almo/ always be5 "s ref]5ce to quantity ( belief2 en\gh p]haps to ju/ify ,de ,morgan's#a rem>k1 t ,probability 0 ! unkn[n ,god :om ! s*oolm5 ignorantly wor%ipp$ :5 !y s dealt ) ?is species ( enunciation1 t x 0 said to be beyond human det]m9ation :e!r !y mo/ tortur$ ! modals1 or ! modals !m4 ,b ?is ref]5ce to quantity ( belief has sometimes be5 direct & imm$iate1 sometimes indirect & aris+ out ( ! nature ( ! subject-matt] ( ! proposition4 ,! fact is1 t t di/9ction betwe5 ! purely subjective & purely objective views ( logic1 :i* ,i h endeav\r$ to br+ out into prom95ce 9 ! elev5? *apt]1 0 n by any means cle>ly recogniz$ 9 e>ly times1 nor inde$ be=e ! "t ( ,kant1 & ! view to be tak5 ( modality naturally %>$ 9 ! consequ5t confusion4 ,?is w1 ,i hope1 be made cle> 9 ! c\rse ( ! foll[+ *apt]1 :i* is int5d$ to give a brief sket* ( ! pr9cipal diff]5t ways 9 :i* ! modality ( propositions has be5 treat$ 9 logic4 ,z x is n propos$ to give any?+ l a regul> hi/ory ( ! subject1 !re w be no necessity to adh]e to any /rict sequ5ce ( "t1 or to discuss ! op9ions ( any writ]s1 except ^? :o may be tak5 z repres5tative ( tol]ably di/9ct views4 ,! outcome ( su* inve/igation w be1 ,i hope1 to conv9ce ! read] 7if1 inde$1 he _h n come to t conviction be=e71 t ! logicians1 aft] hav+ _h a long & fair trial1 h fail$ to make any?+ satisfactory out ( ?is subject ( ! modals by _! me?ods ( enquiry & treatm5t2 & t x ought1 !re=e1 to be bani%$ entirely f t sci5ce1 & relegat$ to ,probability4 #c4 ,f ! e>lie/ /udy ( ! syllogi/ic process x 0 se5 t1 complete z t process is )9 its own doma91 ! doma91 at any rate "u its simple/ treatm5t1 is a v limit$ "o4 ,propositions ( ! pure =m1--,all 7or "s7 ,a is 7or is n7 ,b1--are f\nd 9 practice to =m b a small portion ev5 ( our categorical /atem5ts4 ,we are p]petually meet+ ) o!rs :i* express ! relation ( ,b to ,a ) v>i\s degrees ( necessity or probability2 e4g4 ,a mu/ be ,b1 ,a may be ,b2 or ! effect ( su* facts ^u our judgm5t1 e4g4 ,i am p]fectly c]ta9 t ,a is ,b1 ,i ?9k t ,a may be ,b2 ) _m o!rs ( a m or less simil> type4 ,! "q at once arises1 ,h[ are su* propositions to be treat$8 ,x does n seem to h occurr$ to ! old logicians1 z to "s ( _! successors 9 mod]n times1 simply to reject all consid]ation ( ?is topic4 ,_! fai? 9 ! tru? & complet5ess ( _! sy/em ( inf]5ce 0 f> too firm = !m to suppose x possible t =ms ( proposition univ]sally recogniz$ z significant 9 popul> spee*1 & =ms ( inf]5ce univ]sally recogniz$ !re z valid1 7 to be omitt$ because !y 7 inconv5i5t or complicat$4 #d4 ,"o v simple plan sugge/s itself1 & has inde$ be5 repeat$ly advocat$1 viz4 j to transf] all t is *>act]i/ic ( su* propositions into t conv5i5t receptacle = :at is tr\blesome else:]e1 ! pr$icate4#b ,has n ano!r s-call$ modality be5 ?us got rid (8#c & has x n be5 attempt$ by ! same device to aboli% ! di/9ctive *>act]i/ic ( negative propositions1 viz4 by %ift+ ! negative p>ticle into ! pr$icate8 ,x mu/ be admitt$ t1 up to a c]ta9 po9t1 some?+ may be done 9 ?is way4 ,giv5 ! reason+1 ',^? :o take ars5ic w probably die2 ,a has tak5 x1 !re=e he w probably die2' x is easy to conv]t ?is into an ord9>y syllogism ( ! pure type1 by simply word+ ! major1 ',^? :o take ars5ic are p-:o-w-probably-die1' :5 ! conclusion foll[s 9 ! same =m1 ',a is "o :o-w-probably-die4' ,b ?is device w only c>ry u a v little way4 ,suppose t ! m9or premise also is ( ! same modal description1 e4g4 ',a has probably tak5 ars5ic1' & x w be se5 t we _c relegate ! modality "h also to ! pr$icate )\t be+ br\ght to a /op by f9d+ t !re are f\r t]ms 9 ! syllogism4 ,b ev5 if !re 7 n ?is p>ticul> objection1 x does n appe> t any?+ is to be ga9$ 9 ! way ( intelligibility or me?od by su* a device z ! above4 ,= :at is meant by a modal pr$icate1 by ! pr$icate 'probably mortal1' = in/ance1 9 ! proposition ',all poison+s by ars5ic are probably mortal'8 ,if ! analogy ) ord9>y pure propositions is to hold good1 x mu/ be a pr$icate ref]r+ to ! :ole ( ! subject1 = ! subject is di/ribut$4 ,b !n we are at once laun*$ into ! difficulties discuss$ 9 a =m] *apt] 7,*4 ,,vi4 #ai-be71 :5 we attempt to ju/ify or v]ify ! application ( ! pr$icate4 ,we h to enquire 7at lea/ on ! view adopt$ 9 ?is "w7 :e!r ! application ( ! pr$icate 'probably mortal' to ! :ole ( ! subject1 really means at bottom any?+ else ?an t ! pr$icate 'mortal' is to be appli$ to a portion 7m ?an half7 ( ! memb]s d5ot$ by ! subject4 ,:5 ! transf]5ce ( ! modality to ! pr$icate raises su* intricate que/ions z to ! s5se 9 :i* ! pr$icate is to be int]pret$1 !re is surely no?+ ga9$ by ! /ep4 #e4 ,a second1 & m summ>y way ( %elv+ all difficulties ( ! subject1 s f> at lea/ z logic1 or ! writ]s ^u logic1 are conc]n$1 is f\nd by simply d5y+ t modality has any connection :atev] ) logic4 ,?is is ! c\rse adopt$ by _m mod]n writ]s1 = in/ance1 by ,hamilton & ,mansel1 9 ref]5ce to :om "o _c help rem>k+ t an unduly l>ge portion ( _! logical writ+s seems occupi$ ) tell+ u :at does n belong to logic4 ,!y ju/ify _! rejection on ! gr\nd t ! mode belongs to ! matt]1 & mu/ be det]m9$ by a consid]ation ( ! matt]1 & !re=e is extralogical4 ,to a c]ta9 ext5t ,i agree ) _! gr\nds ( rejection1 = 7z expla9$ 9 ,*apt] ,,vi47 x is n easy to see h[ ! degree ( modality ( any proposition1 :e!r premise or conclusion1 c be ju/ifi$ )\t appeal to ! matt]4 ,b !n que/ions ( ju/ification1 9 any adequate s5se ( ! t]m1 belong to a range ( consid]ations some:at ali5 to ,hamilton's & ,mansel's way ( reg>d+ ! sci5ce4 ,! complete ju/ification ( our inf]5ces is a matt] :i* involves _! tru? or falsehood1 a po9t ) :i* ^! writ]s d n mu* conc]n !mselves1 be+ only occupi$ ) ! consi/5cy ( our reason+s1 n ) _! con=mity ) fact4 ,7 ,i speak+ z a ,hamiltonian ,i %\ld say t modality is =mal r ?an mat]ial1 = ?\gh we _c ju/ify ! degree ( our belief ( a proposition )\t appeal to ! matt]1 we c to a mod]ate degree ( accuracy e/imate x )\t any su* appeal2 & ?is w\ld seem to be q en\gh to w>rant its be+ reg>d$ z =mal4 ,x mu/ be admitt$ t ,hamilton's acc\nt ( ! matt] :5 he is recomm5d+ ! rejection ( ! modals1 is n by any means cle> & consi/5t4 ,he n only fails1 z already rem>k$1 to di/+ui% betwe5 ! =mal & ! mat]ial 79 o!r words1 ! true & ! false7 modality2 b :5 treat+ ( ! =m] he fails to di/+ui% betwe5 ! extremely div]se aspects ( modality :5 view$ f ! ,ari/otelian & ! ,kantian /&-po9ts4 ,( ! am\nt & significance ( ?is diff]5ce we %all speak pres5tly1 b x may be j po9t$ out "h t ,hamilton beg9s 7,vol4 ,i4 p4 #beg7 by reject+ ! modals on ! gr\nd t ! di/9ctions betwe5 ! necess>y1 ! cont+5t1 ! possible1 & ! impossible1 mu/ be :olly re/$ on an appeal to ! matt] ( ! propositions1 9 :i* he is1 ,i ?9k1 q correct4 ,b !n a little fur!r on 7p4 #bfj71 9 expla9+ '! mean+ ( ?ree t]ms :i* are us$ 9 relation to pure & modal propositions1' he gives ! widely diff]5t ,kantian1 or ?ree-fold division into ! apodeictic1 ! ass]tory1 & ! problematic4 ,he does n take ! precaution ( po9t+ out to 8 he>]s ! v diff]5t g5]al views ( logic f :i* ^! two acc\nts ( modality spr+4#d #f4 ,!re is "o k9d ( modal syllogism :i* x w\ld seem unreasonable to reject on ! gr\nd ( its n be+ =mal1 & :i* we may notice 9 pass+4 ,! premise ',any ,a is probably ,b1' is equival5t to ',mo/ ,a are ,b4' ,n[ x is obvi\s t f two su* premises z ',mo/ ,a are ,b1' ',mo/ ,a are ,c1' we c d$uce ! consequ5ce1 ',"s ,c are ,b4' ,s9ce ?is holds good :atev] may be ! nature ( ,a1 ,b1 & ,c1 x is1 accord+ to ord9>y usage ( ! t]m1 a =mal syllogism4 ,mansel1 h[ev]1 refuses to admit t any su* syllogisms belong to =mal logic4 ,8 reasons are giv5 9 a r elaborate review#e & criticism ( "s ( ! logical works ( ,de ,morgan1 to :om ! introduction ( 'num]ically def9ite syllogisms' is ma9ly due4 ,mansel does n take ! p>ticul> example giv5 above1 z he is discuss+ a some:at m compreh5sive algebraic =m4 ,he exam9es x 9 a special num]ical example3#f--ah out ( #ba ,ys are ,x2 #ae out ( #ba ,ys are ,z2 ! conclusion t #ab ,zs are ,x is reject$ f =mal logic on ! gr\nd t ! ari?metical judgm5t involv$ is syn!tical1 n analytical1 & re/s ^u an intuition ( quantity4 ,we _c ent] ^u any exam9ation ( ^! reasons "h2 b x may m]ely be rem>k$ t 8 criticism dem&s ! acceptance ( ! ,kantian doctr9es z to ! nature ( ari?metical judgm5ts1 & t x w\ld be bett] to base ! rejection n on ! gr\nd t ! syllogism is n =mal1 b on ! gr\nd t x is n analytical4 #g4 ,!re is ano!r & practical way ( gett+ rid ( ! p]plexities ( modal reason+ :i* mu/ be notic$ "h4 ,x is ! res\rce ( ord9>y reason]s r ?an ! decision ( pr(ess$ logicians1#g &1 l ! fir/ me?od ( evasion already po9t$ out 9 ?is *apt]1 is ( v p>tial application4 ,x consi/s 9 treat+ ! premises1 dur+ ! process ( reason+1 z if !y 7 pure1 & !n re9troduc+ ! modality into ! conclusion1 z a sort ( qualification ( its full c]ta9ty4 ,:5 ea* ( ! premises is ne>ly c]ta91 or :5 f any cause we are n conc]n$ ) ! ext5t ( _! dep>ture f full c]ta9ty1 ?is r\gh exp$i5t w answ] well en\gh4 ,x is1 ,i appreh5d1 ! process :i* passes ?r\gh ! m9ds ( mo/ p]sons 9 su* cases1 9 s f> z !y reason consci\sly4 ,!y w\ld1 presumably1 9 su* an example z t previ\sly giv5 7#d71 proce$ z if ! premises t '^? :o take ars5ic w die1' & t '! man 9 "q has tak5 x1' 7 q true1 in/ead ( be+ only probably true1 & !y w\ld consequ5tly draw ! conclusion t 'he w\ld die4' ,b be>+ 9 m9d t ! premises are n c]ta91 !y w\ld rememb] t ! conclusion 0 only to be held ) a qualifi$ ass5t4 ,?is !y w\ld express q correctly1 if ! m]e nature & n ! degree ( t ass5t is tak5 into acc\nt1 by say+ t 'he is likely to die4' ,9 ?is case ! modality is reject$ tempor>ily f ! premises to be re9troduc$ into ! conclusion4 ,x is obvi\s t su* a process z ?is is ( a v r\gh & imp]fect k9d4 ,x does1 9 fact1 omit f accurate consid]ation j ! "o po9t n[ "u discussion4 ,x takes no acc\nt ( ! v>y+ %ades ( expression by :i* ! degree ( dep>ture f p]fect conviction is indicat$1 :i* is ( c\rse ! v ?+ ) :i* modality is int5d$ to occupy itself4 ,at be/1 !re=e1 x c\ld only claim to be an extremely rude way ( decid+ que/ions1 ! accurate & sci5tific me?ods ( treat+ :i* are dem&$ ( u4 #h4 ,9 any employm5t ( appli$ logic we h ( c\rse to g ?r\gh su* a process z t j m5tion$4 ,outside ( pure ma!matics x c h>dly ev] be ! case t ! premises f :i* we reason are held ) absolute conviction4 ,h5ce !re mu/ be a lapse f absolute conviction 9 ! conclusion4 ,b we reason on ! hypo!sis t ! premises are true1 & any trifl+ defection f c]ta9ty1 ( :i* we may be consci\s1 is m5tally res]v$ z a qualification to ! conclusion4 ,b su* consid]ations z ^! belong r to ord9>y appli$ logic2 !y am\nt to no?+ m ?an a caution or h9t to be borne 9 m9d :5 ! rules ( ! syllogism1 or ( induction1 are appli$ 9 practice4 ,:51 h[ev]1 we are treat+ ( modality1 ! ext5t ( ! defection f full c]ta9ty is suppos$ to be suffici5tly great = our language to indicate & appreciate x4 ,:at we !n want is ( c\rse a sci5tific discussion ( ! pr9ciples 9 accordance ) :i* ?is dep>ture is to be measur$ & express$1 bo? 9 our premises & 9 our conclusion4 ,su* a plan !re=e = treat+ modality1 z ! "o "u discussion1 is j z mu* a bani%m5t ( x f ! field ( real logical enquiry1 z if we _h det]m9$ av[$ly to reject x f consid]ation4 #i4 ,be=e proce$+ to a discussion ( ! v>i\s ways 9 :i* modality may be treat$ by ^? :o admit x into logic1 some?+ mu/ be said to cle> up a possible s\rce ( confusion 9 ?is "p ( ! subject4 ,9 ! cases ) :i* we h hi!rto be5 mo/ly conc]n$1 9 ! e>li] *apt]s ( ?is "w1 ! *>act]i/ic ( modality 7= 9 ?is *apt] we may ) propriety use ?is logical t]m7 has g5]ally be5 f\nd 9 s+ul> & p>ticul> propositions4 ,x pres5t$ itself :5 we _h to judge ( individual cases f a k ( ! av]age1 & 0 an expression ( ! fact t ! proposition relat+ to ^! individuals ref]r$ to a portion only ( ! :ole class f :i* ! av]age 0 tak54 ,giv5 t ( m5 ( fifty-five1 ?ree out ( five w die 9 ! c\rse ( tw5ty ye>s1 we h _h to d ) propositions ( ! vague =m1 ',x is probable t ,,ab 7( t age7 w die1' or ( ! m precise =m1 ',x is ?ree to two t ,,ab w die1' )9 ! specifi$ "t4 ,"h ! modal proposition naturally pres5ts itself 9 ! =m ( a s+ul> or p>ticul> proposition4 #aj4 ,b :5 we turn to ord9>y logic we may f9d univ]sal propositions spok5 ( z modal4 ,?is mu/ mo/ly be ! case ) ^? :i* are t]m$ necess>y or impossible1 b x may also be ! case ) ! probable4 ,we may meet ) ! =m ',all ,x is probably ,y4' ,adopt+ ! same explanation "h z has be5 ?r\gh\t adopt$ 9 analog\s cases1 we mu/ say t :at is meant by ! modality ( su* a proposition is ! proportional numb] ( times 9 :i* ! univ]sal proposition w\ld be correctly made4 ,& 9 ?is !re is1 s f>1 no difficulty4 ,! only diff]5ce is t :]eas ! ju/ification ( ! =m]1 viz4 ! p>ticul> or individual k9d ( modal1 0 obta9able )9 ! limits ( ! univ]sal proposition :i* includ$ x1 ! ju/ification ( ! modality ( a univ]sal proposition has to be s\ght 9 a gr\p or succession ( o!r propositions4 ,! proposition has to be ref]r$ to "s gr\p ( simil> ones & we h to consid] ! proportion ( cases 9 :i* x w be true4 ,b ?is di/9ction is n at all fundam5tal4 ,x is q true t univ]sal propositions f _! nature are mu* less likely ?an individual ones to be ju/ifi$1 9 practice1 by su* appeal4 ,b1 z has be5 already frequ5tly po9t$ out1 we are n conc]n$ ) ! way 9 :i* our propositions are practically obta9$1 nor ) ! way 9 :i* m5 might f9d x mo/ natural to te/ !m2 b ) t ultimate ju/ification to :i* we appeal 9 ! la/ resort1 & :i* has be5 abundantly %[n to be ( a /ati/ical "*4 ,:51 !re=e1 we say t 'x is probable t all ,x is ,y1' :at we mean is1 t 9 m ?an half ! cases we come across we %\ld be "r 9 s judg+1 & 9 less ?an half ! cases we %\ld be wrong4 #aa4 ,x is at ?is /ep t ! possible ambiguity is enc\nt]$4 ,:5 we talk ( ! *ance t ,all ,x is ,y1 we contemplate or imply ! complem5t>y *ance t x is n s4 ,n[ ?is latt] alt]native is n free f ambiguity4 ,x might happ51 = in/ance1 9 ! cases ( failure1 t no ,x is ,y1 or x might happ5 t "s ,x1 only1 is n ,y2 = bo? ( ^! suppositions contradict ! orig9al proposition1 & are !re=e in/ances ( its failure4 ,9 practice1 no d\bt1 we %\ld h v>i\s recogniz$ rules & inductions to fall back ^u 9 ord] to decide betwe5 ^! alt]natives1 ?\gh1 ( c\rse1 ! appeal to !m w\ld be 9 /rictness extralogical4 ,b ! m]e exi/5ce ( su* an ambiguity1 & ! fact t x c only be cle>$ up by appeal to ! subject-matt]1 are 9 !mselves no real difficulty 9 ! application ( ! conception ( modality to univ]sal propositions z well z to individual ones4 #ab4 ,hav+ notic$ "s ( ! ways 9 :i* ! introduction ( modality into logic has be5 evad$ or reject$1 we mu/ n[ ent] into a brief acc\nt ( its treatm5t by ^? :o h m or less delib]ately admitt$ its claims to acceptance4 ,! fir/ enquiry w be1 ,:at op9ions h be5 held z to ! nature ( modality8 t is1 ,is x prim>ily an affection ( ! matt] ( ! proposition1 &1 if n1 :at is x exactly8 ,9 ref]5ce to ?is enquiry x appe>s to me1 z already rem>k$1 t among/ ! e>li] logicians no su* cle> & consi/5t di/9ction betwe5 ! subjective & objective views ( logic z is n[ commonly ma9ta9$1 c be detect$4#h ,! result ( ?is appe>s 9 _! treatm5t ( modality4 ,?is always _h "s ref]5ce to ! subjective side ( ! proposition1 viz4 9 ?is case to ! nature or quantity ( ! belief ) :i* x 0 ent]ta9$2 b x is equally cle> t ?is *>act]i/ic 0 n e/imat$ at fir/ h&1 s to say1 & 9 itself1 b r f a consid]ation ( ! matt] det]m9+ :at x %\ld be4 ,! commonly accept$ s*ola/ic or ,ari/otelian division1 = in/ance1 is into ! necess>y1 ! cont+5t1 ! possible1 & ! impossible4 ,?is is cle>ly a division accord+ to ! matt] almo/ entirely1 = on ! purely m5tal side ! necess>y & ! impossible w\ld be j ! same2 "o imply+ full conviction ( ! tru? ( a proposition1 & ! o!r ( t ( its contradictory4 ,s too1 on ! same side1 x w\ld n be easy to di/+ui% betwe5 ! cont+5t & ! possible4 ,on ! view 9 "q1 !re=e1 ! modality ( a proposition 0 det]m9$ by a ref]5ce to ! nature ( ! subject-matt]4 ,9 "s propositions ! nature ( ! subject-matt] decid$ t ! pr$icate 0 necess>ily jo9$ to ! subject2 9 o!rs t x 0 impossible t !y %\ld be jo9$2 & s on4 #ac4 ,! artificial "* ( su* a f\r-fold division w be too obvi\s to mod]n m9ds = x to be necess>y to criticize x4 ,a v slight /udy ( nature & consequ5t appreciation ( inductive evid5ce suffice to conv9ce u t ^? uni=mities ^u :i* all connections ( ph5om5a1 :e!r call$ necess>y or cont+5t1 dep5d1 dem& extremely pr(\nd & ext5sive enquiry2 t !y admit ( no su* simple division into cle>ly m>k$ gr\ps2 & t1 !re=e1 ! pure logician _h bett] n m$dle ) !m4#i ,! foll[+ extract f ,grote's ,ari/otle 7,vol4 ,i4 p4 #aib7 w s]ve to %[ ! orig9 ( ?is f\r-fold division1 its con=mity ) ! sci5ce ( ! day1 & consequ5tly its utt] want ( con=mity ) t ( our own "t3--,! di/9ction ( ,problematical & ,necess>y ,propositions corresponds1 9 ! m9d ( ,ari/otle1 to t capital & *>act]i/ic doctr9e ( 8 ,ontology & ,physics1 already t\*$ on 9 ?is *apt]4 ,he ?\ght1 z we h se51 t 9 ! va/ circumf]5tial region ( ! ,kosmos1 f ! out] sid]eal sph]e d[n to ! lun> sph]e1 cele/ial sub/ance 0 a necess>y exi/5ce & en]gy1 sempit]nal & uni=m 9 its rotations & influ5ce2 & t ?r\gh its b5efic5t influ5ce1 p]vad+ ! concavity betwe5 ! lun> sph]e & ! t]re/rial c5tre 7:i* includ$ ! f\r elem5ts ) _! comp\nds7 !re prevail$ a regul>iz+ t5d5cy call$ ,nature2 modifi$1 h[ev]1 & p>tly c\nt]act$ by indep5d5t & irregul> =ces call$ ,spontaneity & ,*ance1 ess5tially unkn[able & unpr$ictable4 ,! irregul> sequ5ces ?us nam$ by ,ari/otle 7 ! objective correlate ( ! ,problematical ,proposition 9 ,logic4 ,9 ^! sublun>y sequ5ces1 z to future "t1 may or may n1 0 all t c\ld be atta9$1 ev5 by ! highe/ k2 c]ta9ty1 ei!r ( affirmation or negation1 0 out ( ! "q4 ,on ! o!r h&1 ! necess>y & uni=m en]gies ( ! cele/ial sub/ance1 =m$ ! objective correlate ( ! ,necess>y ,proposition 9 ,logic2 ?is sub/ance 0 n m]ely an exi/5ce1 b an exi/5ce necess>y & un*angeable444 he consid]s ! ,problematical ,proposition 9 ,logic to be n purely subjective1 z an expression ( ! speak]'s ignorance1 b some?+ m1 namely1 to correlate ) an objective ess5tially unkn[able to all4 #ad4 ,ev5 aft] ?is philosophy began to pass away1 ! divisions ( modality orig9ally f\nd$ ^u x might h prov$1 z ,de ,morgan has rem>k$1#aj ( consid]able s]vice 9 m$ival times4 ,z he says1 p 7 mu* m frequ5tly requir$ to decide 9 "o way or ! o!r ^u a s+le te/imony1 )\t !re be+ a suffici5cy ( specific k to te/ ! /atem5ts made4 ,! old logician did n "k b t any day ( ! week might br+ f ,ca?ay or ,t>t>y an acc\nt ( m5 :o ran on f\r :eels ( fle% & blood1 or grew plant$ 9 ! gr\nd1 l ,polydorus 9 ! neid1 z well evid5c$ z a great _m ne>ly z m>vell\s /ories4 ,h5ce1 9 default ( bett] inductions1 x might h be5 conv5i5t to make r\gh classifications ( ! facts :i* 7 & :i* 7 n to be accept$ on te/imony 7! necess>y1 ! impossible1 c471 & to employ ^! provisional inductions 7:i* is all we %\ld n[ reg>d !m7 z te/+ ! /ories :i* rea*$ him4 ,propositions belong+ to ! class ( ! impossible might be reg>d$ z hav+ an antec$5t presumption aga9/ !m s great z to prevail ov] almo/ any te/imony wor? tak+ acc\nt (1 & s on4 #ae4 ,b ?is old f\r-fold division ( modals cont9u$ to be accept$ & p]petuat$ by ! logicians long aft] all philosophical ju/ification = x _h pass$ away4 ,s f> z ,i h be5 able to asc]ta91 sc>cely any logician ( repute or popul>ity be=e ,kant1 0 bold en\gh to make any important *ange 9 ! way ( reg>d+ !m4#aa ,ev5 ! ,port-,royal ,logic1 f\nd$ z x is on ,c>tesianism1 repeats ! traditional /atem5ts1 ?\gh ) extreme brevity4 ,?is adh]5ce to ! old =ms l$1 x ne$ n be rem>k$1 to consid]able inconsi/5cy & confusion 9 _m cases4 ,^! =ms 7 f\nd$1 z we h se51 on an objective view ( ! prov9ce ( logic1 & ?is view 0 by no means rigidly c>ri$ out 9 _m cases4 ,9 fact x 0 beg9n+ to be ab&on$1 to an ext5t & 9 directions :i* we h n opportunity "h to discuss1 be=e ! influ5ce ( ,kant 0 felt4 ,_m1 = in/ance1 add$ to ! li/ ( ! f\r1 by includ+ ! true & ! false2 occasionally also ! probable1 ! suppos$1 & ! c]ta9 7 add$4 ,?is seems to %[ "s t5d5cy t[>ds ab&on+ ! objective = ! subjective view1 or at lea/ indicates a hesitation betwe5 !m4 #af4 ,) ,kant's view ( modality almo/ e "o is famili>4 ,he divides judgm5ts1 "u ?is head1 into ! apodeictic1 ! ass]tory1 & ! problematic4 ,we %all h to say some?+ ab\t ! numb] & mutual relations ( ^! divisions pres5tly2 we are n[ only conc]n$ ) ! g5]al view :i* !y c>ry out4 ,9 ?is respect x w be obvi\s at once :at a complete *ange ( position has be5 rea*$4 ,! 'necess>y' & ! 'impossible' dem&$ an appeal to ! matt] ( a proposition 9 ord] to recognize !m2 ! 'apodeictic' & ! 'ass]tory'1 on ! o!r h&1 may be true ( almo/ any matt]1 = !y dem& no?+ b an appeal to our consci\sness 9 ord] to di/+ui% betwe5 !m4 ,moreov]1 ! di/9ction betwe5 ! ass]tory & ! problematic is s entirely subjective & p]sonal1 t x may v>y n only betwe5 "o p]son & ano!r1 b 9 ! case ( ! same p]son at diff]5t times4 ,:at "o man kn[s to be true1 ano!r may happ5 to be 9 d\bt ab\t4 ,! apodeictic judgm5t is "o :i* we n only accept1 b :i* we f9d ourselves unable to rev]se 9 ?\ght2 ! ass]tory is simply accept$2 ! problematic is "o ab\t :i* we feel 9 d\bt4 ,?is way ( look+ at ! matt] is ! necess>y outcome ( ! conceptuali/ or ,kantian view ( logic4 ,x has be5 foll[$ by _m logicians1 n only by ^? :o may be call$ foll[]s ( ,kant1 b by almo/ all :o h felt 8 influ5ce4 ,ueb]weg1 = in/ance1 :o is altoge!r at issue ) ,kant on "s fundam5tal po9ts1 adopts x4 #ag4 ,! next "q to be discuss$ is1 ,h[ _m subdivisions ( modality are to be recogniz$8 ,! ,ari/otelian or s*ola/ic logicians1 z we h se51 adopt$ a f\r-fold division4 ,! exact relations ( "s ( ^! to ea* o!r1 especially ! possible & ! cont+5t1 is an extremely obscure po9t1 & "o ab\t :i* ! comm5tators are by no means agre$4 ,z1 h[ev]1 x seems tol]ably cle> t x 0 n consci\sly int5d$ by ! use ( ^! f\r t]ms to exhibit a graduat$ scale ( int5sity ( conviction1 _! correspond5ce ) ! prov9ce ( mod]n probability is b slight1 & ! discussion ( !m1 !re=e1 becomes r a matt] ( special or antiqu>ian int]e/4 ,de ,morgan1 inde$ 7,=mal ,logic1 p4 #bcb71 says t ! s*oolm5 und]/ood by cont+5t m likely ?an n1 & by possible less likely ?an n4 ,i d n "k on :at au?ority ?is /atem5t re/s1 b x cr$its !m ) a mu* ne>] approa* to ! mod]n views ( probability ?an "o w\ld h expect$1 & decid$ly ne>] ?an t ( mo/ ( _! successors4#ab ,! g5]al conclusion at :i* ,i h arriv$1 aft] a reasonable am\nt ( inve/igation1 is t !re 7 two preval5t views on ! subject4 ,"s 7e4g4 ,burg]sdyck1 ,bk4 ,i4 *4 #cb7 admitt$ t !re 7 at bottom only two k9ds ( modality2 ! cont+5t & ! possible be+ equipoll5t1 z also ! necess>y & ! impossible1 provid$ ! "o ass]ts & ! o!r d5ies4 ,?is is ! view to :i* ^? w\ld naturally be l$ :o look$ ma9ly to ! nature ( ! subject-matt]4 ,on ! o!r h&1 ^? :o look$ ma9ly at ! =m ( expression1 w\ld be l$ by ! analogy ( ! f\r =ms ( proposition1 & ! necessity t ea* ( !m %\ld /& 9 def9ite opposition to ea* o!r1 to insi/ ^u a di/9ction betwe5 ! f\r modals4#ac ,!y1 !re=e1 endeav\r$ to introduce a di/9ction by ma9ta9+ 7e4g4 ,crackan?orpe1 ,bk4 ,,iii4 *4 #aa7 t ! cont+5t is t :i* n[ is b may n be1 & ! possible t :i* n[ is n b may be4 ,a few appe> to h made ! di/9ction correspond5t to t betwe5 ! physically & ! logically possible4 #ah4 ,:5 we get to ! ,kantian division we h rea*$ mu* cle>] gr\nd4 ,! mean+ ( ea* ( ^! t]ms is q explicit1 & x is also beyond d\bt t !y h a m def9ite t5d5cy 9 ! direction ( assign+ a graduat$ scale ( conviction4 ,s long z !y are reg>d$ f a metaphysical r ?an a logical /&+ po9t1 !re is mu* to be said 9 _! fav\r4 ,if we use introspection m]ely1 conf9+ ourselves to a /udy ( ! judgm5ts !mselves1 to ! exclusion ( ! gr\nds on :i* !y re/1 !re c]ta9ly does seem a cle> & well-m>k$ di/9ction betwe5 judgm5ts :i* we _c ev5 conceive to be rev]s$ 9 ?\ght2 ^? :i* we c\ld rev]se1 b :i* we accept z true2 & ^? :i* we m]ely ent]ta9 z possible4 ,reg>d$1 h[ev]1 z a logical division1 ,kant's arrangem5t seems to me ( v little s]vice4 ,= su* logical purposes inde$1 z we are n[ conc]n$ )1 x really seems to resolve itself into a two-fold division4 ,! di/9ction betwe5 ! apodeictic & ! ass]tory w be admitt$1 ,i presume1 ev5 by ^? :o accept ! metaphysical or psy*ological !ory ^u :i* x re/s1 to be a diff]5ce :i* conc]ns1 n ! quantity ( belief ) :i* ! judgm5ts are ent]ta9$1 b r ! viol5ce :i* w\ld h to be done to ! m9d by ! attempt to upset !m4 ,ea* is fully believ$1 b ! "o c1 & ! o!r _c1 be controv]t$4 ,! belief ) :i* an ass]tory judgm5t is ent]ta9$ is full belief1 else x w\ld n diff] f ! problematic2 & !re=e 9 reg>d to ! quantity ( belief1 z di/+ui%$ f ! quality or "* ( x1 !re is no diff]5ce betwe5 x & ! apodeictic4 ,x is z ?\gh1 to (f] an illu/ration1 ! index _h be5 already mov$ to ! top ( ! scale 9 ! ass]tory judgm5t1 & all t 0 done to conv]t ?is into an apodeictic "o1 0 to clamp x !re4 ,! only logical diff]5ce :i* !n rema9s is t betwe5 problematic & ass]tory1 ! =m] compreh5d+ all ! judgm5ts z to ! tru? ( :i* we h any degree ( d\bt1 & ! latt] ^? ( :i* we h no d\bt4 ,! :ole range ( ! =m]1 !re=e1 ) :i* ,probability is appropriately occupi$1 is ?r[n undivid$ into a s+le comp>tm5t4 ,we c h>dly speak ( a 'division' :]e "o class includes ev]y?+ up to ! b\nd>y l9e1 & ! o!r is conf9$ to t b\nd>y l9e4 ,practically1 !re=e1 on ?is view1 modality1 z ! ma!matical /ud5t ( ,probability w\ld expect to f9d x1 z completely disappe>s z if x 7 int5d$ to reject x4 #ai4 ,by less consi/5t & sy/ematic ?9k]s1 & by ^? 9 :om +5uity 0 an ov] prom95t feature1 a v>iety ( o!r arrangem5ts h be5 accept$ or propos$4 ,!re is1 ( c\rse1 "s ju/ification = su* attempts 9 ! laudable desire to br+ our logical =ms into bett] h>mony ) ord9>y ?\ght & language4 ,9 practice1 z 0 po9t$ out 9 an e>li] *apt]1 e "o recognizes a great v>iety ( modal =ms1 su* z 'likely1' 'v likely1' 'almo/ c]ta9ly1' & s on almo/ )\t limit 9 ea* direction4 ,x 0 d\btless suppos$ t1 by neglect+ to make use ( te*nical equival5ts = "s ( ^! =ms1 we %\ld lose our logical control ov] c]ta9 possible k9ds ( inf]5ce1 & s f> fall %ort ev5 ( ! precision ( ord9>y ?\ght4 ,) reg>d to su* additional =ms1 x appe>s to me t all ^? :i* h be5 introduc$ by writ]s :o 7 un9flu5c$ by ! ,!ory ( ,probability1 h done little else ?an create additional confusion1 z su* writ]s d n attempt to m>%al _! t]ms 9 ord]1 or to asc]ta9 _! mutual relations4 ,omitt+1 ( c\rse1 =ms obvi\sly ( mat]ial modality1 we h already m5tion$ ! true & ! false2 ! probable1 ! suppos$1 & ! c]ta94 ,^! subdivisions seem to h rea*$ _! climax at a v e>ly /age 9 ,occam 7,prantl1 ,,iii4 #chj71 :o held t a proposition might be modally affect$ by be+ 'v]a1 scita1 falsa1 ignota1 scripta1 prolata1 concepta1 cr$ita1 op9ata1 dubitata4' #bj4 ,s9ce ! gr[? ( ! sci5ce ( ,probability1 logicians h _h bett] opportunities ( kn[+ :at !y _h to aim at2 &1 ?\gh x _c be said t _! attempts h be5 really successful1 ^! are at any rate a decid$ improvem5t ^u ^? ( _! pr$ecessors4 ,dr ,?omson1#ad = in/ance1 gives a n9e-fold division4 ,he says t1 arrang+ ! degrees ( modality 9 an asc5d+ scale1 we f9d t a judgm5t may be ei!r possible1 d\btful1 probable1 morally c]ta9 = ! ?9k] himself1 morally c]ta9 = a class or s*ool1 morally c]ta9 = all1 physically c]ta9 ) a limit1 physically c]ta9 )\t limitation1 & ma!matically c]ta94 ,_m o!r divisions might d\btless be m5tion$1 b1 z e ma!matician w recognize1 ! attempt to secure any g5]al agreem5t 9 su* a matt] ( arrangem5t is q hopeless4 ,x is "h t ! b5eficial influ5ce ( ! ma!matical !ory ( ,probability is to be gratefully ackn[l$g$4 ,z soon z ?is came to be /udi$ x mu/ h be5 p]ceiv$ t 9 attempt+ to m>k (f cle>ly f "o ano!r c]ta9 gradations ( belief1 we %\ld be seek+ = brea*es 9 a cont9u\s magnitude4 ,9 ! advance f a slight presumption to a /rong presumption1 & f t to moral c]ta9ty1 we are mak+ a gradual asc5t1 9 ! c\rse ( :i* !re are no natural halt+-places4 ,! pro( ( ?is cont9uity ne$ n be ent]$ ^u "h1 = ! mat]ials = x w h be5 ga!r$ f almo/ e *apt] ( ?is "w4 ,! read] ne$ m]ely be rem9d$ t ! gr\nds ( our belief1 9 all cases :i* admit ( numb] & measurem5t1 are cle>ly se5 to be ( ?is description2 & t !re=e unless ! belief itself is to be divorc$ f ! gr\nds on :i* x re/s1 :at ?us holds z to _! *>act]i/ics mu/ hold also z to its own4 ,x foll[s1 !re=e1 t modality 9 ! old s5se ( ! ^w1 :]e9 an attempt 0 made to obta9 c]ta9 natural divisions 9 ! scale ( conviction1 mu/ be f9ally ab&on$4 ,all t x endeav\r$ to d c n[ be done incomp>ably bett] by ! !ory ( ,probability1 ) its num]ical scale :i* admits ( indef9ite subdivision4 ,none ( ! old sy/ems ( division c be reg>d$ z a really natural "o2 ^? :i* admit b few divisions be+ f\nd to leave ! :ole range ( ! probable 9 "o unbrok5 class1 & ^? :i* adopt _m divisions laps+ into unavoidable vagu5ess & unc]ta9ty4 #ba4 ,correspond+ to ! di/9ction betwe5 pure & modal propositions1 b ev5 m complicat$ & unsatisfactory 9 its treatm5t1 0 t betwe5 pure & modal syllogisms4 ,! ?+ discuss$ 9 ! case ( ! latt] 01 ( c\rse1 ! effect produc$ ^u ! conclusion 9 respect ( modality1 by ! modal affection ( "o or bo? premises4 ,x is only :5 we rea* su* consid]ations z ^! t we are at all gett+ on to ! gr\nd appropriate to ,probability2 b x is obvi\s t v little c\ld be done ) su* rude mat]ials1 & ! inh]5t clums9ess & complication ( ! :ole modal sy/em come out v cle>ly "h4 ,x 0 9 ref]5ce probably to ?is complication t "s ( ! bitt] say+s#ae ( ! s*oolm5 & o!rs :i* h be5 record$1 7 utt]$4 ,ari/otle has giv5 an intricate inve/igation ( ?is subject1 & 8 foll[]s naturally 7 l$ along a simil> track4 ,x w\ld be q =eign to my purpose 9 ! slight sket* 9 ?is *apt] to attempt to give any acc\nt ( ^! enquiries1 ev5 7 ,i compet5t to d s2 =1 z has be5 po9t$ out1 ! connection betwe5 ! ,ari/otelian modals & ! mod]n view ( ! nature ( ,probability1 ?\gh real1 is exce$+ly slight4 ,x ne$ only be rem>k$ t :at 0 complicat$ en\gh ) f\r modals to be tak5 acc\nt (1 gr[s intricate beyond all endurance :5 su* z ! 'probable' & ! 'true' & ! 'false' h also to be assign$ a place 9 ! li/4 ,! foll[+ examples#af w %[ ! k9d ( discussions ) :i* ! logicians ex]cis$ !mselves4 ',:e!r1 ) "o premise c]ta91 & ! o!r probable1 a c]ta9 conclusion may be inf]r$'3 ',:e!r1 f ! impossible1 ! necess>y c be inf]r$'2 ',:e!r1 ) "o premise necess>y & ! o!r de inesse1 ! conclusion is necess>y'1 & s on1 endlessly4 #bb4 ,on ! ,kantian view ( modality ! discussion ( su* k9ds ( syllogisms becomes at once decid$ly m simple 7= "h b ?ree modes are recogniz$71 & also some:at m closely connect$ ) /rict ,probability1 7= ! modes are m ne>ly ( ! nature ( gradations ( conviction74 ,b1 on ! o!r h&1 !re is less ju/ification = _! introduction1 z logicians might really be expect$ to "k t :at !y are aim+ to effect by _! clumsy contrivances is ! v ?+ :i* ,probability c c>ry out to ! highe/ desir$ degree ( accuracy4 ,! =m] me?ods are z co>se & inaccurate1 comp>$ ) ! latt]1 z 7 ! r\ghe/ measurem5ts ( ,babylonian night-wat*]s comp>$ ) ! ref9$ calculations ( ! mod]n a/ronom]4 ,x is inde$ only "s ( ! g5]al adh]5ts ( ! ,kantian ,logic :o ent] ^u any su* consid]ations z ^!2 "s1 su* z ,hamilton & ,mansel1 entirely reject !m1 z we h se54 ,by ^? :o d treat ( ! subject1 su* conclusions z ! foll[+ are laid d[n2 t :5 bo? premises are apodeictic ! conclusion w be ! same2 s :5 bo? are ass]tory or problematic4 ,if "o is apodeictic & ! o!r ass]tory1 ! latt]1 or 'weak]1' is all t is to be admitt$ = ! conclusion2 & s on4 ,! ,engli% read] w f9d "s acc\nt ( ^! rules 9 ,ueb]weg's ,logic4#ag #bc4 ,b al?\gh ^? modals1 reg>d$ z in/rum5ts ( accurate ?\ght1 h be5 ?us sup]s$$ by ! precise ari?metical expressions ( ,probability1 ! "q /ill rema9s :e!r :at may be t]m$ our popul> modal expressions c\ld n be improv$ & adapt$ to m accurate use4 ,x is true t ! attempt to sep>ate !m f "o ano!r by any fundam5tal di/9ctions is futile1 = ! magnitude ( :i* !y take cognizance is1 z we h rem>k$1 cont9u\s2 b consid]+ ! enorm\s importance ( accurate t]m9ology1 & ( recogniz+ num]ical di/9ctions :]ev] possible1 x w\ld be a real advance if any agreem5t c\ld be arriv$ at ) reg>d to ! use ( modal expressions4 ,we h already notic$ 7,*4 ,,ii4 #af7 "s sugge/ions by ,mr ,galton z to ! possibility ( a natural sy/em ( classification1 re/+ ^u ! regul>ity ) :i* mo/ k9ds ( magnitudes t5d to gr\p !mselves ab\t a mean4 ,x might be propos$1 = in/ance1 t we %\ld agree to apply ! t]m 'good' to ! fir/ qu>t]1 measur+ f ! be/ d[nw>ds2 'indiff]5t' to ! middle half1 & 'bad' to ! la/ qu>t]4 ,!re seems no reason :y a simil>ly improv$ t]m9ology %\ld n "s day be introduc$ into ! ord9>y modal language ( common life4 ,x might be agre$1 = in/ance1 t 'v improbable' %\ld z f> z possible be conf9$ to ^? ev5ts :i* _h odds ( 7say7 m ?an #ii to #a aga9/ !m2 & s on1 ) o!r simil> expressions4 ,!re w\ld1 no d\bt1 be difficulties 9 ! way1 = 9 all applications ( classification we h to surm\nt ! two-fold ob/acles :i* lie 9 ! way1 fir/ly 7to use ,kant's expression7 ( ! faculty ( mak+ rules1 & secondly ( t ( subsumption "u rules4 ,t is to say1 ev5 if we _h agre$ ^u our classes1 !re w\ld /ill be mu* d\bt & dispute1 9 ! case ( ?+s :i* did n readily l5d !mselves to be c\nt$ or measur$1 z to :e!r ! odds 7 m or less ?an ! assign$ quantity4 ,x is true t :5 we "k ! odds = or aga9/ an ev5t1 we c always /ate !m explicitly )\t ! necessity ( fir/ agree+ z to ! usage ( t]ms :i* %all imply !m4 ,b !re w\ld (t5 be circumlocution & p$antry 9 s do+1 & z long z modal t]ms are 9 practical use x w\ld seem t !re c\ld be no h>m1 & might be great good1 9 arriv+ at "s agreem5t z to ! degree ( probability :i* !y %\ld be g5]ally und]/ood to indicate4 ,b5?am1 z is well kn[n1 9 despair ( ev] obta9+ any?+ accurate out ( ! language ( common life on ?is subject1 0 9 fav\r ( a direct appeal to ! num]ical /&>d4 ,he propos$ ! employm5t1 9 judicial trials1 ( an in/rum5t1 graduat$ f #j to #aj1 on :i* scale ! witness 0 to be ask$ to indicate ! degree ( 8 belief ( ! facts to :i* he te/ifi$3 simil>ly ! judge might express ! =ce ) :i* he held 8 conclusion4 ,! use ( su* a num]ical scale1 h[ev]1 0 to be optional only1 n compulsory1 z ,b5?am admitt$ t _m p]sons might feel at a loss ?us to measure ! degree ( _! belief4 7,rationale ( ,judicial ,evid5ce1 ,bk4 ,i41 ,*4 ,,vi47 #bd4 ,?r\gh\t ?is *apt] we h reg>d$ ! modals z ! ne>e/ c\nt]p>t to mod]n ,probability :i* 0 af=d$ by ! old sy/ems ( logic4 ,! reason = s reg>d+ !m is1 t !y repres5t$ "s slight attempt1 rude z x 01 to recognize & measure c]ta9 gradations 9 ! degree ( our conviction1 & to exam9e ! be>+ ( su* consid]ations ^u our logical inf]5ces4 ,b al?\gh x is among/ ! modals t ! g]ms ( ! me?ods ( ,probability are ?us to be s\ght2 ! true subject-matt] ( our sci5ce1 t is1 ! classes ( objects ) :i* x is mo/ appropriately conc]n$1 are r repres5t$ by ano!r "p ( ! s*ola/ic logic4 ,?is 0 ! bran* commonly call$ ,dialectic1 9 ! old s5se ( t t]m4 ,dialectic1 accord+ to ,ari/otle1 seems to h be5 a sort ( si/] art to ,rhetoric4 ,x 0 conc]n$ ) syllogisms diff]+ 9 no way f demon/rative syllogisms1 except t _! premises 7 probable in/ead ( c]ta94 ,premises ( ?is k9d he t]m$ topics1 & ! syllogisms :i* dealt ) !m en?ymemes4 ,!y 7 said to />t f 'signs & likelihoods' r ?an f axioms4#ah #be4 ,! t]ms 9 :i* su* reason+s are commonly describ$ s\nd v mu* l ^? applicable to ,probability1 z we n[ und]/& x4 ,:5 we he> ( likelihood1 & ( probable syllogisms1 our fir/ impression might be t ! inf]5ces involv$ w\ld be ( a simil> "*4#ai ,?is1 h[ev]1 w\ld be errone\s4 ,9 ! fir/ place ! prov9ce ( ?is ,dialectic 0 mu* too wide1 = x cov]$ 9 addition ! :ole field ( :at we %\ld n[ t]m ,sci5tific or ,mat]ial ,induction4 ,! di/9ctive *>act]i/ic ( ! dialectic premises 0 _! want ( c]ta9ty1 & ( su* unc]ta9 premises ,probability 7z ,i h frequ5tly insi/$7 takes acc\nt ( "o class only1 ,induction conc]n+ itself ) ano!r class4 ,aga91 n ! slighte/ attempt 0 made to ent] ^u ! enquiry1 ,h[ unc]ta9 are ! premises8 ,x is only :5 ?is is attempt$ t we c be consid]$ to ent] ^u ! field ( ,probability1 & x is because1 aft] a rude fa%ion1 ! modals attempt$ to grapple ) ?is problem1 t we h reg>d$ !m z 9 any way occupi$ ) our special subject-matt]4 #bf4 ,among/ ! old] logics ) :i* ,i h made any acqua9tance1 t ( ,crackan?orpe gives ! fulle/ discussion ^u ?is subject4 ,he divides 8 treatm5t ( ! syllogism into two p>ts1 occupi$ respectively ) ! 'demon/rative' & ! 'probable' syllogism4 ,to ! latt] a :ole book is devot$4 ,9 ?is ! nature & consequ5ces ( ?irte5 diff]5t 'loci'#bj are inve/igat$1 ?\gh x is n v cle> 9 :at s5se !y c e "o ( !m be reg>d$ z be+ 'probable4' ,x is d\btless true1 t if ! old logicians _h be5 9 possession ( su* premises z mod]n ,probability is conc]n$ )1 & _h adh]$ to _! own way ( treat+ !m1 !y w\ld h _h to place !m among/ su* loci1 & ?us to make ! consid]ation ( !m a "p ( _! ,dialectic4 ,b inasmu* z !re does n seem to h be5 ! slighte/ attempt on _! "p to d m "h ?an recognize ! fact ( ! premises be+ probable2 t is1 s9ce x 0 n attempt$ to measure _! probability & t ( ! conclusion1 ,i _c b reg>d ?is "p ( ,logic z hav+ only ! v slighte/ relation to ,probability z n[ conceiv$4 ,x seems to me little m ?an "o ( ! ways 7describ$ at ! comm5cem5t ( ?is *apt]7 by :i* ! problem ( ,modality is n inde$ reject$1 b practically evad$4 #bg4 ,z ,logic is n ! only sci5ce :i* is directly & prom95tly occupi$ ) que/ions ab\t belief & evid5ce1 s ! difficulties :i* h aris5 !re h be5 by no means unkn[n else:]e4 ,9 respect ( ! modals1 ?is seems to h be5 manife/ly ! case 9 ,jurisprud5ce4 ,"s rem>ks1 !re=e1 may be conv5i5tly made "h ^u ?is application ( ! subject1 ?\gh ( c\rse ) ! brevity suitable on ! "p ( a layman :o has to t\* ^u pr(essional topics4 ,recall = a mom5t :at are ! ess5tials ( modality4 ,^! ,i und]/& to be ! attempt to m>k (f f "o ano!r1 )\t any resort to num]ical notation1 v>y+ degrees ( conviction or belief1 & to det]m9e ! consequ5t effect ( premises1 ?us affect$1 ^u our conclusions4 ,moreov]1 z we _c con/ruct or reta9 a scale ( any k9d )\t employ+ a /&>d f & by :i* to measure x1 ! atta9m5t & recognition ( a /&>d ( c]ta9ty1 or ( "o ( ! o!r degrees ( conviction1 is almo/ insep>ably involv$ 9 ! same enquiry4 ,9 ?is s5se ( ! t]m1 modal difficulties h c]ta9ly %[n !mselves 9 ! dep>tm5t ( ,law4 ,!re h be5 simil> attempts "h1 enc\nt]$ by simil> difficulties1 to come to "s def9ite agreem5t z to a scale ( arrangem5t ( ! degrees ( our ass5t4 ,x is ( c\rse mu* m practicable to secure su* agreem5t 9 ! case ( a special sci5ce1 conf9$ m or less to ! exp]ts1 ?an 9 subjects into :i* all classes ( outsid]s h almo/ equal "r ( entry4 ,! range ( application "u ! =m] circum/ances is n>r[]1 & ! pr(essional exp]ts h acquir$ habits & traditions by :i* ! /&>ds may be reta9$ 9 consid]able integrity4 ,x does n appe>1 h[ev]1 accord+ to all acc\nts1 z if any v /rik+ success _h be5 atta9$ 9 ?is direction by ! lawy]s4 #bh4 ,! difficulty 9 its sci5tific1 or /rictly jurisprud5tial %ape1 seems to h %[n itself pr9cipally 9 ! attempt to arrange legal evid5ce into classes 9 respect ( ! degree ( its cog5cy4 ,?is1 ,i und]/&1 0 ! case 9 ! ,roman law1 & 9 "s ( ! cont95tal sy/ems ( jurisprud5ce :i* took _! rise f ! ,roman law4 ,! direct evid5ce ( s _m witnesses 0 pl5a probatio4 ,!n came m9us pl5a probatio1 !n semipl5 major & semipl5 m9or2 & by add+ toge!r a c]ta9 numb] ( half-pro(s--= in/ance1 by ! production ( a tradesman's acc\nt-books1 plus 8 supplem5t>y oa?--full pro( might be made out4 ,x 0 on ?is pr9ciple t torture 0 employ$ to obta9 a confession4 ,! confession 0 evid5ce suppletory to ! circum/ances :i* 7 held to ju/ify its employm5t4#ba ,accord+ to ,b5?am1#bb ! correspond+ scale 9 ! ,engli% s*ool 03--,positive pro(1 ,viol5t presumption4 ,probable presumption1 ,light or ,ra% presumption4 ,?\gh admitt$ by ,black/one & o!rs1 ,i und]/& t ^! divisions are n at all g5]ally accept$ at ! pres5t day4 #bi4 ,9 ! above we are rem9d$ r ( modal syllogisms4 ,! pr9cipal practical =m 9 :i* ! difficulty und]ly+ ! simple modal propositions pres5ts itself1 is 9 ! attempt to obta9 "s crit]ion ( judicial c]ta9ty4 ,by 'c]ta9ty' "h we mean1 ( c\rse1 n :at ! metaphysicians t]m apodeictic1#bc = t c seldom or nev] be secur$ 9 practical affairs1 b su* a degree ( conviction1 %ort ( ?is1 z e reasonable p]son w feel to be suffici5t = all 8 wants4 ,"h aga91 "o w\ld ?9k1 ! que/ mu/ appe>1 to accurate ?9k]s1 an utt]ly hopeless "o2 an ef=t to discov] natural breaks 9 a cont9u\s magnitude4 ,!re _c inde$ be ! lea/ d\bt t1 among/ limit$ classes ( ke5 & practis$ intellects1 a /&>d ( c]ta9ty1 z ( ev]y?+ else1 might be reta9$ & h&$ d[n ) consid]able accuracy3 ?is is possible 9 matt]s ( ta/e & op9ion :]e p]sonal peculi>ities ( judgm5t are f> m liable to cause disagreem5t & confusion4 ,b !n su* a cons5sus is almo/ entirely an affair ( tact & cu/om2 :]eas :at is want$ 9 ! case 9 "q is "s crit]ion to :i* ! comp>atively un9itiat$ may be able to appeal4 ,! /&>d1 !re=e1 mu/ n m]ely be reta9$ by recollection1 b be g5]ally recognizable by its *>act]i/ics4 ,if su* a crit]ion c\ld be secur$1 its importance c\ld h>dly be ov]rat$4 ,b s f> z "o may judge f ! spee*es ( c\nsel1 ! *>ges ( judges1 & ! v]dicts ( juries1 no?+ really des]v+ ! "n is ev] atta9$4 #cj4 ,! ne>e/ approa*1 p]haps1 to a recogniz$ /&>d is to be f\nd 9 ! frequ5t assurance t juries are n b\nd to convict only 9 case !y h no d\bt ( ! guilt ( ! accus$2 = ! absolute exclusion ( all d\bt1 ! utt] impossibility ( sugge/+ any c\nt] hypo!sis :i* ?is assumes1 is unatta9able 9 human affairs4 ,b1 x is frequ5tly said1 !y are to convict if !y h no 'reasonable d\bt1' no su* d\bt1 t is1 z w\ld be 'a h9drance to act+ 9 ! important affairs ( life4' ,z a caution aga9/ seek+ aft] unatta9able c]ta9ty1 su* advice may be v useful2 b x ne$ h>dly be rem>k$ t ! c]ta9ty ^u :i* we act 9 ! important affairs ( life is no fix$ /&>d1 b v>ies exce$+ly accord+ to ! nature ( ^? affairs4 ,! great] ! rew>d at /ake1 ! great] ! risk we are prep>$ to run1 & conv]sely4 ,h>dly any degree ( c]ta9ty c exi/1 ^u ! security ( :i* we %\ld n be prep>$ to act "u appropriate circum/ances4#bd ,"s writ]s inde$ altoge!r d5y t any /&>d1 9 ! common s5se ( ! ^w1 ei!r is1 or ought to be1 aim$ at 9 legal proce$+s4 ,= in/ance1 ,sir ,j4 ,f4 ,/eph51 9 8 "w on ,engli% ,crim9al ,law1#be aft] notic+ & reject+ su* /&>ds z t la/ indicat$1 comes to ! conclusion t ! only /&>d recogniz$ by our law is t :i* induces juries to convict3--,:at is judicial pro(8 ,t :i* be+ p]mitt$ by law to be giv5 9 evid5ce1 induces twelve m51 *os5 accord+ to ! ,jury ,act1 to say t1 hav+ he>d x1 _! m9ds are satisfi$ ( ! tru? ( ! proposition :i* x affirms4 ,!y may be prejudic$1 !y may be timid1 !y may be ra%1 !y may be ignorant2 b ! oa?1 ! numb]1 & ! prop]ty qualification1 are int5d$1 z f> z possible1 to neutralize ^! disadvantages1 & answ] precisely to ! conditions impos$ ^u /&>ds ( value or l5g?4 7p4 #bfc47 ,to admit ?is is mu* ab\t ! same ?+ z to ab&on su* a /&>d z unatta9able4 ,evid5ce :i* induces a jury to convict may d\btless be a /&>d to me & o!rs ( :at we ought to consid] 'reasonably c]ta91' provid$ ( c\rse t ! v>i\s juries are tol]ably uni=m 9 _! conclusions4 ,b x cle>ly _c be propos$ z a /&>d to ! juries !mselves2 if _! decisions are to be consi/5t & uni=m1 !y want "s ext]nal indication to guide !m4 ,:5 a man is ask+1 ,h[ c]ta9 ought ,i to feel8 to give su* an answ] z ! above is1 surely1 m]ely tell+ him t he is to be z c]ta9 z he is4 ,if1 inde$1 juries compos$ a close pr(ession1 !y might1 z 0 said above1 reta9 a traditional /&>d4 ,b be+1 z !y are1 a selection f ! ord9>y lay public1 _! own decisions 9 ! pa/ c h>dly be held up to !m z a direction :at !y are to d 9 future4 #ca4 ,x w\ld appe> !re=e t we may fairly say t ! ,engli% law1 at any rate1 def9itely rejects ! ma9 assumption ^u :i* ! logical doctr9e ( modality & its legal c\nt]p>t are bas$3 ! assumption1 namely1 t diff]5t grades ( conviction c be m>k$ (f f "o ano!r ) suffici5t accuracy = u to be able to ref] individual cases to _! correspond+ classes4 ,& t ) reg>d to ! collat]al "q ( fix+ a /&>d ( c]ta9ty1 x w g no fur!r ?an pron\nc+1 or imply+1 t we are to be cont5t ) no?+ %ort (1 b ne$ n g beyond1 'reasonable c]ta9ty4' ,?is is a /atem5t ( ! /&>d1 ) :i* ! logician & sci5tific man c easily qu>rel2 & !y may ) mu* reason ma9ta9 t x has n ! slighte/ claim to accuracy1 ev5 if x _h "o to /rict intelligibility4 ,if a man wi%es to "k :e!r 8 pres5t degree ( c]ta9ty is reasonable1 :i!r is he to appeal8 ,he c sc>cely comp>e 8 m5tal /ate ) t :i* is exp]i5c$ 9 '! important affairs ( life1' = ^!1 z already rem>k$1 w\ld indicate no fix$ value4 ,at ! same "t1 "o _c suppose t su* an expression is de/itute ( all signification4 ,p w\ld n cont9ue to use language1 especially 9 matt]s ( p>am\nt importance & int]e/1 )\t mean+ some?+ by x4 ,we are driv5 !re=e to conclude t 'reasonable c]ta9ty' does 9 a rude sort ( way repres5t a traditional /&>d to :i* x is attempt$ to adh]e4 ,z already rem>k$1 ?is is p]fectly practicable 9 ! case ( any class ( pr(essional m51 & !re=e n altoge!r impossible 9 ! case ( ^? :o are (t5 & closely br\ght into connection ) su* a class4 ,?\gh x is h>d to believe t any su* expressions1 :5 us$ = purposes ( ord9>y life1 atta9 at all ne> en\gh to any conv5tional /&>d to be wor? discussion2 yet 9 ! special case ( a jury1 act+ "u ! direct influ5ce ( a judge1 x seems q possible t _! delib]ate ass]tion t !y are 'fully conv9c$' may rea* some:at m ne>ly to a tol]ably fix$ /&>d ?an ord9>y outsid]s w\ld at fir/ ?9k likely4 #cb4 ,are !re !n any means by :i* we c\ld asc]ta9 :at ?is /&>d is2 9 o!r words1 by :i* we c\ld det]m9e :at is ! real wor?1 9 respect ( accuracy1 ( ?is 'reasonable c]ta9ty' :i* ! juries are suppos$ to secure8 ,9 ! abs5ce ( au?oritative decl>ations ^u ! subject1 ! /ud5t ( ,logic & ,probability w\ld naturally resort to two means1 ) a mom5t>y notice ( :i* we w conclude ?is enquiry4 ,! fir/ ( ^! w\ld aim at det]m9+ ! /&>d ( judicial c]ta9ty indirectly1 by simply det]m9+ ! /ati/ical frequ5cy ) :i* ! decisions 7say7 ( a jury 7 f\nd to be correct4 ,?is may seem to be a hopeless task2 & s inde$ x is1 b n s mu* on any !oretic insuffici5cy ( ! det]m9+ elem5ts z on acc\nt ( ! num]\s arbitr>y assumptions :i* atta* to mo/ ( ! problems :i* deal ) ! probability ( te/imony & judgm5ts4 ,x is n necess>y = ?is purpose t we %\ld h an infallible sup]ior c\rt :i* revis$ ! decisions ( ! "o "u consid]ation2#bf x is suffici5t if a l>ge numb] ( ord9>y repres5tative cases are submitt$ to a c\rt consi/+ ev5 ( exactly simil> mat]ials to ! "o ^: decisions we wi% to te/4 ,provid$ always t we make ! mon/r\s assumption t ! judgm5ts ( m5 ab\t matt]s :i* deeply affect !m are 'indep5d5t' 9 ! s5se 9 :i* ! tosses ( p5ce are indep5d5t1 !n ! /ati/ics ( m]e agreem5t & disagreem5t w s]ve our purpose4 ,we might be able to say1 = in/ance1 t a jury ( a giv5 numb]1 decid+ by a giv5 majority1 7 "r n9e times out ( t5 9 _! v]dict4 ,conclusions ( ?is k9d1 9 ref]5ce to ! ,fr5* c\rts1 are :at ,poisson has attempt$ at ! end ( 8 great "w on ! ,probability ( ,judgm5ts2 ?\gh ,i d n suppose t he atta*$ mu* num]ical accuracy to 8 results4 ,a sc>cely m hopeful means w\ld be f\nd by a ref]5ce to c]ta9 cases ( legal 'presumptions4' ,a 'conclusive presumption' is def9$ z foll[s3--,conclusive1 or z !y are else:]e t]m$ imp]ative or absolute presumptions ( law1 are rules det]m9+ ! quantity ( evid5ce requisite = ! support ( any p>ticul> av]m5t :i* is n p]mitt$ to be ov]come by any pro( t ! fact is o!rwise4#bg ,a l>ge numb] ( su* presumptions w be f\nd describ$ 9 ! text-books1 b !y seem to ref] to matt]s f> too vague1 = ! mo/ "p1 to admit ( any r$uction to /ati/ical frequ5cy ( occurr5ce4 ,x is inde$ ma9ta9$ by "s au?orities t any assignm5t ( degree ( ,probability is n _! pres5t object1 b t !y are simply meant to exclude ! tr\blesome delays t w\ld ensue if ev]y?+ 7 consid]$ op5 to d\bt & "q4 ,moreov]1 ev5 if !y did assign a degree ( c]ta9ty ?is w\ld r be an indication ( :at legislators or judges ?\ght reasonable ?an ( :at 0 s consid]$ by ! juries !mselves4 ,!re are inde$ presumptions z to ! "t aft] :i* a man1 if n he>d (1 is suppos$ to be dead 7capable ( dispro(1 ( c\rse1 by 8 reappe>ance74 ,if ?is "t v>i$ ) ! age ( ! man 9 "q1 we %\ld at once h "s su* /&>d z we desire1 = a ref]5ce to ! ,life tables w\ld fix 8 probable duration ( life1 & s det]m9e indirectly ! measure ( probability :i* satisfi$ ! law4 ,b ?is is n ! case2 ! p]iod *os5 is entirely irrespective ( age4 ,! ne>e/ case 9 po9t 7& t does n am\nt to mu*7 :i* ,i h be5 able to asc]ta9 is t ( ! age aft] :i* x has be5 presum$ t a woman 0 incapable ( be>+ *ildr54 ,?is 0 ! age ( #ec4 ,a c]ta9 approa* to a /ati/ical assignm5t ( ! *ances 9 ?is case is to be f\nd 9 ,quetelet's ,physique ,sociale 7,vol4 ,i4 p4 #ahd1 note74 ,accord+ to ! au?orities :i* he !re quotes x w\ld seem t 9 ab\t "o bir? 9 #eejj ! "m 0 ( ! age ( #ej or upw>ds4 ,?is does n q assign ! degree ( :at may be call$ ! priori *ance aga9/ ! occurr5ce ( a bir? at t age1 because ! fact ( hav+ comm5c$ a family at an e>ly age repres5ts "s dim9ution ( ! probability ( cont9u+ x into lat] life4 ,b x s]ves to give "s indication ( :at may be call$ ! odds aga9/ su* an ev5t4 ,x ne$ n be rem>k$ t any su* clues z ^! to ! measure ( judicial c]ta9ty are f> too slight to be ( any real value4 ,!y only des]ve pass+ notice z a possible logical solution ( ! problem 9 "q1 or r z an indication ( ! mode 9 :i*1 9 !ory1 su* a solution w\ld h to be s\ght1 7 ! ,engli% law1 on ^? subjects1 a p]fectly consi/5t s*eme ( sci5tific evid5ce4 ,?is is ! mode 9 :i* "o w\ld1 "u ^? circum/ances1 attempt to extract f its proce$+s an admission ( ! exact measure ( t /&>d ( c]ta9ty :i* x adopt$1 b :i* x decl9$ op5ly to enunciate4 #a4 ,=mal ,logic1 p4 #bcb4 #b4 ,?is appe>s to be ! purport ( "s /atem5ts 9 a v confus$ passage 9 ,:ately's ,logic 7,bk4 ,,ii41 *4 ,,iv4 #a74 ,a modal proposition may be /at$ z a pure "o by atta*+ ! mode to "o ( ! t]ms1 & ! proposition w 9 all respects fall "u ! =ego+ rules2444 ',x is probable t all k is useful2' 'probably useful' is "h ! pr$icate4 ,he draws app>5tly no su* di/9ction z t betwe5 ! true & false modality ref]r$ to 9 ! next note4 ,:at is really surpris+ is t ev5 ,hamilton puts ! two 7! true & ! false modality7 ^u ! same foot+4 ,9 reg>d to ^! ! =m] ! case is precisely ! same2 ! mode is m]ely a "p ( ! pr$icate4 ,logic1 ,i4 #beg4 #c4 ,i allude ( c\rse to su* examples z ',a kill$ ,b unju/ly1' 9 :i* ! kill+ ( ,b by ,a 0 sometimes said to be ass]t$ n simply b ) a modification4 7,hamilton's ,logic1 ,i4 #bef47 ,x is obvi\s t ! modification 9 su* cases is by rights m]ely a "p ( ! pr$icate1 !re be+ no =mal di/9ction betwe5 ',a is ! kill] ( ,b' & ',a is ! unju/ kill] ( ,b4' ,inde$ "s logicians :o 7 too cons]vative to reject ! g5]ic "n ( modality 9 ?is application adopt$ ! common exp$i5t ( introduc+ a specific di/9ction :i* did away ) its mean+1 t]m+ ! spuri\s k9d 'mat]ial modality' & ! g5u9e k9d '=mal modality'4 ,! =m] includ$ all ! cases 9 :i* ! modification belong$ by "r ei!r to ! pr$icate or to ! subject2 ! latt] 0 res]v$ = ! cases 9 :i* ! modification affect$ ! real conjunction ( ! pr$icate ) ! subject4 7,keck]mann1 ,sy/ema ,logic1 ,lib4 ,,ii4 *4 #c47 ,x 01 ,i believe1 a common s*ola/ic di/9ction4 ,= "s acc\nt ( ! dispute z to :e!r ! negative p>ticle 0 to be consid]$ to belong to ! copula or to ! pr$icate1 see ,hamilton's ,logic1 ,i4 #bec4 #d4 ,he has also giv5 a %ort discussion ( ! subject else:]e 7,discussions1 ,ed4 ,,ii4 p4 #gjb71 9 :i* a some:at diff]5t view is tak54 ,! modes are inde$ "h admitt$ into logic1 b only 9 s f> z !y fall by subdivision "u ! relation ( g5us & species1 :i* is ( c\rse tantam\nt to _! entire rejection2 = !y !n diff] 9 no ess5tial way f any o!r examples ( t relation4 #e4 ,lett]s1 ,lectures & ,reviews1 p4 #fa4 ,else:]e 9 ! review 7p4 #de7 he gives :at appe>s to me a some:at diff]5t decision4 #f4 ,x mu/ be rememb]$ t ?is is n "o ( ! proportional propositions ) :i* we h be5 conc]n$ 9 previ\s *apt]s3 x is meant t !re are exactly #ba ,ys1 ( :i* j #ah are ,x1 n t on ! av]age #ah out ( #ba may be s reg>d$4 #g4 ,i consid] h[ev]1 z ,i h said fur!r on 7p4 #cbj71 t ! treatm5t 9 ! old] logics ( ,probable syllogisms1 & ,dialectic syllogisms1 came to some:at ! same ?+ z ?is1 ?\gh !y look$ at ! matt] f a diff]5t po9t ( view1 & express$ x 9 v diff]5t language4 #h4 ,! di/9ction is h[ev] by no means entirely neglect$4 ,?us ,smiglecius1 :5 discuss+ ! modal affections ( c]ta9ty & necessity1 says1 c]titudo ad cognitionem spectat3 necessitas v]o e/ 9 re 7,disputationes2 ,disp4 ,,xiii41 ,qu/4 ,,xii474 #i4 ,x may be rem>k$ t ,:ately 7,logic1 ,bk4 ,,ii4 *4 ,,ii4 #b7 speaks ( necess>y1 impossible & cont+5t matt]1 )\t any app>5t suspicion t !y belong entirely to an obsolete po9t ( view4 #aj4 ,=mal ,logic1 p4 #bcc4 #aa4 ,! subject 0 sometimes altoge!r omitt$1 z by ,wolf4 ,he says a good deal h[ev] ab\t probable propositions & syllogisms1 &1 l ,leibnitz be=e him1 look$ =w>d to a logica probabilium z some?+ new & desirable4 ,i imag9e t he _h be5 influ5c$ by ! writ]s on ,*ances1 z ( ! few :o _h already treat$ t subject ne>ly all ! mo/ important are ref]r$ to 9 "o passage 7,philosophia ,rationalis sive ,logica1 #eic74 ,lamb]t /&s q ap>t4 ,9 ?is respect1 z 9 mo/ o!rs :]e ma!matical conceptions & symbols are involv$1 8 logical attitude is ?or\ghly unconv5tional4 ,see1 = in/ance1 8 *apt] ',von dem ,wahrs*e9li*5'1 9 8 ,neues ,organon4 #ab4 ,i _c f9d ! slighte/ au?ority = ! /atem5t 9 ! elaborate hi/ory ( ,logic by ,prantl4 #ac4 ,hi quatuor modi magnam c5s]i sol5t analogiam hab]e cum quadruplici propositionum 9 quantitate et qualitate v>ietate 7,wallis's ,in/it4 ,logic4 ,bk4 ,,ii4 *4 #h74 #ad4 ,laws ( ,?\ght1 #aah4 #ae4 ,haud scio magis ne doctr9am modalium s*ola/ici ex]cu]9t1 quam ea illos vex>it4 ,c]te usque adeo sudatum hic fuit1 ut dict]io locus sit datus2 ,de modalibus non gu/abit as9us4 ,keck]mann1 ,sy/4 ,log4 ,bk4 ,,ii4 *4 #c4 #af4 ,smiglecii ,disputationes1 ,+ol/adt1 #afah4 ,see also ,prantl's ,ges*i*te d] ,logik 7"u ,occam & ,buridan7 = acc\nts ( ! excessive complication :i* ! subtlety ( ^? le>n$ s*oolm5 evolv$ out ( su* suitable mat]ials4 #ag4 ,translation by ,t4 ,m4 ,l9dsay1 p4 #dci4 #ah4 ,! & !mselves are propositions2 ! =m] /at+ a g5]al probability1 ! latt] a fact1 :i* is kn[n to be an indication1 m or less c]ta91 ( ! tru? ( "s fur!r /atem5t1 :e!r ( a s+le fact1 or ( a g5]al belief4 ,! =m] is a g5]al proposition1 ne>ly1 ?\gh n q1 univ]sal2 z 'mo/ m5 :o envy hate'2 ! latt] is a s+ul> proposition1 :i* h[ev] is n reg>d$ z a sign1 except relatively to "s o!r proposition1 :i* x is suppos$ may by inf]r$ f x4 7,mansel's ,aldri*2 ,app5dix ,f1 :]e an acc\nt w be f\nd ( ! ,ari/otelian en?ymeme1 & dialectic syllogism4 ,also1 ( c\rse1 ,grote's ,ari/otle1 ,topics & else:]e47 #ai4 ,nam 9 hoc etiam diff]t demon/ratio1 s5 demon/rativa argum5tatio1 probabili1 quia 9 ill tam conclusio quam prmiss necess>i sunt2 9 probabili autem argum5tatione sicut conclusio ut probabilis inf]tur ita prmiss ut probabiles aff]untur 7,crackan?orpe1 ,bk4 ,v41 ,*4 #a72 almo/ ! words ) :i* ,de ,morgan di/+ui%es betwe5 logic & probability 9 a passage already cit$ 7see ,*4 ,,vi4 #c74 ,p]haps x 0 a developm5t ( "s su* view z ?is t ,leibnitz look$ =w>d to4 ,j'ai dit plus d'une fois qu'il faudrait une n\velle espce de ,logique1 qui trait]oit des degrs de ,probabilit1 puisqu',ari/ote dans ses ,topiques n'a ri5 mo9s fait que cela 7,n\veaux essais1 ,lib4 ,,iv4 *4 ,,xvi74 ,x is possible1 inde$1 t he _h 9 8 m9d m :at we n[ und]/& by ! ma!matical !ory ( ,probability1 b 9 ! infancy ( a sci5ce x is ( c\rse h>d to say :e!r any p>ticul> subject is def9itely contemplat$ or n4 ,leibnitz 7z ,todhunt] has %[n 9 8 hi/ory7 took ! greate/ int]e/ 9 su* *ance problems z _h yet be5 discuss$4 #bj4 ,by loci 7 und]/ood c]ta9 g5]al classes ( premises4 ,!y /ood1 9 fact1 to ! major premise 9 some:at ! same relation t ! ,category or ,pr$icam5t did to ! t]m4 ,crackan?orpe says ( !m1 s$ duci a loco probabilit] argu5di1 hoc v]e proprium e/ ,argum5tationis probabilis2 et 9 hoc a ,demon/ratione diff]t1 quia ,demon/rator utitur solummodo quatuor ,locis eisque necess>iis4444 ,prt] hos autem1 ex quibus quoque probabilit] argu]e licet1 sunt multo plures ,loci argu5di probabilit]2 ut a ,g5]e1 a ,specie1 ab ,adjuncto1 ab ,oppositis1 et similia 7,logica1 ,lib4 ,v41 *4 ,,ii474 #ba4 ,/eph5's ,g5]al ,view ( ! ,crim9al ,law ( ,engl&1 p4 #bda4 #bb4 ,rationale ( ,judicial ,evid5ce2 ,bk4 ,i4 *4 ,,vi4 #bc4 ,?\gh ?is is claim$ by "s ,kantian logicians2--,nie d>f an e9em angebli*5 ,v]bre*] die gesetzli*e ,/rafe vollzog5 w]d51 bevor er ni*t selb/ das ,v]bre*5 e+e/&54 ,d5n w5n au* alle ,zeugnisse und die brig5 ,anzeig5 wid] ihn wr51 s bleibt do* das ,geg5!il imm] mgli* 7,krug1 ,d5klehre1 #aca74 #bd4 ,z ,mr ,c4 ,j4 ,monro puts x3 ,suppose t a man is suspect$ ( murd]+ 8 daught]4 ,evid5ce :i* w\ld n convict him be=e an ord9>y jury might make a gr& jury f9d a true bill2 evid5ce :i* w\ld n d ?is might make a coron]'s jury br+ 9 a v]dict aga9/ him2 evid5ce :i* w\ld n d ?is w\ld v (t5 prev5t a ,*anc]y judge f appo9t+ ! man gu>dian to a w>d ( ! c\rt2 evid5ce :i* w\ld n affect ! judge's m9d might make a fa!r ?9k twice on 8 dea?-b$ be=e he appo9t$ ! man gu>dian to 8 daught]4 #be4 ,! portions ( ?is "w :i* treat ( ! nature ( pro( 9 g5]al1 & ( judicial pro( 9 p>ticul>1 are well wor? read+ by e logical /ud5t4 ,x appe>s to me1 h[ev]1 t ! au?or goes mu* too f> 9 ! direction ( reg>d+ pro( z subjective1 t is z :at does satisfy p1 r ?an z :at %\ld satisfy !m4 ,he comp>es ! legislative /&>d ( c]ta9ty ) t ( value2 ?is latt] is decl>$ to be a c]ta9 weight ( gold1 irrespective ( ! r>ity or commonness ( t metal4 ,s ) c]ta9ty2 if p gr[ m cr$ul\s ! intr9sic value ( ! /&>d w v>y4 #bf4 ,! "q w be m fully discuss$ 9 a future *apt]1 b a few words may be ins]t$ "h by way ( indication4 ,r$uce ! case to ! simple/ possible elem5ts by suppos+ only two judges or c\rts1 ( ! same av]age correctness ( decision4 ,let ?is be indicat$ by x4 ,!n ! *ance ( _! agree+ is x#b 7#a - x7#b1 = !y agree if bo? are "r or bo? wrong4 ,if ! /ati/ical frequ5cy ( ?is agreem5t is kn[n1 t is1 ! frequ5cy ) :i* ! fir/ judgm5t is confirm$ by ! second1 we h ! means ( det]m9+ x4 #bg4 ,taylor on ,evid5ce3 ! latt] "p ( ! extract does n seem v cle>4 ,,*apt] ,,xiv4 ,,fallacies4 #a4 ,9 works on ,logic a *apt] is g5]ally devot$ to ! discussion ( ,fallacies1 t is1 to ! description & classification ( ! diff]5t ways 9 :i* ! rules ( ,logic may be transgress$4 ,! analogy ( ,probability to ,logic is suffici5tly close to make x advisable to adopt ! same plan "h4 ,9 describ+ 8 own op9ions an au?or is1 ( c\rse1 p]petually oblig$ to describe & criticise ^? ( o!rs :i* he consid]s errone\s4 ,b "s ( ! mo/ widely spread errors f9d no support]s wor? m5tion+1 & exi/ only 9 vague popul> misappreh5sion4 ,x w be f\nd ! be/ arrangem5t1 !re=e1 at ! risk ( occasional repetition1 to collect a few ( ! errors t occur mo/ frequ5tly1 & z f> z possible to trace !m to _! s\rces2 b x w h>dly be wor? ! tr\ble to attempt any regul> sy/em ( arrangem5t & classification4 ,we %all ma9ly conf9e ourselves1 9 accordance ) ! special prov9ce ( ?is "w1 to problems :i* involve que/ions ( logical int]e/1 or to ^? :i* ref] to ! application ( ,probability to moral & social sci5ce4 ,we %all avoid ! discussion ( isolat$ problems 9 games ( *ance & skill except :5 "s error ( pr9ciple seems to be involv$ 9 !m4 #b4 7,i47 ,"o ( ! mo/ f]tile s\rces ( error & confusion ^u ! subject has be5 already sev]al times allud$ to1 & 9 "p discuss$ 9 a previ\s *apt]4 ,?is consi/s 9 *oos+ ! class to :i* to ref] an ev5t1 & !re=e judg+ ( ! r>ity ( ! ev5t & ! consequ5t improbability ( =etell+ x1 aft] x has happ5$1 & !n transf]r+ ! impressions we exp]i5ce to a suppos$ contemplation ( ! ev5t be=eh&4 ,! process 9 itself is p]fectly legitimate 7h[ev] unnecess>y x may be71 s9ce "t does n 9 /rictness ent] at all into que/ions ( ,probability4 ,no error !re=e ne$ arise 9 ?is way1 if we 7 c>eful z to ! class :i* we ?us select$2 b su* c>efulness is (t5 neglect$4 ,an illu/ration may af=d help "h4 ,a man once po9t$ to a small t>get *alk$ ^u a door1 ! t>get hav+ a bullet hole ?r\gh ! c5tre ( x1 & surpris$ "s spectators by decl>+ t he _h fir$ t %ot f an old f[l+-piece at a di/ance ( a hundr$ y>ds1 ,8 /atem5t 0 true en\gh1 b he suppress$ a r important fact4 ,! %ot _h really be5 aim$ 9 a g5]al way at ! b>n-door1 & _h hit x2 ! t>get 0 aft]w>ds *alk$ r\nd ! spot :]e ! bullet /ruck4 ,a deception analog\s to ?is is1 ,i ?9k1 (t5 practis$ unconsci\sly 9 o!r matt]s4 ,we judge ( ev5ts on a simil> pr9ciple1 feel+ & express+ surprise 9 an equally unreasonable way1 & decid+ z to _! occurr5ce on gr\nds :i* are really m]ely a subsequ5t adjunct ( our own4 ,butl]'s rem>ks ab\t '! /ory ( ,cs>1' discuss$ already 9 ! twelf? *apt]1 are ( ?is "*4 ,he selects a s]ies ( ev5ts f hi/ory1 & !n imag9es a p]son guess+ !m correctly :o at ! "t _h n ! hi/ory be=e him4 ,z ,i h already po9t$ out1 x is "o ?+ to be unlikely to guess an ev5t rightly )\t specific evid5ce2 x is ano!r & v diff]5t ?+ to appreciate ! tru? ( a /ory :i* is f\nd$ p>tly or entirely ^u evid5ce4 ,b x is a great mi/ake to transf] to "o ( ^! ways ( view+ ! matt] ! m5tal impressions :i* prop]ly belong to ! o!r4 ,x is l draw+ ! t>get aft]w>ds1 & !n be+ surpris$ to f9d t ! %ot lies 9 ! c5tre ( x4 #c4 ,"o aspect ( ?is fallacy has be5 already discuss$1 b x w s]ve to cle> up difficulties :i* are (t5 felt ^u ! subject if we reexam9e ! "q "u a some:at m g5]al =m4 ,9 ! class ( examples "u discussion we are g5]ally pres5t$ ) an individual :i* is n inde$ def9itely ref]r$ to a class1 b 9 reg>d to :i* we h no great difficulty 9 *oos+ ! appropriate class4 ,n[ suppose we 7 contemplat+ su* an ev5t z ! ?r[+ ( sixes ) a pair ( dice f\r times runn+4 ,su* a ?r[ w\ld be t]m$ a v unlikely ev5t1 z ! odds aga9/ its happ5+ w\ld be #cf #cf #cf #cf - #a to #a or #afgifae to #a4 ,! mean+ ( ^! phrases1 z has be5 abundantly po9t$ out1 is simply t ! ev5t 9 "q occurs v r>ely2 t1 /at$ ) num]ical accuracy1 x occurs once 9 #afgifaf times4 #d4 ,b n[ let u make ! assumption t ! ?r[ has actually occurr$2 let u put ourselves into ! position ( contemplat+ sixes f\r times runn+ :5 x is kn[n or report$ t ?is ?r[ has happ5$4 ,! same phrase1 namely t ! ev5t is a v unlikely "o1 w (t5 be us$ 9 relation to x1 b we %all f9d t ?is phrase may be employ$ to indicate1 on "o occasion or ano!r1 extremely diff]5t mean+s4 7#a7 ,!re is1 fir/ly1 ! mo/ correct mean+4 ,! ev5t1 x is true1 has happ5$1 & we "k :at x is1 & !re=e1 we h n really any occasion to resort to ! rules ( ,probability2 b we c nev]!less conceive ourselves z be+ 9 ! position ( a p]son :o does n "k1 & :o has only ,probability to appeal to4 ,by call+ ! *ances #afgifae to #a aga9/ ! ?r[ we !n mean to imply ! fact1 t inasmu* z su* a ?r[ occurs only once 9 #afgifaf times1 our guess1 7 we to guess1 w\ld be correct only once 9 ! same numb] ( times2 provid$1 t is1 t x is a fair guess1 bas$ simply on ^! /ati/ical gr\nds4 #e4 7#b7 ,b !re is a second & v diff]5t conception sometimes introduc$1 especially :5 ! ev5t 9 "q is suppos$ to be kn[n1 n z above by ! evid5ce ( our exp]i5ce1 b by ! report ( a witness4 ,we may !n mean by ! '*ances aga9/ ! ev5t' 7z 0 po9t$ out 9 ,*apt] ,,xii47 n ! proportional numb] ( times we %\ld be "r 9 guess+ ! ev5t1 b ! proportional numb] ( times ! witness w be "r 9 report+ x4 ,! bases ( our inf]5ce are "h %ift$ on to new gr\nd4 ,9 ! =m] case ! /ati/ics 7 ! ?r[s & _! respective frequ5cy1 n[ !y are ! witnesses' /atem5ts & _! respective tru?fulness4 #f4 7#c7 ,b !re is yet ano!r mean+ sometimes int5d$ to be convey$ :5 p]sons talk ( ! *ances aga9/ su* an ev5t z ! ?r[ 9 "q4 ,!y may mean--n1 ,"h is an ev5t1 h[ (t5 %\ld ,i h guess$ x8--nor1 ,"h is a report1 h[ (t5 w x be correct8--b some?+ diff]5t f ei!r1 namely1 ,"h is an ev5t1 h[ (t5 w x be f\nd to be produc$ by "s "o p>ticul> k9d ( cause8 ,:51 = example1 a man he>s ( dice giv+ ! same ?r[ sev]al times runn+1 & speaks ( ?is z v extraord9>y1 we %all (t5 f9d t he is n m]ely ?9k+ ( ! improbability ( 8 guess be+ "r1 or ( ! report be+ true1 b1 t along ) ?is1 he is introduc+ ! "q ( ! ?r[ hav+ be5 produc$ by fair dice4 ,!re is1 ( c\rse1 no reason :atev] :y su* a "q z ?is %\ld n also be ref]r$ to ,probability1 provid$ always t we c\ld f9d ! appropriate /ati/ics by :i* to judge4 ,^! /ati/ics w\ld be compos$1 n ( ?r[s ( ! p>ticul> dice1 nor ( reports ( ! p>ticul> witness1 b ( ! occasions on :i* su* a ?r[ z ! "o 9 "q respectively _h1 & _h n1 be5 produc$ fairly4 ,! objection to ent]+ ^u ?is view ( ! "q w\ld be t no su* /ati/ics are obta9able1 & t if !y 71 we %\ld pref] to =m our op9ion 7on pr9ciples to be describ$ 9 ,*apt] ,,xvi47 f ! special circum/ances ( ! case r ?an f an appeal to ! av]age4 #g4 ,! read] w easily be able to supply examples 9 illu/ration ( ! di/9ctions j giv52 we w briefly exam9e b "o4 ,i hide a banknote 9 a c]ta9 book 9 a l>ge libr>y1 & leave ! room4 ,a p]son tells me t1 aft] ,i w5t out1 a /rang] came 91 walk$ /raight up to t p>ticul> book1 & took x away ) him4 ,_m p on he>+ ?is acc\nt w\ld reply1 ,h[ extremely improbable6 ,on analys+ ! phrase1 ,i ?9k we %all f9d t c]ta9ly two1 & possibly all ?ree1 ( ! above mean+s might be involv$ 9 ?is exclamation4 7#a7 ,:at may be meant is ?is1--,assum+ t ! report is true1 & ! /rang] innoc5t1 a r>e ev5t has occurr$4 ,_m books might h be5 ?us tak5 )\t t p>ticul> "o be+ select$4 ,i %\ld n !re=e h expect$ ! ev5t1 & :5 x has happ5$ ,i am surpris$4 ,n[ a man has a p]fect "r to be surpris$1 b he has no logical "r 7s long z we conf9e ourselves to ?is view7 to make 8 surprise a gr\nd = disbeliev+ ! ev5t4 ,to d ?is is to fall into ! fallacy describ$ at ! comm5cem5t ( ?is *apt]4 ,! fact ( my n hav+ be5 likely to h guess$ a ?+ be=eh& is no reason 9 itself = d\bt+ x :5 ,i am in=m$ ( x4 7#b7 ,or ,i may /op %ort ( ! ev5ts report$1 & apply ! rules ( ,probability to ! report itself4 ,if s1 :at ,i mean is t su* a /ory z ?is n[ be=e me is ( a k9d v g5]ally false1 & t ,i _c !re=e atta* mu* cr$it to x n[4 7#c7 ,or ,i may accept ! tru? ( ! report1 b d\bt ! fact ( ! /rang] hav+ tak5 ! book at r&om4 ,if s1 :at ,i mean is1 t ( m5 :o take books 9 ! way describ$1 only a small proportion w be f\nd to h tak5 !m really at r&om2 ! majority w d s because !y _h by "s means asc]ta9$1 or come to suspect1 :at !re 0 inside ! book4 ,ea* ( ! above ?ree mean+s is a possible & a legitimate mean+4 ,! only requisite is t we %\ld be c>eful to asc]ta9 :i* ( !m is pres5t to ! m9d1 s z to select ! appropriate /ati/ics4 ,! fir/ makes 9 itself ! mo/ legitimate use ( ,probability2 ! drawback be+ t at ! "t 9 "q ! functions ( ,probability are sup]s$$ by ! ev5t be+ o!rwise kn[n4 ,! second or ?ird1 !re=e1 is ! m likely mean+ to be pres5t to ! m9d1 = 9 ^! cases ,probability1 if x c\ld be practically made use (1 w\ld1 at ! "t 9 "q1 be a means ( draw+ really important inf]5ces4 ,! drawbacks are ! difficulty ( f9d+ su* /ati/ics1 & ! extreme di/urb+ influ5ce ^u ^! /ati/ics ( ! circum/ances ( ! special case4 #h4 7,,ii47 ,closely connect$ ) ! t5d5cy j m5tion$ is t :i* prompts u to conf\nd a true *ance selection ) "o :i* is m or less pick$4 ,:5 we are deal+ ) famili> objects 9 a concrete way1 especially :5 ! great] r>ity corresponds to sup]iority ( quality1 almo/ e "o has le>nt to recognize ! di/9ction4 ,no "o1 = in/ance1 on obs]v+ a f9e body ( troops 9 a =eign t[n1 b w\ld be prompt$ to ask :e!r !y came f an av]age regim5t or f "o t 0 pick$4 ,:5 h[ev] ! di/9ction ref]s to unfamili> objects1 & especially :5 only comp>ative r>ity seems to be involv$1 ! fallacy may assume a r subtle & mislead+ =m1 & seems to des]ve special notice by ! consid]ation ( a few examples4 ,sometimes ! result is n s mu* an actual fallacy z a slight misreckon+ ( ! ord] ( probability ( ! ev5t "u consid]ation4 ,= in/ance1 9 ! ,pyramid "q1 we saw t x made "s diff]5ce :e!r we consid]$ t alone 0 to be tak5 into acc\nt or :e!r we put ?is con/ant into a class ) a small numb] ( o!r simil> ones4 ,9 decid+1 h[ev]1 :e!r or n !re is any?+ rem>kable 9 ! actual fall+ %ort ( ! repres5tation ( ! numb] #g 9 ! evaluation ( 7v4 p4 #bdh7 ! :ole "q turns ^u consid]ations ( ?is k9d4 ,! only enquiry rais$ is :e!r !re is any?+ rem>kable 9 ?is dep>ture f ! mean1 & ! answ] dep5ds ^u :e!r we suppose t we are ref]r+ to a pr$et]m9$ digit1 or to :atev] digit ( ! t5 happ5s to be mo/ above or bel[ ! av]age4 ,or1 take ! case rais$ by ,c\rnot 7,exposition de la ,?orie des ,*ances1 #ajb1 #aad71 t a c]ta9 deviation f ! mean 9 ! case ( ,dep>tm5tal returns ( ! proportion betwe5 male & female bir?s is significant & indicative ( a diff]5ce 9 k9d1 provid$ t we select at r&om a s+le ,fr5* ,dep>tm5t2 b t ! same deviation may be accid5tal if x is ! maximum ( ! respective returns = sev]al ,dep>tm5ts4#a ,! answ] may be giv5 "o way or ! o!r accord+ z we be> ?is consid]ation 9 m9d4 #i4 ,we are peculi>ly liable to be misl$ 9 ?is way :5 we are endeav\r+ to det]m9e ! cause ( "s ph5om5on1 by m]e /ati/ics1 9 entire ignorance z to ! direction 9 :i* ! cause %\ld be expect$4 ,9 su* cases an +5i\s p]son :o *ooses to look ab\t ov] a l>ge field c nev] fail to hit ^u an explanation :i* is plausible 9 ! s5se t x fits 9 ) ! hi!rto obs]v$ facts4 ,) a ti! ( ! tr\ble :i* ,mr ,piazzi ,smy? exp5d$ ^u ! measurem5t ( ! great pyramid1 ,i ?9k ,i w\ld und]take to f9d plausible intimations ( sev]al ( ! important con/ants & /&>ds :i* he discov]$ !re1 9 ! dim5sions ( ! desk at :i* ,i am writ+4 ,! odde/ in/ance ( ?is sort ( conclusion is p]haps to be f\nd 9 ! rese>*es ( a writ] :o has discov]$#b t !re is a connection ( a /rik+ k9d betwe5 ! respective successes ( ! ,ox=d & ! ,cambridge boat 9 ! annual race1 & ! great] & less frequ5cy ( sun-spots4 ,( c\rse our usual practical res\rce 9 su* cases is to make appeal to our previ\s k ( ! subject 9 "q1 :i* enables u to reject z absurd a great numb] ( hypo!ses :i* c nev]!less make a fair %[ :5 !y are all[$ to re/ ^u a limit$ am\nt ( adroitly select$ in/ances4 ,b x mu/ be rememb]$ t if any !ory *ooses to appeal to /ati/ics1 to /ati/ics x mu/ be suff]$ to g = judgm5t4 ,ev5 ! boat race !ory c\ld be e/abli%$ 7if s\nd7 on ?is gr\nd alone4 ,t is1 if x really c\ld be %[n t exp]i5ce 9 ! long run confirm$ ! prepond]ance ( successes on "o side or ! o!r accord+ to ! relative frequ5cy ( ! sun-spots1 we %\ld h to accept ! fact t ! two classes ( ev5ts 7 n really indep5d5t4 ,"o ( ! two1 :i*ev] x may be1 mu/ be suspect$ ( caus+ or influ5c+ ! o!r2 or bo? mu/ be caus$ or influ5c$ by "s common circum/ances4 #aj4 7,,iii47 ,! fallacy describ$ at ! comm5cem5t ( ?is *apt] arose f det]m9+ to judge ( an obs]v$ or report$ ev5t by ! rules ( ,probability1 b employ+ a wrong set ( /ati/ics 9 ! process ( judg+4 ,ano!r fallacy1 closely connect$ ) ?is1 arises f ! practice ( tak+ "s only ( ! *>act]i/ics ( su* an ev5t1 & arbitr>ily conf9+ to ^! ! appeal to ,probability4 ,suppose ,i toss up twelve p5ce & f9d t elev5 ( !m give heads4 ,_m p]sons on witness+ su* an occurr5ce w\ld exp]i5ce a feel+ :i* !y w\ld express by ! rem>k1 ,h[ ne> t 0 to gett+ all heads6 ,& if any ?+ v important 7 /ak$ on ! ?r[ !y w\ld be mu* excit$ at ! occurr5ce4 ,b 9 :at s5se 7 we ne> to twelve8 ,!re is a n uncommon error1 ,i appreh5d1 :i* consi/s 9 unconsci\sly reg>d+ ! elev5 heads z a ?+ :i* is already someh[ secur$1 s t "o might z x 7 keep !m1 & !n take our *ance = secur+ ! rema9+ "o4 ,! elev5 are m5tally set aside1 look$ ^u z c]ta9 7= !y h already happ5$71 & we !n introduce ! notion ( *ance m]ely = ! twelf?4 ,b ?is twelf?1 hav+ also happ5$1 has no bett] claim to su* a di/9ction ?an any ( ! o!rs4 ,if we w introduce ! notion ( *ance 9 ! case ( ! "o t gave tail we mu/ d ! same 9 ! case ( all ! o!rs z well4 ,9 o!r words1 if ! toss] be dissatisfi$ at ! appe>ance ( ! "o tail1 & wi% to cancel x & try 8 luck aga91 he mu/ toss up ! :ole lot ( p5ce aga9 fairly toge!r4 ,9 ?is case1 ( c\rse1 s f> f 8 hav+ a bett] prospect = ! next ?r[ he may ?9k himself 9 v good luck if he makes aga9 z good a ?r[ z ! "o he reject$4 ,:at he is do+ is conf\nd+ ?is case ) t 9 :i* ! ?r[s are really successive4 ,if elev5 heads h be5 toss$ up 9 turn1 we are ( c\rse )9 an ev5 *ance ( gett+ a twelf?2 b ! circum/ances are q diff]5t 9 ! in/ance propos$4 #aa4 ,9 ! above example ! error is transp>5t4 ,b 9 =m+ a judgm5t ^u matt]s ( great] complexity ?an dice & p5ce1 especially 9 ! case ( :at are call$ 'n>r[ escapes1' a mi/ake ( an analog\s k9d is1 ,i appreh5d1 f> f uncommon4 ,a p]son1 = example1 :o has j exp]i5c$ a n>r[ escape w (t5 be fill$ ) surprise & anxiety am\nt+ almo/ to t]ror4 ,! ev5t be+ pa/1 ^! feel+s are1 at ! "t1 9 /rictness inappropriate4 ,if1 z is q possible1 !y are m]ely in/9ctive1 or ! result ( association1 !y d n fall )9 ! prov9ce ( any k9d ( ,logic4 ,if1 h[ev]1 z seems m likely1 !y p>tially arise f a suppos$ transf]5ce ( ourselves into t po9t ( pa/ "t at :i* ! ev5t 0 j ab\t to happ51 & ! production by imag9ation ( ! feel+s we %\ld !n expect to exp]i5ce1 ?is process p>takes ( ! nature ( an inf]5ce1 & c be "r or wrong4 ,9 o!r words1 ! al>m may be proportionate or disproportionate to ! am\nt ( dang] t might fairly h be5 reckon$ ^u 9 su* a hypo!tical anticipation4 ,if ! suppos$ transf] 7 completely c>ri$ out1 !re w\ld be no fallacy2 b x is (t5 v incompletely done1 "s ( ! compon5t p>ts ( ! ev5t be+ suppos$ to be det]m9$ or 'arrang$' 7to use a sport+ phrase7 9 ! =m 9 :i* we n[ "k t !y actually h happ5$1 & only ! rema9+ ones be+ fairly contemplat$ z future *ances4 ,a man1 = example1 is out ) a fri5d1 ^: rifle goes (f by accid5t1 & ! bullet passes ?r\gh 8 hat4 ,he trembles ) anxiety at ?9k+ :at might h happ5$1 & p]haps rem>ks1 ',h[ v ne> ,i 0 to be+ kill$6' ,n[ we may safely assume t he means some?+ m ?an t a %ot pass$ v close to him4 ,he has "s vague idea t1 z he w\ld probably say1 '8 *ance ( be+ kill$ !n 0 v great4' ,8 surprise & t]ror may be 9 great "p physical & in/9ctive1 aris+ simply f ! k t ! %ot _h pass$ v ne> him4 ,b 8 m5tal /ate may be analys$1 & we %all !n mo/ likely f9d1 at bottom1 a fallacy ( ! k9d describ$ above4 ,to speak or ?9k ( *ance 9 connection ) ! incid5t1 is to ref] ! p>ticul> incid5t to a class ( incid5ts ( a simil> "*1 & !n to consid] ! comp>ative frequ5cy ) :i* ! contemplat$ result ensues4 ,n[ ! s]ies :i* we may suppose to be mo/ naturally select$ 9 ?is case is "o compos$ ( %oot+ excursions ) 8 fri5d2 up to ?is po9t ! proce$+s are assum$ to be design$1 beyond x only1 9 ! subsequ5t ev5t1 0 !re accid5t4 ,once 9 a ?\s& times p]haps on su* occasions ! gun w g (f accid5tally2 "o 9 a ?\s& only ( ^? dis*>ges w be direct$ ne> 8 fri5d's head4 ,if we w make ! accid5t a matt] ( ,probability1 we ought by rights 9 ?is way 7to adopt ! language ( ! fir/ example71 to 'toss up aga9' fairly4 ,b we d n d ?is2 we seem to assume = c]ta9 t ! %ot goes )9 an in* ( our heads1 deta* t f ! notion ( *ance at all1 & !n beg9 to introduce ?is notion aga9 = possible deflections f t sav+ in*4 #ab4 7,,iv47 ,we w n[ notice a fallacy connect$ ) ! subjects ( bett+ & gambl+4 ,_m or mo/ ( ! popul> misappreh5sions on ?is subject imply su* utt] ignorance & confusion z to ! f\ndations ( ! sci5ce t x w\ld be ne$less to discuss !m "h4 ,! foll[+ h[ev] is ( a f> m plausible k9d1 & has be5 a s\rce ( p]plexity to p]sons ( consid]able acut5ess4 ,! case1 put into ! simple/ =m1 is z foll[s4#c ,suppose t a p]son ,a is play+ aga9/ ,b1 ,b be+ ei!r ano!r individual or a gr\p ( individuals1 say a gambl+ bank4 ,!y beg9 by toss+ = a %ill+1 & ,a ma9ta9s t he is 9 possession ( a device :i* w insure 8 w9n+4 ,if he does w9 on ! fir/ occasion he has cle>ly ga9$ 8 po9t s f>4 ,if he loses1 he /akes next "t two %ill+s in/ead ( "o4 ,! result ( c\rse is t if he w9s on ! second occasion he replaces 8 =m] loss1 & is left ) "o %ill+ pr(it z well4 ,s he goes on1 d\bl+ 8 /ake aft] e loss1 ) ! obvi\s result t on ! fir/ occasion ( success he makes good all 8 previ\s losses1 & is left ) a %ill+ ov]4 ,b su* an occasion mu/ come soon] or lat]1 by ! assumptions ( *ance on :i* ! game is f\nd$4 ,h5ce x foll[s t he c insure1 soon] or lat]1 be+ left a f9al w9n]4 ,moreov] he may w9 to any am\nt2 fir/ly f ! obvi\s consid]ation t he might make 8 initial /ake z l>ge z he pleas$1 a hundr$ p\nds1 = in/ance1 in/ead ( a %ill+2 & secondly1 because :at he has done once he may d aga94 ,he may put 8 %ill+ by1 & h a second spell ( play1 long or %ort z ! case may be1 ) ! same t]m9ation to x4 ,accord+ly by m]e p]si/5cy he may accumulate any sum ( money he pleases1 9 app>5t defiance ( all t is meant by luck4 #ac4 ,i h class$ ?is op9ion among fallacies1 z ! pres5t is ! mo/ conv5i5t opportunity ( discuss+ x1 ?\gh 9 /rictness x %\ld r be t]m$ a p>adox1 s9ce ! conclusion is p]fectly s\nd4 ,! only fallacy consi/s 9 reg>d+ su* a way ( obta9+ ! result z my/]i\s4 ,on ! contr>y1 !re is no?+ m easy ?an to insure ultimate success "u ! giv5 conditions4 ,! po9t is wor? enquiry1 f ! pr9ciples x involves1 & because ! answ]s commonly giv5 d n q meet ! difficulty4 ,x is sometimes urg$1 = in/ance1 t no bank w\ld or does all[ ! speculator to *oose at w ! am\nt ( 8 /ake1 b puts a limit to ! am\nt = :i* x w cons5t to play4 ,?is is q true1 b is ( c\rse no answ] to ! hypo!tical enquiry be=e u1 :i* assumes t su* a /ate ( ?+s is all[$4 ,aga91 x has be5 urg$ t ! possibility 9 "q turns entirely ^u ! fact t cr$it mu/ be suppos$ to be giv51 = o!rwise ! =tune ( ! play] may n hold out until 8 turn ( luck arrives3--t1 9 fact1 soon] or lat]1 if he goes on long en\gh1 8 =tune w n hold out long en\gh1 & all 8 ga9s w be swept away4 ,x is q true t cr$it is a condition ( success1 b x is 9 no s5se ! cause4 ,we may suppose bo? p>ties to agree at ! outset t !re %all be no paym5ts until ! game be end$1 ,a hav+ ! "r to decide :5 x %all be consid]$ to be end$4 ,x /ill rema9s true t :]eas 9 ord9>y gambl+1 i4e4 ) fix$ or haphaz>d /akes1 ,a c\ld n ensure w9n+ ev5tually to any ext5t1 he c d s if he adopt su* a s*eme z ! "o 9 "q4 ,& ?is is ! /ate ( ?+s :i* seems to call = explanation4 #ad4 ,:at causes p]plexity "h is ! suppos$ fact t 9 "s my/]i\s way c]ta9ty has be5 conjur$ out ( unc]ta9ty2 t 9 a game :]e ! detail$ ev5ts are utt]ly inscrutable1 & :]e ! av]age1 by supposition1 %[s no pref]5ce = ei!r side1 "o p>ty is nev]!less succe$+ someh[ 9 /eadily draw+ ! luck 8 own way4 ,x looks z if x 7 a p>allel case ) t ( a man :o %\ld succe$ by "s device 9 p]man5tly secur+ m ?an half ( ! tosses ) a p5ny :i* 0 nev]!less to be reg>d$ z a p]fectly fair "o4 ,?is is q a mi/ake4 ,! real fact is t ,a does n expose 8 ga9s to *ance at all2 all t he s exposes is ! numb] ( times he has to wait until he ga9s4 ,put su* a case z ?is4 ,i (f] to give a man any sum ( money he *ooses to m5tion provid$ he w at once give x back aga9 to me ) "o p\nd m4 ,x does n ne$ mu* acut5ess to see t x is a matt] ( indiff]5ce to me :e!r he *ooses to m5tion "o p\nd1 or t51 or a hundr$4 ,n[ suppose t in/ead ( leav+ x to 8 *oice :i* ( ^! sums is to be select$ ea* "t1 ! two p>ties agree to leave x to *ance4 ,let !m1 = in/ance1 draw a numb] out ( a bag ea* "t1 & let t be ! sum :i* ,a gives to ,b "u ! prescrib$ conditions4 ,! case is n alt]$4 ,a /ill ga9s 8 p\nd ea* "t1 = ! introduction ( ! elem5t ( *ance has n 9 any way t\*$ ?is4 ,all t x does is to make ?is p\nd ! result ( an unc]ta9 subtraction1 sometimes #aj m9us #i1 sometimes #ej m9us #di1 & s on4 ,x is ^! numb]s only1 n _! diff]5ce1 :i* he submits to luck1 & ?is is ( no consequ5ce :atev]4 ,to sugge/ to any individual or company t !y %\ld cons5t to g on play+ ^u su* t]ms z ^! w\ld be too b>efac$ a proposal4 ,& yet ! case 9 "q is id5tical 9 pr9ciple1 & almo/ id5tical 9 =m1 ) ?is4 ,to (f] to give a man any sum he likes to "n provid$ he gives y back aga9 t same sum plus "o1 & to (f] him any numb] ( t]ms he pleases ( ! s]ies #a1 #b1 #d1 #h1 #af1 c41 provid$ y h ! next t]m ( ! set1 are equival5t4 ,! only diff]5ce is t 9 ! latt] case ! result is atta9$ ) some:at m ( ari?metical p>ade4 ,simil>ly equival5t are ! processes 9 case we pref] to leave x to *ance1 in/ead ( to *oice1 to decide :at sum or :at numb] ( t]ms %all be fix$ ^u4 ,?is latt] is :at is really done 9 ! case 9 "q4 ,a man :o cons5ts to g on d\bl+ 8 /ake e "t he w9s1 is leav+ no?+ else to *ance ?an ! det]m9ation ( ! p>ticul> numb] ( t]ms ( su* a geometrical s]ies :i* %all be all[$ to pass be=e he /ops4 #ae4 ,x may be add$ t !re is no special virtue 9 ! p>ticul> s]ies 9 "q1 viz4 t 9 accordance ) :i* ! /ake is d\bl$ ea* "t4 ,all t is ne$$ is t ! la/ t]m ( ! s]ies %\ld m ?an balance all ! prec$+ ones4 ,any o!r s]ies :i* increas$ fa/] ?an ?is geometrical "o1 w\ld answ] ! purpose z well or bett]4 ,nor is x necess>y1 aga91 t ! game %\ld be an ev5 or 'fair' "o4 ,*ance1 be x rememb]$1 affects no?+ "h b ! numb] ( t]ms to :i* ! s]ies atta9s on ea* occasion1 its f9al result be+ always ari?metically fix$4 ,:5 a p5ny is toss$ up x is only on "o ( e two occasions t ! s]ies runs to m ?an two t]ms1 & s 8 fix$ ga9s come 9 pretty regul>ly4 ,b unless he 0 play+ = a limit$ "t only1 x w\ld n affect him if ! s]ies ran to two hundr$ t]ms2 x w\ld m]ely take him some:at long] to w9 8 /akes4 ,a man might safely1 = in/ance1 cont9ue to lay an ev5 bet t he w\ld get ! s+le prize 9 a lott]y ( a ?\s& tickets1 provid$ he ?us d\bl$1 or m ?an d\bl$1 8 /ake ea* "t1 & unlimit$ cr$it 0 giv54 #af4 ,s reg>d$1 ! problem is simple en\gh1 b !re are two po9ts 9 x to :i* att5tion may conv5i5tly be direct$4 ,9 ! fir/ place1 x s]ves v po9t$ly to rem9d u ( ! di/9ction betwe5 a s]ies ( ev5ts 79 ?is case ! tosses ( ! p5ny7 :i* really are subjects ( *ance1 & our conduct f\nd$ ^u ^! ev5ts1 :i* may or may n be s subject4#d ,x is q possible t ?is latt] may be s contriv$ z to be 9 _m respects a matt] ( absolute c]ta9ty1--a consid]ation1 ,i presume1 famili> en\gh to pr(essional bett+ m54 ,:y is ! ord9>y way ( bett+ on ! ?r[s ( a p5ny fair to bo? p>ties8 ,because a 'fair' s]ies is 'fairly' treat$4 ,! heads & tails occur at r&om1 b on an av]age equally (t51 & ! /akes are ei!r fix$ or also arrang$ at r&om4 ,if a man backs heads e "t = ! same am\nt1 he w ( c\rse 9 ! long run nei!r w9 nor lose4 ,nei!r w he if he v>ies ! /ake e "t1 provid$ he does n v>y x 9 su* a way z to make its am\nt dep5d5t on ! fact ( 8 hav+ won or lo/ ! "t be=e4 ,b he may1 if he pleases1 & ! o!r p>ty cons5ts1 s arrange 8 /akes 7z 9 ! case 9 "q7 t ,*ance1 if "o might s express x1 does n get a fair *ance4 ,"h ! human elem5ts ( *oice & design h be5 s br\ght to be> ^u a s]ies ( ev5ts :i*1 reg>d$ by !mselves1 exhibit no?+ b ! physical *>act]i/ics ( *ance1 t ! latt] elem5ts disappe>1 & we get a result :i* is ari?metically c]ta94 ,o!r analog\s in/ances might be sugge/$1 b ! "o be=e u has ! m]it ( mo/ +5i\sly disguis+ ! actual process4 #ag4 ,! mean+ ( ! rem>k j made w be bett] se5 by a comp>ison ) ! foll[+ case4 ,x has be5 attempt$#e to expla9 ! prepond]ance ( male bir?s ov] female by assum+ t ! *ances ( ! two are equal1 b t ! g5]al desire to h a male heir t5ds to induce _m unions to p]si/ until ! occurr5ce ( ?is ev5t1 & no long]4 ,x is suppos$ t 9 ?is way !re w\ld be a slight prepond]ance ( families :i* consi/$ ( "o son only1 or ( two sons & "o daught]1 & s =?4 ,?is is q fallaci\s 7z _h be5 notic$ by ,laplace1 9 8 ,essai72 & !re c\ld n be a bett] in/ance *os5 ?an ?is to %[ j :at we c d & :at we _c d 9 ! way ( alt]+ ! luck 9 a real *ance-succession ( ev5ts4 ,to suppose t ! numb] ( actual bir?s c\ld be influ5c$ 9 ! way 9 "q is exactly ! same ?+ z to suppose t a numb] ( gambl]s c\ld increase ! ratio ( heads to tails1 to some?+ ov] "o-half1 by ea* h&+ ! co9 to 8 neighb\r z soon z he _h ?r[n a head3 t !y h only to leave (f z soon z head has appe>$2 an absurdity :i* we ne$ n pause to expla9 at ?is /age4 ,! ess5tial po9t ab\t ! ',m>t+ale' is t1 :]eas ! occurr5ce ( ! ev5ts on :i* ! /akes are laid is unaffect$1 ! /akes !mselves c be s adju/$ z to make ! luck sw+ "o way4 #ah4 ,9 ! second place1 ?is example br+s be=e u :at has _h to be s (t5 m5tion$ already1 namely1 t ! s]ies ( ,probability are 9 /rictness suppos$ to be int]m9able4 ,if !re=e we all[ ei!r p>ty to call ^u u to /op1 especially at a po9t :i* j happ5s to suit him1 we may get results decid$ly oppos$ to ! integrity ( ! !ory4 ,9 ! case be=e u x is a necess>y /ipulation = ,a t he may be all[$ to leave (f :5 he wi%es1 t is at "o ( ! po9ts at :i* ! ?r[ is 9 8 fav\r4 ,)\t ?is /ipulation he may be left a los] to any am\nt4 ,introduce ! supposition t "o p>ty may arbitr>ily call = a /oppage :5 x suits him & refuse to p]mit x soon]1 & almo/ any sy/em ( :at w\ld be o!rwise fair play may be conv]t$ into a v "o-sid$ arrangem5t4 ,inde$1 9 ! case 9 "q1 ,a ne$ n adopt ?is device ( d\bl+ ! /akes e "t he loses4 ,he may play ) a fix$ /ake1 & nev]!less insure t "o p>ty %all w9 any assign$ sum1 assum+ t ! game is ev5 & t he is p]mitt$ to play on cr$it4 #ai4 7,v47 ,a common mi/ake is to assume t a v unlikely ?+ w n happ5 at all4 ,x is a mi/ake :i*1 :5 ?us /at$ 9 words1 is too obvi\s to be committ$1 = ! mean+ ( an unlikely ?+ is "o t happ5s at r>e int]vals2 if x 7 n assum$ t ! ev5t w\ld happ5 sometimes x w\ld n be call$ unlikely1 b impossible4 ,?is is an error :i* c\ld sc>cely occur except 9 vague popul> misappreh5sion1 & is s abundantly refut$ 9 works on ,probability1 t x ne$ only be t\*$ ^u briefly "h4 ,x foll[s ( c\rse1 f our def9ition ( ,probability1 t to speak ( a v r>e comb9ation ( ev5ts z "o t is 'sure nev] to happ51' is to use language incorrectly4 ,su* a phrase may pass curr5t z a loose popul> exagg]ation1 b 9 /rictness x involves a contradiction4 ,! tru? ab\t su* r>e ev5ts _c be bett] describ$ ?an 9 ! foll[+ quotation f ,de ,morgan3#f-- ,x is said t no p]son ev] does arrive at su* extremely improbable cases z ! "o j cit$ draw+ ! same ball five times runn+ out ( a bag conta9+ tw5ty balls4 ,t a giv5 individual %\ld nev] ?r[ an ace twelve times runn+ on a s+le die1 is by f> ! mo/ likely2 inde$1 s remote are ! *ances ( su* an ev5t 9 any twelve trials 7m ?an #b1jjj1jjj1jjj to #a aga9/ x7 t x is unlikely ! exp]i5ce ( any giv5 c\ntry1 9 any giv5 c5tury1 %\ld furni% x4 ,b let u /op = a mom5t1 & ask ourselves to :at ?is argum5t applies4 ,a p]son :o r>ely t\*es dice w h>dly believe t d\blets sometimes occur ?ree times runn+2 "o :o h&les !m frequ5tly kn[s t su* is sometimes ! fact4 ,e v practis$ us] ( ^? implem5ts has se5 /ill r>] sequ5ces4 ,n[ suppose t a society ( p]sons _h ?r[n ! dice s (t5 z to secure a run ( six aces obs]v$ & record$1 ! prec$+ argum5t w\ld /ill be us$ aga9/ twelve4 ,& if ano!r society _h practis$ long en\gh to see twelve aces foll[+ ea* o!r1 !y might /ill employ ! same me?od ( d\bt+ z to a run ( tw5ty-f\r2 & s on1 ad inf9itum4 ,! p[] ( imag9+ cases :i* conta9 long comb9ations s mu* exce$s t ( exhibit+ & arrang+ !m1 t x is easy to assign a telegraph :i* %\ld make a sep>ate signal = e gra9 ( s& 9 a globe z l>ge z ! visible univ]se1 ^u ! hypo!sis ( ! mo/ space-p5etrat+ a/ronom]4 ,! fallacy ( ! prec$+ objection lies 9 suppos+ ev5ts 9 numb] beyond our exp]i5ce1 compos$ entirely ( sequ5ces su* z fall )9 our exp]i5ce4 ,x makes ! pa/ necess>ily conta9 ! :ole1 z to ! quality ( its compon5ts2 & judges by samples4 ,n[ ! lea/ cauti\s buy] ( gra9 requires to exam9e a h&ful be=e he judges ( a bu%el1 & a bu%el be=e he judges ( a load4 ,b relatively to su* enorm\s numb]s ( comb9ations z are frequ5tly propos$1 our exp]i5ce does n des]ve ! title ( a h&ful z comp>$ ) a bu%el1 or ev5 ( a s+le gra94 #bj4 ,! orig9 ( ?is invet]ate mi/ake is n difficult to be acc\nt$ =4 ,x arises1 no d\bt1 f ! exig5cies ( our practical life4 ,no man c be> 9 m9d e cont+5cy to :i* he may be expos$4 ,if !re=e we are ev] to d any?+ at all 9 ! _w1 a l>ge numb] ( ! r>] cont+5cies mu/ be left entirely out ( acc\nt4 ,& ! necessity ( ?is oblivion is /r5g!n$ by ! %ortness ( our life4 ,ma!matically speak+1 x w\ld be said to be c]ta9 t any "o :o lives long en\gh w be bitt5 by a mad dog1 = ! ev5t is n an impossible1 b only an improbable "o1 & mu/ !re=e come to pass 9 "t4 ,b ?is & an indef9ite numb] ( o!r disagreeable cont+5cies h on mo/ occasions to be entirely ignor$ 9 practice1 & !nce !y come almo/ necess>ily to drop equally out ( our ?\ght & expectation4 ,& :5 ! ev5t is "o 9 itself ( no importance1 l a r>e ?r[ ( ! dice1 a great ef=t ( imag9ation may be requir$1 on ! "p ( p]sons n accu/om$ to ab/ract ma!matical calculation1 to enable !m to realize ! ?r[ z be+ ev5 possible4 ,attempts h sometimes be5 made to e/imate :at extremity ( unlikelihood ought to be consid]$ z equival5t to ?is practical z]o po9t ( belief4 ,9 s f> z su* attempts are c>ri$ out by logicians1 or by ^? :o are unwill+ to resort to ma!matical valuation ( *ances1 !y mu/ be reg>d$ z m]ely a special =m ( ! modal difficulties discuss$ 9 ! la/ *apt]1 & ne$ n !re=e be reconsid]$ "h2 b a ^w or two may be add$ conc]n+ ! views ( "s :o h look$ at ! matt] f ! ma!matician's po9t ( view4 ,! pr9cipal ( ^! is p]haps ,buffon4 ,he has arriv$ at ! e/imate 7,ari?mtique ,morale ,,viii47 t ?is practical z]o is equival5t to a *ance ( #a_/aj1jjj4 ,! gr\nds = select+ ?is fraction are f\nd 9 ! fact t1 accord+ to ! tables ( mortality accessible to him1 x repres5ts ! *ance ( a man ( #ef dy+ 9 ! c\rse ( ! next day4 ,b s9ce no man "u common circum/ances takes ! *ance into ! slighte/ consid]ation1 x foll[s t x is practically e/imat$ z hav+ no value4 ,x is obvi\s t ?is result is almo/ entirely arbitr>y1 & 9 fact 8 reasons _c be reg>d$ z any?+ m ?an a sl5d] ju/ification f exp]i5ce = adopt+ a conv5i5tly simple fraction2 a ju/ification h[ev] :i* w\ld app>5tly h be5 equally available 9 ! case ( any o!r fractions ly+ )9 wide limits ( ! "o select$4#g #ba4 ,!re is "o p>ticul> =m ( ?is error1 :i*1 f ! importance occasionally atta*$ to x1 des]ves p]haps m special exam9ation4 ,z /at$ above1 !re c be no d\bt t1 h[ev] unlikely an ev5t may be1 if we 7loosely speak+7 v>y ! circum/ances suffici5tly1 or if1 9 o!r words1 we keep on try+ long en\gh1 we %all meet ) su* an ev5t at la/4 ,if we toss up a pair ( dice a few times we %all get d\blets2 if we try long] ) ?ree we %all get triplets1 & s on4 ,h[ev] unusual ! ev5t may be1 ev5 7 x sixes a ?\s& times runn+1 x w come "s "t or o!r if we h only pati5ce & vitality en\gh4 ,n[ apply ?is result to ! lett]s ( ! alphabet4 ,suppose t "o lett] at a "t is drawn f a bag :i* conta9s !m all1 & is !n replac$4 ,if ! lett]s 7 writt5 d[n "o aft] ano!r z !y occurr$1 x w\ld commonly be expect$ t !y w\ld be f\nd to make m]e nons5se1 & w\ld nev] arrange !mselves into ! words ( any language kn[n to m54 ,no m !y w\ld 9 g5]al1 b x is a commonly accept$ result ( ! !ory1 & "o :i* we may assume ! read] to be ready to admit )\t fur!r discussion1 t1 if ! process 7 cont9u$ long en\gh1 words mak+ s5se w\ld appe>2 nay m1 t any book we *ose to m5tion1--,milton's ,p>adise ,lo/ or ! plays ( ,%akespe>e1 = example1--w\ld be produc$ 9 ?is way at la/4 ,x w\ld take m days ?an we h space 9 ?is volume to repres5t 9 figures1 to make tol]ably c]ta9 ( obta9+ ! =m] ( ^! works by ?us draw+ lett]s out ( a bag1 b ! desir$ result w\ld be obta9$ at l5g?4#h ,n[ _m p h n unnaturally ?\ght x d]ogatory to g5ius to sugge/ t its productions c\ld h also be5 obta9$ by *ance1 :il/ o!rs h gone on to argue1 ,if ?is be ! case1 might n ! _w itself 9 ?is mann] h be5 produc$ by *ance8 #bb4 ,we w beg9 ) ! comp>atively simple1 det]m9ate1 & intelligible problem ( ! possible production ( ! works ( a great human g5ius by *ance4 ,) reg>d to ?is possibility1 x may be a consolation to "s timid m9ds to be rem9d$ t ! p[] ( produc+ ! works ( a ,%akespe>e1 9 "t1 is n conf9$ to consummate g5ius & to m]e *ance4 ,!re is a ?ird alt]native1 viz4 t ( purely me*anical proc$ure4 ,any "o1 d[n almo/ to an idiot1 might d x1 if he took suffici5t "t ab\t ! task4 ,= suppose t ! requir$ numb] ( lett]s 7 procur$ & arrang$1 n by *ance1 b design$ly1 & accord+ to rules sugge/$ by ! !ory ( p]mutations3 ! lett]s ( ! alphabet & ! numb] ( !m to be employ$ be+ f9ite1 e ord] 9 :i* !y c\ld occur w\ld come 9 its due turn1 & !re=e e ?+ :i* c be express$ 9 language w\ld be arriv$ at "s "t or o!r4 ,!re is really no?+ t ne$ %ock any "o 9 su* a result4 ,its possibility arises f ! foll[+ cause4 ,! numb] ( lett]s1 & !re=e ( words1 at our disposal is limit$2 :atev] !re=e we may desire to express 9 language necess>ily becomes subject to correspond+ limitation4 ,! possible v>iations ( ?\ght are lit]ally inf9ite1 s are ^? ( spok5 language 7by intonation ( ! voice1 c472 b :5 we come to words !re is a limitation1 ! nature ( :i* is di/9ctly conceivable by ! m9d1 ?\gh ! re/riction is "o t 9 practice w nev] be appreciable1 ow+ to ! fact t ! numb] ( comb9ations :i* may be produc$ is s enorm\s z to surpass all p[] ( ! imag9ation to realize4#i ,! answ] !re=e is pla91 & x is "o t w apply to _m o!r cases z well1 t to put a f9ite limit ^u ! numb] ( ways 9 :i* a ?+ c be done1 is to det]m9e t any "o :o is able & will+ to try long en\gh %all succe$ 9 do+ x4 ,if a great g5ius condesc5ds to p]=m x "u ^! circum/ances1 he mu/ submit to ! possibility ( hav+ 8 claims rivall$ or disput$ by ! *ance-man & idiot4 ,if ,%akespe>e 7 limit$ to ! use ( eight or n9e assign$ words1 ! "t )9 :i* ! latt] ag5ts might claim equality ) him w\ld n be v great4 ,z x is1 hav+ _h ! range ( ! ,engli% language at 8 disposal1 8 reputation is n 9 dang] ( be+ assail$ by any su* me?ods4 #bc4 ,! case ( ! possible production ( ! _w by *ance leads u into an altoge!r diff]5t region ( discussion4 ,we are n "h deal+ ) figures ! nature & use ( :i* are )9 ! fair p[]s ( ! und]/&+1 h[ev] ! imag9ation may break d[n 9 attempt+ to realize ! smalle/ fraction ( _! full significance4 ,! und]/&+ itself is w&]+ out ( its prop] prov9ce1 = ! conditions ( ! problem _c be assign$4 ,:5 we draw lett]s out ( a bag we "k v well :at we are do+2 b :at is really meant by produc+ a _w by *ance8 ,by analogy ( ! =m] case1 we may assume t "s k9d ( ag5t is presuppos$2--p]haps !re=e ! foll[+ supposition is less absurd ?an any o!r4 ,imag9e "s be+1 n a ,creator b a sort ( ,demiurgus1 :o has _h a quantity ( mat]ials put into 8 h&s1 & he assigns !m _! collocations & _! laws ( action1 bl9dly & at haphaz>d3 :at are ! odds t su* a _w z we actually exp]i5ce %\ld h be5 br\ght ab\t 9 ?is way8 ,if x 7 wor? :ile s]i\sly to set ab\t answ]+ su* a "q1 & if "s "o w\ld furni% u ) ! numb] ( ! lett]s ( su* an alphabet1 & ! l5g? ( ! "w to be writt5 ) !m1 we c\ld proce$ to indicate ! result4 ,b s mu* z ?is may surely be affirm$ ab\t x2--t1 f> f m]ely f9d+ ! l5g? ( ?is small volume insuffici5t = conta9+ ! figures 9 :i* ! adv]se odds w\ld be giv51 all ! pap] :i* ! _w has hi!rto produc$ w\ld be us$ up be=e we _h got f> on our way 9 writ+ !m d[n4 #bd4 ,! mo/ s$uctive =m 9 :i* ! difficulty ab\t ! occurr5ce ( v r>e ev5ts g5]ally pres5ts itself is probably ?is4 ',y admit 7"s p]sons w be dispos$ to say7 t su* an ev5t may sometimes happ52 nay1 t x does sometimes happ5 9 ! inf9ite c\rse ( "t4 ,h[ !n am ,i to "k t ?is occasion is n "o ( ^! possible occurr5ces8' ,to ?is1 "o answ] only c be giv51--! same :i* mu/ always be giv5 :]e /ati/ics & probability are conc]n$1--',! pres5t may be su* an occasion1 b x is inconceivably unlikely t x %\ld be "o4 ,among/ c\ntless billions ( times 9 :i* y1 & su* z y1 urge ?is1 "o p]son only w be ju/ifi$2 & x is n likely t y are t "o1 or t ?is is t occasion4' #be4 ,!re is ano!r =m ( ?is practical inability to di/+ui% betwe5 "o high numb] & ano!r 9 ! e/imation ( *ances1 :i* des]ves pass+ notice f its importance 9 argum5ts ab\t h]$ity4 ,p w (t5 urge an objection to ! doctr9e t qualities1 m5tal & bodily1 are transmitt$ f ! p>5ts to ! (fspr+1 on ! gr\nd t !re are a multitude ( in/ances to ! contr>y1 9 fact a great majority ( su* in/ances4 ,to raise ?is objection implies an utt] want ( appreciation ( ! v great odds :i* possibly may exi/1 & :i* ! argum5t 9 support ( h]$ity implies d exi/ aga9/ any giv5 p]son be+ di/+ui%$ = intellectual or o!r em95ce4 ,?is is d\btless p>tly a matt] ( def9ition1 dep5d+ ^u ! degree ( r>ity :i* we consid] to be impli$ by em95ce2 b tak+ any reasonable s5se ( ! t]m1 we %all readily see t a v great proportion ( failures may /ill leave an enorm\s prepond]ance ( evid5ce 9 fav\r ( ! h]$ity doctr9e4 ,take1 = in/ance1 t degree ( em95ce :i* is impli$ by be+ "o ( f\r ?\s&4 ,?is is a consid]able di/9ction1 ?\gh1 s9ce !re are ab\t two ?\s& su* p]sons to be f\nd among/ ! total adult male population ( ,great ,brita91 x is f> f imply+ any conspicu\s g5ius4 ,n[ suppose t 9 exam9+ ! cases ( a l>ge numb] ( ! *ildr5 ( su* p]sons1 we _h f\nd t #aii out ( #bjj ( !m fail$ to rea* ! same di/9ction4 ,_m p]sons w\ld conclude t ?is 0 pretty conclusive evid5ce aga9/ any h]$it>y transmission4 ,to be able to adduce only "o fav\rable1 z aga9/ #aii ho/ile in/ances1 w\ld to !m repres5t ! entire break-d[n ( any su* !ory4 ,! error1 ( c\rse1 is obvi\s en\gh1 & "o :i*1 ) ! figures ?us be=e him1 h>dly any "o c\ld fail to avoid4 ,b if "o may judge f common conv]sation & o!r su* s\rces ( in=mation1 x is f\nd 9 practice exce$+ly difficult adequately to reta9 ! conviction t ev5 ?\gh only "o 9 #bjj in/ances 7 fav\rable1 ?is w\ld repres5t odds ( ab\t #bj to #a 9 fav\r ( ! !ory4 ,if h]$it>y transmission did n prevail1 only "o 9 #djjj sons w\ld ?us rival _! fa!rs2 b we f9d actually1 let u say 7we are ( c\rse tak+ imag9>y proportions "h71 t "o 9 #bjj does4 ,h5ce1 if ! /ati/ics are l>ge en\gh to be satisfactory1 !re has be5 "s influ5ce at "w :i* has improv$ ! *ances ( m]e co9cid5ce 9 ! ratio ( #bj to #a4 ,we are 9 fact s little able to realise ! mean+ ( v l>ge numb]s1--t is1 to reta9 ! ratios 9 ! m9d1 :]e l>ge numb]s are conc]n$1--t unless we repeat$ly *eck ourselves by ari?metical consid]ations we are too apt to treat & e/imate all beyond c]ta9 limits z equally va/ & vague4 #bf4 7,,vi47 ,9 discuss+ ! nature ( ! connexion betwe5 ,probability & ,induction1 we exam9$ ! claims ( a rule commonly giv5 = inf]r+ ! probability t an ev5t :i* _h be5 repeat$ly obs]v$ w\ld recur aga94 ,i endeav\r$ to %[ t all attempts to obta9 & prove su* a rule 7 necess>ily futile2 if ^! reasons 7 conclusive ! employm5t ( su* a rule mu/ ( c\rse be reg>d$ z fallaci\s4 ,a few examples may conv5i5tly be add$ "h1 t5d+ to %[ h[ in/ead ( !re be+ m]ely a s+le rule ( succession we might bett] divide ! possible =ms into ?ree classes4 7#a7 ,9 "s cases :5 a ?+ has be5 obs]v$ to happ5 sev]al times x becomes 9 consequ5ce m likely t ! ?+ %\ld happ5 aga94 ,?is agrees ) ! ord9>y =m ( ! rule1 & is probably ! case ( mo/ frequ5t occurr5ce4 ,! necess>y vagu5ess ( expression :5 we talk ( ! 'happ5+ ( a ?+' makes x q impossible to tol]ate ! rule 9 ?is g5]al =m1 b if we specialize x a little we %all f9d x assume a m famili> %ape4 ,if1 = example1 we h obs]v$ two or m prop]ties to be frequ5tly associat$ toge!r 9 a succession ( individuals1 we %all conclude ) "s =ce t !y w be f\nd to be s connect$ 9 future4 ,! /r5g? ( our conviction h[ev] w dep5d n m]ely on ! numb] ( obs]v$ co9cid5ces1 b on f> m complicat$ consid]ations2 = a discussion ( :i* ! read] mu/ be ref]r$ to regul> treatises on ,inductive evid5ce4 ,or aga91 if we h obs]v$ "o ( two ev5ts succe$ ! o!r sev]al times1 ! occurr5ce ( ! =m] w excite 9 mo/ cases "s degree ( expectation ( ! latt]4 ,z be=e1 h[ev]1 ! degree ( our expectation is n to be assign$ by any simple =mula2 x w dep5d 9 "p ^u ! suppos$ intimacy ) :i* ! ev5ts are connect$4 ,to attempt to lay d[n def9ite rules ^u ! subject w\ld lead to a discussion ^u laws ( causation1 & ! circum/ances "u :i* _! exi/5ce may be inf]r$1 & !re=e any fur!r consid]ation ( ! matt] mu/ be ab&on$ "h4 #bg4 7#b7 ,or1 secondly1 ! pa/ recurr5ce may 9 itself give no valid gr\nds = inf]5ce ab\t ! future2 ?is is ! case :i* mo/ prop]ly belongs to ,probability4#aj ,t x does s belong w be easily se5 if we be> 9 m9d ! fundam5tal conception ( ! sci5ce4 ,we are !re introduc$ to a s]ies1--= purposes ( inf]5ce an indef9itely ext5d$ s]ies1--( t]ms1 ab\t ! details ( :i*1 in=mation1 except on c]ta9 po9ts1 is n giv52 our k be+ conf9$ to ! /ati/ical fact1 t1 say1 "o 9 t5 ( !m has "s attribute :i* we w call ,x4 ,suppose n[ t five ( ^! t]ms 9 succession h be5 ,x1 :at h9t does ?is give ab\t ! six? be+ also an ,x8 ,cle>ly none at all2 ?is pa/ fact tells u no?+2 ! =mula = our inf]5ce is /ill precisely :at x 0 be=e1 t "o 9 t5 be+ ,x x is "o to n9e t ! next t]m is ,x4 ,& h[ev] _m t]ms 9 succession _h be5 ( "o k9d1 precisely ! same =mula w\ld /ill be giv54 #bh4 ,! way 9 :i* ev5ts w ju/ify ! answ] giv5 by ?is =mula is (t5 misund]/ood4 ,= ! b5efit !re=e ( ^? unacqua9t$ ) "s ( ! conceptions famili> to ma!maticians1 a few words ( explanation may be add$4 ,suppose !n t we h _h ,x twelve times 9 succession4 ,?is is cle>ly an anomal\s /ate ( ?+s4 ,to suppose any?+ l ?is cont9u+ to occur w\ld be obvi\sly 9 opposition to ! /ati/ics1 :i* ass]t t 9 ! long run only "o 9 t5 is ,x4 ,b h[ is ?is anomaly got ov]8 ,9 o!r words1 h[ d we obviate ! conclusion t ,x's mu/ occur m frequ5tly ?an once 9 t5 times1 aft] su* a long succession ( !m z we h n[ _h8 ,_m p seem to believe t !re mu/ be a dim9ution ( ,x's aft]w>ds to c\nt]balance _! pa/ prepond]ance4 ,?is h[ev] w\ld be q a mi/ake2 ! proportion 9 :i* !y occur 9 future mu/ rema9 ! same ?r\gh\t2 x _c be alt]$ if we are to adh]e to our /ati/ical =mula4 ,! fact is t ! rectification ( ! exceptional di/urbance 9 ! proportion w be br\ght ab\t simply by ! cont9ual influx ( fre% t]ms 9 ! s]ies4 ,^! w 9 ! long run neutralize ! di/urbance1 n by any special adaptation1 z x 71 = ! purpose1 b by ! m]e weight ( _! ov]:elm+ numb]s4 ,at e /age !re=e1 9 ! succession1 :atev] might h be5 ! numb] & nature ( ! prec$+ t]ms1 x w /ill be true to say t "o 9 t5 ( ! t]ms w be an ,x4 ,if we _h to d only ) a f9ite numb] ( t]ms1 h[ev] l>ge t numb] might be1 su* a di/urbance z we h spok5 ( w\ld1 x is true1 ne$ a special alt]ation 9 ! subsequ5t proportions to neutralize its effects4 ,b :5 we h to d ) an inf9ite numb] ( t]ms1 ?is is n ! case2 ! 'limit' ( ! s]ies1 :i* is :at we !n h to deal )1 is unaffect$ by ^! tempor>y di/urbances4 ,9 ! cont9u$ progress ( ! s]ies we %all f9d1 z a matt] ( fact1 m & m ( su* di/urbances1 & ^! ( a m & m exceptional "*4 ,b :atev] ! po9t we may occupy at any "t1 if we look =w>d or backw>d into ! indef9ite ext5sion ( ! s]ies1 we %all /ill see t ! ultimate limit to ! proportion 9 :i* its t]ms are arrang$ rema9s ! same2 & x is ) ?is limit1 z above m5tion$1 t we are conc]n$ 9 ! /rict rules ( ,probability4 ,! mo/ famili> example1 p]haps1 ( ?is k9d is t ( toss+ up a p5ny4 ,suppose we h _h f\r heads 9 succession2 p#aa h tol]ably realiz$ by n[ t 'head ! fif? "t' is /ill an ev5 *ance1 z 'head' 0 ea* "t be=e1 & w be ev] aft]4 ,! prec$+ p>agraph expla9s h[ x is t ^! occasional di/urbances 9 ! av]age become neutraliz$ 9 ! long run4 #bi4 7#c7 ,!re are o!r cases :i*1 ?\gh r>e1 are by no means unkn[n1 9 :i* su* an inf]5ce z t obta9$ f ! ,rule ( ,succession w\ld be ! direct rev]se ( ! tru?4 ,! (t5] a ?+ happ5s1 x may be1 ! m unlikely x is to happ5 aga94 ,?is is ! case :5ev] we are draw+ ?+s f a limit$ s\rce 7z balls f a bag )\t replac+ !m71 or :5ev] ! act ( repetition itself t5ds to prev5t ! succession 7z 9 giv+ false al>ms74 ,i am q ready to admit t we believe ! results describ$ 9 ! la/ two classes on ! /r5g? ( "s su* g5]al ,inductive rule1 or r pr9ciple1 z t involv$ 9 ! fir/4 ,b x w\ld be a great error to conf\nd ?is ) an admission ( ! validity ( ! rule 9 ea* special in/ance4 ,we are speak+ ab\t ! application ( ! rule to individual cases1 or classes ( cases2 ?is is q a di/9ct ?+1 z 0 po9t$ out 9 a previ\s *apt]1 f giv+ ! gr\nds on :i* we re/ ! rule itself4 ,if a man 7 to lay x d[n z a univ]sal rule1 t ! te/imony ( all p]sons 0 to be believ$1 & we adduc$ an in/ance ( a man hav+ li$1 x w\ld n be consid]$ t he sav$ 8 rule by %[+ t we believ$ t x 0 a lie on ! ^w ( o!r p]sons4 ,b x is p]fectly consi/5t to give z a m]ely g5]al1 b n univ]sal1 rule1 t ! te/imony ( m5 is cr$ible2 !n to sep>ate (f a second class ( m5 ^: ^w is n to be tru/$1 & f9ally1 if any "o wants to "k our gr\nd = ! second rule1 to re/ x ^u ! fir/4 ,if we 7 speak+ ( necess>y laws1 su* a conflict z ?is w\ld be z hopeless z ! old ',cretan' puzzle 9 logic2 b 9 in/ances ( ,inductive & ,analogical ext5sion x is p]fectly h>mless4 #cj4 ,a famili> example w s]ve to br+ out ! ?ree diff]5t possible conclusions m5tion$ above4 ,we h obs]v$ x ra9 on t5 successive days4 ,a & ,b conclude respectively = & aga9/ ra9 on ! elev5? day2 ,c ma9ta9s t ! pa/ ra9 af=ds no data :atev] = an op9ion4 ,:i* is "r8 ,we really _c det]m9e priori4 ,an appeal mu/ be made to direct obs]vation1 or means mu/ be f\nd = decid+ on indep5d5t gr\nds to :i* class we are to ref] ! in/ance4 ,if1 = example1 x 7 kn[n t e c\ntry produces its own ra91 we %\ld *oose ! ?ird rule1 = x w\ld be a case ( draw+ f a limit$ supply4 ,if aga9 we _h reasons to believe t ! ra9 = our c\ntry might be produc$ any:]e on ! globe1 we %\ld probably conclude t ! pa/ ra9fall ?rew no light :atev] on ! prospect ( a cont9uance ( wet wea!r1 & !re=e take ! second4 ,or if1 f9ally1 we knew t ra9 came 9 long spells or seasons1 z 9 ! tropics1 !n ! occurr5ce ( t5 wet days 9 succession w\ld make u believe t we _h ent]$ on "o ( ^! seasons1 & t !re=e ! next day w\ld probably resemble ! prec$+ t54 ,s9ce !n all ^! =ms ( su* an ,inductive rule are possible1 & we h (t5 no priori gr\nds = pref]r+ "o to ano!r1 x w\ld seem to be unreasonable to attempt to e/abli% any univ]sal =mula ( anticipation4 ,all t we c d is to asc]ta9 :at are ! circum/ances "u :i* "o or o!r ( ^! rules is1 z a matt] ( fact1 f\nd to be applicable1 & to make use ( x "u ^? circum/ances4 #ca4 7,,vii47 ,9 ! cases discuss$ 9 7,v47 ! almo/ inf9itely small *ances ) :i* we 7 conc]n$ 7 rightly neglect$ f all practical consid]ation1 h[ev] prop] x might be1 on speculative gr\nds1 to keep our m9ds op5 to _! actual exi/5ce4 ,b x has (t5 occurr$ to me t !re is a common error 9 neglect+ to take !m into acc\nt :5 !y may1 ?\gh individually small1 make up = _! m9ut5ess by _! numb]4 ,z ! ma!matician w\ld express x1 !y may occasionally be capable ( be+ integrat$ into a f9ite or ev5 consid]able magnitude4 ,= in/ance1 we may be confront$ ) a difficulty out ( :i* !re appe>s to be only "o appreciably possible mode ( escape4 ,! attempt is made to =ce u into accept+ ?is1 h[ev] great ! odds app>5tly are aga9/ x1 on ! gr\nd t improbable z x may seem1 x is at any rate va/ly m probable ?an any ( ! o!rs4 ,i c q admit t1 on practical gr\nds1 we may (t5 f9d x reasonable to adopt ?is c\rse2 = we c only act on "o supposition1 & we naturally & rightly *oose1 out ( a quantity ( improbabilities1 ! lea/ improbable4 ,b :5 we are n =c$ to act1 no su* decisive pref]5ce is dem&$ ( u4 ,x is !n p]fectly reasonable to refuse ass5t to ! propos$ explanation2 ev5 to say di/9ctly t we d n believe x1 & at ! same "t to decl9e1 at pres5t1 to accept any o!r explanation4 ,we rema91 9 fact1 9 a /ate ( susp5se ( judgm5t1 a /ate p]fectly "r & reasonable s long z no action dem&+ a specific *oice is =c$ ^u u4 ,"o alt]native may be decid$ly probable z comp>$ ) any o!r individually1 b decid$ly improbable z comp>$ ) all o!rs collectively4 ,?is 9 itself is intelligible en\gh2 :at p (t5 fail to see is t !re is no necess>y contradiction betwe5 say+ & feel+ ?is1 & yet be+ prep>$ vigor\sly to act1 :5 action is =c$ ^u u1 z ?\gh ?is alt]native 7 really ! true "o4 #cb4 ,to take a specific in/ance1 ?is way ( reg>d+ ! matt] has (t5 occurr$ to me 9 disputes ^u ',spirituali/' manife/ations4 ,ass5t is urg$ ^u u because1 x is said1 no o!r possible solution c be sugge/$4 ,x may be q true t app>5tly ov]:elm+ difficulties may lie z aga9/ ea* sep>ate alt]native solution2 b is x always suffici5tly realiz$ h[ num]\s su* solutions may be8 ,no matt] t ea* individually may be almo/ incr$ible3 !y ought all to be mass$ toge!r & ?r[n into ! scale aga9/ ! pr(f]$ solution1 :5 ! only "q ask$ is1 ,are we to accept ?is solution8 ,!re is no unfairness 9 su* a c\rse4 ,we are p]fectly ready to adopt ! same plan aga9/ any o!r individual alt]native1 :5ev] any p]son takes to claim+ ?is z ! solution ( ! difficulty4 ,we are look+ at ! matt] f a purely logical po9t ( view1 & are q will+1 s f>1 to place e solution1 spirituali/ or o!rwise1 ^u ! same foot+4 ,! p>tisans ( e alt]native are 9 some:at ! same position z ! memb]s ( a delib]ative assembly1 9 :i* no "o w support ! motion ( any o!r memb]4 ,e "o c aid effectively 9 reject+ e o!r motion1 b no "o c succe$ 9 pass+ 8 own4 ,pressure ( urg5t necessity may possibly =ce !m out ( ?is /ate ( practical inaction1 by1 s to say1 break+ ?r\gh ! opposition at "s po9t ( lea/ resi/ance2 b unless aid$ by "s su* pressure !y are left 9 a /ate ( hopeless dead-lock4 #cc4 ,assum+ t ! spirituali/ic solution admits (1 & is to receive1 sci5tific treatm5t1 ?is1 x seems to me1 is ! conclusion to :i* "o might sometimes be l$ 9 ! face ( ! evid5ce (f]$4 ,we might h to say to e individual explanation1 ,x is incr$ible1 ,i _c accept x2 & unless circum/ances %\ld 7:i* x is h>dly possible t !y %\ld7 =ce u to a ha/y decision1--a decision1 rememb]1 :i* ne$ indicate no pref]5ce ( ! judgm5t beyond :at is j suffici5t to turn ! scale 9 its fav\r z aga9/ any o!r s+le alt]native1--we leave ! matt] ?us 9 abeyance4 ,x w v likely be urg$ t "o ( ! explanations 7assum+ t all ! possible ones _h be5 includ$7 mu/ be true2 ?is we readily admit4 ,x w probably also be urg$ t 7on ! (t5-quot$ pr9ciple ( ,butl]7 we ought =?) to accept ! "o :i*1 z comp>$ ) ! o!rs1 is ! mo/ plausible1 :atev] its absolute wor? may be4 ,?is seems di/9ctly an error4 ,to say t su* & su* an explanation is ! "o we %\ld accept1 if circum/ances compell$ u to anticipate our decision1 is q compatible ) its pres5t rejection4 ,! only rational position surely is t ( admitt+ t ! tru? is some:]e among/ ! v>i\s alt]natives1 b confess+ pla9ly t we h no su* pref]5ce = "o ov] ano!r z to p]mit our say+ any?+ else ?an t we disbelieve ea* "o ( !m4 #cd4 7,,viii47 ,! v common fallacy ( 'judg+ by ! ev5t1' z x is g5]ally t]m$1 des]ves pass+ notice "h1 z x cle>ly belongs to ,probability r ?an to ,logic2 ?\gh its nature is s obvi\s to ^? :o h grasp$ ! g5]al pr9ciples ( our sci5ce1 t a v few words ( rem>k w suffice4 ,9 "o s5se e proposition mu/ cons5t to be judg$ by ! ev5t1 s9ce ?is is m]ely1 9 o!r words1 submitt+ x to ! te/ ( exp]i5ce4 ,b !re is ! wide/ diff]5ce betwe5 ! te/ appropriate to a univ]sal proposition & t appropriate to a m]ely proportional or /ati/ical "o4 ,! =m] is subv]t$ by a s+le exception2 ! latt] n m]ely admits exceptions1 b implies !m4 ,no?+1 h[ev]1 is m common ?an to blame advice 79 o!rs7 because x has happ5$ to turn out un=tunately1 or to claim cr$it = x 79 oneself7 because x has happ5$ to succe$4 ,( c\rse if ! conclusion 0 av[$ly "o ( a probable k9d we mu/ be prep>$ ) complac5cy to accept a ho/ile ev5t1 or ev5 a succession ( !m2 x is n until ! succession %[s a disposition to cont9ue ov] long t suspicion & d\bt %\ld arise1 & !n only by a comp>ison ( ! degree ( ! assign$ probability1 & ! magnitude ( ! dep>ture f x :i* exp]i5ce exhibits4 ,= any s+le failure ! reply mu/ be1 '! advice 0 s\nd' 7suppos+1 t is1 t x 0 to be ju/ifi$ 9 ! long run71 '& ,i %all (f] x aga9 "u ! same circum/ances4' #ce4 ,! di/9ction drawn 9 ! above in/ance des]ves c>eful consid]ation2 = ow+ to ! wide diff]5ce betwe5 ! k9d ( propositions dealt ) 9 ,probability & 9 ord9>y ,logic1 & ! consequ5t diff]5ce 9 ! nature ( ! pro( (f]$1 x is q possible = argum5ts ( ! same g5]al appe>ance to be valid 9 ! =m] & fallaci\s 9 ! latt]1 & conv]sely4 ,= in/ance1 take ! well-kn[n fallacy :i* consi/s 9 simply conv]t+ a univ]sal affirmative1 i4e4 9 pass+ f ,all ,a is ,b to ,all ,b is ,a4 ,:51 z 9 common ,logic1 ! conclusion is to be z c]ta9 z ! premise1 !re is n a ^w to be said = su* a /ep4 ,b if we look at ! process ) ! m indulg5t eye ( ,induction or ,probability we see t a v fair case may sometimes be made out = x4 ,! m]e fact t ',"s ,b is ,a' raises a c]ta9 presumption t any p>ticul> ,b tak5 at r&om w be an ,a4 ,!re is "s reason1 at any rate1 = ! belief1 ?\gh 9 ! abs5ce ( /ati/ics z to ! relative frequ5cy ( ,a & ,b we are unable to assign a value to ?is belief4 ,i suspect t !re may be _m cases 9 :i* a man has inf]r$ t "s p>ticul> ,b is an ,a on ! gr\nd t ,all ,a is ,b1 :o might ju/ly plead 9 8 behalf t he nev] meant x to be a necess>y1 b only a probable inf]5ce4 ,! same rem>ks w ( c\rse apply also to ! logical fallacy ( ,undi/ribut$ ,middle4 ,n[ = a case ( ! opposite k9d1 i4e4 "o 9 :i* ,probability fails u1 :]eas ! circum/ances seem closely analog\s to ^? 9 :i* ord9>y inf]5ce w\ld be able to make a /&4 ,suppose t ,i "k t "o lett] 9 a million is lo/ :5 9 *>ge ( ! po/4 ,i write to a fri5d & get no answ]4 ,h ,i any reason to suppose t ! fault lies ) him8 ,"h is an ev5t 7viz4 ! loss ( ! lett]7 :i* has c]ta9ly happ5$2 & we suppose t1 ( ! only two causes to :i* x c be assign$1 ! 'value1' i4e4 /ati/ical frequ5cy1 ( "o is accurately assign$1 does x n seem natural to suppose t some?+ c be inf]r$ z to ! likelihood t ! o!r cause _h be5 op]ative8 ,to say t no?+ c be kn[n ab\t its adequacy "u ^! circum/ances looks at fir/ sight l ass]t+ t an equation 9 :i* !re is only "o unkn[n t]m is !oretically insoluble4 ,z examples ( ?is k9d h be5 amply discuss$ 9 ! *apt] ^u ,inv]se rules ( ,probability ,i ne$ d no m "h ?an rem9d ! read] t no conclusion :atev] c be drawn z to ! likelihood t ! fault lay ) my fri5d r ?an ) ! ,po/ ,(fice4 ,unless we ei!r "k1 or make "s assumption ab\t1 ! frequ5cy ) :i* he neglects to answ] ! lett]s he receives1 ! problem rema9s insoluble4 ,! reason :y ! app>5t analogy1 indicat$ above1 to an equation ) only "o unkn[n quantity1 fails to hold good1 is t = ! purposes ( ,probability !re are really two unkn[n quantities4 ,:at we deal ) are proportional or /ati/ical propositions4 ,n[ we are only told t 9 ! in/ance 9 "q ! lett] 0 lo/1 n t !y 7 f\nd to be lo/ 9 su* & su* a proportion ( cases4 ,_h ?is latt] in=mation be5 giv5 to u we %\ld really h _h b "o unkn[n quantity to det]m9e1 viz4 ! relative frequ5cy ) :i* my correspond5t neglects to answ] 8 lett]s1 & we c\ld !n h det]m9$ ?is ) ! greate/ ease4 #a4 ,discuss$ by ,mr ,f4 ,y4 ,edgewor?1 9 ! ,phil4 ,mag4 = ,april1 #ahhg4 #b4 ,j\rnal ( ! ,/ati/ical ,soc4 7,vol4 ,,xlii4 p4 #cbh7 ,d>e "o suspect a joke8 #c4 ,x appe>s to h be5 long kn[n to gambl]s "u ! "n ( ! ,m>t+ale4 ,!re is a pap] by ,babbage 7,trans4 ( ,royal ,soc4 ( ,ed9burgh1 = #ahbc7 :i* discusses c]ta9 po9ts connect$ ) x1 b sc>cely t\*es on ! subject ( ! sections :i* foll[4 #d4 ,att5tion w be fur!r direct$ to ?is di/9ction 9 ! *apt] on ,insurance & ,gambl+4 #e4 ,z by ,prvo/ 9 ! ,biblio?que ,univ]selle de ,g5ve1 ,oct4 #ahbi4 ,! explanation is not$1 & app>5tly accept$1 by ,quetelet 7,physique ,sociale1 ,i4 #aga74 #f4 ,essay on ,probabilities1 p4 #abf4 #g4 ,?is !oretical or absolute neglect ( :at is v r>e mu/ n be confus$ ) ! practical neglect sometimes recomm5d$ by a/ronomical & o!r obs]v]s4 ,a crit]ion1 kn[n z ,*auv5et's1 = indicat+ ! limits ( su* rejection w be f\nd describ$ 9 ,mr ,m]riman's ,lea/ ,squ>es 7p4 #aff74 ,b ?is re/s on ! und]/&+ t a small] balance ( error w\ld ?us result 9 ! long run4 ,! v r>e ev5t is delib]ately reject$1 n ov]look$4 #h4 ,! process ( calculation may be readily indicat$4 ,!re are1 say1 ab\t #cej1jjj lett]s 9 ! "w 9 "q4 ,s9ce any ( ! #bf lett]s ( ! alphabet may be drawn ea* "t1 ! possible numb] ( comb9ations w\ld be #bfcej1jjj2 a numb] :i*1 z may easily be inf]r$ f a table ( log>i?ms1 w\ld dem& = its expression ne>ly #ejj1jjj figures4 ,only "o ( ^! comb9ations is fav\rable1 if we reject v>iations ( spell+4 ,h5ce unity divid$ by ?is numb] w\ld repres5t ! *ance ( gett+ ! desir$ result by successive r&om selection ( ! requir$ numb] ( #cej1jjj lett]s4 ,if ?is *ance is ?\ght too small1 & any "o asks h[ (t5 ! above r&om selection mu/ be repeat$ 9 ord] to give him odds ( #b to #a 9 fav\r ( success1 ?is also c be easily %[n4 ,if ! *ance ( an ev5t on ea* occasion is #a_/n1 ! *ance ( gett+ x once at lea/ 9 n trials is #a - 77n - #a7_/n7n2 = we %all d ?is unless we fail n times runn+4 ,:5 7z 9 ! case 9 "q7 n is v l>ge1 ?is may be %[n algebraically to be equival5t to odds ( ab\t #b to #a4 ,t is1 :5 we h drawn ! requisite quantity ( lett]s a numb] ( times equal to ! inconceivably great numb] above repres5t$1 x is /ill only #b to #a t we %all h secur$ :at we want3--& !n we h to recognize x4 #i4 ,! longe/ life :i* c\ld reasonably be attribut$ to any language w\ld ( c\rse dw9dle into utt] insignificance 9 ! face ( su* p]iods ( "t z are be+ "h ari?metically contemplat$4 #aj4 ,we are "h assum+ ( c\rse t ! ultimate limit to :i* our av]age t5ds is kn[n1 ei!r f k ( ! causes or f previ\s ext5sive exp]i5ce4 ,we are assum+ t e4g4 ! die is kn[n to be a fair "o2 if ?is is n kn[n b a possible bias has to be inf]r$ f its obs]v$ p]=mances1 ! case falls "u ! =m] head4 #aa4 ,except inde$ ! gambl]s4 ,accord+ to a gambl+ acqua9tance :om ,h\d91 ! conjur]1 describes himself z hav+ met at ,spa1 ! (t5] a p>ticul> comb9ation has occurr$ ! m c]ta9 x is t x w n be repeat$ at ! next c\p3 ?is is ! gr\ndwork ( all !ories ( probabilities & is t]m$ ! maturity ( *ances 7,c>d-%>p+ expos$1 p4 #he74 ,,*apt] ,,xv4 ,,insurance ,,& ,,gambl+4 #a4 ,if ! read] w recall to m9d ! fundam5tal po/ulate ( ! ,sci5ce ( ,probability1 e/abli%$ & expla9$ 9 ! fir/ few *apt]s1 & s abundantly illu/rat$ s9ce1 he w readily recognize t ! two opposite *>act]i/ics ( individual irregul>ity & av]age regul>ity w naturally be diff]5tly e/imat$ by diff]5t m9ds4 ,to "s p]sons ! elem5ts ( unc]ta9ty may be s pa9ful1 ei!r 9 !mselves or 9 _! consequ5ces1 t !y are anxi\s to adopt "s means ( dim9i%+ !m4 ,to o!rs ! ultimate regul>ity ( life1 at any rate )9 c]ta9 dep>tm5ts1 its monotony z !y consid] x1 may be s we>isome t !y equally wi% to effect "s alt]ation & improvem5t 9 its *>act]i/ics4 ,we %all discuss briefly ^! m5tal t5d5cies1 & ! mo/ simple & obvi\s modes ( satisfy+ !m4 ,to "s p]sons1 z we h said1 ! _w is all too full ( *ange & irregul>ity & consequ5t unc]ta9ty4 ,civilization has done mu* to dim9i% ^! *>act]i/ics 9 c]ta9 directions1 b x has unque/ionably aggravat$ !m 9 o!r directions1 & x might n be v easy to say ) c]ta9ty 9 :i* ( ^! respects its op]ation has be51 at pres5t1 on ! :ole mo/ effective4 ,! dim9ution ( irregul>ity is exemplifi$1 among/ o!r ?+s1 9 ! case ( ! /aple products :i* supply our necess>y food & clo?+4 ,) respect to !m1 fam9e & sc>city are by comp>ison almo/ unkn[n n[1 at any rate 9 tol]ably civiliz$ communities4 ,z a consequ5ce ( ?is1 & ( ! va/ improvem5ts 9 ! means ( transport+ goods & convey+ intellig5ce1 ! fluctuations 9 ! price ( su* articles are mu* less ?an !y once 74 ,9 o!r directions1 h[ev]1 ! rev]se has be5 ! case4 ,fa%ion1 = in/ance1 n[ induces s _m p 9 e l>ge community simultane\sly to desire ! same ?+1 t great fluctuations 9 value may ensue4 ,moreov] a :ole gr\p ( causes 7to ent] ^u any discussion ( :i* w\ld be to tr5* ^u ! gr\nd ( ,political ,economy7 comb9e to produce great & frequ5t v>iations 9 matt]s conc]n+ cr$it & ! curr5cy1 :i* =m]ly _h no exi/5ce4 ,bankruptcy1 = in/ance1 is f ! nature ( ! case1 almo/ :olly a creation ( mod]n times4 ,we w n attempt to /rike any balance betwe5 ^! opposite results ( mod]n civilization1 beyond rem>k+ t 9 matt]s ( prime importance ! actual unc]ta9ties h be5 probably on ! :ole dim9i%$1 :]eas 9 ^? :i* affect ! pocket r ?an ! life1 !y h be5 r increas$4 ,x might also be argu$ ) "s plausibility t 9 cases :]e ! actual unc]ta9ties h n become great]1 !y h = all practical purposes done s1 by _! consequ5ces frequ5tly becom+ m s]i\s1 or by our e/imate ( ^! consequ5ces becom+ high]4 #b4 ,h[ev] ! above "q1 z to ! ultimate balance ( ga9 or loss1 %\ld be decid$1 !re c be no d\bt t _m p]sons f9d ! pres5t am\nt ( unc]ta9ty 9 "s ( ! affairs ( life great] ?an suits _! ta/e4 ,h[ are !y to dim9i% x8 ,some?+ ( c\rse may be done1 z reg>ds ! individual cases1 by prud5ce & =esight4 ,our h\ses may be built ) a view n to take fire s readily1 or precautions may be tak5 t !re %all be fire-eng9es at h&4 ,9 ! w>d+ (f ( dea? f disease & accid5t1 some?+ may be done by e "o :o *ooses to live prud5tly4 ,precautions ( ! above k9d1 h[ev]1 d n introduce any que/ions ( ,probability4 ,^! latt] consid]ations only come 9 :5 we beg9 to invoke ! regul>ity ( ! av]age to save u f ! irregul>ities ( ! details4 ,we _c1 x is true1 remove ! unc]ta9ty 9 itself1 b we c s act t ! consequ5ces ( t unc]ta9ty %all be less to u1 or to ^? 9 :om we are int]e/$4 ,take ! case ( ,life ,insurance4 ,a pr(essional man :o has no?+ b ! income he e>ns to dep5d ^u1 kn[s t ! :ole ( t income may vani% 9 a mom5t by 8 dea?4 ,?is is a /ate ( ?+s :i* he _c prev5t2 & if he 7 ! only "o 9 su* a position1 or 7 unable or unwill+ to comb9e ) 8 fell[-m51 !re w\ld be no?+ m to be done 9 ! matt] except to live )9 8 income z mu* z possible1 & s leave a m>g9 ( sav+s4 #c4 ,!re is h[ev] an easy mode ( escape = him4 ,all t he has to d is to agree ) a numb] ( o!rs1 :o are 9 ! same position z himself1 to make up1 s to say1 a common purse4 ,!y may resolve t ^? ( _! numb] :o live to "w beyond ! av]age l5g? ( life %all contribute to support ! families ( ^? :o die e>li]4 ,if a few only concurr$ 9 su* a resolution !y w\ld n ga9 v mu*1 = !y w\ld /ill be remov$ by b a slight /ep f t unc]ta9ty :i* !y are seek+ to escape4 ,:at is ess5tial is t a consid]able numb] %\ld ?us comb9e s z to get ! b5efit ( t comp>ative regul>ity :i* ! av]age1 z is well kn[n1 almo/ always t5ds to exhibit4 #d4 ,! above simple consid]ations really conta9 ! ess5ce ( all insurance4 ,su* po9ts z ! fact t ! agreem5t = indemnity ext5ds only to a c]ta9 def9ite sum ( money2 & t in/ead ( call+ = an occasional g5]al contribution at ! "t ( ! dea? ( ea* memb] !y sub/itute a fix$ annual premium1 out ( ! proce$s ( :i* ! paym5t is to be made1 are m]ely accid5ts ( conv5i5ce & arrangem5t4 ,insurance is simply equival5t to a mutual contract among/ ^? :o dread ! consequ5ces ( ! unc]ta9ty ( _! life or employm5t1 t !y w employ ! aggregate regul>ity to neutralize z f> z possible ! individual irregul>ity4 ,!y "k t = e "o :o ga9s by su* a contract ano!r w lose z mu*2 or if "o ga9s a great deal _m mu/ h lo/ a little4 ,!y "k also t h>dly any ( _! numb] c expect to f9d ! arrangem5t a 'fair' "o1 9 ! s5se t !y j get back aga9 :at !y h paid 9 premiums1 aft] d$uct+ ! necess>y exp5ses ( managem5t2 b !y delib]ately pref] ?is /ate ( ?+s4 ,!y consi/ ( a body ( p]sons :o ?9k x decid$ly bett] to leave beh9d !m a comp>atively fix$ =tune1 r ?an "o :i* is extremely unc]ta9 9 am\nt2 al?\gh !y are p]fectly aw>e t1 ow+ to ! unavoidable exp5ses ( manag+ ! affairs ( su* a society1 ! comp>atively fix$ sum1 s to be left1 w be a trifle less ?an ! av]age =tunes :i* w\ld h be5 left _h no su* sy/em ( insurance be5 adopt$4 ,z ?is is n a regul> treatise ^u ,insurance no m ne$ be said ^u ! exact nature ( su* societies1 beyond po9t+ out t !y are ( v>i\s diff]5t k9ds4 ,sometimes !y really are :at we h comp>$ !m )1 viz4 mutual agreem5ts among/ a gr\p ( p]sons to make up ea* o!r's losses to a c]ta9 ext5t4 ,into ?is category fall ! ,mutual ,insurance ,societies1 ,b5efit ,societies1 ,trades ,unions 79 respect ( "s ( _! functions71 toge!r ) innum]able o!r societies :i* g by v>i\s names4 ,sometimes !y are companies work$ by proprietors or %>ehold]s = a pr(it1 l any o!r indu/rial ent]prise4 ,?is is ! case1 ,i believe1 ) ! majority ( ! ord9>y ,life ,insurance ,societies4 ,sometimes1 aga91 x is ! ,/ate :i* und]takes ! managem5t1 z 9 ! case ( our ,po/ ,(fice ,insurance bus9ess4 #e4 ,x is cle> t !re is no necess>y limit to ! range ( application ( ?is pr9ciple4#a ,x is q conceivable t ! majority ( ! inhabitants ( "s nation might be s enam\r$ ( security t !y %\ld devise a gr& insurance society to cov] almo/ e conc]n 9 life4 ,!y c\ld n inde$ aboli% unc]ta9ty1 = ! conditions ( life are v f> f p]mitt+ ?is1 b !y c\ld )\t mu* difficulty get rid ( ! wor/ ( ! consequ5ces ( x4 ,!y might det]m9e to insure n m]ely _! lives1 h\ses1 %ips1 & o!r ?+s 9 respect ( :i* sudd5 & total loss is possible1 b also to insure _! bus9ess2 9 ! s5se ( avoid+ n only bankruptcy1 b ev5 casual bad ye>s1 on ! same pr9ciple ( commutation4 ,unfamili> z su* an aim may appe> :5 introduc$ 9 ?is language1 x is nev]!less "o :i* "u a "n ( suspici\s import to ! cons]vative classes has _h a good deal ( att5tion direct$ to x4 ,x is really sc>cely any?+ else ?an ,communism1 :i* might inde$ be def9$ z a univ]sal & compulsory#b insurance society :i* is to take acc\nt ( all dep>tm5ts ( bus9ess1 &1 9 "s at lea/ ( its =ms1 to invade ! prov9ce ( social & dome/ic life z well4 ,al?\gh no?+ s compreh5sive z ?is is likely to be practically c>ri$ out on any v l>ge scale1 x des]ves notice t ! pr9ciple itself is /eadily spread+ 9 e direction 9 matt]s ( detail4 ,x is1 = in/ance1 ! great compla9t aga9/ ,trades ,unions t !y too (t5 seek to secure ^! results 9 respect ( ! equalization ( ! workm5's wages1 ?us insur+ to "s degree aga9/ incompet5ce1 z !y rightly & wisely d aga9/ illness & loss ( "w4 ,aga91 !re is ! ,tradesman's ,mutual ,protection ,society1 :i* insures aga9/ ! occasional loss entail$ by ! necessity ( hav+ to conduct prosecutions at law4 ,!re are societies 9 _m t[ns = ! prosecution ( petty !fts1 ) ! object ( escap+ ! same unc]ta9 & p]haps s]i\s loss4 ,among/ in/ances ( insurance = ! p r ?an by !m1 !re is ( c\rse ! giant example ( ! ,engli% ,poor ,law1 9 :i* ! resemblance to an initial ,communi/ic sy/em becomes v m>k$4 ,! poor are insur$ aga9/ loss ( "w aris+ n only f illness & old age1 b f any cause except wilful idl5ess4 ,!y d n1 x is true1 pay ! :ole premium1 b s9ce !y mo/ly be> "s portion ( ! burd5 ( municipal & c\nty taxation !y mu/ c]ta9ly be consid]$ z pay+ a "p ( ! premium4 ,9 "s bran*es also ( ! public & private s]vices ! sy/em is adopt$ ( d$uct+ a p]c5tage f ! wage or sal>y1 = ! purpose ( a semi-compulsory insurance aga9/ dea?1 illness or sup]annuation4 #f4 ,closely connect$ ) ,insurance1 z an application ( ,probability1 ?\gh ( c\rse by contra/1 /&s ,gambl+4 ,?\gh we _c1 9 /rictness1 t]m ei!r ( ^! practices ! conv]se ( ! o!r1 x seems nev]!less correct to say t !y spr+ f opposite m5tal t5d5cies4 ,"s p]sons1 z has be5 said1 f9d life too monoton\s = _! ta/e1 or r ! region ( :at c be pr$ict$ ) c]ta9ty is too l>ge & pr$om9ant 9 _! e/imation4 ,!y c easily adopt two c\rses = secur+ ! *anges !y desire4 ,!y may1 = "o ?+1 aggravate & int5sify ! results ( ev5ts :i* are comp>atively incapable ( prevision1 ^! ev5ts n be+ 9 !mselves ( suffici5t importance to excite any /rong emotions4 ,! mo/ obvi\s way ( do+ ?is is by bett+ ^u !m4 ,or aga91 !y may inv5t games or o!r pursuits1 ! individual cont+5cies ( :i* are entirely remov$ f all possible human prevision1 & !n make heavy money consequ5ces dep5d ^u ^! cont+5cies4 ,?is is gambl+ prop]1 c>ri$ on mo/ly by means ( c>ds & dice & ! r\lette4 ,! gambl+ _s1 z we h said1 seeks = ! excitem5t ( unc]ta9ty & v>iety4 ,:5 !re=e p make a long cont9u$ practice ( play+1 especially if ! /akes = :i* !y play are mod]ate 9 comp>ison ) _! =tune1 ?is unc]ta9ty f ! nature ( ! case beg9s to dim9i%4 ,! ?or\ghly practis$ gambl]1 if he possesses m ?an usual skill 79 games :]e skill c\nts = some?+71 mu/ be reg>d$ z a man foll[+ a pr(ession1 ?\gh a pr(ession = ! mo/ "p ( a risky & excit+ k9d1 to say no?+ ( its ignoble & (t5 di%one/ "*4 ,if1 on ! o!r h&1 8 skill is bel[ ! av]age1 or ! game is "o 9 :i* skill does n tell & ! odds are slightly 9 fav\r ( 8 antagoni/1 z 9 ! gam+ tables1 "o light 9 :i* he c be reg>d$ is t ( a man :o is foll[+ a fav\rite amusem5t2 if ?is amusem5t involves a con/ant annual outlay on 8 "p1 t is no?+ m ?an :at has to be said ( mo/ o!r amusem5ts4 #g4 ,we _c1 ( c\rse1 give su* a rational explanation z ! above 9 e case4 ,!re are pl5ty ( novices1 & pl5ty ( fanatics1 :o g on /eadily los+ 9 ! full conviction t !y w ev5tually come out w9n]s4 ,b x is h>d to believe t su* ignorance1 or su* intellectual twi/1 c really be s widely preval5t z w\ld be requisite to con/itute !m ! rule r ?an ! exception4 ,!re mu/ surely be "s v g5]al impulse :i* is gratifi$ by su* res\rces1 & x is n easy to see :at else ?is c be ?an a love ( t v>iety & consequ5t excitem5t :i* c only be f\nd 9 p]fection :]e exact prevision is impossible4 ,x is ( c\rse v difficult to make any g5]alization "h z to ! comp>ative preval5ce ( v>i\s motives among/ mank9d2 b :5 "o consid]s :at is ! diff]5ce :i* mo/ quiet ord9>y :i/ play]s feel betwe5 a game = 'love' & "o 9 :i* !re is a small /ake1 "o _c b assign a high value to ! influ5ce ( a wi% to emphasize ! excitem5t ( loss & ga94 ,i w\ld n = a mom5t und]rate ! practical dang]s :i* are f\nd to att5d ! practice ( gambl+4 ,x is rem>k$ t ! gambl]1 if he cont9ues to play = a long "t1 is "u an almo/ irresi/ible impulse to increase 8 /akes1 & s re-introduce ! elem5t ( unc]ta9ty4 ,x is 9 fact ?is t5d5cy to be ?us l$ on1 :i* makes ! pr9cipal dang] & mis*ief ( ! practice4 ,risk & unc]ta9ty are /ill su* normal *>act]i/ics ( ev5 civiliz$ life1 t ! m]e ext5sion ( su* t5d5cies into new fields does n 9 itself (f] any v al>m+ prospect4 ,x is only to be deprecat$ 9 s f> z !re is a dang]1 :i* exp]i5ce %[s to be no trifl+ "o1 t ! fasc9ation f\nd 9 ! pursuit %\ld lead m5 into foll[+ x up into excessive l5g?s4#c #h4 ,! above g5]al treatm5t ( ,gambl+ & ,insurance seems to me ! only rational & s\nd pr9ciple ( division2--namely1 t on :i* ! diff]5t practices :i*1 "u v>i\s names1 are kn[n z gambl+ or insurance1 are arrang$ 9 accordance ) ! _s ( :i* !y are ! outcome1 & !re=e ( ! results :i* !y are design$ to secure4 ,if we 7 to attempt to judge & arrange !m accord+ to ! names :i* !y curr5tly be>1 we %\ld f9d ourselves l$ to no k9d ( sy/ematic division :atev]2 ! fact be+ t s9ce !y all alike involve1 z _! ess5tial *>act]i/ic1 paym5ts & receipts1 "o or bo? ( :i* are necess>ily unc]ta9 9 _! date or am\nt1 ! names may (t5 be int]*ang$4 ,= in/ance1 a lott]y & an ord9>y insurance society aga9/ accid5t1 if we m]ely look to ! processes p]=m$ 9 !m1 are to all int5ts & purposes id5tical4 ,9 ea* alike !re is a small paym5t :i* is c]ta9 9 am\nt1 & a great receipt :i* is unc]ta9 9 am\nt4 ,a great _m p]sons pay ! small premium1 :]eas a few only ( _! numb] obta9 a prize1 ! re/ gett+ no return :atev] = _! outlay4 ,9 ea* case alike1 also1 ! aggregate receipts & losses are int5d$ to balance ea* o!r1 aft] all[+ = ! pr(its ( ^? :o c>ry on ! und]tak+4 ,b ( c\rse :5 we take into acc\nt ! occasions ^u :i* ! insur]s get _! prizes1 we see t !re is all ! diff]5ce 9 ! _w betwe5 receiv+ !m at haphaz>d1 z 9 a lott]y1 & receiv+ !m z a p>tial set-(f to a brok5 limb or injur$ con/itution1 z 9 ! insurance society4 ,aga91 ! language ( bett+ may be easily made to cov] almo/ e k9d ( insurance4 ,inde$ ,de ,morgan has describ$ life insurance z a bet :i* ! individual makes ) ! company1 t he w n live beyond a c]ta9 age4 ,if he dies "y1 he is pecuni>ily a ga9]1 if he dies late he is a los]4#d ,"h1 too1 ?\gh ! expression is te*nically q correct 7s9ce any su* delib]ate risk ( money1 ^u an unproductive v5ture1 may fall "u ! def9ition ( a bet71 !re is ! broade/ di/9ction betwe5 bett+ ) no o!r view :atev] ?an t ( risk+ money1 & bett+ ) ! view ( dim9i%+ risk & loss z mu* z possible4 ,9 fact1 if ! language ( sport+ life is to be introduc$ into ! matt]1 we ought1 ,i presume1 to speak ( ! insur] z 'h$g+' aga9/ 8 dea?4 #i4 ,aga91 9 ,tont9es we h a sy/em ( :at is (t5 call$ ,insurance1 & 9 c]ta9 po9ts rightly s1 b :i* is to all int5ts & purposes simply & absolutely a gambl+ transaction4 ,!y h be5 entirely ab&on$1 ,i believe1 = "s "t1 b 7 once r popul>1 especially 9 ,france4 ,on ?is plan ! ,/ate1 or :atev] society manages ! bus9ess1 does n ga9 any?+ until ! la/ memb] ( ! ,tont9e is dead4 ,z ! numb] ( ! survivors dim9i%es1 ! same sum-total ( annuities /ill cont9ues to be paid among/ !m1 z long z any are left alive1 s t ea* receives a gradually increas+ sum4 ,h5ce ^? :o die e>ly1 in/ead ( receiv+ ! mo/1 z on ! ord9>y plan1 receive ! lea/2 = at ! dea? ( ea* memb] ! annuity ceases absolutely1 s f> z he & 8 relations are conc]n$4 ,! :ole affair !re=e is to all int5ts & purposes a gigantic sy/em ( bett+1 to see :i* c live ! longe/2 ! ,/ate be+ ! common /ake-hold]1 & receiv+ a heavy commission = its sup]9t5d5ce1 ?is commission be+ naturally its sole motive = enc\rag+ su* a transaction4 ,x is record$ ( "o ( ! ,fr5* ,tont9es#e t a wid[ ( #ig 0 left1 z ! la/ survivor1 to receive an annuity ( #gc1ejj livres dur+ ! re/ ( ! life :i* %e c\ld manage to drag on aft] t age2--%e hav+ orig9ally subscrib$ a s+le sum ( #cjj livres only4 ,x is obvi\s t su* a sy/em z ?is1 ?\gh x may sometimes g by ! "n ( insurance1 is utt]ly oppos$ to ! _s ( true insurance1 s9ce x t5ds to aggravate exi/+ inequalities ( =tune in/ead ( to mitigate !m4 ,! insur] "h bets t he w die old2 9 ord9>y insurance he bets t he w die "y4 ,aga91 to take "o f9al in/ance1 common op9ion (t5 reg>ds ! bank or company :i* keeps a r\ge et noir table1 & ! individuals :o risk _! money at x1 z be+ bo? alike engag$ 9 gambl+4 ,s !y may be1 te*nically1 b = all practical purposes su* a bank is z sure & safe a bus9ess z t ( any ord9>y insurance society1 & probably f> /eadi] 9 its receipts ?an ! majority ( ord9>y trades 9 a manufactur+ or comm]cial city4 ,! bank goes 9 = _m & small transactions1 9 proportion to its capital2 _! cu/om]s1 v (t51 9 proportion to _! incomes g 9 = v heavy transactions4 ,t ! =m] comes out a ga9] ye> aft] ye> dep5ds1 ( c\rse1 ^u ! fact t ! tables are notori\sly slightly 9 _! fav\r4 ,b ! /ead9ess ( ^! ga9s :5 comp>$ ) ! un/ead9ess ( ! individual losses dep5ds simply ^u1--9 fact1 is m]ely an illu/ration (1--! "o great p]man5t contra/ :i* lies at ! basis ( all reason+ 9 ,probability4 #aj4 ,we h s f> reg>d$ ,insurance & ,gambl+ z be+ ea* ! product ( a natural impulse1 & z hav+ ea*1 if we look m]ely to exp]i5ce1 a great mass ( human judgm5t 9 its fav\r4 ,! popul> moral judgm5t1 h[ev]1 :i* applauds ! "o & condemns ! o!r re/s 9 great "p ^u an assumption1 :i* has d\btless mu* tru? 9 x1 b :i* is (t5 int]pret$ ) an absolut5ess :i* leads to error 9 ea* direction2--! duty ( insurance be+ too p]emptorily urg$ ^u e "o1 & ! practice ( gambl+ too univ]sally reg>d$ z involv+ a sacrifice ( real self-int]e/1 z be+ 9 fact little bett] ?an a p]si/5t blund]4 ,! assumption 9 "q seems to be extract$ f ! ackn[l$g$ advantages ( insurance1 & !n invok$ to condemn ! practice ( gambl+4 ,b 9 s do+ ! fact does n seem to be suffici5tly recogniz$ t ! latt] practice1 if we m]ely look to ! ext5t & antiquity ( ! tacit vote ( mank9d 9 its fav\r1 might surely claim to c>ry ! day4 ,x is ( c\rse obvi\s t 9 all cases ) :i* we are conc]n$1 ! aggregate weal? is unalt]$2 money be+ m]ely transf]r$ f "o p]son to ano!r4 ,! loss ( "o is precisely equival5t to ! ga9 ( ano!r4 ,at lea/ ?is is ! approximation to ! tru? ) :i* we f9d x conv5i5t to />t4#f ,n[ if ! happ9ess :i* is yield$ by weal? 7 always 9 direct proportion to its am\nt1 x is n easy to see :y insurance %\ld be advocat$ or gambl+ condemn$4 ,9 ! case ( ! latt] ?is is obvi\s en\gh4 ,i h lo/ #ej1 say1 b o!rs 7"o or m z ! case may be7 h ga9$ x1 & ! increase ( _! happ9ess w\ld exactly balance ! dim9ution ( m9e4 ,9 ! case ( ,insurance !re is a slight complication1 aris+ f ! fact t ! fall+ 9 ( ! policy does n happ5 at r&om 7o!rwise1 z already po9t$ out1 x w\ld be simply a lott]y71 b is made cont+5t ^u "s k9d ( loss1 :i* x is int5d$ z f> z possible to balance4 ,i insure myself on a railway j\rney1 break my leg 9 an accid5t1 &1 hav+ paid ?reep5ce = my ticket1 receive say #bjj comp5sation f ! insurance company4 ,! same rem>ks1 h[ev]1 apply "h2 ! happ9ess ,i acquire by ?is #bjj w\ld only j balance ! aggregate loss ( ! #af1jjj :o h paid _! ?reep5ces & receiv$ no return = !m1 7 happ9ess always directly proportional to weal?4 #aa4 ,! practice ( ,insurance does n1 ,i ?9k1 give rise to _m que/ions ( !oretic int]e/1 & ne$ n !re=e deta9 u long]4 ,! fact is t x has h>dly yet be5 appli$ suffici5tly long & widely1 or to matt]s :i* admit ( suffici5tly accurate /ati/ical treatm5t1 except 9 "o dep>tm5t4 ,?is1 ( c\rse1 is ,life ,insurance2 b ! subject is "o :i* requires con/ant att5tion to details ( /ati/ics1 & is 7rightly7 ma9ly c>ri$ out 9 /rict accordance ) r\t9e4 ,z an illu/ration ( ?is we ne$ m]ely ref] to ! works ( ,de ,morgan1--a pr(essional actu>y z well z a writ] on ! !ory ( ,probability1--:o has f\nd b little opportunity to aid 8 speculative treatm5t ( ,probability by examples drawn f ?is class ( consid]ations4 ,) ,gambl+ x is o!rwise4 ,n only h a v>iety ( int]e/+ s+le problems be5 discuss$ 7( :i* ! ,pet]sburg problem is ! be/ kn[n7 b sev]al speculative que/ions ( consid]able importance h be5 rais$4 ,"o ( ^! conc]ns ! disadvantages ( ! practice ( gambl+4 ,!re h be5 a numb] ( writ]s :o1 n cont5t ) dwell+ ^u ! obvi\s moral & indirect mis*ief :i* results1 9 ! %ape ( ov]-excitem5t1 consequ5t gre$1 )drawal f ! /eady bus9ess habits :i* alone insure prosp]ity 9 ! long run1 div]sion ( weal? into di%one/ h&s1 c41 h endeav\r$ to demon/rate ! necess>y loss caus$ by ! practice4 #ab4 ,^! attempts may be divid$ into two classes4 ,!re are 7#a7 ^? :i* appeal to m]ely num]ical consid]ations1 & 7#b7 ^? :i* introduce :at is call$ ! 'moral' z di/+ui%$ f ! ma!matical value ( a future cont+5cy4 7#a7 ,= in/ance1 an +5i\s attempt has be5 made by ,mr ,:itwor? to prove t gambl+ is necess>ily disadvantage\s on purely ma!matical gr\nds4 ,:5 two p]sons play aga9/ ea* o!r "o ( ! two mu/ be ru9$ soon] or lat]1 ev5 ?\gh ! game be a fair "o1 suppos+ t !y g on play+ long en\gh2 ! "o ) ! small] income hav+ ( c\rse ! wor/ *ance ( be+ ! lucky survivor4 ,if "o ( !m has a f9ite1 & ! o!r an inf9ite income1 x mu/ cle>ly be ! =m] :o w be ! ultimate suff]] if !y g on long en\gh4 ,x is !n ma9ta9$ t ?is is 9 fact e individual gambl]'s position1 no "o is re/rict$ to gambl+ ) "o s+le oppon5t2 ! speculator deals ) ! public at l>ge1 ) a _w ^: res\rces are practically unlimit$4 ,!re is a prospect t 8 op]ations may t]m9ate to 8 own disadvantage1 ?r\gh 8 hav+ no?+ m to /ake2 b !re is no prospect t x w t]m9ate to 8 advantage ?r\gh ! exhau/ion ( ! res\rces ( ! _w4 ,e "o :o gambles is c>ry+ on an unequal w>f>e3 he is rang$ ) a re/rict$ capital aga9/ an adv]s>y ^: means are inf9ite4#g ,9 ! above argum5t x is surely ov]look$ t ! adv]s>ies aga9/ :om he plays are n "o body ) a common purse1 l ! bank 9 a gambl+ e/abli%m5t4 ,ea* ( ^! adv]s>ies is 9 exactly ! same position z he himself is1 & a precisely simil> pro( might be employ$ to %[ t ea* ( !m mu/ be ev5tually ru9$ :i* is ( c\rse a r$uction to absurdity4 ,gambl+ c only transf] money f "o play] to ano!r1 & !re=e none ( x c be actually lo/4 #ac4 ,:at really becomes ( ! money1 :5 !y play to extremity1 is n difficult to see4 ,fir/ suppose a limit$ numb] ( play]s4 ,if !y g on long en\gh1 ! money w at la/ all f9d its way into ! pocket ( "s "o ( _! numb]4 ,if _! =tunes 7 orig9ally equal1 ea* /&s ! same *ance ( be+ ! lucky survivor2 9 :i* case we _c ass]t1 on any num]ical gr\nds1 t ! prospect ( ! play is disadvantage\s to any "o ( !m4 ,if _! =tunes 7 unequal1 ! "o :o _h ! l>ge/ sum to beg9 ) c be %[n to h ! be/ *ance1 accord+ to "s assignable law1 ( be+ left ! f9al w9n]2 9 :i* case x mu/ be j z advantage\s = him1 z x 0 disadvantage\s = 8 less weal?y competitors4 ,:51 in/ead ( a limit$ numb] ( play]s1 we suppose an unlimit$ numb]1 ea* z he is ru9$ retir+ f ! table & lett+ ano!r come 91 ! results are m complicat$1 b _! g5]al t5d5cy c be readily di/+ui%$4 ,if we suppos$ t no "o retir$ except :5 he 0 ru9$1 we %\ld h a /ate ( ?+s 9 :i* all ! old play]s 7 gr[+ gradually ri*]4 ,9 ?is case ! prospect be=e ! new com]s w\ld /eadily gr[ worse & worse1 = _! *ance ( w9n+ aga9/ su* ri* oppon5ts w\ld be exce$+ly small4 ,b z ?is is an unreasonable supposition1 we ought r to assume t n only d ! ru9$ victims retire1 b also t ^? :o h ga9$ =tunes ( a c]ta9 am\nt retire also1 s t ! aggregate & av]age weal? ( ! gambl+ body rema9s pretty /eady4 ,:at *ance any giv5 play] has ( be+ ru9$1 & h[ long he may expect to hold out be=e be+ ru9$1 w dep5d ( c\rse ^u ! initial incomes ( ! play]s1 ! rules ( ! game1 ! /akes = :i* !y play1 & o!r consid]ations4 ,b x is cle> t = all t is lo/ by "o1 a precisely equal sum mu/ be ga9$ by o!rs1 & t !re=e any p>ticul> gambl] c only be caution$ be=eh& t 8 conduct is n to be recomm5d$1 by appeal+ to "s su* suppositions z ^? already m5tion$ 9 a =m] section4 #ad4 ,z an additional ju/ification ( ?is view ! read] may obs]ve t ! /ate ( ?+s 9 ! la/ example is "o :i*1 express$ 9 some:at diff]5t language & ) a slight alt]ation ( circum/ances1 is be+ incessantly c>ri$ on ^u a gigantic scale ^u e side ( u4 ,call x ! competition ( m]*ants & trad]s 9 a comm]cial c\ntry1 & ! g5]al results are famili> en\gh4 ,x is true t 9 s f> z skill comes into ! "q1 !y are n prop]ly gambl]s2 b 9 s f> z *ance & risk d1 !y may be fairly s t]m$1 & 9 _m bran*es ( bus9ess ?is mu/ necess>ily be ! case to a v consid]able ext5t4 ,:5ev] bus9ess is c>ri$ on 9 a reckless way1 ! comp>ison is on g5]al gr\nds fair en\gh4 ,9 ea* case alike we f9d "s retir+ ru9$1 & "s mak+ _! =tunes2 & 9 ea* case alike also ! *ances1 coet]is p>ibus1 lie ) ^? :o h ! l>ge/ =tunes4 ,e "o is1 9 a s5se1 /ruggl+ aga9/ ! collective comm]cial _w1 b s9ce ea* ( 8 competitors is do+ ! same1 we cle>ly c\ld n caution any ( !m 7except inde$ ! poor] ones7 t _! ef=ts mu/ f9ally end 9 disadvantage4 #ae4 ,if we wi% to see ?is result display$ 9 its mo/ decisive =m we may f9d a good analogy 9 a v diff]5t class ( ev5ts1 viz4 9 ! fate ( surnames4 ,we are all gambl]s 9 ?is respect1 & ! game is c>ri$ out to ! la/ f>?+ ) a rig\r unkn[n at ,newm>ket or ,monte ,c>lo4 ,9 its complete treatm5t ! subject is a v intricate "o1#h b a simple example w s]ve to display ! g5]al t5d5cy4 ,suppose a colony compris+ #ajjj c\ples ( diff]5t surnames1 & suppose t ea* ( ^! has f\r *ildr5 :o gr[ up to m>ry4 ,approximately1 "o 9 #af ( ^! families w consi/ ( girls only2 & !re=e1 "u ord9>y conv5tions1 ab\t #fb ( ! names w h disappe>$ = ev] aft] ! next g5]ation4 ,f\r aga9 out ( #af w h b "o boy1 ea* ( :om w ( c\rse be 9 ! same position z 8 fa!r1 viz4 ! sole repres5tative ( 8 "n4 ,accord+ly 9 ! next g5]ation "o 9 #af ( ^! names w aga9 drop out1 & s ! process cont9ues4 ,! numb] :i* disappe>s 9 ea* successive g5]ation becomes small]1 z ! /ability ( ! survivors becomes great] ow+ to _! l>g] numb]s4 ,b !re is no *eck to ! process4 #af4 ,! analogy "h is a v close "o1 ! names :i* ?us disappe> correspond+ to ! gambl]s :o retire ru9$ & ^? :i* increase 9 numb] correspond+ to ! lucky w9n]s4 ,! ultimate goal 9 ea* case alike1--( c\rse an exce$+ly remote "o1--is ! exclusive survival ( "o at ! exp5se ( all ! o!rs4 ,t "o surname does ?us drop out aft] ano!r mu/ h /ruck e "o :o has made any enquiry into family g5ealogy1 & v>i\s fanciful acc\nts h be5 giv5 by ^? unfamili> ) ! !ory ( probability4 ,:at is (t5 apt to be ov]look$ is ! extreme slightness ( :at may be t]m$ ! turn ( ! tables 9 fav\r ( ! survival at ea* g5]ation4 ,9 ! above num]ical example we h made an extravagantly fav\rable supposition1 by assum+ t ! population d\bles at e g5]ation4 ,9 an old & ?ickly populat$ c\ntry :]e ! numb]s increase v sl[ly1 we %\ld be mu* ne>] ! m>k 9 assum+ t ! av]age effective family1--t is1 ! av]age numb] ( *ildr5 :o live to m>ry1--0 only two4 ,9 ?is case e family :i* 0 repres5t$ at any "t by b a s+le male w\ld h b ?ree *ances 9 f\r ( surviv+ ext9ction1 & ( c\rse ! process ( ?9n+ out w\ld be a m rapid "o4 #ag4 ,! mo/ int]e/+ class ( attempts to prove ! disadvantages ( gambl+ appeal to :at is te*nically call$ 'moral expectation' z di/+ui%$ f 'ma!matical expectation4' ,! latt] may be def9$ simply z ! av]age money value ( ! v5ture 9 "q2 t is1 x is ! product ( ! am\nt to be ga9$ 7or lo/7 & ! *ance ( ga9+ 7or los+7 x4 ,= in/ance1 if ,i bet f\r to "o 9 sov]eigns aga9/ ! occurr5ce ( ace ) a s+le die !re w\ld be1 on ! av]age ( _m ?r[s1 a loss ( f\r p\nds aga9/ a ga9 ( five p\nds on ea* set ( six occurr5ces2 i4e4 !re w\ld be an av]age ga9 ( ?ree %ill+s & f\rp5ce on ea* ?r[4 ,?is is call$ ! true or ma!matical expectation4 ,! s-call$ 'moral expectation'1 on ! o!r h&1 is ! subjective value ( ?is ma!matical expectation4 ,t is1 in/ead ( reckon+ a money =tune 9 ! ord9>y way1 z :at x is1 ! attempt is made to reckon x at :at x is felt to be4 ,! elem5ts ( computation !re=e become1 n p\nds & %ill+s1 b sums ( pleasure enjoy$ actually or 9 prospect4 ,accord+ly :5 reckon+ ! pres5t value ( a future ga91 we mu/ n[ multiply1 n ! objective b ! subjective value1 by ! *ance we h ( secur+ t ga94 ,) reg>d to ! exact relation ( ?is moral =tune to ! physical v>i\s m or less arbitr>y assumptions h be5 made4 ,"o writ] 7,buffon7 consid]s t ! moral value ( any giv5 sum v>ies inv]sely ) ! total weal? ( ! p]son :o ga9s x4 ,ano!r 7,d4 ,b]n\lli7 />t+ f a diff]5t assumption1 :i* we %all pres5tly h to notice m p>ticul>ly1 makes ! moral value ( a =tune v>y z ! log>i?m ( its actual am\nt4#i ,a ?ird 7,cram]7 makes x v>y ) ! squ>e root ( ! am\nt4 #ah4 ,hi/orically1 ^! proposals h sprung f ! wi% to reconcile ! conclusions ( ! ,pet]sburg problem ) ! dictates ( practical common s5se2 =1 by sub/itut+ ! moral = ! physical e/imate ! total value ( ! expectation c\ld be r$uc$ to a f9ite sum4 ,on ?is gr\nd !re=e su* proposals h no great int]e/1 =1 z we h se51 !re is no s]i\s difficulty 9 ! problem :5 rightly und]/ood4 ,^! same proposals h[ev] h be5 employ$ 9 ord] to prove t gambl+ is necess>ily disadvantage\s1 & ?is to bo? p>ties4 ,take1 = in/ance1 ,b]n\lli's supposition4 ,x c be readily %[n t if two p]sons ea* ) a sum ( #ej to />t ) *oose to risk1 say1 #aj ^u an ev5 wag] !re w be a loss ( happ9ess z a result2 = ! pleasure ga9$ by ! possessor ( #fj w n be equal to t :i* is lo/ by ! man :o leaves (f ) #dj4aj #ai4 ,?is is ! =m ( argum5t commonly adopt$2 b1 z x /&s1 x does n seem conclusive4 ,x may surely be repli$ t all :i* is ?us prov$ is t inequality is bad1 on ! gr\nd t two =tunes ( #ej are bett] ?an "o ( #fj & "o ( #dj4 ,conceive = in/ance t ! orig9al =tunes _h be5 #fj & #dj respectively1 ! ev5t may result 9 an increase ( happ9ess2 = ?is w c]ta9ly be ! case if ! ri*] man loses & ! =tunes are ?us equaliz$4 ,?is is q true2 & we are !re=e oblig$ to %[1--:at c be v easily %[n1--t if ! o!r alt]native _h tak5 place & ! two =tunes _h be5 made /ill m unequal 7viz4 #fe & #ce respectively7 ! happ9ess ?us lo/ w\ld m ?an balance :at w\ld h be5 ga9$ by ! equalization4 ,& s9ce ^! two suppositions are equally likely !re w be a loss 9 ! long run4 ,! consid]ation j adduc$ seems h[ev] to %[ t ! common way ( /at+ ! conclusion is r mislead+2 & t1 on ! assumption 9 "q z to ! law ( dep5d5ce ( happ9ess on weal?1 x really is ! case t ! effective elem5t 9 r5d]+ gambl+ disadvantage\s is its t5d5cy to ! increase ( ! inequality 9 ! di/ribution ( weal?4 #bj4 ,?is raises two que/ions1 "o ( "s speculative int]e/ 9 connection ) our subject1 & ! o!r ( supreme importance 9 ! conduct ( life4 ,! fir/ is ?is3 q ap>t f any p>ticul> assumption :i* we make ab\t moral =tunes or laws ( v>iation ( happ9ess1 is x ! fact t gambl+ t5ds to increase ! exi/+ inequalities ( weal?8 ,!oretically !re is no d\bt t ?is is s4 ,take ! simple/ case & suppose two p toss+ = a p\nd4 ,if _! =tunes 7 equal to beg9 ) !re mu/ be resultant inequality4 ,if !y 7 unequal !re is an ev5 *ance ( ! inequality be+ increas$ or dim9i%$2 b s9ce ! increase is proportionally great] ?an ! decrease1 ! f9al result rema9s ( ! same k9d z :5 ! =tunes 7 equal4#aa ,tak+ a m g5]al view ! same conclusion und]lies all our reason+ z to ! av]ages ( l>ge numb]s1 viz4 t ! resultant div]g5cies increase absolutely 7h[ev] !y dim9i% relatively7 z ! numb]s become great]4 ,& ( c\rse we ref] to ^! absolute div]g5cies :5 we are talk+ ( ! di/ribution ( weal?4 #ba4 ,?is is ! !oretic conclusion4 ,h[ f> ! actual practice ( gambl+ introduces c\nt]act+ ag5cies mu/ be left to ! det]m9ation ( ^? :o are compet5t to pron\nce4 ,s f> z outsid]s are au?oris$ to judge f :at !y read 9 ! newspap]s & o!r public s\rces ( in=mation1 x w\ld appe> t ^! c\nt]act+ ag5cies are v consid]able1 & t 9 consequ5ce x is a r insecure argum5t to advance aga9/ gambl+4 ,_m a l>ge =tune has notori\sly be5 squ&]$ on ! race-c\rse or 9 gambl+ saloons1 & mo/ c]ta9ly a l>ge portion1 if n ! major "p1 has gone to swell ! incomes ( _m :o 7 by comp>ison poor4 ,b ! solution ( ?is "q mu/ cle>ly be left to ^? :o h bett] opportunities ( kn[+ ! facts ?an is to be expect$ on ! "p ( writ]s on ,probability4 #bb4 ,! g5]al conclusion to be drawn is t ^? :o invok$ ?is pr9ciple ( moral =tune z an argum5t aga9/ gambl+ 7 really rais+ a mu* m intricate & f>-rea*+ problem ?an !y 7 aw>e (4 ,:at !y 7 at "w ^u 0 ! "q1 ,:at is ! di/ribution ( weal? :i* t5ds to secure ! maximum ( happ9ess8 ,is ?is be/ secur$ by equality or inequality8 ,_h !y really foll[$ out ! doctr9e on :i* _! d5unciation ( gambl+ 0 f\nd$ !y ought to h adopt$ ! ,sociali/'s ideal z be+ di/9ctly t :i* t5ds to increase happ9ess4 ,& !y ought to h br\ght "u ! same disapprobation :i* !y express$ aga9/ gambl+ all ^? t5d5cies ( mod]n civiliz$ life :i* "w 9 ! same direction4 ,= in/ance2 ke5 competition1 speculative op]ations1 ext5d$ facilities ( cr$it1 me*anical inv5tions1 enl>gem5t ( bus9ess op]ations into va/ firms3--all ^!1 & o!r simil> t5d5cies too num]\s to m5tion "h1 h _h "s influ5ce 9 ! way ( add+ to exi/+ inequalities4 ,!y are1 or h be51 9 consequ5ce d5\nc$ by sociali/s3 are we hone/ly to br+ !m to ?is te/ 9 ord] to asc]ta9 :e!r or n !y are to be condemn$8 ,! read] :o wi%es to see :at sort ( problems ?is assumption ( 'moral =tune' ought to introduce may be recomm5d$ to read ,mr ,f4 ,y4 ,edgewor?'s ,ma!matical ,psy*ics1 ! only "w ) :i* ,i am acqua9t$ :i* treats ( ^! que/ions4 #a4 ,! "q ( ! advisability ( inoculation aga9/ ! small-pox1 :i* gave rise to mu* discussion among/ ! writ]s on ,probability dur+ ! la/ c5tury1 is a case 9 po9t ( ! same pr9ciples appli$ to a v diff]5t k9d ( in/ance4 ,! loss aga9/ :i* ! insurance 0 direct$ 0 dea? by small-pox1 ! premium paid 0 ! illness & o!r inconv5i5ce1 & ! v small risk ( dea?1 f ! inoculation4 ,! disputes :i* !nce arose among/ writ]s on ! subject involv$ ! same difficulties z to ! balance betwe5 c]ta9 mod]ate loss & cont+5t great loss4 ,9 ! sev5te5? c5tury x seems to h be5 an occasional practice1 be=e a j\rney into ! ,m$it]ranean1 to insure aga9/ capture by ,moori% pirates1 ) a view to secure hav+ ! ransom paid4 7,see1 = an acc\nt ( "s extraord9>y developm5ts ( ! insurance pr9ciple1 ,wal=d's ,insurance ,guide & ,h&book4 ,x is n writt5 9 a v sci5tific _s1 b x conta9s mu* in=mation on all matt]s connect$ ) insurance47 #b4 ,all t is meant by ! above comp>ison is t ! ideal aim$ at by ,communism is simil> to t ( ,insurance4 ,if we look at ! processes by :i* x w\ld be c>ri$ out1 & ! means = en=c+ x1 ! matt] w\ld ( c\rse assume a v diff]5t aspect4 ,simil>ly ) ! action ( ,trades ,unionism ref]r$ to 9 ! next p>agraph4 #c4 ,"o ( ! be/ discussions t ,i h rec5tly se5 on ^! subjects1 by a writ] at once ?or\ghly compet5t & well in=m$1 is 9 ,mr ,proctor's ,*ance & ,luck4 ,x appe>s to me h[ev] t he runs into an extreme 9 8 d5unciation n ( ! folly b ( ! di%one/y ( all gambl+4 ,surely also x is a /ra9$ use ( language to speak ( all lott]ies z 'unfair' & ev5 'sw9dl+' on ! gr\nd t ! sum-total ( :at !y di/ribute 9 prizes is less ?an t ( :at !y receive 9 paym5ts4 ,! diff]5ce1 9 respect ( in=mation delib]ately )held & false reports wilfully spread1 betwe5 mo/ ( ! lott]ies t h be5 support$1 & ! bubble companies :i* ju/ly des]ve ! "n ( sw9dles1 ought to prev5t ! same "n be+ appli$ to bo?4 #d4 ,a fire insurance is a simple bet betwe5 ! (fice & ! p>ty1 & a life insurance is a collection ( wag]s4 ,!re is some?+ ( ! pr9ciple ( a wag] 9 e transaction 9 :i* ! results ( a future ev5t are to br+ ga9 or loss4 ,p5ny ,cyclopdia1 "u ! head ( ,wag]4 #e4 ,encyclopdie ,me?odique1 "u ! head ( ,tont9es4 #f4 ,( c\rse1 if we introduce consid]ations ( ,political ,economy1 corrections w h to be made4 ,= "o ?+1 e ,insurance ,(fice is1 z ,de ,morgan repeat$ly insi/s1 a ,sav+s ,bank z well z an ,insurance ,(fice4 ,! ,(fice inve/s ! premiums1 & c !re=e af=d to pay a l>g] sum ?an w\ld o!rwise be ! case4 ,aga91 9 ! case ( gambl+1 a l>ge loss ( capital by any "o w almo/ necess>ily involve an actual de/ruction ( weal?2 to say no?+ ( ! fact t1 practically1 gambl+ (t5 causes a con/ant transf] ( weal? f productive to unproductive purposes4 #g4 ,*oice & ,*ance1 ,ed4 ,,ii4 p4 #bjh4 #h4 ,x 01 ,i believe1 fir/ treat$ z a s]i\s problem by ,mr ,galton4 7,see ! ,j\rnal ,an?rop4 ,in/4 ,vol4 ,,iv4 #ahge1 :]e a complete ma!matical solution is indicat$ by ,mr ,h4 ,w4 ,watson47 #i4 ,b]n\lli himself does n seem to h bas$ 8 conclusions ^u actual exp]i5ce4 ,b x is a notewor?y fact t ! assumption ) :i* he />ts1 viz4 t ! subjective value ( any small increm5t 7dx7 is inv]sely proportional to ! sum !n possess$ 7x71 & :i* leads at once to ! log>i?mic law above m5tion$1 is id5tical ) "o :i* is n[ famili> en\gh to e psy*ologi/4 ,x is :at is commonly call$ ,fe*n]'s ,law1 :i* he has e/abli%$ by aid ( an enorm\s am\nt ( c>eful exp]im5t 9 ! case ( a numb] ( our simple s5sations4 ,b ,i d n believe t he has made any claim t su* a law holds good 9 ! f> m intricate dep5d5ce ( happ9ess ^u weal?4 #aj4 ,! =mula expressive ( ?is moral happ9ess is c log x_/a2 :]e x /&s = ! physical =tune possess$ at ! "t1 & a = t small value ( x at :i* happ9ess is suppos$ to disappe>3 c be+ an arbitr>y con/ant4 ,let two p]sons1 ^: =tune is x1 risk y on an ev5 bet4 ,!n ! balance1 z reg>ds happ9ess1 mu/ be drawn betwe5 c log x_/a & #a_/b;c log 7x y7_/a #a_/b;c log 7x - y7_/a1 or log x#b & log7x y77x - y71 or x#b & x#b - y#b1 ! =m] ( :i* is necess>ily ! great]4 #aa4 ,?is may be se5 m cle>ly z foll[s4 ,suppose two pair ( gambl]s1 ea* pair consi/+ ( m5 possess+ #ej & #cj respectively4 ,n[ if we suppose ! ri*] man to w9 9 "o case & ! poor] 9 ! o!r ^! two results w be a fair repres5tation ( ! av]age2 = !re are only two alt]natives & ^! w be equally frequ5t 9 ! long run4 ,x is obvi\s t we h _h two =tunes ( #ej & two ( #cj conv]t$ into "o ( #bj1 two ( #dj1 & "o ( #fj4 ,& ?is is cle>ly an increase ( inequality4 ,,*apt] ,,xvi4 ,,! ,,application ,,( ,,probability ,,to ,,te/imony4 #a4 ,on ! pr9ciples :i* h be5 adopt$ 9 ?is "w1 x becomes que/ionable :e!r sev]al classes ( problems :i* may seem to h acquir$ a prescriptive "r to admission1 w n h to be exclud$ f ! sci5ce ( ,probability4 ,! mo/ important1 p]haps1 ( ^! ref] to :at is commonly call$ ! cr$ibility ( te/imony1 e/imat$ ei!r at fir/ h& & directly1 or z influ5c+ a juryman1 & s rea*+ u ?r\gh 8 sagacity & tru/wor?9ess4 ,almo/ e treatise ^u ! sci5ce conta9s a discussion ( ! pr9ciples accord+ to :i* cr$it is to be atta*$ to comb9ations ( ! reports ( witnesses ( v>i\s degrees ( tru/wor?9ess1 or ! v]dicts ( juries consi/+ ( l>g] or small] numb]s4 ,a great mod]n ma!matician1 ,poisson1 has writt5 an elaborate treatise expressly ^u ?is subject2 :il/ a consid]able portion ( ! works ( ,laplace1 ,de ,morgan1 & o!rs1 is devot$ to an exam9ation ( simil> enquiries4 ,x w\ld be presumptu\s to diff] f su* au?orities z ^!1 except ^u ! /ronge/ gr\nds2 b ,i confess t ! extraord9>y +5uity & ma!matical ability :i* h be5 devot$ to ^! problems1 consid]$ z que/ions 9 ,probability1 fails to conv9ce me t !y ought to h be5 s consid]$4 ,! foll[+ are ! pr9cipal gr\nds = ?is op9ion4 #b4 ,x w be rememb]$ t 9 ! c\rse ( ! *apt] on ,induction we ent]$ into a detail$ inve/igation ( ! process dem&$ ( u :51 in/ead ( ! appropriate propositions f :i* ! inf]5ce 0 to be made be+ set be=e u1 ! individual pres5t$ himself1 & ! task 0 impos$ ^u u ( select+ ! requisite gr\ps or s]ies to :i* to ref] him4 ,9 o!r words1 in/ead ( calculat+ ! *ance ( an ev5t f det]m9ate conditions ( frequ5cy ( its occurr5ce 7^! be+ ei!r obta9$ by direct exp]i5ce1 or d$uctively inf]r$7 we h to select ! conditions ( frequ5cy out ( a plurality ( m or less suitable ones4 ,:5 ! problem is pres5t$ to u at su* a /age z ?is1 we may ( c\rse assume t ! prelim9>y process ( obta9+ ! /ati/ics :i* are ext5d$ into ! proportional propositions has be5 already p]=m$2 we may suppose !re=e t we are already 9 possession ( a quantity ( su* propositions1 our pr9cipal rema9+ d\bt be+ z to :i* ( !m we %\ld !n employ4 ,?is selection 0 %[n to be to a c]ta9 ext5t arbitr>y2 =1 ow+ to ! fact ( ! individual possess+ a l>ge numb] ( diff]5t prop]ties1 he became 9 consequ5ce a memb] ( diff]5t s]ies or gr\ps1 :i* might pres5t diff]5t av]ages4 ,we mu/ n[ exam9e1 some:at m fully ?an we did be=e1 ! practical conditions "u :i* any difficulty aris+ f ?is s\rce ceases to be ( importance4 #c4 ,"o condition ( ?is k9d is v simple & obvi\s4 ,x is t ! diff]5t /ati/ics ) :i* we are pres5t$ %\ld n 9 reality (f] mat]ially diff]5t results1 ,if1 = in/ance1 we 7 enquir+ into ! probability ( a man ag$ =ty dy+ )9 ! ye>1 we might if we pleas$ take into acc\nt ! fact ( 8 hav+ r$ hair1 or 8 hav+ be5 born 9 a c]ta9 c\nty or t[n4 ,ea* ( ^! circum/ances w\ld s]ve to specialize ! individual1 & !re=e to re/rict ! limits ( ! /ati/ics :i* 7 applicable to 8 case4 ,b ! consid]ation ( su* qualities z ^! w\ld ei!r leave ! av]age precisely z x 01 or produce su* an unimportant alt]ation 9 x z no "o w\ld ?9k ( tak+ into acc\nt4 ,?\gh we c\ld h>dly say ) c]ta9ty ( any conceivable *>act]i/ic t x has absolutely no be>+ on ! result1 we may /ill feel v confid5t t ! be>+ ( su* *>act]i/ics z ^! is utt]ly insignificant4 ,( c\rse 9 ! extreme case ( ! ?+s mo/ p]fectly suit$ to ! ,calculus ( ,probability1 viz4 games ( pure *ance1 ^! subsidi>y *>act]i/ics are q irrelevant4 ,any fur!r p>ticul>s ab\t ! *>act]i/ics ( ! c>ds 9 a really fair pack1 beyond ^? :i* are famili> to all ! play]s1 w\ld convey no in=mation :atev] ab\t ! result4 ,or aga92 al?\gh ! diff]5t sets ( /ati/ics may n z above give almo/ id5tical results1 yet !y may d :at practically comes to v mu* ! same ?+1 t is1 arrange !mselves into a small numb] ( gr\ps1 all ( ! /ati/ics 9 any "o gr\p practically co9cid+ 9 _! results4 ,if = example a consumptive man desir$ to insure 8 life1 !re w\ld be a m>k$ diff]5ce 9 ! /ati/ics accord+ z we took 8 peculi> /ate ( heal? into acc\nt or n4 ,we %\ld "h h two sets ( /ati/ics1 s cle>ly m>k$ (f f "o ano!r t !y might almo/ rank ) ! di/9ctions ( natural k9ds1 & :i* w\ld 9 consequ5ce (f] decid$ly diff]5t results4 ,if we 7 to specialize /ill fur!r1 by tak+ into acc\nt insignificant qualities l ^? m5tion$ 9 ! la/ p>agraph1 we might inde$ get m limit$ sets ( /ati/ics applicable to p]sons /ill m closely resembl+ ! individual 9 "q1 b ^! w\ld n diff] suffici5tly 9 _! results to make x wor? our :ile to d s4 ,9 o!r words1 ! diff]5t propositions :i* are applicable to ! case 9 po9t arrange !mselves into a limit$ numb] ( gr\ps1 :i*1 & :i* only1 ne$ be tak5 into acc\nt2 :5ce ! range ( *oice among/ !m is v mu* dim9i%$ 9 practice4 #d4 ,! reasons = ! conditions above describ$ are n difficult to detect4 ,:]e ^! conditions exi/ ! process ( select+ a s]ies or class to :i* to ref] any individual is v simple1 & ! selection is1 = ! p>ticul> purposes ( inf]5ce1 f9al4 ,9 any case ( insurance1 = example1 ! "q we h to decide is ( ! v simple k9d2 ,is ,a4 ,b4 a man ( a c]ta9 age8 ,if s "o 9 fifty 9 8 circum/ances w die 9 ! c\rse ( ! ye>4 ,if any fur!r que/ions h to be decid$ !y w\ld be ( ! foll[+ description4 ,is ,a4 ,b4 a heal?y man8 ,does he foll[ a dang]\s trade8 ,b "h too ! classes 9 "q are b few1 & ! limits by :i* !y are b\nd$ are tol]ably precise2 s t ! ref]5ce ( an individual to "o or o!r ( !m is easy4 ,& :5 we h once *os5 our class we rema9 untr\bl$ by any fur!r consid]ations2 = s9ce no o!r /ati/ics are suppos$ to (f] a mat]ially diff]5t av]age1 we h no occasion to take acc\nt ( any o!r prop]ties ?an ^? already notic$4 ,! case ( games ( *ance1 already ref]r$ to1 (f]s ( c\rse an in/ance ( ^! conditions 9 an almo/ ideal /ate ( p]fection2 ! same circum/ances :i* fit !m s em95tly = ! purposes ( fair gambl+1 fitt+ !m equally to become examples 9 ,probability4 ,:5 a die is to be ?r[n1 all p]sons alike /& on precisely ! same foot+ ( k & ( ignorance ab\t ! result2 ! only data to :i* any "o c\ld appeal be+ t ea* face turns up on an av]age once 9 six times4 #e4 ,let u n[ exam9e h[ f> ! above conditions are fulfill$ 9 ! case ( problems :i* discuss :at is call$ ! cr$ibility ( te/imony4 ,! foll[+ w\ld be a fair specim5 ( "o ( ! elem5t>y enquiries out ( :i* ^! problems are compos$2--,"h is a /atem5t made by a witness :o lies once 9 t5 times1 :at am ,i to conclude ab\t its tru?8 ,objections might fairly be rais$ aga9/ ! possibility ( ?us assign+ a man 8 place ^u a graduat$ scale ( m5dacity4 ,?is h[ev] we w pass ov]1 & w assume t ! witness goes ab\t ! _w be>+ /amp$ someh[ on 8 face ! appropriate class to :i* he belongs1 & consequ5tly1 ! degree ( cr$it to :i* he has a claim on su* g5]al gr\nds4 ,b !re are o!r & /rong] reasons aga9/ ! admissibility ( ?is class ( problems4 #f4 ,t :i* has be5 describ$ 9 ! previ\s sections z ! 'individual' :i* _h to be assign$ to an appropriate class or s]ies ( /ati/ics is1 ( c\rse1 9 ?is case1 a /atem5t4 ,9 ! p>ticul> in/ance 9 "q ?is individual /atem5t is already assign$ to a class1 t namely ( /atem5ts made by a witness ( a giv5 degree ( v]acity2 b x is cle>ly optional ) u :e!r or n we *oose to conf9e our att5tion to ?is class 9 =m+ our judgm5t2 at lea/ x w\ld be optional :5ev] we 7 practically call$ on to =m an op9ion4 ,b 9 ! case ( ?is /atem5t1 z 9 t ( ! mortality ( ! man ^: insurance we 7 discuss+1 !re are a multitude ( o!r prop]ties obs]vable1 besides ! "o :i* is suppos$ to m>k ! giv5 class4 ,j z 9 ! latt] !re 7 7besides 8 age71 ! place ( 8 bir?1 ! nature ( 8 occupation1 & s on2 s 9 ! =m] !re are 7besides its be+ a /atem5t by a c]ta9 k9d ( witness71 ! fact ( its be+ utt]$ at a c]ta9 "t & place & "u c]ta9 circum/ances4 ,at ! "t ! /atem5t is made all ^! qualities or attributes ( ! /atem5t are pres5t to u1 & we cle>ly h a "r to take into acc\nt z _m ( !m z we please4 ,n[ ! "q at pres5t be=e u seems to be simply ?is2--,are ! consid]ations1 :i* we might ?us introduce1 z immat]ial to ! result 9 ! case ( ! tru? ( a /atem5t ( a witness1 z ! correspond+ consid]ations are 9 ! case ( ! insurance ( a life8 ,!re c surely be no hesitation 9 ! reply to su* a "q4 ,"u ord9>y circum/ances we soon "k all t we c "k ab\t ! conditions :i* det]m9e u 9 judg+ ( ! prospect ( a man's dea?1 & we !re=e re/ cont5t ) g5]al /ati/ics ( mortality2 b no "o :o he>d a witness speak w\ld ?9k ( simply appeal+ to 8 figure ( v]acity1 ev5 suppos+ t ?is _h be5 au?oritatively communicat$ to u4 ,! circum/ances "u :i* ! /atem5t is made in/ead ( be+ insignificant1 are ( ov]:elm+ importance4 ,! appe>ance ( ! witness1 ! tone ( 8 voice1 ! fact ( 8 hav+ objects to ga91 toge!r ) a c\ntless multitude ( o!r circum/ances :i* w\ld gradually come to light z we reflect ^u ! matt]1 w\ld make any s5sible man disc>d ! assign$ av]age f 8 consid]ation4 ,he w\ld1 9 fact1 no m ?9k ( judg+ 9 ?is way ?an he w\ld ( appeal+ to ! ,c>lisle or ,nor?ampton tables ( mortality to det]m9e ! probable l5g? ( life ( a soldi] :o 0 already 9 ! mid/ ( a battle4 #g4 ,x _c be repli$ t "u ^! circum/ances we /ill ref] ! witness to a class1 & judge ( 8 v]acity by an av]age ( a m limit$ k9d2 t we inf]1 = example1 t ( m5 :o look & act l him "u su* circum/ances1 a mu* l>g] proportion1 say n9e-t5?s1 are f\nd to lie4 ,!re is no appeal to a class 9 ?is way at all1 !re is no imm$iate ref]5ce to /ati/ics ( any k9d :atev]2 at lea/ none :i* we are consci\s ( us+ at ! "t1 or to :i* we %\ld ?9k ( resort+ = ju/ification aft]w>ds4 ,! decision seems to dep5d ^u ! quickness ( ! obs]v]'s s5ses & ( 8 appreh5sion g5]ally4 ,/ati/ics ab\t ! v]acity ( witnesses seem 9 fact to be p]man5tly z inappropriate z all o!r /ati/ics occasionally may be4 ,we may "k accurately ! p]c5tage ( recov]ies aft] amputation ( ! leg2 b :at surgeon w\ld ?9k ( =m+ 8 judgm5t solely by su* tables :5 he _h a case be=e him8 ,we ne$ n d5y1 ( c\rse1 t ! op9ion he might =m ab\t ! pati5t's prospects ( recov]y might ultimately re/ ^u ! proportions ( dea?s & recov]ies he might h previ\sly witness$4 ,b if ?is 7 ! case1 ^! data are ly+1 z "o may say1 obscurely 9 ! backgr\nd4 ,he does n appeal to !m directly & imm$iately 9 =m+ 8 judgm5t4 ,!re has be5 a f> m important int]m$iate process ( appreh5sion & e/imation ( :at is ess5tial to ! case & :at is n4 ,%>p s5ses1 memory1 judgm5t1 & practical sagacity h _h to be call$ into play1 & !re is n !re=e ! same direct consci\s & sole appeal to /ati/ics t !re 0 be=e4 ,! surgeon may h 9 8 m9d two or ?ree in/ances 9 :i* ! op]ation p]=m$ 0 equally sev]e1 b 9 :i* ! pati5t's con/itution 0 diff]5t2 ! latt] elem5t !re=e has to be prop]ly all[$ =4 ,!re may be o!r in/ances 9 :i* ! con/itution 0 simil>1 b ! op]ation m sev]e2 & s on4 ,h5ce1 al?\gh ! ultimate appeal may be to ! /ati/ics1 x is n s directly2 _! value has to be e/imat$ ?r\gh ! some:at hazy m$ium ( our judgm5t & memory1 :i* places !m "u a v diff]5t aspect4 #h4 ,any "o :o kn[s any?+ ( ! game ( :i/ may supply an apposite example ( ! di/9ction "h insi/$ on1 by recall+ to m9d ! alt]ation 9 ! nature ( our inf]5ces z ! game progresses4 ,at ! comm5cem5t ( ! game our sole appeal is rightfully made to ! !ory ( ,probability4 ,all ! rules ^u :i* ea* play] acts1 & !re=e ^u :i* he inf]s t ! o!rs w act1 re/ ^u ! obs]v$ frequ5cy 7or r ^u ! frequ5cy :i* calculation assures u w be obs]v$7 ) :i* su* & su* comb9ations ( c>ds are f\nd to occur4 ,:y are we told1 if we h m ?an f\r trumps1 to lead !m out at once8 ,because we are conv9c$1 on pure gr\nds ( probability1 capable ( be+ /at$ 9 ! /ricte/ /ati/ical =m1 t 9 a majority ( in/ances we %all draw our oppon5t's trumps1 & !re=e be left ) ! comm&4 ,simil>ly ) e o!r rule :i* is recogniz$ 9 ! e>ly "p ( ! play4 ,b z ! play progresses all ?is is *ang$1 & t[>ds its conclusion !re is b little reliance ^u any rules :i* ei!r we or o!rs c\ld base ^u /ati/ical frequ5cy ( occurr5ce1 obs]v$ or inf]r$4 ,a multitude ( o!r consid]ations h come 92 we beg9 to be influ5c$ p>tly by our k ( ! "* & practice ( our p>tn] & oppon5ts2 p>tly by a rapid comb9ation ( a multitude ( judgm5ts1 f\nd$ ^u our obs]vation ( ! actual c\rse ( play1 ! gr\nds ( :i* we c\ld h>dly realize or describe at ! "t & :i* may h be5 =gott5 s9ce4 ,t is1 ! p>ticul> comb9ation ( c>ds1 n[ be=e u1 does n readily fall into any well-m>k$ class to :i* alone x c reasonably be ref]r$ by e "o :o has ! facts be=e him4 #i4 ,a criticism some:at resembl+ ! above has be5 giv5 by ,mill 7,logic1 ,bk4 ,,iii4 ,*ap4 ,,xviii4 #c7 ^u ! applicability ( ! !ory ( ,probability to ! cr$ibility ( witnesses4 ,b he has add$ o!r reasons :i* d n appe> to me to be equally valid2 he says common s5se w\ld dictate t x is impossible to /rike a g5]al av]age ( ! v]acity1 & o!r qualifications = true te/imony1 ( mank9d or any class ( !m2 & if x 7 possible1 su* an av]age w\ld be no guide1 ! cr$ibility ( almo/ e witness be+ ei!r bel[ or above ! av]age1 ,! latt] objection w\ld h[ev] apply ) equal =ce to e/imat+ ! l5g? ( a man's life f tables ( mortality2 = ! cr$ibility ( diff]5t witnesses c sc>cely h a wid] range ( v>iation ?an ! l5g? ( diff]5t lives4 ,if /ati/ics ( cr$ibility c\ld be obta9$1 & c\ld be conv5i5tly appeal$ to :5 !y 7 obta9$1 !y might furni% u 9 ! long run ) z accurate inf]5ces z any o!r /ati/ics ( ! same g5]al description4 ,^! /ati/ics w\ld h[ev] 9 practice naturally & rightly be neglect$1 because !re c h>dly fail to be circum/ances 9 ea* individual /atem5t :i* w\ld m appropriately ref] x to "s new class dep5d+ on diff]5t /ati/ics1 & af=d+ a f> bett] *ance ( our be+ "r 9 t p>ticul> case4 ,9 mo/ in/ances ( ! k9d 9 "q1 inde$1 su* a *ange is ?us produc$ 9 ! mode ( =mation ( our op9ion1 t1 z already po9t$ out1 ! m5tal op]ation ceases to be 9 any prop] s5se f\nd$ on appeal to /ati/ics4#a #aj4 ,! ,*ance problems :i* are conc]n$ ) te/imony are n altoge!r conf9$ to su* in/ances z ^? hi!rto ref]r$ to4 ,?\gh we mu/1 z x appe>s to me1 reject all attempts to e/imate ! cr$ibility ( any p>ticul> witness1 or to ref] him to any assign$ class 9 respect ( 8 tru/wor?9ess1 & consequ5tly ab&on z unsuitable any ( ! num]\s problems :i* />t f su* data z 'a witness :o is wrong once 9 t5 times1' yet x does n foll[ t te/imony may n to a slight ext5t be treat$ by our sci5ce 9 a some:at diff]5t mann]4 ,we may be q unable to e/imate1 except 9 ! r\ghe/ possible way1 ! v]acity ( any p>ticul> witness1 & yet x may be possible to =m "s k9d ( op9ion ^u ! v]acity ( c]ta9 classes ( witnesses2 to say1 = in/ance1 t ,europeans are sup]ior 9 ?is way to ,ori5tals4 ,s we might attempt to expla9 :y1 & to :at ext5t1 an op9ion 9 :i* ! judgm5ts ( t5 p]sons1 say jurors1 concur1 is sup]ior to "o 9 :i* five only concur4 ,some?+ may also be done t[>ds lay+ d[n ! pr9ciples 9 accordance ) :i* we are to decide :e!r1 & :y1 extraord9>y /ories des]ve less cr$5ce ?an ord9>y ones1 ev5 if we _c arrive at any precise & def9ite decision ^u ! po9t4 ,?is la/ "q is fur!r discuss$ 9 ! c\rse ( ! next *apt]4 #aa4 ,! *ange ( view 9 accordance ) :i* x foll[s t que/ions ( ! k9d j m5tion$ ne$ n be entirely reject$ f sci5tific consid]ation1 pres5ts itself 9 o!r directions also4 ,x has1 = in/ance1 be5 already po9t$ out t ! individual *>act]i/ics ( any sick man's disease w\ld be q suffici5tly important 9 mo/ cases to prev5t any surgeon f judg+ ab\t 8 recov]y by a g5u9e & direct appeal to /ati/ics1 h[ev] su* consid]ations might indirectly op]ate ^u 8 judgm5t4 ,b if an op9ion _h to be =m$ ab\t a consid]able numb] ( cases1 say 9 a l>ge hospital1 /ati/ics might aga9 come prom95tly into play1 & be rightly recogniz$ z ! pr9cipal s\rce ( appeal4 ,we %\ld feel able to comp>e "o hospital1 or "o me?od ( treatm5t1 ) ano!r4 ,! gr\nd ( ! diff]5ce is obvi\s4 ,x arises f ! fact t ! *>act]i/ics ( ! individuals1 :i* made u s ready to des]t ! av]age :5 we _h to judge ( !m sep>ately1 d n produce ! same di/urbance :5 7 h to judge ab\t a gr\p ( cases4 ,! av]ages !n become ! mo/ secure & available gr\nd on :i* to =m an op9ion1 & !re=e ,probability aga9 becomes applicable4 ,b al?\gh "s resort to ,probability may be admitt$ 9 su* cases z ^!1 x nev]!less does n appe> to me t !y c ev] be reg>d$ z p>ticul>ly appropriate examples to illu/rate ! me?ods & res\rces ( ! !ory4 ,inde$ x is sc>cely possible to resi/ ! conviction t ! ref9em5ts ( ma!matical calculation h "h be5 pu%$ to l5g?s utt]ly unju/ifiable1 :5 we be> 9 m9d ! impossibility ( obta9+ any correspond+ degree ( accuracy & precision 9 ! data f :i* we h to />t4 ,to cite b "o in/ance4 ,x w\ld be h>d to f9d a case 9 :i* love ( consi/5cy has prevail$ ov] common s5se to su* an ext5t z 9 ! admission ( ! conclusion t x is unimportant :at are ! numb]s = & aga9/ a p>ticul> /atem5t1 provid$ ! actual majority is ! same4 ,t is1 ! unanim\s judgm5t ( a jury ( eight is to c\nt = ! same z a majority ( t5 to two 9 a jury ( twelve4 ,& yet ?is conclusion is admitt$ by ,poisson4 ,! assumptions "u :i* x foll[s w be indicat$ 9 ! c\rse ( ! next *apt]4 ,aga91 p]fect indep5d5ce among/ ! witnesses or jurors is an almo/ necess>y po/ulate4 ,b :]e c ?is be secur$8 ,to say no?+ ( direct collusion1 human be+s are 9 almo/ all in/ances greatly "u ! influ5ce ( sympa?y 9 =m+ _! op9ions4 ,?is influ5ce1 "u ! v>i\s names ( political bias1 class prejudice1 local feel+1 & s on1 always exi/s to a suffici5t degree to induce a cauti\s p]son to make _m ( ^? individual corrections :i* we saw to be necess>y :5 we 7 e/imat+ ! tru/wor?9ess1 9 any giv5 case1 ( a s+le witness2 t is1 !y are suffici5t to de/roy mu*1 if n all1 ( ! confid5ce ) :i* we resort to /ati/ics & av]ages 9 =m+ our judgm5t4 ,s9ce !n ?is ,essay is ma9ly devot$ to expla9+ & e/abli%+ ! g5]al pr9ciples ( ! sci5ce ( ,probability1 we may v fairly be excus$ f any fur!r treatm5t ( ?is subject1 beyond ! brief discussions :i* are giv5 9 ! next *apt]4 #a4 ,x may be rem>k$ also t !re is ano!r reason :i* t5ds to dissuade u f appeal+ to pr9ciples ( ,probability 9 ! majority ( ! cases :]e te/imony has to be e/imat$4 ,x (t51 p]haps usually happ5s1 t we are n absolutely =c$ to come to a decision2 at lea/ s f> z ! acquitt+ ( an accus$ p]son may be consid]$ z avoid+ a decision4 ,x may be ( mu* great] importance to u to atta9 n m]ely tru? on ! av]age1 b tru? 9 ea* individual in/ance1 s t we _h r n =m an op9ion at all ?an =m "o ( :i* we c only say 9 its ju/ification t x w t5d to lead u "r 9 ! long run4 ,,*apt] ,,xvii4 ,,on ,,! ,,cr$ibility ,,( ,,extraord9>y ,,/ories4 #a4 ,x is n[ "t to recur = full] inve/igation to an enquiry :i* has be5 already briefly t\*$ ^u m ?an once2 t is1 ! validity ( te/imony to e/abli%1 z x is frequ5tly express$1 an o!rwise improbable /ory4 ,x w be rememb]$ t 9 a previ\s *apt] 7! twelf?7 we devot$ "s exam9ation to an ass]tion by ,butl]1 :i* seem$ to be to "s ext5t c\nt5anc$ by ,mill1 t a great improbability be=e ! pro( might become b a v small improbability aft] ! pro(4 ,9 opposition to ?is x 0 po9t$ out t ! diff]5t e/imates :i* we und\bt$ly =m$ ( ! cr$ibility ( ! examples adduc$1 _h no?+ to d ) ! fact ( ! ev5t be+ pa/ or future1 b arose f a v diff]5t cause2 t ! conception ( ! ev5t :i* we ent]ta9 at ! mom5t 7:i* is all t is !n & !re actually pres5t to u1 & z to ! correctness ( :i* z a repres5tation ( facts we h to make up our m9ds7 comes be=e u 9 two v diff]5t ways4 ,9 "o in/ance x 0 a m]e guess ( our own :i* we knew f /ati/ics w\ld be "r 9 a c]ta9 proportion ( cases2 9 ! o!r in/ance x 0 ! ass]tion ( a witness1 & !re=e ! appeal 0 n n[ prim>ily to /ati/ics ( ! ev5t1 b to ! tru/wor?9ess ( ! witness4 ,! conception1 or 'ev5t' if we w s t]m x1 _h 9 fact pass$ out ( ! category ( guesses 7on /ati/ical gr\nds71 into t ( ass]tions 7mo/ likely re/+ on "s specific evid5ce71 & w\ld !re=e be naturally reg>d$ 9 a v diff]5t light4 #b4 ,b x may seem z if ?is pr9ciple w\ld lead u to some:at />tl+ conclusions4 ,=1 by transf]r+ ! appeal f ! frequ5cy ) :i* ! ev5t occurs to ! tru/wor?9ess ( ! witness :o makes ! ass]tion1 is x n impli$ t ! probability or improbability ( an ass]tion dep5ds solely ^u ! v]acity ( ! witness8 ,if s1 ought n any /ory :atev] to be believ$ :5 x is ass]t$ by a tru?ful p]son8 ,9 ord] to settle ?is "q we mu/ look a little m closely into ! circum/ances "u :i* su* te/imony is commonly pres5t$ to u4 ,z x is ( c\rse necess>y1 = cle>ness ( exposition1 to take a num]ical example1 let u suppose t a giv5 /atem5t is made by a witness :o1 on ! :ole & 9 ! long run1 is "r 9 :at he says n9e times out ( t54#a ,"h !n is an av]age giv5 to u1 an av]age v]acity t is1 :i* includes all ! p>ticul> /atem5ts :i* ! witness has made or w make4 #c4 ,n[ x has be5 abundantly %[n 9 a =m] *apt] 7,*4 ,,ix4 #ad-cb7 t ! m]e fact ( a p>ticul> av]age hav+ be5 assign$1 is no reason = our be+ =c$ inv>iably to adh]e to x1 ev5 9 ^? cases 9 :i* our mo/ natural & appropriate gr\nd ( judgm5t is f\nd 9 an appeal to /ati/ics & av]ages4 ,! g5]al av]age may con/antly h to be correct$ 9 ord] to meet m accurately ! circum/ances ( p>ticul> cases4 ,9 /ati/ics ( mortality1 = in/ance2 in/ead ( resort+ to ! wid] tables furni%$ by p 9 g5]al ( a giv5 age1 we (t5 pref] ! n>r[] tables furni%$ by m5 ( a p>ticul> pr(ession1 abode1 or mode ( life4 ,! read] may h[ev] be conv5i5tly rem9d$ "h t 9 s do+ we mu/ n suppose t we are able1 by any su* device1 9 any special or peculi> way to secure tru?4 ,! g5]al av]age1 if p]si/5tly adh]$ to ?r\gh\t a suffici5tly wide & v>i$ exp]i5ce1 w\ld 9 ! long run t5d to give u ! tru?2 all ! advantage :i* ! m special av]ages c secure = u is to give u ! same t5d5cy to ! tru? ) few] & slight] ab]rations4 #d4 ,return+ !n to our witness1 we "k t if we h a v great _m /atem5ts f him ^u all possible subjects1 we may feel conv9c$ t 9 n9e out ( t5 ( ^! he w tell u ! tru?1 & t 9 ! t5? case he w g wrong4 ,?is is no?+ m ?an a matt] ( def9ition or consi/5cy4 ,b _c we d bett] ?an ?us rely ^u 8 g5]al av]age8 ,_c we1 9 almo/ any giv5 case1 specialize x by att5d+ to v>i\s *>act]i/ic circum/ances 9 ! nature ( ! /atem5t :i* he makes2 j z we specialize 8 prospects ( mortality by att5d+ to circum/ances 9 8 con/itution or mode ( life8 ,und\bt$ly we may d ?is2 & 9 any ( ! practical cont+5cies ( life1 suppos+ t we 7 at all guid$ by consid]ations ( ?is nature1 we %\ld act v fooli%ly if we did n adopt "s su* plan4 ,two me?ods ( ?us correct+ ! av]age may be sugge/$3 "o ( !m be+ t :i* practical sagacity w\ld be mo/ likely to employ1 ! o!r t :i* is almo/ univ]sally adopt$ by writ]s on ,probability4 ,! =m] attempts to make ! correction by ! foll[+ consid]ations3 in/ead ( rely+ ^u ! witness' g5]al av]age1 we assign to x a sort ( conjectural correction to meet ! case be=e u1 f\nd$ on our exp]i5ce or obs]vation2 t is1 we appeal to exp]i5ce to e/abli% t /ories ( su* & su* a k9d are m or less likely to be true1 z ! case may be1 ?an /ories 9 g5]al4 ,! o!r proce$s ^u a diff]5t & some:at m me?odical plan4 ,x is "h endeav\r$ to %[1 by an analysis ( ! nature & numb] ( ! s\rces ( error 9 ! cases 9 "q1 t su* & su* k9ds ( /ories mu/ be m or less likely to be correctly report$1 & ?is 9 c]ta9 num]ical proportions4 #e4 ,be=e proce$+ to a discussion ( ^! me?ods a di/9ction mu/ be po9t$ out to :i* writ]s ^u ! subject h n always att5d$1 or at any rate to :i* !y h n g5]ally suffici5tly direct$ _! read]s' att5tion4#b ,!re are1 broadly speak+1 two diff]5t ways 9 :i* we may suppose te/imony to be giv54 ,x may1 9 ! fir/ place1 take ! =m ( a reply to an alt]native "q1 a "q1 t is1 fram$ to be answ]$ by yes or no4 ,"h1 ( c\rse1 ! possible answ]s are mutually contradictory1 s t if "o ( !m is n correct ! o!r mu/ be s3--,has ,a happ5$1 yes or no8 ,! common mode ( illu/rat+ ?is k9d ( te/imony num]ically is by suppos+ a lott]y ) a prize & blanks1 or a bag ( balls ( two col\rs only1 ! witness kn[+ t !re are only two1 or at any rate be+ conf9$ to nam+ "o or o!r ( !m4 ,if !y are black & :ite1 & he errs :5 black is drawn1 he mu/ say ':ite1' ,! reason = ! prom95ce assign$ to examples ( ?is class is1 probably1 t !y correspond to ! v important case ( v]dicts ( juries2 juries be+ suppos$ to h no?+ else to d ?an to say 'guilty' or 'n guilty4' ,on ! o!r h&1 ! te/imony may take ! =m ( a m orig9al /atem5t or piece ( in=mation4 ,in/ead ( say+1 ,did ,a happ58 we may ask1 ,:at happ5$8 ,"h if ! witness speaks tru? he mu/ be suppos$1 z be=e1 to h b "o way ( do+ s2 = ! occurr5ce ( "s specific ev5t 0 ( c\rse contemplat$4 ,b if he errs he has _m ways ( go+ wrong1 possibly an inf9ite numb]4 ,ord9>ily h[ev] 8 possible false /atem5ts are assum$ to be limit$ 9 numb]1 z mu/ g5]ally be m or less ! result 9 practice4 ,?is case is repres5t$ num]ically by suppos+ ! balls 9 ! bag n to be ( two col\rs only1 b to be all di/9ct f ea* o!r2 say by _! be+ all numb]$ successively4 ,x may ( c\rse be object$ t a l>ge numb] ( ! /atem5ts t are made 9 ! _w are n 9 any way answ]s to que/ions1 ei!r ( ! alt]native or ( ! op5 k9d4 ,= in/ance1 a man simply ass]ts t he has drawn ! sev5 ( spades f a pack ( c>ds2 & we d n "k p]haps :e!r he _h be5 ask$ ',has t c>d be5 drawn8' or ',:at c>d has be5 drawn8' or inde$ :e!r he _h be5 ask$ any?+ at all4 ,/ill m might ?is be s 9 ! case ( any ord9>y hi/orical /atem5t4 ,?is objection is q to ! po9t1 & mu/ be recogniz$ z con/itut+ an additional difficulty4 ,all t we c d is to endeav\r1 z be/ we may1 to asc]ta91 f ! circum/ances ( ! case1 :at numb] ( alt]natives ! witness may be suppos$ to h _h be=e him4 ,:5 he simply te/ifies to "s matt] well kn[n to be 9 dispute1 & does n g mu* into detail1 we may fairly consid] t !re 7 practically only ! two alt]natives be=e him ( say+ 'yes' or 'no4' ,:51 on ! o!r h&1 he tells a /ory ( a m orig9al k9d1 or 7:at comes to mu* ! same ?+7 goes into details1 we mu/ reg>d him z hav+ a wide comp>ative range ( alt]natives be=e him4 ,^! two classes ( examples1 viz4 t ( ! black & :ite balls1 9 :i* only "o =m ( error is possible1 & ! numb]$ balls1 9 :i* !re may be _m =ms ( error1 are ! only two :i* we ne$ notice4 ,9 practice x w\ld seem t !y may gradually m]ge into ea* o!r1 accord+ to ! v>y+ ways 9 :i* we *oose to frame our "q4 ,besides ask+1 ,did y see ,a /rike ,b8 &1 ,:at did y see8 we may introduce any numb] ( int]m$iate lead+ que/ions1 z1 ,:at did ,a d8 ,:at did he d to ,b8 & s on4 ,9 ?is way we may gradually n>r[ ! possible op5+s to wrong /atem5t1 & s approa* to ! direct alt]native "q4 ,b x is cle> t all ^! cases may be repres5t$ num]ically by a suppos$ dim9ution 9 ! numb] ( ! balls :i* are ?us di/+ui%$ f ea* o!r4 #f4 ,( ! two plans m5tion$ 9 #d we w beg9 ) ! latt]1 z x is ! only me?odical & sci5tific "o :i* has be5 propos$4 ,suppose t !re is a bag ) #ajjj balls1 only "o ( :i* is :ite1 ! re/ be+ all black4 ,a ball is drawn at r&om1 & our witness ^: v]acity is #i_/aj reports t ! :ite ball 0 drawn4 ,take a great _m ( 8 /atem5ts ^u ?is p>ticul> subject1 say #aj1jjj2 t is1 suppose t #aj1jjj balls hav+ be5 successively drawn out ( ?is bag1 or bags ( exactly ! same k9d1 he makes 8 report 9 ea* case4 ,8 #aj1jjj /atem5ts be+ tak5 z a fair sample ( 8 g5]al av]age1 we %all f9d1 by supposition1 t #i out ( e #aj ( !m are true & ! rema9+ "o false4 ,:at w be ! nature ( ^! false /atem5ts8 ,"u ! circum/ances 9 "q1 he hav+ only "o way ( go+ wrong1 ! answ] is easy4 ,9 ! #aj1jjj draw+s ! :ite ball w\ld come out #aj times1 & !re=e be rightly ass]t$ #i times1 :il/ on ! "o ( ^! occasions on :i* he goes wrong he has no?+ to say b 'black4' ,s ) ! #iiij occasions on :i* black is drawn2 he is "r & says black on #hiia ( !m1 & is wrong & !re=e says :ite on #iii ( !m4 ,on ! :ole1 !re=e1 we conclude t out ( e #ajjh times on :i* he says t :ite is drawn he is wrong #iii times & "r only #i times4 ,t is1 8 special v]acity1 z we may t]m x1 = cases ( ?is description1 has be5 r$uc$ f #i_/aj to #i_/ajjh4 ,z x w\ld commonly be express$1 ! latt] fraction repres5ts ! *ance t ?is p>ticul> /atem5t ( 8 is true4#c #g4 ,we w n[ take ! case 9 :i* ! witness has _m ways ( go+ wrong1 in/ead ( m]ely "o4 ,suppose t ! balls 7 all numb]$1 f #a to #a1jjj1 & ! witness kn[s ?is fact4 ,a ball is drawn1 & he tells me t x 0 numb]$ #be1 :at are ! odds t he is "r8 ,proce$+ z be=e1 9 #aj1jjj draw+s ?is ball w\ld be obta9$ #aj times1 & correctly nam$ #i times4 ,b on ! #iiij occasions on :i* x 0 n drawn !re w\ld be a diff]5ce1 = ! witness has n[ _m op5+s = error be=e him4 ,x is1 h[ev]1 g5]ally consid]$ reasonable to assume t 8 errors w all take ! =m ( ann\nc+ wrong numb]s2 & t1 !re be+ no app>5t reason :y he %\ld *oose "o numb] r ?an ano!r1 he w be likely to ann\nce all ! wrong ones equally (t54 ,h5ce 8 #iii errors1 in/ead ( all lead+ him n[ back aga9 to "o spot1 w be uni=mly spread ov] z _m di/9ct ways ( go+ wrong4 ,on "o only ( ^! occasions1 !re=e1 w he m5tion #be z hav+ be5 drawn4 ,x foll[s !re=e t out ( e #aj times t he names #be he is "r #i times2 s t 9 ?is case 8 av]age or g5]al tru?fulness applies equally well to ! special case 9 po9t4 #h4 ,) reg>d to ! tru? ( ^! conclusions1 x mu/ ( c\rse be admitt$ t if we grant ! validity ( ! assumptions ab\t ! limits )9 :i* ! blund]+ or m5dacity ( ! witness are conf9$1 & ! complete imp>tiality ) :i* 8 answ]s are dispos$ )9 ^? limits1 ! reason+ is p]fectly s\nd4 ,b are n ^! assumptions extremely arbitr>y1 t is1 are n our lott]ies & bags ( balls r5d]$ p]fectly precise 9 _m respects 9 :i*1 9 ord9>y life1 ! conditions suppos$ to correspond to !m are s vague & unc]ta9 t no su* me?od ( reason+ becomes practically available8 ,suppose t a p]son :om ,i h long kn[n1 & ( ^: measure ( v]acity & judgm5t ,i may be suppos$ !re=e to h acquir$ "s k1 in=ms me t !re is some?+ to my advantage if ,i *oose to g to c]ta9 tr\ble or exp5se 9 ord] to secure x4 ,z reg>ds ! g5]al v]acity ( ! witness1 !n1 !re is no difficulty2 we suppose t ?is is det]m9$ = u4 ,b z reg>ds 8 /ory1 difficulty & vagu5ess em]ge at e po9t4 ,:at is ! numb] ( balls 9 ! bag "h8 ,:at 9 fact are ! nature & cont5ts ( ! bag out ( :i* we suppose ! draw+ to h be5 made8 ,x does n seem t ! mat]ials = any rational judgm5t exi/ "h4 ,b if we are to get at any su* am5d$ figure ( v]acity z ^? atta9$ 9 ! above example1 ^! que/ions mu/ necess>ily be answ]$ ) "s degree ( accuracy2 = ! ma9 po9t ( ! me?od consi/s 9 det]m9+ h[ (t5 ! ev5t mu/ be consid]$ n to happ51 & !nce inf]r+ h[ (t5 ! witness w be l$ wrongly to ass]t t x has happ5$4 ,x is n ( c\rse d5i$ t consid]ations ( ! k9d 9 "q h "s influ5ce ^u our decision1 b only t ?is influ5ce c\ld "u any ord9>y circum/ances be submitt$ to num]ical det]m9ation4 ,we are d\btless liable to h in=mation giv5 to u t we h come 9 = "s k9d ( =tune1 = in/ance1 :5 no su* good luck has really befall5 u2 & ?is n once only b repeat$ly4 ,b :o c give ! fa9te/ intimation ( ! nature & numb] ( ! occasions on :i*1 a blank be+ ?us really drawn1 a prize w nev]!less be falsely ann\nc$8 ,x appe>s to me !re=e t num]ical results ( any practical value c seldom1 if ev]1 be look$ = f ?is me?od ( proc$ure4 #i4 ,our conclusion 9 ! case ( ! lott]y1 or1 :at comes to ! same ?+1 9 ! case ( ! bag ) black & :ite balls1 has be5 que/ion$ or object$ to#d on ! gr\nd t x is contr>y to all exp]i5ce to suppose t ! te/imony ( a mod]ately good witness c\ld be s enorm\sly depreciat$ "u su* circum/ances4 ,i %\ld pref] to base ! objection on ! gr\nd t exp]i5ce sc>cely ev] pres5ts su* circum/ances z ^? suppos$2 b if we po/ulate _! exi/5ce ! giv5 conclusion seems correct en\gh4 ,assume t a man is m]ely requir$ to say yes or no2 assume also a gr\p or succession ( cases 9 :i* no %\ld rightly be said v mu* (t5] ?an yes4 ,!n1 assum+ almo/ any g5]al tru?fulness ( ! witness1 we may easily suppose ! rightful occasions = d5ial to be s mu* ! m frequ5t t a majority ( 8 affirmative answ]s w actually occur z false 'noes' r ?an z correct 'ayes4' ,?is ( c\rse l[]s ! av]age value ( 8 'ayes1' & r5d]s !m comp>atively untru/wor?y4 ,consid] ! foll[+ example4 ,i h a g>d5] :om ,i tru/ z to all ord9>y matt]s ( fact4 ,if he 7 to tell me "s morn+ t my dog _h run away ,i %\ld fully believe him4 ,he tells me h[ev] t ! dog has gone mad4 ,surely ,i %\ld accept ! /atem5t ) mu* hesitation1 & on ! gr\nds indicat$ above4 ,x is n t he is m likely to be wrong :5 ! dog is mad2 b t exp]i5ce %[s t !re are o!r compla9ts 7e4g4 fits7 :i* are f> m common ?an madness1 & t mo/ ( ! ass]tions ( madness are errone\s ass]tions ref]r+ to ^!4 ,?is seems a some:at p>allel case to t 9 :i* we f9d t mo/ ( ! ass]tions t a :ite ball _h be5 drawn are really false ass]tions ref]r+ to ! draw+ ( a black ball4 ,practically ,i d n ?9k t any "o w\ld feel a difficulty 9 ?us exorbitantly disc\nt+ "s p>ticul> ass]tion ( a witness :om 9 mo/ o!r respects he fully tru/$4 #aj4 ,!re is "o p>ticul> case :i* has be5 reg>d$ z a difficulty 9 ! way ( ?is treatm5t ( ! problem1 b :i* seems to me to be a decid$ confirmation ( x2 always1 be x und]/ood1 )9 ! v n>r[ & artificial limits to :i* we mu/ suppose ourselves to be conf9$4 ,?is is ! case ( a witness ^: v]acity is j "o-half2 t is1 "o :o1 :5 a m]e yes or no is dem&$ ( him1 is z (t5 wrong z "r4 ,9 ! case ( any o!r assign$ degree ( v]acity x is extremely difficult to get any?+ approa*+ to a confirmation f practical judgm5t & exp]i5ce4 ,we are n accu/om$ to e/imate ! m]its ( witnesses 9 ?is way1 & h>dly appreciate :at is meant by 8 num]ical degree ( tru?fulness4 ,b z reg>ds ! man ^: v]acity is "o-half1 we are 7z ,mr ,c4 ,j4 ,monro has v +5i\sly sugge/$7 only too well acqua9t$ ) su* witnesses1 ?\gh "u a some:at diff]5t "n2 = ?is is really no?+ else ?an ! case ( a p]son confid5tly answ]+ a "q ab\t a subject-matt] ( :i* he kn[s no?+1 & c !re=e only give a m]e guess4 ,n[ 9 ! case ( ! lott]y ) "o prize1 :5 ! witness ^: v]acity is "o-half tells u t we h ga9$ ! prize1 we f9d on calculation t 8 te/imony goes = absolutely no?+2 ! *ances t we h got ! prize are j ! same z !y w\ld be if he _h nev] op5$ 8 lips1 viz4 #a_/ajjj4 ,b cle>ly ?is is :at ought to be ! result1 = ! witness :o kn[s no?+ ab\t ! matt] leaves x exactly z he f\nd x4 ,he is inde$1 9 /rictness1 sc>cely a witness at all2 = ! natural function ( a witness is to exam9e ! matt]1 & s to add confirmation1 m or less1 accord+ to 8 judgm5t & probity1 b at any rate to (f] an improvem5t ^u ! m]e guess]4 ,if1 h[ev]1 we w give he$ to 8 m]e guess we are do+ j ! same ?+ z if we 7 to guess ourselves1 9 :i* case ( c\rse ! odds t we are "r are simply measur$ by ! frequ5cy ( occurr5ce ( ! ev5ts4 ,we _c q s readily apply ! same rule to ! o!r case1 namely to t ( ! numb]$ balls1 = !re ! witness :o is "r e o!r "t may really be a v fair1 or ev5 excell5t1 witness4 ,if he has _m ways ( go+ wrong1 & yet is "r 9 half 8 /atem5ts1 x is cle> t he mu/ h tak5 "s degree ( c>e1 & _c h m]ely guess$4 ,9 a case ( yes or no1 any "o c be "r e o!r "t1 b x is diff]5t :]e tru? is s+le & error is manifold4 ,to repres5t ! case ( a simply wor?less witness :5 !re 7 #ajjj balls & ! draw+ ( "o assign$ ball 0 9 "q1 we %\ld h to put 8 figure ( v]acity at #a_/ajjj4 ,if ?is 7 done we %\ld ( c\rse get a simil> result4 #aa4 ,x des]ves notice !re=e t ! figure ( v]acity1 or fraction repres5t+ ! g5]al tru?fulness ( a witness1 is 9 a way relative1 n absolute2 t is1 x dep5ds ^u1 & v>ies )1 ! g5]al "* ( ! answ] :i* he is suppos$ to give4 ,two witnesses ( equal intr9sic v]acity & wor?1 "o ( :om conf9$ himself to say+ yes & no1 :il/ ! o!r v5tur$ to make m orig9al ass]tions1 w\ld be repres5t$ by diff]5t fractions2 ! =m] hav+ set himself a mu* easi] task ?an ! latt]4 ,! real caution & tru?fulness ( ! witness are only "o factor1 !re=e1 9 8 actual figure ( v]acity2 ! o!r factor consi/s ( ! nature ( 8 ass]tions1 z j po9t$ out4 ,! ord9>y plan !re=e1 9 su* problems1 ( assign+ an av]age tru?fulness to ! witness1 & accept+ ?is alike 9 ! case ( ea* ( ! two k9ds ( answ]s1 ?\gh conv5i5t1 seems sc>cely s\nd4 ,?is consid]ation w\ld h[ev] be ( mu* m importance 7 n ! discussions ^u ! subject ma9ly conc]n$ ) only "o description ( answ]1 namely t ( ! 'yes or no' k9d4 #ab4 ,s mu* = ! me?odical way ( treat+ su* a problem4 ,! way 9 :i* x w\ld be tak5 9 h& by ^? :o _h made no /udy ( ,probability is v diff]5t4 ,x w\ld1 ,i appreh5d1 /rike !m z foll[s4 ,!y w\ld say to !mselves1 ,"h is a /ory relat$ by a witness :o tells ! tru?1 say1 n9e times out ( t54 ,b x is a /ory ( a k9d :i* exp]i5ce %[s to be v g5]ally made untruly1 say #ii times out ( #ajj4 ,hav+ !n ^! opposite inducem5ts to belief1 !y w\ld attempt 9 "s way to /rike a balance betwe5 !m4 ,no?+ 9 ! nature ( a /rict rule c\ld be giv5 to enable !m to decide h[ !y might escape out ( ! difficulty4 ,probably1 9 s f> z !y did n judge at haphaz>d1 !y w\ld be guid$ by /ill fur!r resort to exp]i5ce1 or unconsci\s recollections ( its previ\s tea*+s1 9 ord] to settle :i* ( ! two oppos+ inductions 0 bett] entitl$ to c>ry ! day 9 ! p>ticul> case be=e !m4 ,! read] w readily see t any g5]al solution ( ! problem1 :5 ?us pres5t$1 is impossible4 ,x is simply ! n[ famili> case 7,*ap4 ,,ix4 #ad-cb7 ( an individual :i* belongs equally to two di/9ct1 or ev51 9 respect ( _! *>act]i/ics1 oppos+ classes4 ,we _c decide (f-h& to :i* ( ! two its *>act]i/ics mo/ naturally & rightly ref] x4 ,a fre% induction is ne$$ 9 ord] to settle ?is po9t4 #ac4 ,rules h inde$ be5 sugge/$ by v>i\s writ]s 9 ord] to extricate u f ! difficulty4 ,! controv]sy ab\t miracles has probably be5 ! mo/ f]tile occasion = sugge/ions ( ?is k9d on "o side or ! o!r4 ,x is to ?is controv]sy1 presumably1 t ! phrase is due1 s (t5 employ$ 9 discussions ^u simil> subjects1 'a conte/ ( opposite improbabilities4' ,:at is meant by su* an expression is cle>ly ?is3 t 9 =m+ a judgm5t ^u ! tru? ( c]ta9 ass]tions we may f9d t !y are compris$ 9 two v di/9ct classes1 s t1 accord+ z we reg>d$ !m z belong+ to "o or ! o!r ( ^! di/9ct classes1 our op9ion z to _! tru? w\ld be v diff]5t4 ,su* an ass]tion belongs to "o class1 ( c\rse1 by its be+ a /atem5t ( a p>ticul> witness1 or k9d ( witness2 x belongs to ! o!r by its be+ a p>ticul> k9d ( /ory1 "o ( :at is call$ an improbable nature4 ,its belong+ to ! =m] class is s f> fav\rable to its tru?1 its belong+ to ! latt] is s f> ho/ile to its tru?4 ,x seems to be assum$1 9 speak+ ( a conte/ ( opposite improbabilities1 t :5 ^! diff]5t s\rces ( conviction co-exi/ toge!r1 !y w\ld ea* 9 "s way reta9 _! probative =ce s z to produce a conte/1 end+ g5]ally 9 a victory to "o or o!r ( !m4 ,hume1 = in/ance1 speaks ( our d$uct+ "o probability f ! o!r1 & apportion+ our belief to ! rema9d]4#e ,?omson1 9 8 ,laws ( ,?\ght1 speaks ( "o probability z entirely sup]s$+ ! o!r4 #ad4 ,x does n appe> to me t ! slighte/ philosophical value c be atta*$ to any su* rules z ^!4 ,!y d\btless may1 & inde$ w1 hold 9 individual cases1 b !y _c lay claim to any g5]ality4 ,ev5 ! notion ( a conte/1 z any necess>y +r$i5t 9 ! case1 mu/ be laid aside4 ,= let u ref] aga9 to ! way 9 :i* ! p]plexity arises1 & we %all readily see1 z has j be5 rem>k$1 t x is no?+ m ?an a p>ticul> exemplification ( a difficulty :i* has already be5 recogniz$ z incapable ( solution by any g5]al priori me?od ( treatm5t4 ,all t we are suppos$ to h be=e u is a /atem5t4 ,on ?is occasion x is made by a witness :o lies1 say1 once 9 t5 times 9 ! long run2 t is1 :o mo/ly tells ! tru?4 ,b on ! o!r h&1 x is a /atem5t :i* exp]i5ce1 d]iv$ f a v>iety ( witnesses on v>i\s occasions1 assures u is mo/ly false2 /at$ num]ically x is f\nd1 let u suppose1 to be false #ii times 9 a hundr$4 ,n[1 z 0 %[n 9 ! *apt] on ,induction1 we are ?us br\ght to a complete dead lock4 ,our sci5ce (f]s no pr9ciples by :i* we c =m an op9ion1 or attempt to decide ! matt] "o way or ! o!r2 =1 z we f\nd1 !re are an indef9ite numb] ( conclusions :i* are all equally possible4 ,= in/ance1 all ! witness' extraord9>y ass]tions may be true1 or !y may all be false1 or !y may be divid$ into ! true & ! false 9 any proportion :atev]4 ,hav+ gone s f> 9 our appeal to /ati/ics z to recognize t ! witness is g5]ally "r1 b t 8 /ory is g5]ally false1 we _c /op !re4 ,we ought to make /ill fur!r appeal to exp]i5ce1 & asc]ta9 h[ x /&s ) reg>d to 8 /ories :5 !y are ( t p>ticul> nature3 or r1 = ?is w\ld be to make a ne$lessly n>r[ ref]5ce1 h[ x /&s ) reg>d to /ories ( t k9d :5 advanc$ by witnesses ( 8 g5]al "*1 position1 sympa?ies1 & s on4#f #ae4 ,t extraord9>y /ories are 9 _m cases1 probably 9 a great majority ( cases1 less tru/wor?y ?an o!rs mu/ be fully admitt$4 ,t is1 if we 7 to make two di/9ct classes ( su* /ories respectively1 we %\ld f9d t ! same witness1 or simil> witnesses1 7 proportionally m (t5 wrong :5 ass]t+ ! =m] ?an :5 ass]t+ ! latt]4 ,b x does n by any means appe> to me t ?is mu/ always be ! case4 ,we may well conceive1 = in/ance1 t ) "s p ! m]e fact ( ! /ory be+ ( a v unusual "* may make !m m c>eful 9 :at !y /ate1 s z actually to add to _! v]acity4 ,if ?is 7 s we might be ready to accept _! extraord9>y /ories ) ev5 m read9ess ?an _! ord9>y ones4 ,su* a supposition z t j made does n seem to me by any means =c$4 ,put su* a case z ?is3 let u suppose t two p]sons1 "o ( !m a man ( m]ely ord9>y probity & intellig5ce1 ! o!r a sci5tific naturali/1 make a /atem5t ab\t "s common ev5t4 ,we believe !m bo?4 ,let !m n[ ea* report "s extraord9>y lusus natur or mon/rosity :i* !y pr(ess to h se54 ,mo/ p]sons1 we may presume1 w\ld receive ! /atem5t ( ! naturali/ 9 ?is latt] case almo/ z readily z 9 ! =m]3 :]eas :5 ! same /ory came f ! unsci5tific obs]v] x w\ld be receiv$ ) consid]able hesitation4 ,:5ce arises ! diff]5ce8 ,f ! conviction t ! naturali/ w be f> m c>eful1 & !re=e to ! full z accurate1 9 matt]s ( ?is k9d z 9 ^? ( ! mo/ ord9>y description1 :]eas ) ! o!r man we feel by no means ! same confid5ce4 ,ev5 if any "o is n prep>$ to g ?is l5g?1 he w probably admit t ! diff]5ce ( cr$it :i* he w\ld atta* to ! two k9ds ( /ory1 respectively1 :5 !y came f ! naturali/1 w\ld be mu* less ?an :at x w\ld be :5 !y came f ! o!r man4 #af4 ,:il/ we are on ?is "p ( ! subject1 x mu/ be po9t$ out t !re is consid]able ambiguity & consequ5t confusion ab\t ! use ( ! t]m 'an extraord9>y /ory4' ,)9 ! prov9ce ( pure ,probability x ought to mean simply a /ory :i* ass]ts an unusual ev5t4 ,at lea/ ?is is ! view :i* has be5 adopt$ & ma9ta9$1 x is hop$ consi/5tly1 ?r\gh\t ?is "w4 ,s long z we adh]e to ?is s5se we "k precisely :at we mean by ! t]m4 ,x has a purely objective ref]5ce2 x simply connotes a v l[ degree ( relative /ati/ical frequ5cy1 actual or prospective4 ,out ( a great numb] ( ev5ts we suppose a selection ( "s p>ticul> k9d to be contemplat$1 :i* occurs relatively v seldom1 & ?is is t]m$ an unusual or extraord9>y ev5t4 ,x foll[s1 z 0 abundantly %[n 9 a =m] *apt]1 t ow+ to ! r>ity ( ! ev5t we are v little dispos$ to expect its occurr5ce 9 any giv5 case4 ,our guess ab\t x1 9 case we ?us anticipat$ x1 w\ld v seldom be ju/ifi$1 & we are !re=e apt to be mu* surpris$ :5 x does occur4 ,?is1 ,i take x1 is ! only legitimate s5se ( 'extraord9>y' s f> z ,probability is conc]n$4 ,b !re is ano!r & v diff]5t use ( ! ^w1 :i* belongs to ,induction1 or r to ! sci5ce ( evid5ce 9 g5]al1 m ?an to t limit$ portion ( x t]m$ ,probability4 ,9 ?is s5se ! 'extraord9>y1' & /ill m ! 'improbable1' ev5t is n m]ely "o ( extreme /ati/ical r>ity1 :i* we c\ld n expect to guess aright1 b :i* on mod]ate evid5ce we may pretty readily accept2 x is r "o :i* possesses1 s to say1 an actual evid5ce-resi/+ p[]4 ,x may be some?+ :i* affects ! cr$ibility ( ! witness at ! f\nta9-head1 :i* makes1 t is1 8 /atem5ts ^u su* a subject ess5tially inf]ior to ^? on o!r subjects4 ,?is is ! case1 = in/ance1 ) any?+ :i* excites 8 prejudices or passions or sup]/itions4 ,9 ^! cases x w\ld seem unreasonable to attempt to e/imate ! cr$ibility ( ! witness by calculat+ 7z 9 #f7 h[ (t5 8 errors w\ld mislead u ?r\gh 8 hav+ be5 wrongly br\ght to an affirmation in/ead ( adh]+ correctly to a negation4 ,we %\ld r be dispos$ to put our correction on ! witness' av]age v]acity at once4 #ag4 ,9 true ,probability1 z has j be5 rem>k$1 e ev5t has its own def9itely recognizable degree ( frequ5cy ( occurr5ce4 ,x may be excessively r>e1 r>e to any extreme we l to po/ulate1 b /ill e "o :o und]/&s & admits ! data ^u :i* its occurr5ce dep5ds w be able to appreciate )9 :at range ( exp]i5ce x may be expect$ to pres5t itself4 ,we d n expect x 9 any individual case1 nor )9 any brief range1 b we d confid5tly expect x )9 an adequately ext5sive range4 ,h[ !re=e c miracul\s /ories be simil>ly tak5 acc\nt (1 :5 ! disputants1 on "o side at lea/1 are n prep>$ to admit _! actual occurr5ce any:]e or at any "t8 ,h[ c any arrangem5t ( bags & balls1 or o!r me*anical or num]ical illu/rations ( unlikely ev5ts1 be admitt$ z fairly illu/rative ( miracul\s occurr5ces1 or inde$ ( _m ( ^? :i* come "u ! designation ( 'v extraord9>y' or 'highly improbable'8 ,^? :o conte/ ! occurr5ce ( a p>ticul> miracle1 z report$ by ?is or t n>rator1 d n admit t miracles are to be confid5tly expect$ soon] or lat]4 ,x is n a "q z to :e!r :at mu/ happ5 sometimes has happ5$ "s p>ticul> "t1 & !re=e no illu/ration ( ! k9d c be reg>d$ z apposite4 ,h[ unsuitable ^! m]ely r>e ev5ts1 h[ev] excessive _! r>ity may be1 are z examples ( miracul\s ev5ts1 w be evid5t f a s+le consid]ation4 ,no "o1 ,i presume1 :o admitt$ ! occasional occurr5ce ( an exce$+ly unusual comb9ation1 w\ld be 9 mu* d\bt if he consid]$ t he _h actually se5 x himself4#g ,on ! o!r h&1 few m5 ( any really sci5tific turn w\ld readily accept a miracle ev5 if x appe>$ to happ5 "u _! v eyes4 ,!y might be /agg]$ at ! "t1 b !y w\ld probably soon come to discr$it x aft]w>ds1 or s expla9 x z to evacuate x ( all t is meant by miracul\s4 #ah4 ,x appe>s to me !re=e1 on ! :ole1 t v little c be made ( ^! problems ( te/imony 9 ! way 9 :i* x is g5]ally int5d$ t !y %\ld be treat$2 t is1 9 obta9+ specific rules = ! e/imation ( ! te/imony "u any giv5 circum/ances4 ,assum+ t ! v]acity ( ! witness c be measur$1 we enc\nt] ! real difficulty 9 ! utt] impossibility ( det]m9+ ! limits )9 :i* ! failures ( ! ev5t 9 "q are to be consid]$ to lie1 & ! degree ( explicitness ) :i* ! witness is suppos$ to answ] ! enquiry address$ to him2 bo? ( ^! be+ *>act]i/ics ( :i* x is necess>y to h a num]ical e/imate be=e we c consid] ourselves 9 possession ( ! requisite data4 ,s9ce !re=e ! practical res\rce ( mo/ p]sons1 viz4 t ( putt+ a direct & imm$iate correction1 ( c\rse ( a some:at conjectural nature1 ^u ! g5]al tru/wor?9ess ( ! witness1 by a consid]ation ( ! nature ( ! circum/ances "u :i* 8 /atem5t is made1 is ess5tially unsci5tific & irr$ucible to rule2 x really seems to me t !re is some?+ to be said 9 fav\r ( ! simple plan ( tru/+ 9 all cases alike to ! witness' g5]al v]acity4#h ,t is1 :e!r 8 /ory is ord9>y or extraord9>y1 we may resolve to put x on ! same foot+ ( cr$ibility1 provid$ ( c\rse t ! ev5t is fully recogniz$ z "o :i* does or may occasionally happ54 ,x is true t we %all ?us g con/antly a/ray1 & may d s to a great ext5t1 s t if !re 7 any rational & precise me?od ( specializ+ 8 tru/wor?9ess1 accord+ to ! nature ( 8 /ory1 we %\ld be on mu* firm] gr\nd4 ,b at lea/ we may ?us "k :at to expect on ! av]age4 ,provid$ we h a suffici5t numb] & v>iety ( /atem5ts f him1 & always take !m at ! same con/ant rate or degree ( tru/wor?9ess1 we may succe$ 9 balanc+ & correct+ our conduct 9 ! long run s z to avoid any ru9\s error4 #ai4 ,a few words may n[ be add$ ab\t ! comb9ation ( te/imony4 ,no new pr9ciples are introduc$ "h1 ?\gh ! consequ5t complication is naturally great]4 ,let u suppose two witnesses1 ! v]acity ( ea* be+ #i_/aj4 ,n[ suppose #ajj /atem5ts made by ! pair2 accord+ to ! plan ( proce$+ adopt$ be=e1 we %\ld h !m bo? "r #ha times & bo? wrong once1 9 ! rema9+ #ah cases "o be+ "r & ! o!r wrong4 ,b s9ce !y are bo? suppos$ to give ! same acc\nt1 :at we h to comp>e toge!r are ! numb] ( occasions on :i* !y agree & are "r1 & ! total numb] on :i* !y agree :e!r "r or wrong4 ,! ratio ( ! =m] to ! latt] is ! fraction :i* expresses ! tru/wor?9ess ( _! comb9ation ( te/imony 9 ! case 9 "q4 ,9 attempt+ to decide ?is po9t ! only difficulty is 9 det]m9+ h[ (t5 !y w be f\nd to agree :5 !y are bo? wrong1 = cle>ly !y mu/ agree :5 !y are bo? "r4 ,?is enquiry turns ( c\rse ^u ! numb] ( ways 9 :i* !y c succe$ 9 go+ wrong4 ,suppose fir/ ! case ( a simple yes or no 7z 9 #f71 & take ! same example1 ( a bag ) #ajjj balls1 9 :i* "o only is :ite4 ,proce$+ z be=e1 we %\ld f9d t out ( #ajj1jjj draw+s 7! numb] requir$ 9 ord] to obta9 a complete cycle ( all possible occurr5ces1 z well z ( all possible reports ab\t !m7 ! two witnesses agree 9 a correct report ( ! appe>ance ( :ite 9 #ha1 & agree 9 a wrong report ( x 9 #iii4 ,! ,probability !re=e ( ! /ory :5 s atte/$ is #ha_/ajhj2 ! fact !re=e ( two su* witnesses ( equal v]acity hav+ concurr$ makes ! report ne>ly #i times z likely z :5 x re/$ ^u ! au?ority ( only "o ( !m4#i #bj4 ,:5 h[ev] ! witnesses h _m ways ( go+ wrong1 ! fact ( _! agree+ makes ! report f> m likely to be true4 ,= in/ance1 9 ! case ( ! #ajjj numb]$ balls1 x is v unlikely t :5 !y bo? mi/ake ! numb] !y %\ld 7)\t collusion7 happ5 to make ! same mis/atem5t4 ,:]eas1 9 ! la/ case1 e comb9$ mis/atem5t necess>ily l$ !m bo? to ! ass]tion t ! ev5t 9 "q _h happ5$1 we %\ld n[ f9d t only once 9 #iii #iii times w\ld !y bo? be l$ to ass]t t "s giv5 numb] 7say1 z be=e1 #be7 _h be5 drawn4 ,! odds 9 fav\r ( ! ev5t 9 fact n[ become #hjiai_/hjibj1 :i* are enorm\sly great] ?an :5 !re 0 only "o witness4 ,x appe>s !re=e t :5 two1 & ( c\rse /ill m :5 _m1 witnesses agree 9 a /atem5t 9 a matt] ab\t :i* !y might make _m & v>i\s errors1 ! comb9ation ( _! fav\rable te/imony adds enorm\sly to ! likelihood ( ! ev5t2 provid$ always t !re is no *ance ( collusion4 ,& 9 ! extreme case ( ! opportunities = error be+1 z !y well may be1 practically inf9ite 9 numb]1 su* comb9ation w\ld produce almo/ p]fect c]ta9ty4 ,b !n ?is condition1 viz4 abs5ce ( collusion1 v seldom c be secur$4 ,practically our ma9 s\rce ( error & suspicion is 9 ! possible exi/5ce ( "s k9d ( collusion4 ,s9ce we c seldom entirely get rid ( ?is dang]1 & :5 x exi/s x c nev] be submitt$ to num]ical calculation1 x appe>s to me t comb9ation ( te/imony1 9 reg>d to detail$ acc\nts1 is yet m unfitt$ = consid]ation 9 ,probability ?an ev5 t ( s+le te/imony4 #ba4 ,! impossibility ( any adequate or ev5 appropriate consid]ation ( ! cr$ibility ( miracul\s /ories by ! rules ( ,probability has be5 already notic$ 9 #ag4 ,b1 s9ce ! gr\nds ( ?is impossibility are (t5 v insuffici5tly appreciat$1 a few pages may conv5i5tly be add$ "h ) a view to en=c+ ?is po9t4 ,if x be reg>d$ z a digression1 ! importance ( ! subject & ! p]si/5cy ) :i* v>i\s writ]s h at "o "t or ano!r attempt$ to treat x by ! rules ( our sci5ce mu/ be ! excuse = ent]+ ^u x4 ,a necess>y prelim9>y w be to decide ^u "s def9ition ( a miracle4 ,x w1 we may suppose1 be admitt$ by mo/ p]sons t 9 call+ a miracle 'a susp5sion ( a law ( causation1' we are giv+ :at1 ?\gh x may n am\nt to an adequate def9ition1 is at lea/ true z a description4 ,x is true1 ?\gh x may n be ! :ole tru?4 ,:atev] else ! miracle may be1 ?is is its physical aspect3 ?is is ! po9t at :i* x comes into contact ) ! subject-matt] ( sci5ce4 ,if x 7 n consid]$ t any susp5sion ( causation 7 involv$1 ! ev5t w\ld be reg>d$ m]ely z an ord9>y "o to :i* "s special significance 0 atta*$1 t is1 z a type or symbol r ?an a miracle4 ,x is ?is aspect moreov] ( ! miracle :i* is n[ expos$ to ! ma9 brunt ( ! attack1 & 9 support ( :i* !re=e ! def5ce has g5]ally be5 c>ri$ on4 ,n[ x is obvi\s t ?is1 l mo/ o!r def9itions or descriptions1 makes "s assumption z to matt]s ( fact1 & involves some?+ ( a !ory4 ,! assumption cle>ly is1 t laws ( causation prevail univ]sally1 or almo/ univ]sally1 ?r\gh\t nature1 s t infractions ( !m are m>k$ & exceptional4 ,?is assumption is made1 b x does n appe> t any?+ m ?an ?is is necess>ily requir$2 t is1 !re is no?+ :i* ne$ necess>ily make u side ) ei!r ( ! two pr9cipal s*ools :i* are divid$ z to ! nature ( ^! laws ( causation4 ,! def9ition w s]ve equally well :e!r we und]/& by law no?+ m ?an uni=mity ( antec$5t & consequ5t1 or :e!r we ass]t t !re is "s deep] & m my/]i\s tie betwe5 ! ev5ts ?an m]e sequ5ce4 ,! use ( ! t]m 'causation' 9 ?is m9imum ( signification is common to bo? s*ools1 ?\gh ! "o might consid] x inadequate2 we may speak1 !re=e1 ( 'susp5sions ( causation' )\t committ+ ourselves to ei!r4 #bb4 ,x %\ld be obs]v$ t ! aspect ( ! "q sugge/$ by ?is def9ition is "o f :i* we c h>dly escape4 ,attempts inde$ h be5 sometimes made to avoid ! necessity ( any assumption z to ! univ]sal preval5ce ( law & ord] 9 nature1 by def9+ a miracle f a diff]5t po9t ( view4 ,a miracle may be call$1 = in/ance1 'an imm$iate ex]tion ( creative p[]1' 'a sign ( a revelation1' or1 /ill m vaguely1 an 'extraord9>y ev5t4' ,b no?+ w\ld be ga9$ by adopt+ any su* def9itions z ^!4 ,h[ev] !y might satisfy ! !ologian1 ! /ud5t ( physical sci5ce w\ld n re/ cont5t ) !m = a mom5t4 ,he w\ld at once ass]t 8 own belief1 & t ( o!r sci5tific m51 9 ! exi/5ce ( univ]sal law1 & enquire :at 0 ! connection ( ! def9ition ) ?is doctr9e4 ,an answ] w\ld imp]atively be dem&$ to ! "q1 ,does ! miracle1 z y h describ$ x1 imply an infraction ( "o ( ^! laws1 or does x n8 ,& an answ] mu/ be giv51 unless inde$ we reject 8 assumption by d5y+ our belief 9 ! exi/5ce ( ?is univ]sal law1 9 :i* case ( c\rse we put ourselves out ( ! pale ( argum5t ) him4 ,! necessity ( hav+ to recognize ?is fact is gr[+ ^u m5 day by day1 ) ! increas$ /udy ( physical sci5ce4 ,& s9ce ?is aspect ( ! "q has to be met "s "t or o!r1 x is z well to place x 9 ! front4 ,! difficulty1 9 its sci5tific =m1 is ( c\rse a mod]n "o1 = ! doctr9e out ( :i* x arises is mod]n4 ,b x is only "o in/ance1 out ( _m t might be m5tion$1 9 :i* ! gr[? ( "s philosophical conception has gradually affect$ ! nature ( ! dispute1 & at la/ %ift$ ! position ( ! battle-gr\nd1 9 "s discussion ) :i* x might n at fir/ h appe>$ to h any connection :atev]4 #bc4 ,s f> our pa? is pla94 ,up to ?is po9t disciples ( v diff]5t s*ools may advance toge!r2 = 9 lay+ d[n ! above doctr9e we h c>efully ab/a9$ f imply+ or admitt+ t x conta9s ! :ole tru?4 ,b f ?is po9t two pa?s bran* out be=e u1 pa?s z diff]5t f ea* o!r 9 _! "*1 orig91 & direction1 z c well be conceiv$4 ,z ?is enquiry is only a digression1 we may conf9e ourselves to /at+ briefly :at seem to be ! *>act]i/ics ( ea*1 )\t attempt+ to give ! argum5ts :i* might be us$ 9 _! support4 7,i47 ,on ! "o h&1 we may assume t ?is pr9ciple ( causation is ! ultimate "o4 ,by s t]m+ x1 we d n mean t x is "o f :i* we consci\sly />t 9 our inve/igations1 z we d f ! axioms ( geometry1 b r t x is ! f9al result t[>ds :i* we f9d ourselves drawn by a /udy ( nature4 ,f9d+ t1 ?r\gh\t ! scope ( our enquiries1 ev5t foll[s ev5t 9 nev]-fail+ uni=mity1 & f9d+ moreov] 7"s might add7 t ?is exp]i5ce is support$ or ev5 dem&$ by a t5d5cy or law ( our nature 7x does n matt] "h h[ we describe x71 we may come to reg>d ?is z ! "o fundam5tal pr9ciple on :i* all our enquiries %\ld re/4 7,,ii47 ,or1 on ! o!r h&1 we may admit a class ( pr9ciples ( a v diff]5t k9d4 ,all[+ t !re is ?is uni=mity s f> z our exp]i5ce ext5ds1 we may yet admit :at c h>dly be o!rwise describ$ ?an by call+ x a ,sup]9t5d+ ,provid5ce1 t is1 a ,s*eme or ,ord]1 9 ref]5ce to :i* ,design may be pr$icat$ )\t us+ m]ely metaphorical language4 ,to adopt an aptly *os5 di/9ction1 x is n to be und]/ood z ov]-rul+ ev5ts1 b r z und]ly+ !m4 #bd4 ,n[ x is q cle> t accord+ z we come to ! discussion ( any p>ticul> miracle or extraord9>y /ory "u "o or o!r ( ^! prepossessions1 ! "q ( its cr$ibility w assume a v diff]5t aspect4 ,x is sometimes ov]look$ t al?\gh a diff]5ce ab\t facts is "o ( ! conditions ( a bon fide argum5t1 a diff]5ce :i* rea*es to ultimate pr9ciples is fatal to all argum5t4 ,! possibility ( pres5t conflict is bani%$ 9 su* a case z absolutely z t ( future concord4 ,a l>ge am\nt ( popul> lit]ature on ! subject ( miracles seems to lab\r "u ?is defect4 ,argum5ts are /at$ & exam9$ = & aga9/ ! cr$ibility ( miracul\s /ories )\t ! disputants appe>+ to h any adequate conception ( ! *asm :i* sep>ates "o side f ! o!r4 #be4 ,! foll[+ illu/ration may s]ve 9 "s degree to %[ ! sort ( inconsi/5cy ( :i* we are speak+4 ,a sailor reports t 9 "s remote coral isl& ( ! ,pacific1 on :i* he _h l&$ by himself1 he _h f\nd a numb] ( /ones on ! bea* dispos$ 9 ! exact =m ( a cross4 ,n[ if we conceive a debate to arise ab\t ! tru? ( 8 /ory1 9 :i* x is attempt$ to decide ! matt] simply by consid]ations ab\t ! validity ( te/imony1 )\t introduc+ ! "q ( ! exi/5ce ( inhabitants1 & ! nature ( _! cu/oms1 we %all h "s notion ( ! unsatisfactory nature ( _m ( ! curr5t argum5ts ab\t miracles4 ,all illu/rations ( ?is subject are imp]fect1 b a case l ?is1 9 :i* a suppos$ trace ( human ag5cy is detect$ int]f]+ ) ! ord]ly sequ5ce ( o!r & non-intellig5t natural causes1 is z mu* to ! po9t z any illu/ration c be4 ,! ?+ omitt$ "h f ! discussion is cle>ly ! "o important ?+4 ,if we suppose t !re is no inhabitant1 we %all probably disbelieve ! /ory1 or consid] x to be grossly exagg]at$4 ,if we suppose t !re are inhabitants1 ! "q is at once resolv$ into a diff]5t & some:at m intricate "o4 ,! cr$ibility ( ! witness is n ! only elem5t1 b we %\ld necess>ily h to take into consid]ation ! "* ( ! suppos$ inhabitants1 & ! object ( su* an action on _! "p4 #bf4 ,consid]ations ( ?is "* are d\btless (t5 introduc$ into ! discussion1 b x appe>s to me t !y are introduc$ to a v inadequate ext5t4 ,x is (t5 urg$1 aft] ,paley1 ',once believe 9 a ,god1 & miracles are n incr$ible4' ,su* an admission surely dem&s "s modification & ext5sion4 ,x %\ld r be /at$ ?us1 ,believe 9 a ,god ^: work+ may be trac$ ?r\gh\t ! :ole moral & physical _w4 ,x am\nts1 9 fact1 to ?is2--,admit t !re may be a design :i* we c trace someh[ or o!r 9 ! c\rse ( ?+s2 admit t we are n :olly conf9$ to trac+ ! connection ( ev5ts1 or foll[+ out _! effects1 b t we c =m "s idea1 feeble & imp]fect ?\gh x be1 ( a s*eme4#aj ,paley's advice s\nds too mu* l say+1 ,admit t !re are fairies1 & we c acc\nt = our cups be+ crack$4 ,! admission is n to be made 9 s (f-h& a mann]4 ,to any "o lab\r+ "u ! difficulty we are speak+ (1 ?is belief 9 a ,god almo/ out ( any con/ant relation to nature1 :om we !n imag9e to occasionally manife/ himself 9 a p]haps irregul> mann]1 is altoge!r impossible4 ,! only =m "u :i* belief 9 ! ,deity c ga9 entrance into 8 m9d is z ! controll+ ,_s ( an inf9ite & ord]ly sy/em4 ,9 fact1 x appe>s to me1 p>adoxical z ! sugge/ion may appe>1 t x might ev5 be m easy = a p]son ?or\ghly imbu$ ) ! _s ( ,inductive sci5ce1 ?\gh an a!i/1 to believe 9 a miracle :i* =m$ a "p ( a va/ sy/em1 ?an = su* a p]son1 z a !i/1 to accept an isolat$ miracle4 #bg4 ,x is !re=e ) great prud5ce t ,hume1 & o!rs aft] him1 h practically insi/$ on comm5c+ ) a discussion ( ! cr$ibility ( ! s+le miracle1 treat+ ! "q z ?\gh ! ,*ri/ian ,revelation c\ld be adequately reg>d$ z a succession ( su* ev5ts4 ,z well might "o consid] ! liv+ body to be repres5t$ by ! aggregate ( ! limbs :i* compose x4 ,:at is to be compla9$ ( 9 s _m popul> discussions on ! subject is ! entire abs5ce ( any recognition ( ! diff]5t gr\nd on :i* ! attack]s & def5d]s ( miracles are s (t5 really /&+4 ,pro(s & illu/rations are produc$ 9 endless numb]1 :i* involv+1 z !y almo/ all d 9 ! m9d ( ! disputants on "o side at lea/1 t v pr9ciple ( causation1 ! abs5ce ( :i* 9 ! case 9 "q !y are int5d$ to e/abli%1 !y fail 9 ! s+le ess5tial po9t4 ,to attempt to induce any "o to disbelieve 9 ! exi/5ce ( physical causation1 9 a giv5 in/ance1 by means ( illu/rations :i* to him seem only additional examples ( ! pr9ciple 9 "q1 is l try+ to make a dam1 9 ord] to /op ! fl[ ( a riv]1 by %ovell+ 9 sn[4 ,su* illu/rations are pl5tiful 9 times ( controv]sy1 b be+ 9 reality only modifi$ =ms ( t :i* !y are appli$ to c\nt]act1 !y *ange _! %ape at _! fir/ contact ) ! disbeliev]'s m9d1 & only help to swell ! flood :i* !y 7 int5d$ to *eck4 #a4 ,reasons 7 giv5 9 ! la/ *apt] aga9/ ! propriety ( apply+ ! rules ( ,probability ) any /rictness to su* examples z ^!4 ,b al?\gh all approa* to num]ical accuracy is unatta9able1 we d und\bt$ly recognize 9 ord9>y life a di/9ction betwe5 ! cr$ibility ( "o witness & ano!r2 su* a r\gh practical di/9ction w be q suffici5t = ! purposes ( ?is *apt]4 ,= conv5i5ce1 & to illu/rate ! !ory1 ! examples are be/ /at$ 9 a num]ical =m1 b x is n int5d$ !reby to imply t any su* accuracy is really atta9able 9 practice4 #b4 ,i mu/ plead guilty to ?is *>ge myself1 9 ! fir/ edition ( ?is "w4 ,! result 0 to make ! treatm5t ( ?is "p ( ! subject obscure & imp]fect1 & 9 "s respects errone\s4 #c4 ,! g5]aliz$ algebraical =m ( ?is result is z foll[s4 ,let p be ! priori probability ( an ev5t1 & x be ! cr$ibility ( ! witness4 ,!n1 if he ass]ts t ! ev5t happ5$1 ! probability t x really did happ5 is px_/7px 7#a - p77#a - x772 :il/ if he ass]ts t x did n happ5 ! probability t x did happ5 is p7#a - x7_/7p7#a - x7 7#a - p7x74 ,9 illu/ration ( "s rem>ks to be pres5tly made1 ! read] w notice t on mak+ ei!r ( ^! expressions p1 we obta9 9 ea* case x #a_/b4 ,t is1 a witness ^: v]acity #a_/b leaves ! priori probability ( an ev5t 7( ?is k9d7 unaffect$4 ,if1 on ! o!r h&1 we make ^! expressions equal to x & #a - x respectively1 we obta9 9 ea* case p #a_/b4 ,t is1 :5 an ev5t 7( ?is k9d7 is z likely to happ5 z n1 ! ord9>y v]acity ( ! witness 9 respect ( x rema9s unaffect$4 #d4 ,todhunt]'s ,hi/ory1 p4 #djj4 ,philosophical ,magaz9e1 ,july1 #ahfd4 #e4 ,:5 !re=e ^! two k9ds ( exp]i5ce are contr>y1 we h no?+ to d b subtract ! "o f ! o!r1 & embrace an op9ion1 ei!r on "o side or ! o!r1 ) t assurance :i* arises f ! rema9d]4 7,essay on ,miracles47 #f4 ,consid]ations ( ?is k9d h inde$ be5 introduc$ into ! ma!matical treatm5t ( ! subject4 ,! common algebraical solution ( ! problem 9 #e 7to beg9 ) ! simple/ case7 is ( c\rse z foll[s4 ,let p be ! antec$5t probability ( ! ev5t1 & t ! measure ( ! tru?fulness ( ! witness2 !n ! *ance ( 8 /atem5t be+ true is pt_/7pt 7#a - p77#a - t774 ,?is supposes him to lie z mu* :5 ! ev5t does n happ5 z :5 x does4 ,b we may meet ! cases suppos$ 9 ! text by assum+ t t' is ! measure ( 8 v]acity :5 ! ev5t does n happ51 s t ! above =mula becomes pt_/7pt 7#a - p77#a - t'774 ,"h t' & t measure respectively 8 tru/wor?9ess 9 usual & unusual ev5ts4 ,z a =mal solution ?is c]ta9ly meets ! objections /at$ above 9 #ad & #ae4 ,! det]m9ation h[ev] ( t' w\ld dem&1 z ,i h rem>k$1 cont9ually r5ew$ appeal to exp]i5ce4 ,9 any case ! practical me?ods :i* w\ld be adopt$1 if any plans ( ! k9d indicat$ above 7 resort$ to1 seem to me to diff] v mu* f t adopt$ by ! ma!maticians1 9 _! _s & plan4 #g4 ,laplace1 = in/ance 7,essai1 ed4 #ahbe1 p4 #adi71 says t if we saw #ajj dies 7kn[n ( c\rse to be fair ones7 all give ! same face1 we %\ld be bewild]$ at ! "t1 & ne$ confirmation f o!rs1 b t1 aft] due exam9ation1 no "o w\ld feel oblig$ to po/ulate halluc9ation 9 ! matt]4 ,b ! *ance ( ?is occurr5ce is repres5t$ by a fraction ^: num]ator is #a1 & d5om9ator conta9s #gg figures1 & is !re=e utt]ly inappreciable by ! imag9ation4 ,x mu/ be admitt$1 ?\gh1 t !re is some?+ hypo!tical ab\t su* an example1 = we c\ld n really "k t ! dies 7 fair ) a confid5ce ev5 di/antly approa*+ su* prodigi\s odds4 ,9 o!r words1 x is difficult "h to keep ap>t ^? diff]5t aspects ( ! "q discuss$ 9 ,*ap4 ,,xiv4 #bh-cc4 #h4 ,9 ! fir/ edition ?is 0 /at$1 z x n[ seems to me1 9 decid$ly too unqualifi$ a mann]4 ,x mu/ be rememb]$1 h[ev]1 t 7z 0 %[n 9 #g7 ?is plan is really ! be/ !oretical "o :i* c be adopt$ 9 c]ta9 cases4 #i4 ,x is on ?is pr9ciple t ! rem>kable conclusion m5tion$ on p4 #dje is bas$4 ,suppose an ev5t ^: probability is p2 & t1 ( a numb] ( witnesses ( ! same v]acity 7y71 m ass]t t x happ5$1 & n d5y ?is4 ,g5]aliz+ ! ari?metical reason+ giv5 above we see t ! *ance ( ! ev5t be+ ass]t$ v>ies z pym 7#a - y7n 7#a - p7 yn 7#a - y7m2 7viz4 z ! *ance t ! ev5t happ5s1 & t m are "r & n are wrong2 plus ! *ance t x does n happ51 & t n are "r & m are wrong74 ,& ! *ance ( its be+ rightly ass]t$ z pym 7#a - y7n4 ,!re=e ! *ance t :5 we h an ass]tion be=e u x is a true "o is pym 7#a - y7n ---------------------------------------- ------ pym 7#a - y7n 7#a - p7 yn 7#a - y7m1 :i* is equal to pym-n -------------------------------- pym-n 7#a - p7 7#a - y7m-n4 ,b ?is la/ expression repres5ts ! probability ( an ass]tion :i* is unanim\sly support$ by m - n su* witnesses4 #aj4 ,! /ress :i* ,butl] lays ^u ?is notion ( a s*eme is1 ,i ?9k1 "o great m]it ( 8 ,analogy4 ,,*apt] ,,xviii4 ,,! ,,nature ,,& ,,use ,,( ,,an ,,av]age1 ,,& ,,on ,,! ,,diff]5t ,,k9ds ,,( ,,av]age4#a #a4 ,!re is mu* ne$ ( "s good acc\nt1 accessible to ! ord9>y ,engli% read]1 ( ! nature & prop]ties ( ! pr9cipal k9ds ( ,mean4 ,! common text-books ( ,algebra sugge/ t !re are only ?ree su*1 viz4 ! ari?metical1 ! geometrical & ! h>monical3--?us includ+ two ) :i* ! /ati/ician has little or no?+ to d1 & exclud+ two or m ) :i* he %\ld h a great deal to d4 ,! be/ ?ree ref]5ces ,i c give ! read] are ! foll[+4 7#a7 ,! article ,moy5ne 9 ! ,dictionnaire des ,sci5ces ,mdicales1 by ,dr ,b]tillon4 ,?is is writt5 some:at f ! ,quetelet po9t ( view4 7#b7 ,a pap] by ,fe*n] 9 ! ,abh&lung5 d4 ,ma?4 phys4 ,classe d4 ,kn4 ,s*s4 ,gesells*aft d4 ,wiss4 #ahgh2 pp4 #a-gf4 ,?is conta9s a v int]e/+ discussion1 especially = ! /ati/ician1 ( a numb] ( diff]5t k9ds ( mean4 ,8 acc\nt ( ! m$ian is rem>kably full & valuable4 ,b little ma!matical k is dem&$4 7#c7 ,a pap] by ,mr ,f4 ,y4 ,edgewor? 9 ! ,camb4 ,phil4 ,trans4 = #ahhe1 entitl$ ,obs]vations & ,/ati/ics4 ,?is dem&s "s ma!matical k4 ,in/ead ( deal+1 z su* inve/igations g5]ally d1 ) only "o ,law ( ,error & ) only "o k9d ( mean1 x cov]s a wide field ( inve/igation4 #a4 ,we h _h su* frequ5t occasion to ref] to av]ages1 & to ! k9d ( uni=mity :i* !y are apt to display 9 contra/ ) individual objects or ev5ts1 t x w n[ be conv5i5t to discuss some:at m m9utely :at are ! diff]5t k9ds ( available av]age1 & :at exactly are ! functions !y p]=m4 ,! fir/ vague notion ( an av]age1 z we n[ und]/& x1 seems to me to involve little m ?an t ( a some?+ int]m$iate to a numb] ( objects4 ,! objects mu/ ( c\rse resemble ea* o!r 9 c]ta9 respects1 o!rwise we %\ld n ?9k ( class+ !m toge!r2 & !y mu/ also diff] 9 c]ta9 respects1 o!rwise we %\ld n di/+ui% betwe5 !m4 ,:at ! av]age does = u1 "u ?is primitive =m1 is to enable u conv5i5tly to reta9 ! gr\p toge!r z a :ole4 ,t is1 x furni%es a sort ( repres5tative value ( ! quantitative aspect ( ! ?+s 9 "q1 :i* w s]ve = c]ta9 purposes to take ! place ( any s+le memb] ( ! gr\p4 ,x w\ld seem !n t ! fir/ dawn ( ! conception :i* sci5ce r$uces to accuracy "u ! designation ( an av]age or mean1 & !n proce$s to subdivide into v>i\s di/9ct species ( means1 pres5ts itself z p]=m+ "s ( ! functions ( a g5]al "n4 ,= :at is ! ma9 use ( a g5]al "n8 ,x is to r$uce a plurality ( objects to unity2 to gr\p a numb] ( ?+s toge!r by ref]5ce to "s qualities :i* !y possess 9 common4 ,! ord9>y g5]al "n re/s ^u a consid]able v>iety ( attributes1 mo/ly ( a qualitative "*1 :]eas ! av]age1 9 s f> z x s]ves ! same sort ( purpose1 re/s r ^u a s+le quantitative attribute4 ,x directs att5tion to a c]ta9 k9d & degree ( magnitude4 ,:5 ! grazi] says ( 8 %eep t '"o ) ano!r !y w fet* ab\t #ej %ill+s1' or ! f>m] buys a lot ( poles :i* 'run to ab\t #aj feet1' x is true t !y are n /rictly us+ ! equival5t ( ei!r a g5]al or a collective "n4 ,b !y are com+ v ne> to su* use1 9 pick+ out a sort ( type or specim5 ( ! magnitude to :i* att5tion is to be direct$1 & 9 class+ ! :ole gr\p by its resemblance to ?is type4 ,! grazi] is ?9k+ ( 8 %eep3 n 9 a m]ely g5]al s5se1 z %eep1 & !re=e "u t "n or conception1 b z %eep ( a c]ta9 approximate money value4 ,"s w be m1 "s less1 b !y are all ne> en\gh to ! assign$ value to be conv5i5tly class$ toge!r z if by a "n4 ,_m ( our r\gh quantitative designations seem to be ( ?is k9d1 z :5 we speak ( 'eight-day clocks' or 'twelve-/one m51' c42 unless ( c\rse we int5d 7z we sometimes d 9 ^! cases7 to assign a maximum or m9imum value4 ,x is n inde$ easy to see h[ else we c\ld readily convey a m]ely g5]al notion ( ! quantitative aspect ( ?+s1 except by select+ a type z above1 or by assign+ c]ta9 limits )9 :i* ! ?+s are suppos$ to lie4 #b4 ,s f> !re is n necess>ily any idea introduc$ ( comp>ison1--( comp>ison1 t is1 ( "o gr\p ) ano!r1--by aid ( su* an av]age4 ,z soon z we beg9 to ?9k ( ?is we h to be m precise 9 say+ :at we mean by an av]age4 ,we c easily see t ! numb] ( possible k9ds ( av]age1 9 ! s5se ( int]m$iate values1 is v great2 is1 9 fact1 indef9itely great4 ,out ( ! g5]al conception ( an int]m$iate value1 obta9$ by "s treatm5t ( ! orig9al magnitudes1 we c elicit z _m subdivisions z we please1 by v>i\s modes ( treatm5t4 ,!re are h[ev] only ?ree or f\r :i* = our purposes ne$ be tak5 into acc\nt4 7#a7 ,9 ! fir/ place !re is ! ari?metical av]age or mean4 ,! rule = obta9+ ?is is v simple3 add all ! magnitudes toge!r1 & divide ! sum by _! numb]4 ,?is is ! only k9d ( av]age ) :i* ! unsci5tific m9d is ?or\ghly famili>4 ,b we mu/ n let ?is simplicity & famili>ity bl9d u to ! fact t !re are def9ite reasons = ! employm5t ( ?is av]age1 & t x is !re=e appropriate only 9 def9ite circum/ances4 ,! reason :y x af=ds a safe & accurate int]m$iate value = ! actual div]g5t values1 is t = _m ( ! ord9>y purposes ( life1 su* z pur*ase & sale1 we come to exactly ! same result1 :e!r we take acc\nt ( ^? exi/5t div]g5ces1 or suppose all ! objects equat$ to _! av]age4 ,:at ! grazi] mu/ be und]/ood to mean1 if he wi%es to be accurate1 by say+ t ! av]age price ( 8 %eep is #ej %ill+s1 is1 t s f> z t flock is conc]n$ 7& s f> z he is conc]n$71 x comes to exactly ! same ?+1 :e!r !y are ea* sold at diff]5t prices1 or are all sold at ! 'av]age' price4 ,accord+ly1 :5 he comp>es 8 sales ( "o ye> ) ^? ( ano!r2 :5 he says t la/ ye> ! %eep av]ag$ #dh %ill+s aga9/ ! #ej ( ?is ye>2 ! employm5t ( ?is repres5tative or av]age value is a great simplification1 & is p]fectly accurate = ! purpose 9 "q4 #c4 7#b7 ,n[ consid] ?is case4 ,a c]ta9 population is f\nd to h d\bl$ itself 9 #ajj ye>s3 c we talk ( an 'av]age' increase "h ( #a p] c5t4 annually8 ,! circum/ances are n q ! same z 9 ! =m] case1 b ! analogy is suffici5tly close = our purpose4 ,! answ] is decid$ly1 ,no4 ,if #ajj articles ( any k9d are sold = #ajj1 we say t ! av]age price is #a4 ,by ?is we mean t ! total am\nt is ! same :e!r ! entire lot are sold = #ajj1 or :e!r we split ! lot up into individuals & sell ea* ( ^! = #a4 ,! av]age price "h is a conv5i5t fictiti\s sub/itute1 :i* c be appli$ = ea* individual )\t alt]+ ! aggregate total4 ,if !re=e ! "q be1 ,w a suppos$ increase ( #a p4 c4 9 ea* ( ! #ajj ye>s be equival5t to a total increase to d\ble ! orig9al am\nt8 we are propos+ a closely analog\s "q4 ,& ! answ]1 z j rem>k$1 mu/ be 9 ! negative4 ,an annual increase ( #a p4 c4 cont9u$ = #ajj ye>s w m ?an d\ble ! total2 x w multiply x by ab\t #b4g4 ,! true annual increm5t requir$ is measur$ by sqrt#ajjb2 t is1 ! population may be said to h increas$ 'on ! av]age' #j4g p4 c4 annually4 ,we are ?us direct$ to ! second k9d ( av]age discuss$ 9 ! ord9>y text-books ( algebra1 viz4 ! geometrical4 ,:5 only two quantities are conc]n$1 ) a s+le int]m$iate value betwe5 !m1 ! geometrical mean con/itut+ ?is la/ is be/ describ$ z ! mean proportional betwe5 ! two =m]4 ,?us1 s9ce #c 3 sqrt#ae 33 sqrt#ae 3 #e1 sqrt#ae is ! geometrical mean betwe5 #c & #e4 ,:5 a numb] ( geometrical means h to be int]pos$ betwe5 two quantities1 !y are to be s *os5 t e t]m 9 ! entire succession %all be> ! same con/ant ratio to its pr$ecessor4 ,?us1 9 ! example 9 ! la/ p>agraph1 #ii int]m$iate /eps 7 to be int]pos$ betwe5 #a & #b1 ) ! condition t ! #ajj ratios ?us produc$ 7 to be all equal4 ,x w\ld seem !re=e t :]ev] accurate quantitative results are conc]n$1 ! selection ( ! appropriate k9d ( av]age mu/ dep5d ^u ! answ] to ! "q1 ,:at p>ticul> int]m$iate value may be safely sub/itut$ = ! actual v>iety ( values1 s f> z ! precise object 9 view is conc]n$8 ,?is is an aspect ( ! subject :i* w h to be m fully consid]$ 9 ! next *apt]4 ,b x may safely be laid d[n t = purposes ( g5]al comp>ison1 :]e accurate num]ical relations are n requir$1 almo/ any k9d ( int]m$iate value w answ] our purpose1 provid$ we adh]e to ! same ?r\gh\t4 ,?us1 if we want to comp>e ! /atures ( ! inhabitants ( diff]5t c\nties or di/ricts 9 ,engl&1 or ( ,engli%m5 g5]ally ) ^? ( ,fr5*m51 or to asc]ta9 :e!r ! /ature ( "s p>ticul> class or di/rict is increas+ or dim9i%+1 x really does n seem to matt] :at sort ( av]age we select provid$1 ( c\rse1 t we adh]e to ! same ?r\gh\t our inve/igations4 ,a v l>ge am\nt ( ! "w p]=m$ by av]ages is ( ?is m]ely comp>ative or non-quantitative description2 or1 at any rate1 no?+ m ?an ?is is really requir$4 ,?is be+ s1 we %\ld naturally resort to ! ari?metical av]age2 p>tly because1 hav+ be5 long 9 ! field1 x is univ]sally und]/ood & appeal$ to1 & p>tly because x happ5s to be rem>kably simple & easy to calculate4 #d4 ,! ari?metical mean is = mo/ ord9>y purposes ! simple/ & be/4 ,inde$1 :5 we are deal+ ) a small numb] ( some:at artificially select$ magnitudes1 x is ! only mean :i* any "o w\ld ?9k ( employ+4 ,we %\ld n1 = in/ance1 apply any o!r me?od to ! results ( a few doz5 measurem5ts ( l5g?s or e/imates ( prices4 ,:51 h[ev]1 we come to consid] ! results ( a v l>ge numb] ( measurem5ts ( ! k9d :i* c be gr\p$ toge!r into "s sort ( 'probability curve' we beg9 to f9d t !re is m ?an "o alt]native be=e u4 ,beg9 by recurr+ to ! famili> curve repres5t$ on p4 #bi2 or1 bett] /ill1 to ! initial =m ( x repres5t$ 9 ! next *apt] 7p4 #dgf74 ,we see t !re are ?ree diff]5t ways 9 :i* we may describe ! v]tex ( ! curve4 ,we may call x ! position ( ! maximum ord9ate2 or t ( ! c5tre ( ! curve2 or 7z w be se5 h]eaft]7 ! po9t to :i* ! ari?metical av]age ( all ! diff]5t values ( ! v>iable magnitude directs u4 ,^! ?ree are all di/9ct ways ( describ+ a position2 b :5 we are deal+ ) a symmetrical curve at all resembl+ ! b9omial or expon5tial =m !y all ?ree co9cide 9 giv+ ! same result3 z !y obvi\sly d 9 ! case 9 "q4 ,z soon1 h[ev]1 z we come to consid] ! case ( asymmetrical1 or lop-sid$ curves1 ! indications giv5 by ^! ?ree me?ods w be z a rule q di/9ct2 & !re=e ! two =m] ( ^! des]ve brief notice z repres5t+ diff]5t k9ds ( means f ! ari?metical or ord9>y "o4 ,we %all see t !re is some?+ ab\t ea* ( !m :i* recomm5ds x to common s5se z be+ 9 "s way natural & appropriate4 #e4 7#c7 ,! fir/ ( ^! selects f among/ ! v>i\s diff]5t magnitudes t p>ticul> "o :i* is mo/ frequ5tly repres5t$4 ,x has n acquir$ any te*nical designation1#a except 9 s f> z x is ref]r$ to1 by its graphical repres5tation1 z ! maximum ord9ate me?od4 ,b ,i suspect t "s appeal to su* a mean or /&>d is really f> f uncommon1 & t if we c\ld draw out into cle>ness ! conceptions lat5t 9 ! judgm5ts ( ! comp>atively uncultivat$1 we %\ld f9d t !re 7 v>i\s classes ( cases 9 :i* ?is mean 0 naturally employ$4 ,suppose1 = in/ance1 t !re 0 a fi%]y 9 :i* ! fi% v>i$ v mu* 9 size b 9 :i* ! commone/ size 0 some:at ne> ! l>ge/ or ! smalle/4 ,if ! m5 7 9 ! habit ( sell+ _! fi% by weight1 x is probable t !y w\ld be=e long beg9 to acquire "s k9d ( notion ( :at is meant by ! ari?metical mean or av]age1 & w\ld p]ceive t ?is 0 ! mo/ appropriate te/4 ,b if ! fi% 7 sort$ into sizes1 & sold by numb]s 9 ea* ( ^! sizes1 ,i suspect t ?is appeal to a maximum ord9ate w\ld beg9 to take ! place ( ! o!r4 ,t is1 ! mo/ num]\s class w\ld come to be select$ z a sort ( type by :i* to comp>e ! same fi%]y at "o "t & ano!r1 or "o fi%]y ) o!rs4 ,!re is also1 z we %all see 9 ! next *apt]1 "s sci5tific gr\nd = ! pref]5ce ( ?is k9d ( mean 9 peculi> cases2 viz4 :]e ! quantities ) :i* we deal are true 'errors1' 9 ! e/imate ( "s magnitude1 & :]e also x is ( mu* m importance to be exactly "r1 or v ne>ly "r1 ?an to h m]ely a l[ av]age ( error4 #f4 7#d7 ,! rema9+ k9d ( mean is t :i* is n[ com+ to be call$ ! m$ian4 ,x is "o ) :i* ! writ+s ( ,mr ,galton h done s mu* to famili>ize /ati/icians1 & is be/ describ$ z foll[s4 ,conceive all ! objects 9 "q to be m>%all$ 9 ! ord] ( _! magnitude2 or1 :at comes to ! same ?+1 conceive !m sort$ into a numb] ( equally num]\s classes2 !n ! middle "o ( ! r[1 or ! middle "o 9 ! middle class1 w be ! m$ian4 ,i d n ?9k t ?is k9d ( mean is at all g5]ally recogniz$ at pres5t1 b if ,mr ,galton's s*eme ( natural measurem5t by :at he calls p]-c5tiles %\ld come to be g5]ally adopt$1 su* a te/ w\ld become an important "o4 ,!re are "s conspicu\s advantages ab\t ?is k9d ( mean4 ,= "o ?+1 9 mo/ /ati/ical enquiries1 x is f> ! simple/ to calculate2 &1 :at is m1 ! process ( det]m9+ x s]ves also to assign ano!r important elem5t to be pres5tly notic$1 viz4 ! 'probable error4' ,!n aga91 z ,fe*n] notes1 :]eas 9 ! ari?metical mean a few exceptional & extreme values w (t5 cause p]plexity by _! comp>ative prepond]ance1 9 ! case ( ! m$ian 7:]e _! numb] only & n _! extreme magnitude is tak5 into acc\nt7 ! importance ( su* di/urbance is dim9i%$4 #g4 ,a simple illu/ration w s]ve to indicate h[ ^! ?ree k9ds ( mean coalesce into "o :5 we are deal+ ) symmetrical ,laws ( ,error1 b become q di/9ct z soon z we come to consid] ^? :i* are unsymmetrical4 ,figure3 ,v>i\s def9itions ( ! mean4 ,suppose t1 9 measur+ a magnitude along ,,obdc1 :]e ! extreme limits are ,,ob & ,,oc1 ! law ( error is repres5t$ by ! triangle ,,bac3 ! l5g? ,,od w be at once ! ari?metical mean1 ! m$ian1 & ! mo/ frequ5t l5g?3 its frequ5cy be+ repres5t$ by ! maximum ord9ate ,,ad4 ,b n[ suppose1 on ! o!r h&1 t ! extreme l5g?s are ,,od & ,,oc1 & t ! triangle ,,adc repres5ts ! law ( error4 ,! mo/ frequ5t l5g? w be ! same z be=e1 ,,od1 m>k$ by ! maximum ord9ate ,,ad4 ,b ! mean value w n[ be ,,ox1 :]e ,,dx #a_/c ,,dc2 & ! m$ian w be ,,oy1 :]e ,,dy 7#a - #a_/sqrt#b7 ,,dc4 ,ano!r example1 tak5 f natural ph5om5a1 may be f\nd 9 ! heights ( ! b>omet] z tak5 at ! same h\r on successive days4 ,s f> z #dheg ( ^! may be reg>d$ z furni%+ a suffici5tly /able basis ( exp]i5ce1 x c]ta9ly seems t ! result+ curve ( frequ5cy is asymmetrical4 ,! mean height "h 0 f\nd to be #bi4ih3 ! m$ian 0 #cj4ja3 ! mo/ frequ5t height 0 #cj4je4 ,! close approximation among/ ^! is an indication t ! asymmetry is slight4#b #h4 ,x mu/ be cle>ly und]/ood t ! av]age1 ( :atev] k9d x may be1 f ! m]e fact ( its be+ a s+le sub/itute = an actual plurality ( obs]v$ values1 mu/ let slip a consid]able am\nt ( in=mation4 ,9 fact x is only introduc$ = economy4 ,x may entail no loss :5 us$ = "s "o assign$ purpose1 z 9 our example ab\t ! %eep2 b = purposes 9 g5]al x _c possibly take ! place ( ! orig9al div]sity1 by yield+ all ! in=mation :i* !y conta9$4 ,if all ?is is to be reta9$ we mu/ resort to "s o!r me?od4 ,practically we g5]ally d "o ( two ?+s3 ei!r 7#a7 we put all ! figures d[n 9 /ati/ical tables1 or 7#b7 we appeal to a diagram4 ,?is la/ plan is conv5i5t :5 ! data are v num]\s1 or :5 we wi% to display or to discov] ! nature ( ! law ( facility "u :i* !y range4 ,! m]e assignm5t ( an av]age lets drop ne>ly all ( ?is1 conf9+ itself to ! indication ( an int]m$iate value4 ,x gives a middle po9t ( "s k9d1 b says no?+ :atev] z to h[ ! orig9al magnitudes 7 gr\p$ ab\t ?is po9t4 ,= in/ance1 :e!r two magnitudes _h be5 respectively #be & #bg1 or #ae & #cg1 !y w\ld yield ! same ari?metical av]age ( #bf4 #i4 ,to break (f at ?is /age w\ld cle>ly be to leave ! problem 9 a v imp]fect condition4 ,we !re=e naturally seek = "s simple te/ :i* %all indicate h[ closely ! sep>ate results 7 gr\p$ ab\t _! av]age1 s z to recov] "s "p ( ! in=mation :i* _h be5 let slip4 ,if any "o 7 approa*+ ?is problem entirely anew1--t is1 if he _h no k ( ! ma!matical exig5cies :i* att5d ! !ory ( ,lea/ ,squ>es1--,i appreh5d t !re is b "o way 9 :i* he w\ld set ab\t ! bus9ess4 ,he w\ld say1 ,! av]age :i* we h already obta9$ gave u a r\gh indication1 by assign+ an int]m$iate po9t among/ ! orig9al magnitudes4 ,if we want to supplem5t ?is by a r\gh indication z to h[ ne> toge!r ^! magnitudes lie1 ! be/ way w be to treat _! dep>tures f ! mean 7:at are te*nically call$ ! errors7 9 precisely ! same way1 viz4 by assign+ _! av]age4 ,suppose !re are #ac m5 ^: heights v>y by equal diff]5ces f #e feet to #f feet1 we %\ld say t _! av]age height 0 #ff in*es1 & _! av]age dep>ture f ?is av]age 0 #c-c_/ac in*es4 ,look$ at f ?is po9t ( view we %\ld !n proce$ to try h[ ea* ( ! above-nam$ av]ages w\ld answ] ! purpose4 ,two ( !m1--viz4 ! ari?metical mean & ! m$ian1--w answ] p]fectly2 &1 z we %all imm$iately see1 are frequ5tly us$ = ! purpose4 ,s too we c\ld1 if we pleas$1 employ ! geometrical mean1 ?\gh su* employm5t w\ld be t$i\s1 ow+ to ! difficulty ( calculation4 ,! 'maximum ord9ate' cle>ly w\ld n answ]1 s9ce x w\ld g5]ally 7v4 ! diagram on p4 #ddc7 ref] u back aga9 to ! av]age already obta9$1 & !re=e give no in=mation4 ,! only po9t "h ab\t :i* any d\bt c\ld arise conc]ns :at is call$ 9 algebra ! sign ( ! errors4 ,two equal & opposite errors1 add$ algebraically1 w\ld cancel ea* o!r4 ,b :51 z "h1 we are reg>d+ ! errors z sub/antive quantities1 to be consid]$ on _! own acc\nt1 we att5d only to _! real magnitude1 & !n ^! equal & opposite errors are to be put ^u exactly ! same foot+4 #aj4 ,( ! v>i\s means already discuss$1 two1 z j rem>k$1 are 9 common use4 ,"o ( ^! is famili>ly kn[n1 9 a/ronomical & o!r calculations1 z ! ',mean ,error1' & is s absolutely an application ( ! same pr9ciple ( ! ari?metical mean to ! errors1 t has be5 already appli$ to ! orig9al magnitudes1 t x ne$s no fur!r explanation4 ,?us 9 ! example 9 ! la/ section ! mean ( ! heights 0 #ff in*es1 ! mean ( ! errors 0 #c-c_/ac in*es4 ,! o!r is ! ,m$ian1 ?\gh "h x is always kn[n "u ano!r "n1 i4e4 z ! ',probable ,error'2--a te*nical & decid$ly mislead+ t]m4 ,x is briefly def9$ z t error :i* we are z likely to exce$ z to fall %ort (3 o!rwise phras$1 if we 7 to arrange all ! errors 9 ! ord] ( _! magnitude1 x corresponds to t "o ( !m :i* j bisects ! r[4 ,x is !re=e ! 'm$ian' error3 or1 if we arrange all ! magnitudes 9 successive ord]1 & divide !m into f\r equally num]\s classes1--:at ,mr ,galton calls 'qu>tiles1'--! fir/ & ?ird ( ! consequ5t divisions w m>k ! limits ( ! 'probable error' on ea* side1 :il/ ! middle "o w m>k ! 'm$ian4' ,?is m$ian1 z 0 rem>k$1 co9cides1 9 symmetrical curves1 ) ! ari?metical mean4 ,x is be/ to /& by accept$ nom5clature1 b ! read] mu/ und]/& t su* an error is n 9 any /rict s5se 'probable4' ,x is inde$ highly improbable t 9 any p>ticul> in/ance we %\ld happ5 to get j ?is error3 9 fact1 if we *ose to be precise & to reg>d x z "o exact magnitude out ( an inf9ite numb]1 x w\ld be inf9itely unlikely t we %\ld hit ^u x4 ,nor c x be said to be probable t we %all be )9 ?is limit ( ! tru?1 =1 by def9ition1 we are j z likely to exce$ z to fall %ort4 ,z already rem>k$ 7see note on p4 #dda71 ! 'maximum ord9ate' w\ld h ! be/ "r to be reg>d$ z indicat+ ! really mo/ probable value4 #aa4 7#e7 ,! error ( mean squ>e4 ,z previ\sly sugge/$1 ! plan :i* w\ld naturally be adopt$ by any "o :o _h no conc]n ) ! high] ma!matics ( ! subject1 w\ld be to take ! 'mean error' = ! purpose ( ! indication 9 view4 ,b a v diff]5t k9d ( av]age is g5]ally adopt$ 9 practice to s]ve z a te/ ( ! am\nt ( div]g5ce or disp]sion4 ,suppose t we h ! magnitudes x#a1 x#b1 444 xn2 _! ord9>y av]age is #a_/n 7x#a x#b 444 xn71 & _! 'errors' are ! diff]5ces betwe5 ?is & x#a1 x#b1 444 xn4 ,call ^! errors e#a1 e#b1 444 en1 !n ! ari?metical mean ( ^! errors 7irrespective ( sign7 is #a_/n 7e#a e#b 444 en74 ,! ,error ( ,mean ,squ>e1#c on ! o!r h&1 is ! squ>e root ( #a_/n 7e#ab e#bb 444 en#b74 ,! reasons = employ+ ?is latt] k9d ( av]age 9 pref]5ce to any ( ! o!rs w be indicat$ 9 ! foll[+ *apt]4 ,at pres5t we are conc]n$ only ) ! g5]al logical nature ( an av]age1 & x is !re=e suffici5t to po9t out t any su* int]m$iate value w answ] ! purpose ( giv+ a r\gh & summ>y indication ( ! degree ( clos5ess ( approximation :i* our v>i\s measures display to ea* o!r & to _! common av]age4 ,if we 7 to speak respectively ( ! 'fir/' & ! 'second av]age1' we might say t ! =m] ( ^! assigns a r\gh s+le sub/itute = ! plurality ( orig9al values1 :il/ ! latt] gives a simil> r\gh e/imate ( ! degree ( _! dep>ture f ! =m]4 #ab4 ,s f> we h only be5 consid]+ ! g5]al nature ( an av]age1 & ! pr9cipal k9ds ( av]age practically 9 use4 ,we mu/ n[ enquire m p>ticul>ly :at are ! pr9cipal purposes = :i* av]ages are employ$4 ,9 ?is respect ! fir/ ?+ we h to d is to raise d\bts 9 ! read]'s m9d on a subject on :i* he p]haps has n hi!rto felt ! slighte/ d\bt4 ,e "o is m or less famili> ) ! practice ( appeal+ to an av]age 9 ord] to secure accuracy4 ,b di/9ctly :at we beg9 by do+ is to sacrifice accuracy2 = 9 place ( ! plurality ( actual results we get a s+le result :i* v possibly does n agree ) any "o ( !m4 ,if ,i f9d ! temp]ature 9 diff]5t p>ts ( a room to be diff]5t1 b say t ! av]age temp]ature is #fa1 !re may p]haps be b few p>ts ( ! room :]e ?is exact temp]ature is realiz$4 ,& if ,i say t ! av]age /ature ( a c]ta9 small gr\p ( m5 is #fh in*es1 x is probable t no "o ( !m w pres5t precisely ?is height4 ,! pr9cipal way 9 :i* accuracy c be ?us secur$ is :5 :at we are really aim+ at is n ! magnitudes be=e u b some?+ else ( :i* !y are an indication4 ,if !y are !mselves 'inaccurate1'--we %all see pres5tly t ?is ne$s "s explanation1--!n ! s+le av]age1 :i* 9 itself agrees p]haps ) none ( !m1 may be mu* m ne>ly :at we are actually 9 want (4 ,we %all f9d x conv5i5t to subdivide ?is view ( ! subject into two p>ts2 by consid]+ fir/ ^? cases 9 :i* quantitative consid]ations ent] b slightly1 & 9 :i* no det]m9ation ( ! p>ticul> ,law ( ,error involv$ is dem&$1 & secondly ^? 9 :i* su* det]m9ation _c be avoid$4 ,! latt] are only notic$ 9 pass+ "h1 z a sep>ate *apt] is res]v$ = _! full] consid]ation4 #ac4 ,! process1 z a practical "o1 is famili> en\gh to almo/ ev]ybody :o has to "w ) measures ( any k9d4 ,suppose1 = in/ance1 t ,i am measur+ any object ) a brass rod :i*1 z we "k1 exp&s & contracts accord+ to ! temp]ature4 ,! results w v>y slightly1 be+ sometimes a little too great & sometimes a little too small4 ,all ^! v>iations are physical facts1 & if :at we 7 conc]n$ ) 0 ! prop]ties ( brass !y w\ld be ! "o important fact = u4 ,b :5 we are conc]n$ ) ! l5g? ( ! object measur$1 ^! facts become sup]flu\s & mislead+4 ,:at we want to d is to escape _! influ5ce1 & ?is we are enabl$ to effect by tak+ _! 7ari?metical7 av]age1 provid$ only !y are z (t5 9 excess z 9 defect4#d ,= ?is purpose all t is necess>y is t equal excesses & defects %\ld be equally preval5t4 ,x is n necess>y to "k :at is ! law ( v>iation1 or ev5 to be assur$ t x is ( "o p>ticul> k9d4 ,provid$ only t x is 9 ! language ( ! diagram on p4 #bi1 symmetrical1 !n ! ari?metical av]age ( a suitable & suitably v>i$ numb] ( measurem5ts w be free f ?is s\rce ( di/urbance4 ,& :at holds good ( ?is cause ( v>iation w hold good ( all o!rs :i* obey ! same g5]al conditions4 ,9 fact ! equal preval5ce ( equal & opposite errors seems to be ! sole & suffici5t ju/ification ( ! famili> process ( tak+ ! av]age 9 ord] to secure accuracy4 #ad4 ,we mu/ n[ make ! di/9ction to :i* att5tion requires s (t5 to be drawn 9 ^! subjects betwe5 ! cases 9 :i* !re respectively is1 & is n1 "s objective magnitude aim$ at3 a di/9ction :i* ! common use ( ! same ^w errors is s apt to obscure4 ,:5 we talk$1 9 ! case ( ! brass rod1 ( excesses & defects be+ equal1 we meant exactly :at we said1 viz4 t = e case 9 :i* ! 'true' l5g? 7i4e4 t det]m9$ by ! au?oriz$ /&>d7 is exce$$ by a giv5 fraction ( an in*1 !re w be a correspond+ case 9 :i* !re is an equal defect4 ,on ! o!r h&1 :5 !re is no su* fix$ objective /&>d ( ref]5ce1 x w\ld appe> t all t we mean by equal excesses & defects is p]man5t symmetry ( arrangem5t4 ,9 ! case ( ! measur+ rod we 7 able to />t ) some?+ :i* exi/$1 s to say1 be=e its v>iations2 b 9 _m cases any />t+ po9t :i* we c f9d is solely det]m9$ by ! av]age4 ,suppose1 = in/ance1 we take a great numb] ( obs]vations ( ! height ( ! b>omet] at a c]ta9 place1 at all times & seasons & 9 all wea!rs1 we %\ld g5]ally consid] t ! av]age ( all ^! %[$ ! 'true' height = t place4 ,:at we really mean is t ! height at any mom5t is det]m9$ p>tly 7& pr9cipally7 by ! height ( ! column ( air above x1 b p>tly also by a numb] ( o!r ag5cies su* z local temp]ature1 moi/ure1 w9d1 c4 ,^! are sometimes m & sometimes less effective1 b _! range be+ tol]ably con/ant1 & _! di/ribution ?r\gh ?is range be+ tol]ably symmetrical1 ! av]age ( "o l>ge bat* ( obs]vations w be almo/ exactly ! same z t ( any o!r4 ,?is con/ancy ( ! av]age is its tru?4 ,i am q aw>e t we f9d x difficult n to suppose t !re mu/ be some?+ m ?an ?is con/ancy1 b we are probably apt to be misl$ by ! analogy ( ! o!r class ( cases1 viz4 ^? 9 :i* we are really aim+ at "s sort ( m>k4 #ae4 ,z reg>ds ! practical me?ods available = det]m9+ ! v>i\s k9ds ( av]age !re is v little to be said2 z ! ari?metical rules are simple & def9ite1 & involve no?+ m ?an ! inevitable drudg]y att5dant ^u deal+ ) long r[s ( figures4 ,p]haps ! mo/ important contribution to ?is "p ( ! subject is furni%$ by ,mr ,galton's sugge/ion to sub/itute ! m$ian = ! mean1 & ?us to elicit ! av]age ) suffici5t accuracy by ! m]e act ( gr\p+ a numb] ( objects toge!r4 ,?us he has giv5 an +5i\s sugge/ion = obta9+ ! av]age height ( a numb] ( m5 )\t ! tr\ble & risk ( measur+ !m all4 ,a b>b>ian *ief might (t5 be induc$ to m>%all 8 m5 9 ! ord] ( _! heights1 or 9 t ( ! popul> e/imate ( _! skill 9 any capacity2 b x w\ld require "s app>atus & a great deal ( "t to measure ea* man sep>ately1 ev5 suppos+ x possible to ov]come ! usually /rong repugnance ( unciviliz$ p to any su* proce$+ 7,phil4 ,mag4 ,jan4 #ahge74 ,t is1 x be+ kn[n f wide exp]i5ce t ! heights ( any tol]ably homog5e\s set ( m5 are apt to gr\p !mselves symmetrically1--! condition = ! co9cid5ce ( ! ?ree pr9cipal k9ds ( mean1--! middle man ( a r[ ?us arrang$ 9 ord] w repres5t ! mean or av]age man1 & him we may subject to measurem5t4 ,moreov]1 s9ce ! int]m$iate heights are mu* m ?ickly repres5t$ ?an ! extreme ones1 a mod]ate error 9 ! selection ( ! c5tral man ( a long r[ w only entail a v small error 9 ! selection ( ! correspond+ height4 #af4 ,we c n[ conv5i5tly recur to a subject :i* has be5 already notic$ 9 a =m] *apt]1 viz4 ! attempt :i* is sometimes made to e/abli% a di/9ction betwe5 an av]age & a mean4 ,x has be5 propos$ to conf9e ! =m] t]m to ! cases 9 :i* we are deal+ ) a fictiti\s result ( our own con/ruction1 t is1 ) a m]e ari?metical d$uction f ! obs]v$ magnitudes1 & to apply ! latt] to cases 9 :i* !re is suppos$ to be "s objective magnitude peculi>ly repres5tative ( ! av]age4 ,recur to ! ?ree pr9cipal classes1 ( ?+s appropriate to ,probability1 :i* 7 sket*$ out 9 ,*4 ,,ii4 #d4 ,! fir/ ( ^! compris$ ! results ( games ( *ance4 ,toss a die t5 times3 ! total numb] ( pips on ! upp] side may v>y f t5 up to sixty4 ,suppose x to be ?irty4 ,we !n say t ! av]age ( ?is bat* ( t5 is ?ree4 ,take ano!r set ( t5 ?r[s1 & we may get ano!r av]age1 say f\r4 ,!re is cle>ly no?+ objective peculi>ly correspond+ 9 any way to ^! av]ages4 ,no d\bt if we g on long en\gh we %all f9d t ! av]ages t5d to c5tre ab\t #c4e3 we !n call ?is ! av]age1 or ! 'probable' numb] ( po9ts2 & ?is ultimate av]age might h be5 pretty con/antly ass]t$ be=eh& f our k ( ! con/itution ( a die4 ,x has h[ev] no o!r tru? or reality ab\t x ( ! nature ( a type3 x is simply ! limit t[>ds :i* ! av]ages t5d4 ,! next class is t occupi$ by ! memb]s ( mo/ natural gr\ps ( objects1 especially z reg>ds ! *>act]i/ics ( natural species4 ,some:at simil> rem>ks may be repeat$ "h4 ,!re is v frequ5tly a 'limit' t[>ds :i* ! av]ages ( increas+ numb]s ( individuals t5d to approa*2 & !re is c]ta9ly "s temptation to reg>d ?is limit z be+ a sort ( type :i* all _h be5 int5d$ to resemble z closely z possible4 ,b :5 we look$ clos]1 we f\nd t ?is view c\ld sc>cely be ju/ifi$2 all :i* c\ld be safely ass]t$ 0 t ?is type repres5t$1 = ! "t be+1 ! mo/ num]\s specim5s1 or ^? :i* "u exi/+ conditions c\ld mo/ easily be produc$4 ,! rema9+ class /&s on a some:at diff]5t gr\nd4 ,:5 we make a succession ( m or less successful attempts ( any k9d1 we get a correspond+ s]ies ( deviations f ! m>k at :i* we aim$4 ,^! we may treat ari?metically1 & obta9 _! av]ages1 j z 9 ! =m] cases4 ,^! av]ages are fictions1 t is to say1 !y are artificial d$uctions ( our own :i* ne$ n necess>ily h any?+ objective correspond+ to !m4 ,9 fact1 if !y be av]ages ( a few only !y mo/ probably w n h any?+ ?us correspond+ to !m4 ,any?+ answ]+ to a type c only be s\ght 9 ! 'limit' t[>ds :i* !y ultimately t5d1 = ?is limit co9cides ) ! fix$ po9t or object aim$ at4 #ag4 ,fully admitt+ ! great value & int]e/ ( ,quetelet's "w 9 ?is direction1--he 0 c]ta9ly ! fir/ to direct public att5tion to ! fact t s _m classes ( natural objects display ! same *>act]i/ic prop]ty1--x nev]!less does n seem desirable to attempt to m>k su* a di/9ction by any special use ( ^! te*nical t]ms4 ,! objections are pr9cipally ! two foll[+4 ,9 ! fir/ place1 a s+le anti!sis1 l ?is betwe5 an av]age & a mean1 appe>s to sugge/ a v mu* simpl] /ate ( ?+s ?an is actually f\nd to exi/ 9 nature4 ,a ref]5ce to ! ?ree classes ( ?+s j m5tion$1 & a consid]ation ( ! wide range & div]sity includ$ 9 ea* ( !m1 w s]ve to rem9d u n only ( ! v gradual & ins5sible advance f :at is ?us reg>d$ z 'fictiti\s' to :at is claim$ z 'real2' b also ( ! important fact t :]eas ! 'real type' may be ( a fluctuat+ & evanesc5t "*1 ! 'fiction' may 7z 9 games ( *ance7 be app>5tly fix$ = ev]4 ,provid$ only t ! conditions ( production rema9 /able1 av]ages ( l>ge numb]s w always practically pres5t mu* ! same g5]al *>act]i/ics4 ,! f> m important di/9ction lies betwe5 ! av]age ( a few1 ) its fluctuat+ values & v imp]fect & occasional atta9m5t ( its ultimate goal1 & ! av]age ( _m & its gradually close approximation to its ultimate value3 i4e4 to its objective po9t ( aim if !re happ5 to be su*4 ,!n1 aga91 ! consid]ations adduc$ 9 ?is *apt] w %[ t )9 ! field ( ! av]age itself !re is f> m v>iety ?an ,quetelet seems to h recogniz$4 ,he did n inde$ q ignore ?is v>iety1 b he practically conf9$ himself almo/ entirely to ^? symmetrical arrangem5ts 9 :i* ?ree ( ! pr9cipal means coalesce into "o4 ,we %\ld f9d x difficult to c>ry out 8 di/9ction 9 less simple cases4 ,= in/ance1 :5 !re is "s degree ( asymmetry1 x is ! 'maximum ord9ate' :i* w\ld h to be consid]$ z a 'mean' to ! exclusion ( ! o!rs2 = no appeal to an ari?metical av]age w\ld guide u to ?is po9t1 :i* h[ev] is to be reg>d$1 if any c be s reg>d$1 z m>k+ out ! position ( ! ultimate type4 #ah4 ,we h sev]al times po9t$ out t x is a *>act]i/ic ( ! ?+s ) :i* ,probability is conc]n$ to pres5t1 9 ! long run1 a cont9ually int5sify+ uni=mity4 ,& ?is has be5 frequ5tly describ$ z :at happ5s 'on ! av]age4' ,n[ an objection may v possibly be rais$ aga9/ reg>d+ an arrangem5t ( ?+s by virtue ( :i* ord] ?us em]ges out ( disord] z des]v+ any special notice1 on ! gr\nd t f ! nature ( ! ari?metical av]age x c\ld n possibly be o!rwise4 ,! process by :i* an av]age is obta9$1 x may be urg$1 insures ?is t5d5cy to equalization among/ ! magnitudes ) :i* x deals4 ,= in/ance1 let !re be a p>ty ( t5 m51 ( :om f\r are tall & f\r are %ort1 & take ! av]age ( any five ( !m4 ,s9ce ?is numb] _c be made up ( tall m5 only1 or ( %ort m5 only1 x /&s to reason t ! av]ages _c diff] s mu* among/ !mselves z ! s+le measures c4 ,is n !n ! equaliz+ process1 x may be ask$1 :i* is obs]vable on increas+ ! range ( our obs]vations1 "o :i* c be %[n to foll[ f necess>y laws ( ari?metic1 & "o !re=e :i* might be ass]t$ priori8 ,:atev] =ce !re may be 9 ! above objection arises pr9cipally f ! limitations ( ! example select$1 9 :i* ! numb] *os5 0 s l>ge a proportion ( ! total z to exclude ! b>e possibility ( only extreme cases be+ conta9$ )9 x4 ,z mu* confusion is (t5 felt "h betwe5 :at is necess>y & :at is matt] ( exp]i5ce1 x w be well to look at an example some:at m closely1 9 ord] to det]m9e exactly :at are ! really necess>y consequ5ces ( ! av]ag+ process4 #ai4 ,suppose !n t we take t5 digits at r&om f a table 7say7 ( log>i?ms4 ,unless 9 ! highly unlikely case ( our hav+ happ5$ ^u ! same digit t5 times runn+1 ! av]age ( ! t5 mu/ be int]m$iate betwe5 ! possible extremes4 ,e conception ( an av]age ( any sort n m]ely involves1 b actually means1 ! tak+ ( some?+ int]m$iate betwe5 ! extremes4 ,! av]age !re=e ( ! t5 mu/ lie clos] to #d4e 7! av]age ( ! extremes7 ?an did "s ( ! s+le digits4 ,n[ suppose we take #ajjj su* digits in/ead ( #aj4 ,we c say no?+ m ab\t ! l>g] numb]1 ) demon/rative c]ta9ty1 ?an we c\ld be=e ab\t ! small]4 ,if !y 7 unequal to beg9 ) 7i4e4 if !y 7 n all ! same7 !n ! av]age mu/ be int]m$iate1 b m ?an ?is _c be prov$ ari?metically4 ,by comp>ison ) su* purely ari?metical consid]ations !re is :at may be call$ a physical fact und]ly+ our confid5ce 9 ! gr[+ /ability ( ! av]age ( ! l>g] numb]4 ,x is t ! con/itu5t elem5ts f :i* ! av]age is d$uc$ w !mselves betray a gr[+ uni=mity3--t ! proportions 9 :i* ! diff]5t digits come out w become m & m ne>ly equal z we take l>g] numb]s ( !m4 ,if ! proportions 9 :i* ! #ajjj digits 7 di/ribut$ 7 ! same z ^? ( ! #aj ! av]ages w\ld be ! same4 ,x is obvi\s !re=e t ! ari?metical process ( obta9+ an av]age goes a v little way t[>ds secur+ ! /rik+ k9d ( uni=mity :i* we f9d to be actually pres5t$4 #bj4 ,!re is ano!r way 9 :i* ! same ?+ may be put4 ,x is sometimes said t :atev] may h be5 ! arrangem5t ( ! orig9al elem5ts ! process ( cont9ual av]ag+ w necess>ily produce ! peculi> b9omial or expon5tial law ( arrangem5t4 ,?is /atem5t is p]fectly true 7) c]ta9 safegu>ds7 b x is n 9 any way oppos$ to :at has be5 said above4 ,let u take = consid]ation ! example above ref]r$ to4 ,! arrangem5t ( ! individual digits 9 ! long run is ! simple/ possible4 ,x w\ld be repres5t$1 9 a diagram1 n by a curve b by a f9ite /raight l9e1 = ea* digit occurs ab\t z (t5 z any o!r1 & ?is exhau/s all ! 'arrangem5t' t c be detect$4 ,n[1 :5 we consid] ! results ( tak+ av]ages ( t5 su* digits1 we see at once t !re is an op5+ = a m ext5sive arrangem5t4 ,! totals may range f #j up to #ajj1 & !re=e ! av]age w h #ajj values f #j to #i2 & :at we f9d is t ! frequ5cy ( ^! numb]s is det]m9$ accord+ to ! ,b9omial#e or ,expon5tial ,law4 ,! mo/ frequ5t result is ! true mean1 viz4 #d4e1 & f ?is !y dim9i% 9 ea* direction t[>ds #j & #aj1 :i* w ea* occur b once 7on ! av]age7 9 #ajaj occasions4 ,! explanation "h is ( ! same k9d z 9 ! =m] case4 ,! resultant arrangem5t1 s f> z ! av]ages are conc]n$1 is only 'necess>y' 9 ! s5se t x is a necess>y result ( c]ta9 physical assumptions or exp]i5ces4 ,if all ! digits t5d to occur ) equal frequ5cy1 & if !y are 'indep5d5t' 7i4e4 if ea* is associat$ indiff]5tly ) e o!r71 !n x is an ari?metical consequ5ce t ! av]ages :5 arrang$ 9 respect ( _! magnitude & preval5ce w display ! ,law ( ,facility above indicat$4 ,exp]i5ce1 s f> z x c be appeal$ to1 %[s t ! true r&omness ( ! selection ( ! digits1--i4e4 _! equally frequ5t recurr5ce1 & ! imp>tiality ( _! comb9ation1--is v fairly secur$ 9 practice4 ,accord+ly ! !oretic d$uction t :atev] may h be5 ! orig9al ,law ( ,facility ( ! individual results we %all always f9d ! famili> ,expon5tial ,law ass]t+ itself z ! law ( ! av]ages1 is fairly ju/ifi$ by exp]i5ce 9 su* a case4 ,! fur!r discussion ( c]ta9 corrections & ref9em5ts is res]v$ to ! foll[+ *apt]4 #ba4 ,9 reg>d to ! ?ree k9ds ( av]age employ$ to te/ ! am\nt ( disp]sion1--i4e4 ! mean error1 ! probable error1 & ! error ( mean squ>e1--two important consid]ations mu/ be borne 9 m9d4 ,!y w bo? recur = full] discussion & ju/ification 9 ! c\rse ( ! next *apt]1 :5 we come to t\* ^u ! ,me?od ( ,lea/ ,squ>es1 b _! significance = logical purposes is s great t !y ought n to be entirely pass$ by at pres5t4 7#a7 ,9 ! fir/ place1 !n1 x mu/ be rem>k$ t 9 ord] to "k :at 9 any case is ! real value ( an error we ought 9 /rictness to "k :at is ! position ( ! limit or ultimate av]age1 = ! am\nt ( an error is always !oretically measur$ f ?is po9t4 ,b ?is is in=mation :i* we d n always possess4 ,recurr+ once m to ! ?ree pr9cipal classes ( ev5ts ) :i* we are conc]n$1 we c readily see t 9 ! case ( games ( *ance we mo/ly d possess ?is k4 ,in/ead ( appeal+ to exp]i5ce to asc]ta9 ! limit1 we practically d$uce x by simple me*anical or ari?metical consid]ations1 & !n ! 'error' 9 any individual case or gr\p ( cases is obvi\sly f\nd by comp>+ ! results ?us obta9$ ) t :i* !ory in=ms u w\ld ultimately be obta9$ 9 ! long run4 ,9 ! case ( delib]ate ef=ts at an aim 7! ?ird class7 we may or may n "k accurately ! value or position ( ?is aim4 ,9 a/ronomical obs]vations we d n "k x1 & ! me?od ( ,lea/ ,squ>es is a me?od = help+ u to asc]ta9 x z well z we c2 9 su* exp]im5tal results z fir+ at a m>k we d "k x1 & may ?us te/ ! nature & am\nt ( our failure by direct exp]i5ce4 ,9 ! rema9+ case1 namely t ( :at we h t]m$ natural k9ds or gr\ps ( ?+s1 n only d we n "k ! ultimate limit1 b its exi/5ce is always at lea/ d\btful1 & 9 _m cases may be confid5tly d5i$4 ,:]e x does exi/1 t is1 :]e ! type seems = all practical purposes p]man5tly fix$1 we c only asc]ta9 x by a labori\s resort to /ati/ics4 ,hav+ done ?is1 we may !n te/ by x ! results ( obs]vations on a small scale4 ,= in/ance1 if we f9d t ! ultimate proportion ( male to female bir?s is ab\t #ajf to #ajj1 we may !n comp>e ! /ati/ics ( "s p>ticul> di/rict or t[n & speak ( ! consequ5t 'error1' viz4 ! dep>ture1 9 t p>ticul> & special di/rict1 f ! g5]al av]age4 ,:at we h !re=e to d 9 ! va/ majority ( practical cases is to take ! av]age ( a f9ite numb] ( measurem5ts or obs]vations1--( all ^?1 9 fact1 :i* we h 9 h&1--& take ?is z our />t+ po9t 9 ord] to measure ! errors4 ,! errors 9 fact are n kn[n = c]ta9 b only probably calculat$4 ,?is h[ev] is n s mu* ( a !oretic defect z x may seem at fir/ sight2 = inasmu* z we seldom h to employ ^! me?ods1--= purposes ( calculation1 t is1 z di/+ui%$ f m]e illu/ration1--except = ! purpose ( discov]+ :at ! ultimate av]age is1 x w\ld be a sort ( petitio pr9cipii to assume t we _h already secur$ x4 ,b x is wor? :ile consid]+ :e!r x is desirable to employ "o & ! same t]m = 'errors' kn[n to be su*1 & ^: am\nt c be assign$ ) c]ta9ty1 & = 'errors' :i* are only probably su* & ^: am\nt c be only probably assign$4 ,9 fact x has be5 propos$#f to employ ! two t]ms 'error' & 'residual' respectively to di/+ui% betwe5 ! magnitudes ?us det]m9$1 t is1 betwe5 ! 7g5]ally unkn[n7 actual error & ! obs]v$ error4 #bb4 7#b7 ,! o!r po9t involves ! "q to :at ext5t ei!r ( ! fir/ two te/s 7pp4 #ddf1g7 ( ! clos5ess ) :i* ! v>i\s results h gr\p$ !mselves ab\t _! av]age is tru/wor?y or complete4 ,! answ] is t !y are necess>ily incomplete4 ,no s+le e/imate or magnitude c possibly give u an adequate acc\nt ( a numb] ( v>i\s magnitudes4 ,! po9t is a v important "o2 & is n1 ,i ?9k1 suffici5tly att5d$ to1 ! consequ5ce be+1 z we %all see h]eaft]1 t x is f> too summ>ily assum$ t a me?od :i* yields ! result ) ! lea/ 'error ( mean squ>e' mu/ necess>ily be ! be/ result = all purposes4 ,x is n h[ev] by any means cle> t a te/ :i* answ]s be/ = "o purpose mu/ d s = all4 ,x mu/ be cle>ly und]/ood t ea* ( ^! te/s is an 'av]age1' & t e av]age necess>ily rejects a mass ( v>i$ detail by sub/itut+ = x a s+le result4 ,we _h1 say1 a lot ( /atures3 s _m ( #fj in*es1 s _m ( #fa1 c4 ,we replace ^! by an 'av]age' ( #fh1 & !reby drop a mass ( in=mation4 ,a portion ( ?is we !n seek to recov] by reconsid]+ ! 'errors' or dep>tures ( ^! /atures f _! av]age4 ,z be=e1 h[ev]1 in/ead ( giv+ ! full details we sub/itute an av]age ( ! errors4 ,! only diff]5ce is t in/ead ( tak+ ! same k9d ( av]age 7i4e4 ! ari?metical7 we (t5 pref] to adopt ! "o call$ ! 'error ( mean squ>e4' #bc4 ,a "q may be rais$ "h :i* is ( suffici5t importance to des]ve a %ort consid]ation4 ,:5 we h got a set ( measurem5ts be=e u1 :y is x g5]ally held to be suffici5t simply to assign3 7#a7 ! mean value2 & 7#b7 ! mean dep>ture f ?is mean8 ,! answ] is1 ( c\rse1 p>tly giv5 by ! fact t we are only suppos$ to be 9 want ( a r\gh approximation3 b !re is m to be said ?an ?is4 ,a fur!r ju/ification is to be f\nd 9 ! fact t we assume t we ne$ only contemplate ! possibility ( a s+le ,law ( ,error1 or at any rate t ! dep>tures f ! famili> ,law w be b trifl+4 ,9 o!r words1 if we recur to ! figure on p4 #bi1 we assume t !re are only two unkn[n quantities or disposable con/ants to be assign$2 viz4 fir/1 ! position ( ! c5tre1 &1 secondly1 ! degree ( ecc5tricity1 if "o may s t]m x1 ( ! curve4 ,! det]m9ation ( ! mean value directly & at once assigns ! =m]1 & ! det]m9ation ( ! mean error 79 ei!r ( ! ways ref]r$ to already7 indirectly assigns ! latt] by conf9+ u to "o alone ( ! possible curves indicat$ 9 ! figure4 ,except = ! assumption ( "o su* ,law ( ,error ! det]m9ation ( ! mean error w\ld give b a slight intimation ( ! sort ( outl9e ( our ,curve ( ,facility4 ,we might !n h f\nd x conv5i5t to adopt "s plan ( successive approximation1 by add+ a ?ird or f\r? 'mean4' ,j z we assign ! mean value ( ! magnitude1 & its mean dep>ture f ?is mean2 s we might take ?is mean error 7h[ev] det]m9$7 z a fre% />t+ po9t1 & assign ! mean dep>ture f x4 ,if ! po9t 7 wor? fur!r discussion we might easily illu/rate by means ( a diagram ! sort ( successive approximations :i* su* indications w\ld yield z to ! ultimate =m ( ! ,curve ( ,facility or ,law ( ,error4 99 99 99 99 99 ,z ?is volume is writt5 ma9ly = ^? :o take an int]e/ 9 ! logical que/ions involv$1 r ?an z an introduction to ! actual processes ( calculation1 ma!matical details h be5 ?r\gh\t avoid$ z mu* z possible4 ,= ?is reason comp>atively few ref]5ces h be5 made to ! expon5tial equation ( ! ,law ( ,error1 or to ! correspond+ ',probability integral1' tables ( :i* are giv5 9 sev]al h&books on ! subject4 ,!re are two po9ts h[ev] 9 connection ) ^! p>ticul> topics z to :i* difficulties are1 or %\ld be1 felt by s _m /ud5ts t "s notice may be tak5 ( !m "h 7#a7 ,9 reg>d to ! ord9>y algebraical expression = ! law ( error1 viz4 y 7h_/sqrt7 e-h#bx#b1 x w h be5 obs]v$ t ,i h always spok5 ( y z be+ proportional to ! numb] ( errors ( ! p>ticul> magnitude x4 ,x w\ld h>dly be correct to say1 absolutely1 t y repres5ts t numb]1 because ( c\rse ! actual numb] ( errors ( any precise magnitude1 :]e cont9uity ( possibility is assum$1 mu/ be indef9itely small4 ,if !re=e we want to pass f ! cont9u\s to ! discrete1 by asc]ta9+ ! actual numb] ( errors betwe5 two consecutive divisions ( our scale1 :51 z usual 9 measurem5ts1 all )9 c]ta9 limits are ref]r$ to "s "o precise po9t1 we mu/ modify our =mula4 ,9 accordance ) ! usual diff]5tial notation1 we mu/ say t ! numb] ( errors fall+ into "o subdivision 7dx7 ( our scale is dx 7h_/sqrt7 e-h#b x#b1 :]e dx is a 7small7 unit ( l5g?1 9 :i* bo? h-#a & x mu/ be measur$4 ,! difficulty felt by mo/ /ud5ts is 9 apply+ ! =mula to actual /ati/ics1 9 o!r words 9 putt+ 9 ! correct units4 ,to take an actual num]ical example1 suppose t #adfj m5 h be5 measur$ 9 reg>d to _! height true to ! ne>e/ in*1 & let x be kn[n t ! modulus "h is #c4f in*es4 ,!n dx #a 7in*72 h-#a #c4f in*es4 ,n[ sum 7h_/sqrt7 e-h#bx#b dx #a2 t is1 ! sum ( all ! consecutive possible values is equal to unity4 ,:5 !re=e we want ! sum1 z "h1 to be #adfj1 we mu/ express ! =mula ?us2--y #adfj_/7sqrt #c4f7 e-7x_/#c4f7b1 or y #bbh e-7x_/#c4f7b4 ,"h x /&s = ! numb] ( in*es measur$ f ! c5tral or mean height1 & y /&s = ! numb] ( m5 ref]r$ to t height 9 our /ati/ical table4 7,! values ( e-t#b = successive values ( t are giv5 9 ! h&books47 ,= illu/ration ,i give ! calculat$ numb]s by ?is =mula = values ( x f #j to #h in*es1 ) ! actual numb]s obs]v$ 9 ! ,cambridge measurem5ts rec5tly set on foot by ,mr ,galton4 in*es calculat$ obs]v$ x #j y #bbh #bca x #a y #bab #bah x #b y #aff #agj x #c y #aaa #aaj x #d y #hb #ff x #e y #cb #ca x #f y #aa #aj x #g y #d #f x #h y #a #c ,"h ! av]age height 0 #fi in*es3 dx1 z /at$1 #a in*4 ,by say+1 'put x #j1' we mean1 calculate ! numb] ( m5 :o are assign$ to #fi in*es2 i4e4 :o fall betwe5 #fh4e & #fi4e4 ,by say+1 'put x #d1' we mean1 calculate ! numb] :o are assign$ to #fe or to #gc2 i4e4 :o lie betwe5 #fd4e & #fe4e1 or betwe5 #gb4e & #gc4e4 ,! obs]v$ results1 x w be se51 keep pretty close to ! calculat$3 9 ! case ( ! =m] ! means ( equal & opposite div]g5ces f ! mean h be5 tak51 ! actual results n be+ always ! same 9 opposite directions4 7#b7 ,! o!r po9t conc]ns ! int]pretation ( ! famili> probability integral1 7#b_/sqrt7 integral#jt e-t#b dt4 ,e "o :o has calculat$ ! *ance ( an ev5t1 by ! help ( ! tables ( ?is integral giv5 9 s _m h&books1 kn[s t if we assign any num]ical value to t1 ! correspond+ value ( ! above expression assigns ! *ance t an error tak5 at r&om %all lie )9 t same limit1 viz4 t4 ,?us put t #a4e1 & we h ! result #j4if2 t is1 only #d p] c5t4 ( ! errors w exce$ '"o & a half4' ,b :5 we ask1 '"o & a half' :at8 ! answ] w\ld n always be v ready4 ,z usual1 ! ma9 difficulty ( ! beg9n] is n to manipulate ! =mul1 b to be q cle> ab\t 8 units4 ,x w be se5 at once t ?is case diff]s f ! prec$+ 9 t we _c n[ *oose our unit z we please4 ,:]e1 z "h1 !re is only "o v>iable 7t71 if we 7 all[$ to select our own unit1 ! in*1 foot1 or :atev] x might be1 we might get q diff]5t results4 ,accord+ly "s comp>atively natural unit mu/ h be5 *os5 = u 9 :i* we are b\nd to reckon1 j z 9 ! circul> measurem5t ( an angle z di/+ui%$ f t by degrees4 ,! answ] is t ! unit "h is ! modulus1 & t to put 't #a4e' is to say1 'suppose ! error half z great aga9 z ! modulus'2 ! modulus itself be+ an error ( a c]ta9 assignable magnitude dep5d+ ^u ! nature ( ! measurem5ts or obs]vations 9 "q4 ,we %all see ?is bett] if we put ! integral 9 ! =m 7#b_/sqrt7 integral#j;hx e-h#b x#b d7hx72 :i* is precisely equival5t1 s9ce ! value ( a def9ite integral is indep5d5t ( ! p>ticul> v>iable employ$4 ,"h hx is ! same z x 3 #a_/;h2 i4e4 x is ! ratio ( x to #a_/;h1 or x measur$ 9 t]ms ( #a_/;h4 ,b #a_/;h is ! modulus 9 ! equation 7y 7h_/sqrt7 e-h#b x#b7 = ! law ( error4 ,9 o!r words ! num]ical value ( an error 9 ?is =mula1 is ! numb] ( times1 :ole or fractional1 :i* x conta9s ! modulus4 #a4 ,?is k9d ( mean is call$ by ,fe*n] & o!rs ! di*te/e ,w]?4 ,! mo/ appropriate appeal to x t ,i h se5 is by ,pr(4 ,lexis 7,mass5]s*e9ung51 p4 #db7 :]e he %[s t x indicates cle>ly a sort ( normal l5g? ( human life1 ( ab\t #gj ye>s2 a result :i* is almo/ entirely mask$ :5 we appeal to ! ari?metical av]age4 ,?is mean ought to be call$ ! 'probable' value 7a "n h[ev] 9 possession ( ano!r7 on ! gr\nd t x indicates ! po9t ( likelie/ occurr5ce2 i4e4 if we comp>e all ! indef9itely small & equal units ( v>iation1 ! "o correspond+ to ?is w t5d to be mo/ frequ5tly repres5t$4 #b4 ,a diagram illu/rative ( ?is numb] ( results 0 giv5 9 ,nature 7,sept4 #a1 #ahhg74 ,9 calculat+1 z above1 ! diff]5t means1 ,i may rem>k t ! orig9al results 7 giv5 to ?ree decimal places2 b1 9 class+ !m1 only "o place 0 not$4 ,t is1 #bi4i includes all values betwe5 #bi4ijj & #bi4iii4 ,?us ! value mo/ frequ5tly ent]$ 9 my tables 0 #cj4j1 b on ! usual pr9ciples ( int]polation ?is is reckon$ z #cj4je4 #c4 ,!re is "s ambiguity 9 ! phraseology 9 use "h4 ,?us ,airy commonly uses ! expression ',error ( ,mean ,squ>e' to repres5t1 z "h1 sqrt7sum e#b7_/n4 ,gall[ay commonly speaks ( ! ',mean ,squ>e ( ! ,errors' to repres5t 7sum e#b7_/n4 ,i %all adh]e to ! =m] usage & repres5t x briefly by ,e4,m4,s4 ,/ill m un=tunate 7to my ?9k+7 is ! employm5t1 by ,mr ,m]riman & o!rs1 ( ! expression ',mean ,error1' 7widely 9 use 9 its m natural signification17 z ! equival5t ( ?is ,e4,m4,s4 ,! te*nical t]m ',fluctuation' is appli$ by ,mr ,f4 ,y4 ,edgewor? to ! expression 7#b sum e#b7_/n4 #d4 ,practically1 ( c\rse1 we %\ld all[ = ! expansion or contraction4 ,b = purposes ( logical explanation we may conv5i5tly take ?is v>iation z a specim5 ( "o ( ^? di/urbances :i* may be neutralis$ by resort to an av]age4 #e4 ,m /rictly mult9omial3 ! relative frequ5cy ( ! diff]5t numb]s be+ indicat$ by ! coeffici5ts ( ! p[]s ( x 9 ! developm5t ( 7#a x x#b 444 x#i7aj4 #f4 ,by ,mr ,m]riman1 9 8 "w on ,lea/ ,squ>es4 ,,*apt] ,,xix4 ,,! ,,!ory ,,( ,,! ,,av]age ,,z ,a ,,means ,,( ,,approximation ,,to ,,! ,,tru?4 #a4 ,9 ! la/ *apt] we 7 occupi$ ) ! ,av]age ma9ly "u its qualitative r ?an its quantitative aspect4 ,t is1 we discuss$ its g5]al nature1 its pr9cipal v>ieties1 & ! ma9 uses to :i* x c\ld be put 9 ord9>y life or 9 reason+ processes :i* did n claim to be v exact4 ,x is n[ "t to ent] m m9utely into ! specific "q ( ! employm5t ( ! av]age 9 ! way peculi>ly appropriate to ,probability4 ,t is1 we mu/ be suppos$ to h a c]ta9 numb] ( measurem5ts1--9 ! wide/ s5se ( t t]m1--plac$ be=e u1 & to be prep>$ to answ] su* que/ions z2 ,:y d we take _! av]age8 ,) :at degree ( confid5ce8 ,mu/ we 9 all cases take ! av]age1 &1 if s1 "o always ( ! same k9d8 ,! subject ^u :i* we are ?us ent]+ is "o :i*1 "u its mo/ g5]al !oretic treatm5t1 has p]haps giv5 rise to m pr(\nd inve/igation1 to a great] v>iety ( op9ion1 & 9 consequ5ce to a m ext5sive hi/ory & lit]ature1 ?an any o!r s+le problem )9 ! range ( ma!matics4#a ,b1 9 spite ( ?is1 ! ma9 logical pr9ciples und]ly+ ! me?ods & processes 9 "q are n1 ,i appreh5d1 p>ticul>ly difficult to grasp3 ?\gh1 ow+ to ! extremely te*nical /yle ( treatm5t adopt$ ev5 9 comp>atively elem5t>y discussions ( ! subject1 x is f> f easy = ^? :o h b a mod]ate comm& ( ma!matical res\rces to dis5tangle ^! pr9ciples f ! symbols 9 :i* !y are clo!d4 ,! pres5t *apt] conta9s an attempt to remove ^! difficulties1 s f> z a g5]al compreh5sion ( ! subject is conc]n$4 ,z ! treatm5t ?us adopt$ involves a consid]able numb] ( subdivisions1 ! read] w probably f9d x conv5i5t to ref] back occasionally to ! table ( cont5ts at ! comm5cem5t ( ?is volume4 #b4 ,! subject1 9 ! =m 9 :i* we %all discuss x1 w be n>r[$ to ! consid]ation ( ! av]age1 on acc\nt ( ! comp>ative simplicity & v wide preval5ce ( ?is aspect ( ! problem4 ,! problem is h[ev] v commonly ref]r$ to1 ev5 9 non-ma!matical treatises1 z ! ,rule or ,me?od ( ,lea/ ,squ>es2 ! fact be+ t1 9 su* cases z we %all be conc]n$ )1 ! ,rule ( ,lea/ ,squ>es resolves itself into ! simpl] & m famili> process ( tak+ ! ari?metical av]age4 ,a v simple example1--"o giv5 by ,h]s*el1--w expla9 ! g5]al nature ( ! task "u a slightly wid] treatm5t1 & w s]ve to ju/ify ! famili> designation4 ,suppose t a man _h be5 fir+ = "s "t ) a pi/ol at a small m>k1 say a waf] on a wall4 ,we may take x = grant$ t ! %ot-m>ks w\ld t5d to gr\p !mselves ab\t ! waf] z a c5tre1 ) a d5sity v>y+ 9 "s way inv]sely ) ! di/ance f ! c5tre4 ,b n[ suppose t ! waf] :i* m>k$ ! c5tre 0 remov$1 s t we c\ld see no?+ b ! surface ( ! wall spott$ ) ! %ot-m>ks2 & t we 7 ask$ to guess ! position ( ! waf]4 ,_h !re be5 only "o %ot1 common s5se w\ld sugge/ our assum+ 7( c\rse v prec>i\sly7 t ?is m>k$ ! real c5tre4 ,_h !re be5 two1 common s5se w\ld sugge/ our tak+ ! mid-po9t betwe5 !m4 ,b if ?ree or m 7 involv$1 common s5se w\ld be at a loss4 ,x w\ld feel t "s int]m$iate po9t ought to be select$1 b w\ld n see its way to a m precise det]m9ation1 because its famili> reliance1--! ari?metical av]age1--does n seem at h& "h4 ,! rule 9 "q tells u h[ to proce$4 ,x directs u to select t po9t :i* w r5d] ! sum ( ! squ>es ( all ! di/ances ( ! v>i\s %ot-m>ks f x ! lea/ possible4#b ,?is is m]ely by way ( illu/ration1 & to ju/ify ! famili> designation ( ! rule4 ,! sort ( cases ) :i* we %all be exclusively occupi$ are ^? comp>atively simple ones 9 :i* only l9e> magnitude1 or "s quality :i* c be adequately repres5t$ by l9e> magnitude1 is ! object "u consid]ation4 ,9 respect ( ^! ! ,rule ( ,lea/ ,squ>es r$uces itself to ! process ( tak+ ! av]age1 9 ! mo/ famili> s5se ( t t]m1 viz4 ! ari?metical mean2 & a s+le ,law ( ,error1 or its graphical equival5t1 a ,curve ( ,facility1 w suffice accurately to indicate ! comp>ative frequ5cy ( ! diff]5t am\nts ( ! "o v>iable magnitude involv$4 #c4 ,we may conv5i5tly "h aga9 call att5tion to a misconception or confusion :i* has be5 already notic$ 9 a =m] *apt]4 ,x is t ( conf\nd+ ! ,law ( ,error ) ! ,me?od ( ,lea/ ,squ>es4 ,^! are ?+s ( an entirely di/9ct k9d4 ,! =m] is ( ! nature ( a physical fact1 & its production is "o :i* 9 _m cases is entirely beyond our control4 ,! latt]1--or any simplifi$ application ( x1 su* z ! ari?metical av]age1--is no law :atev] 9 ! physical s5se4 ,x is r a precept or rule = our guidance4 ,! ,law /ates1 9 any giv5 case1 h[ ! errors t5d to occur 9 respect ( _! magnitude & frequ5cy4 ,! ,me?od directs u h[ to treat ^! errors :5 any numb] ( !m are pres5t$ to u4 ,no d\bt !re is a relation betwe5 ! two1 z w be po9t$ out 9 ! c\rse ( ! foll[+ pages2 b !re is no?+ really to prev5t u f us+ ! same me?od = diff]5t laws ( error1 or diff]5t me?ods = ! same law4 ,9 s do+1 ! "q ( di/9ct "r & wrong w\ld seldom be involv$1 b r "o ( m or less propriety4 #d4 ,! read] mu/ und]/&1--z 0 impli$ 9 ! illu/ration ab\t ! pi/ol %ots1--t ! ultimate problem be=e u is an inv]se "o4 ,t is1 we are suppos$ to h a mod]ate numb] ( 'errors' be=e u & we are to und]take to say :]eab\ts is ! c5tre f :i* !y div]ge4 ,?is resembles ! det]m9ation ( a cause f ! obs]vation ( an effect4 ,b1 z mo/ly happ5s 9 inv]se problems1 we mu/ comm5ce ) ! consid]ation ( ! direct problem4 ,9 o!r words1 s f> z conc]ns ! case be=e u1 we %all h to beg9 by suppos+ t ! ultimate object ( our aim1--t is1 ! true c5tre ( our curve ( frequ5cy1--is already kn[n to u3 9 :i* case all t rema9s to be done is to /udy ! consequ5ces ( tak+ av]ages ( ! magnitudes :i* con/itute ! errors4 #e4 ,we %all1 = ! pres5t1 conf9e our rem>ks to :at mu/ be reg>d$ z ! typical case :]e consid]ations ( ,probability are conc]n$2 viz4 t 9 :i* ! law ( arrangem5t or developm5t is ( ! ,b9omial k9d4 ,! nature ( ?is law 0 expla9$ 9 ,*ap4 ,,ii41 :]e x 0 %[n t ! frequ5cy ( ! respective numb]s ( occurr5ces 0 regulat$ 9 accordance ) ! magnitude ( ! successive t]ms ( ! expansion ( ! b9omial 7#a #a7n4 ,x 0 also po9t$ out t :5 n becomes v great1 t is1 :5 ! numb] ( influ5c+ circum/ances is v l>ge1 & _! relative individual influ5ce correspond+ly small1 ! =m assum$ by a curve drawn ?r\gh ! summits ( ord9ates repres5t+ ^! successive t]ms ( ! b9omial t5ds t[>ds t assign$ by ! equation y ,ae-h#bx#b4 ,= all practical purposes !re=e we may talk indiff]5tly ( ! ,b9omial or ,expon5tial law2 if only on ! gr\nd t ! arrangem5t ( ! actual ph5om5a on "o or o!r ( ^! two s*emes w\ld soon become indi/+ui%able :5 ! numb]s involv$ are l>ge4 ,b !re is ano!r gr\nd ?an ?is4 ,ev5 :5 ! ph5om5a !mselves repres5t a cont9u\s magnitude1 our measurem5ts ( !m1--:i* are all ) :i* we c deal1--are discont9u\s4 ,suppose we _h be=e u ! accurate heights ( a million adult m54 ,= all practical purposes ^! w\ld repres5t ! v>iations ( a cont9u\s magnitude1 = ! diff]5ces betwe5 two successive magnitudes1 especially ne> ! mean1 w\ld be inappreciably small4 ,b our tables w probably repres5t !m only to ! ne>e/ in*4 ,we h s _m assign$ z #fi in*es2 s _m z #gj2 & s on4 ,! tabul> /atem5t 9 fact is ( mu* ! same "* z if we 7 assign+ ! numb] ( 'heads' 9 a toss ( a h&ful ( p5ce2 t is1 z if we 7 deal+ ) discont9u\s numb]s on ! b9omial1 r ?an ) a cont9u\s magnitude on ! expon5tial arrangem5t4 #f4 ,conf9+ ourselves !n1 = ! pres5t1 to ?is g5]al head1 ( ! b9omial or expon5tial law1 we mu/ di/+ui% two sep>ate cases 9 respect ( ! k we may possess z to ! g5]at+ circum/ances ( ! v>iable magnitudes4 7#a7 ,!re is1 fir/1 ! case 9 :i* ! conditions ( ! problem are det]m9able priori3 t is1 :]e we are able to say1 prior to specific exp]i5ce1 h[ frequ5tly ea* comb9ation w occur 9 ! long run4 ,9 ?is case ! ma9 or ultimate object = :i* we are suppos+ t ! av]age is employ$1--i4e4 t ( discov]+ ! true mean value1--is sup]s$$4 ,we are able to say :at ! mean or c5tral value 9 ! long run w be2 & !re=e !re is no occasion to set ab\t det]m9+ x1 ) "s tr\ble & unc]ta9ty1 f a small numb] ( obs]vations4 ,/ill x is necess>y to discuss ?is case c>efully1 because its assumption is a necess>y l9k 9 ! reason+ 9 o!r cases4 ,?is comp>atively priori k may pres5t itself 9 two diff]5t degrees z respects its complet5ess4 ,9 ! fir/ place x may1 s f> z ! circum/ances 9 "q are conc]n$1 be absolutely complete4 ,consid] ! results :5 a h&ful ( t5 p5ce is repeat$ly toss$ up4 ,we "k precisely :at ! mean value is "h1 viz4 equal division ( heads & tails3 we "k also ! *ance ( six heads & f\r tails1 & s on4 ,t is1 if we _h to plot out a diagram %[+ ! relative frequ5cy ( ea* comb9ation1 we c\ld d s )\t appeal+ to exp]i5ce4 ,we c\ld draw ! appropriate b9omial curve f ! g5]at+ conditions giv5 9 ! /atem5t ( ! problem4 ,b n[ consid] ! results ( fir+ at a t>get consi/+ ( a long & n>r[ /rip1 ( :i* "o po9t is m>k$ z ! c5tre ( aim4#c ,"h 7assum+ t !re are no causes at "w to produce p]man5t bias7 we "k t ?is c5tre w correspond to ! mean value4 ,& we "k also1 9 a g5]al way1 t ! disp]sion on ea* side ( ?is w foll[ a b9omial law4 ,b if we attempt$ to plot out ! proportions1 z 9 ! prec$+ case1 by erect+ ord9ates :i* %\ld repres5t ea* degree ( frequ5cy z we rec$$ fur!r f ! mean1 we %\ld f9d t we c\ld n d s4 ,fre% data mu/ be giv5 or inf]r$4 ,a good m>ksman & a bad m>ksman w bo? di/ribute _! %ot accord+ to ! same g5]al law2 b ! rapidity ) :i* ! %ots ?9 (f z we rec$e f ! c5tre w be diff]5t 9 ! two cases4 ,ano!r 'con/ant' is dem&$ be=e ! curve ( frequ5cy c\ld be correctly trac$ out4 #g4 7#b7 ,! second division1 to be next consid]$1 corresponds = all logical purposes to ! fir/4 ,x comprises ! cases 9 :i* ?\gh we h no priori k z to ! situation ab\t :i* ! values w t5d to clu/] 9 ! long run1 yet we h suffici5t exp]i5ce at h& to assign x ) practical c]ta9ty4 ,consid] = in/ance ! tables ( human /ature4 ,^! are (t5 v ext5sive1 includ+ t5s or hundr$s ( ?\s&s4 ,9 su* cases ! mean or c5tral value is det]m9able ) j z great c]ta9ty z by any priori rule4 ,t is1 if we took ano!r hundr$ ?\s& measurem5ts f ! same class ( population1 we %\ld feel secure t ! av]age w\ld n be alt]$ by any magnitude :i* our measur+ in/rum5ts c\ld practically appreciate4 #h4 ,b ! m]e assignm5t ( ! mean or c5tral value does n "h1 any m ?an 9 ! prec$+ case1 give u all t we want to "k4 ,x might s happ5 t ! mean height ( two populations 0 ! same1 b t ! law ( disp]sion ab\t t mean 0 v diff]5t3 s t a man :o 9 "o s]ies 0 an exceptional giant or dw>f %\ld1 9 ! o!r1 be 9 no wise rem>kable4 ,to expla9 ! process ( ?us det]m9+ ! actual magnitude ( ! disp]sion w\ld dem& too mu* ma!matical detail2 b "s indication may be giv54 ,:at we h to d is to det]m9e ! con/ant h 9 ! equation#d y 7h_/sqrt7 e-h#b x#b4 ,9 te*nical language1 :at we h to d is to det]m9e ! modulus ( ?is equation4 ,! quantity #a_/;h 9 ! above expression is call$ ! modulus4 ,x measures ! degree ( contraction or disp]sion ab\t ! mean indicat$ by ?is equation4 ,:5 x is l>ge ! disp]sion is consid]able2 t is ! magnitudes are n closely cr[d$ up t[>ds ! c5tre1 :5 x is small !y are ?us cr[d$ up4 ,! small] ! modulus 9 ! curve repres5t+ ! ?ickness ) :i* ! %ot-m>ks clu/]$ ab\t ! c5tre ( ! t>get1 ! bett] ! m>ksman4 #i4 ,!re are sev]al ways ( det]m9+ ! modulus4 ,9 ! fir/ ( ! cases discuss$ above1 :]e our !oretical k is complete1 we are able to calculate x priori f our k ( ! *ances4 ,we %\ld naturally adopt ?is plan if we 7 toss+ up a l>ge h&ful ( p5ce4 ,! usual po/]iori plan1 :5 we h ! measurem5ts ( ! magnitudes or obs]vations be=e u1 is ?is3--,take ! mean squ>e ( ! errors1 & d\ble ?is2 ! result gives ! squ>e ( ! modulus4 ,suppose1 = in/ance1 t we _h ! five magnitudes1 #d1 #e1 #f1 #g1 #h4 ,! mean ( ^! is #f3 ! 'errors' are respectively #b1 #a1 #j1 #a1 #b4 ,!re=e ! 'modulus squ>$' is equal to #aj_/e2 i4e4 ! modulus is sqrt#b4 ,_h ! magnitudes be5 #b1 #d1 #f1 #h1 #aj2 repres5t+ ! same mean 7#f7 z be=e1 b display+ a great] disp]sion ab\t x1 ! modulus w\ld h be5 l>g]1 viz4 sqrt#h in/ead ( sqrt#b4 ,mr ,galton's me?od is m ( a graphical nature4 ,x is describ$ 9 a pap] on ,/ati/ics by ,int]comp>ison 7,phil4 ,mag4 #ahge71 & else:]e4 ,x may be indicat$ z foll[s4 ,suppose t we 7 deal+ ) a l>ge numb] ( measurem5ts ( human /ature1 & conceive t all ! p]sons 9 "q 7 m>%all$ 9 ! ord] ( _! height4 ,select ! av]age height1 z m>k$ by ! c5tral man ( ! r[4 ,suppose him to be #fi in*es4 ,!n raise 7or depress7 ! scale f ?is po9t until x /&s at su* a height z j to include "o half ( ! m5 above 7or bel[7 ! mean4 7,9 practice ?is w\ld be f\nd to require ab\t #a4ga in*es3 t is1 "o qu>t] ( any l>ge gr\p ( su* m5 w fall betwe5 #fi & #gj4ga in*es47 ,divide ?is numb] by #j4dgfi & we h ! modulus4 ,9 ! case 9 "q x w\ld be equal to ab\t #c4f in*es4 ,"u ! assumption ) :i* we />t1 viz4 t ! law ( error displays itself 9 ! famili> b9omial =m1 or 9 "s =m approximat+ to ?is1 ! ?ree me?ods indicat$ above w co9cide 9 _! result4 ,:]e !re is any d\bt on ?is head1 or :]e we d n feel able to calculate be=eh& :at w be ! rate ( disp]sion1 we mu/ adopt ! second plan ( det]m9+ ! modulus4 ,?is is ! only univ]sally applicable mode ( calculation3 9 fact t x %\ld yield ! modulus is a tru? ( def9ition2 = 9 det]m9+ ! error ( mean squ>e we are really do+ no?+ else ?an det]m9+ ! modulus1 z 0 po9t$ out 9 ! la/ *apt]4 #aj4 ,! position !n :i* we h n[ rea*$ is ?is4 ,tak+ x = grant$ t ! ,law ( ,error w fall into ! symbolic =m express$ by ! equation y 7h_/sqrt7 e-h#b x#b1 we h rules at h& by :i* h may be det]m9$4 ,we !re=e1 = ! purposes 9 "q1 "k all ab\t ! curve ( frequ5cy3 we c trace x out on pap]3 giv5 "o value1--say ! c5tral "o1--we c det]m9e any o!r value at any di/ance f ?is4 ,t is1 kn[+ h[ _m m5 9 a million1 say1 are #fi in*es high1 we c det]m9e )\t direct obs]vation h[ _m w be #fg1 #fh1 #gj1 #ga1 & s on4 ,we c n[ adequately discuss ! pr9cipal "q ( logical int]e/ be=e u2 viz4 :y d we take av]ages or means8 ,:at is ! exact nature & am\nt ( ! advantage ga9$ by s do+8 ,! advanc$ /ud5t w\ld ( c\rse pref] to "w out ! answ]s to ^! que/ions by appeal+ at once to ! ,law ( ,error 9 its ultimate or expon5tial =m4 ,b ,i feel conv9c$ t ! be/ me?od = ^? :o wi% to ga9 a cle> conception ( ! logical nature ( ! process involv$1 is to beg9 by treat+ x z a "q ( comb9ations su* z we are famili> ) 9 elem5t>y algebra2 9 o!r words to take a f9ite numb] ( errors & to see :at comes ( av]ag+ ^!4 ,we c !n proce$ to "w out ari?metically ! results ( comb9+ two or m ( ! errors toge!r s z to get a new s]ies1 n cont5t+ ourselves ) ! g5]al "* m]ely ( ! new law ( error1 b actually calculat+ :at x is 9 ! giv5 case4 ,= ! sake ( simplicity we w n take a s]ies ) a v l>ge numb] ( t]ms 9 x1 b x w be well to h en\gh ( !m to secure t our law ( error %all r\ghly approximate 9 its =m to ! /&>d or expon5tial law4 ,= ?is purpose ! law ( error or div]g5ce giv5 by suppos+ our ef=t to be affect$ by t5 causes1 ea* ( :i* produces an equal error1 b :i* error is equally likely to be positive & negative 7or1 z x might p]haps be express$1 't5 equal & indiff]5tly additive & subtractive causes'7 w suffice4 ,?is is ! l[e/ numb] =m$ accord+ to ! ,b9omial law1 :i* w furni% to ! eye a fair indication ( ! limit+ or ,expon5tial law4#e ,! :ole numb] ( possible cases "h is #baj or #ajbd2 t is1 ?is is ! numb] requir$ to exhibit n only all ! cases :i* c occur 7= !re are b elev5 really di/9ct cases71 b also ! relative frequ5cy ) :i* ea* ( ^! cases occurs 9 ! long run4 ,( ?is total1 #beb w be situat$ at ! mean1 repres5t+ ! 'true' result1 or t giv5 :5 five ( ! causes ( di/urbance j neutralize ! o!r five4 ,aga91 #baj w be at :at we w call "o unit's di/ance f ! mean1 or t giv5 by six causes comb9+ aga9/ f\r2 & s on2 until at ! extreme di/ance ( five places f ! mean we get b "o result1 s9ce 9 only "o case out ( ! #ajbd w all ! causes comb9e toge!r 9 ! same direction4 ,! set ( #ajbd ef=ts is !re=e a fair repres5tation ( ! di/ribution ( an inf9ite numb] ( su* ef=ts4 ,a graphical repres5tation ( ! arrangem5t is giv5 "h4 ,figure3 ,b9omial di/ribution = ! t5? p[]4 #aa4 ,?is repres5t+ a complete set ( s+le obs]vations or ef=ts1 :at w be ! numb] & arrangem5t 9 ! correspond+ set ( comb9$ or r$uc$ obs]vations1 say ( two toge!r8 ,) reg>d to ! numb] we mu/ be> 9 m9d t ?is is n a case ( ! comb9ations ( ?+s :i* _c be repeat$2 = any giv5 error1 say ! extreme "o at ,f1 c obvi\sly be repeat$ twice runn+4 ,su* a repetition w\ld be a piece ( v bad luck no d\bt1 b be+ possible x mu/ h its place 9 ! set4 ,n[ ! possible numb] ( ways ( comb9+ #ajbd ?+s two toge!r1 :]e ! same ?+ may be repeat$ twice runn+1 is #ajbd #ajbd or #ajdhegf4 ,?is !n is ! numb] 9 a complete cycle ( ! results tak5 two & two toge!r4 #ab4 ,s mu* = _! numb]2 n[ = _! arrangem5t or di/ribution4 ,:at we h to asc]ta9 is1 fir/ly1 h[ _m times ea* possible pair ( obs]vations w pres5t itself2 &1 secondly1 :]e ! new results1 obta9$ f ! comb9ation ( ea* pair1 are to be plac$4 ,) reg>d to ! fir/ ( ^! enquiries2--x w be readily se5 t on "o occasion we %all h ,f repeat$ twice2 on #bj occasions we %all h ,f comb9$ ) ,e 7= ,f com+ fir/ we may h x foll[$ by any "o ( ! #aj at ,e1 or any "o ( ^! may be foll[$ by ,f72 ,e c be repeat$ 9 #aj #aj1 or #ajj ways1 & s on4 ,n[ = ! position ( ea* ( ^! r$uc$ obs]vations1 ! relative frequ5cy ( ^: compon5t elem5ts has ?us be5 po9t$ out4 ,?is is easy to det]m9e1 = :5 we take two errors !re is 7z 0 se57 sc>cely any o!r mode ( treatm5t ?an t ( select+ ! mid-po9t betwe5 !m2 ?is mid-po9t ( c\rse becom+ id5tical ) ea* ( !m :5 ! two happ5 to co9cide4 ,x w be se5 !re=e t ,f w recur once on ! new arrangem5t1 viz4 by its be+ repeat$ twice on ! old "o4 ,g midway betwe5 ,e & ,f1 w be giv5 #bj times4 ,e1 on our new arrangem5t1 c be got at 9 two ways1 viz4 by its be+ repeat$ twice 7:i* w happ5 #ajj times71 & by its be+ obta9$ z ! mid-po9t betwe5 ,d & ,f 7:i* w happ5 #ij times74 ,h5ce ,e w occur #aij times altoge!r4 ,! read] :o *ooses to take ! tr\ble may "w out ! frequ5cy ( all possible occurr5ces 9 ?is way1 & if ! object 7 simply to illu/rate ! pr9ciple 9 accordance ) :i* !y occur1 ?is might be ! be/ way ( proce$+4 ,b z he may soon be able to obs]ve1 & z ! ma!matician w\ld at once be able to prove1 ! new 'law ( facility ( error' c be got at m quickly d$uctively1 viz4 by tak+ ! successive t]ms ( ! expansion ( 7#a #a7bj4 ,!y are giv51 bel[ ! l9e1 9 ! figure on p4 #dgf4 #ac4 ,!re are two app>5t ob/acles to any direct comp>ison betwe5 ! di/ribution ( ! old set ( simple obs]vations1 & ! new set ( comb9$ or r$uc$ ones4 ,9 ! fir/ place1 ! numb] ( ! latt] is mu* great]4 ,?is1 h[ev]1 is readily met by r$uc+ !m bo? to ! same scale1 t is by mak+ ! same total numb] ( ea*4 ,9 ! second place1 half ( ! new positions h no repres5tatives among/ ! old1 viz4 ^? :i* occur midway betwe5 ,f & ,e1 ,e & ,d1 & s on4 ,?is c be met by ! usual plan ( int]polation1 viz4 by fill+ 9 su* gaps by e/imat+ :at w\ld h be5 ! numb] at ! miss+ po9ts1 on ! same scale1 _h !y be5 occupi$4 ,draw a curve ?r\gh ! v]tices ( ! ord9ates at ,a1 ,b1 ,c1 c41 & ! l5g?s ( ! ord9ates at ! int]m$iate po9ts w v fairly repres5t ! correspond+ frequ5cy ( ! errors ( ^? magnitudes respectively4 ,:5 ! gaps are ?us fill$ up1 & ! numb]s ?us r$uc$ to ! same scale1 we h a p]fectly fair basis ( comp>ison4 7,see figure on next page47 ,simil>ly we might proce$ to gr\p or 'r$uce' ?ree obs]vations1 or any great] numb]4 ,! numb] ( possible gr\p+s naturally becomes v mu* l>g]1 be+ 7#ajbd7c :5 !y are tak5 ?ree toge!r4 ,z soon z we get to ?ree or m obs]vations1 we h 7z already po9t$ out7 a v>iety ( possible modes ( treatm5t or r$uction1 ( :i* t ( tak+ ! ari?metical mean is b "o4 #ad4 ,! foll[+ figure is int5d$ to illu/rate ! nature ( ! advantage secur$ by ?us tak+ ! ari?metical mean ( sev]al obs]vations4 ,! curve ,,abcd repres5ts ! arrangem5t ( a giv5 numb] ( 'errors' suppos$ to be dispos$ accord+ to ! b9omial law already m5tion$1 :5 ! angles h be5 smoo!d (f by draw+ a curve ?r\gh !m4 ,a',,cd' repres5ts ! simil> arrangem5t ( ! same numb] :5 giv5 n z simple errors1 b z av]ages ( pairs ( errors4 ,a,,bd1 aga91 repres5ts ! simil> arrangem5t obta9$ z av]ages ( errors tak5 ?ree toge!r4 ,!y are drawn z c>efully to scale z ! small size ( ! figure p]mits4 ,figure3 ,gaussian di/ributions = two or ?ree obs]vations4 #ae4 ,a glance at ! above figure w expla9 to ! read]1 bett] ?an any v]bal description1 ! full significance ( ! /atem5t t ! result ( comb9+ two or m measurem5ts or obs]vations toge!r & tak+ ! av]age ( !m1 in/ead ( /opp+ %ort at ! s+le elem5ts1 is to make l>ge errors comp>atively m sc>ce4 ,! advantage is ( ! same g5]al description z t ( fi%+ 9 a lake :]e1 ( ! same numb] ( fi%1 !re are m big & few] little ones ?an 9 ano!r wat]3 ( dipp+ 9 a bag :]e ( ! same numb] ( co9s !re are m sov]eigns & few] %ill+s2 & s on4 ,! extreme importance1 h[ev]1 ( obta9+ a p]fectly cle> conception ( ! subject may r5d] x desirable to "w ?is out a little m fully 9 detail4 ,= "o ?+1 !n1 x mu/ be cle>ly und]/ood t ! result ( a set ( 'av]ages' ( errors is no?+ else ?an ano!r set ( 'errors1' ,no device c make ! atta9m5t ( ! true result c]ta91--to suppose ! contr>y w\ld be to misconceive ! v f\ndations ( ,probability1--no device ev5 c obviate ! possibility ( be+ actually worse (f z ! result ( our lab\r4 ,! av]age ( two1 ?ree1 or any l>g] numb] ( s+le results1 may give a worse result1 i4e4 "o fur!r f ! ultimate av]age1 ?an 0 giv5 by ! fir/ obs]vation we made4 ,we mu/ simply fall back ^u ! ju/ification t big deviations are r5d]$ sc>c] 9 ! long run4 ,aga92 x may be po9t$ out t ?\gh1 9 ! above inve/igation1 we h spok5 only ( ! ari?metical av]age z commonly und]/ood & employ$1 ! same g5]al results w\ld be obta9$ by resort+ to almo/ any symmetrical & regul> mode ( comb9+ our obs]vations or errors4 ,! two ma9 features ( ! regul>ity display$ by ! ,b9omial ,law ( facility 7 7#a7 ultimate symmetry ab\t ! c5tral or true result1 & 7#b7 increas+ relative frequ5cy z ?is c5tre 0 approa*$4 ,a v little consid]ation w %[ t x is no peculi> pr]ogative ( ! ari?metical mean to reta9 ! =m] ( ^! & to increase ! latt]4 ,9 say+ ?is1 h[ev]1 a di/9ction mu/ be att5d$ to = :i* x w be conv5i5t to ref] to a figure4 #af4 ,suppose t ,o1 9 ! l9e ,d',,od1 0 ! po9t aim$ at by any s]ies ( measurem5ts2 or1 :at comes to ! same ?+ = our pres5t purpose1 0 ! ultimate av]age ( all ! measurem5ts made4 ,:at we mean by a symmetrical arrangem5t ( ! values 9 reg>d to ,o1 is t = e error ,,ob1 !re %all be 9 ! long run a precisely correspond+ opposite "o ,,ob'2 s t :5 we erect ! ord9ate ,,bq1 indicat+ ! frequ5cy ) :i* ,b is yield$1 we mu/ erect an equal "o ,b',q'4 ,accord+ly ! two halves ( ! curve on ea* side ( ,p1 viz4 ,,pq & ,,pq' are precisely alike4 ,figure3 ,symmetry ( a di/ribution4 ,x !n readily foll[s t ! second>y curve1 viz4 t m>k+ ! law ( frequ5cy ( ! av]ages ( two or m simple errors1 w also be symmetrical4 ,consid] any ?ree po9ts ,b1 ,c1 ,d3 to ^! correspond ano!r ?ree ,b'1 ,c'1 ,d'4 ,x is obvi\s !re=e t any regul> & symmetrical mode ( deal+ ) all ! gr\ps1 ( :i* ,,bcd is a sample1 w result 9 symmetrical arrangem5t ab\t ! c5tre ,o4 ,! ord9>y famili> ari?metical av]age is b "o out ( _m su* modes4 ,"o way ( describ+ x is by say+ t ! av]age ( ,b1 ,c1 ,d1 is assign$ by *oos+ a po9t su* t ! sum ( ! squ>es ( its di/ances f ,b1 ,c1 ,d1 is a m9imum4 ,b we might h select$ a po9t su* t ! cubes1 or ! f\r? p[]s1 or any high] p[]s %\ld be a m9imum4 ,^! w\ld all yield curves resembl+ 9 a g5]al way ! dott$ l9e 9 our figure4 ,( c\rse !re w\ld be insup]able practical objections to any su* c\rses z ^!2 = ! lab\r ( calculation w\ld be enorm\s1 & ! results s f> f be+ bett] w\ld be worse ?an ^? af=d$ by ! employm5t ( ! ord9>y av]age4 ,b s f> z conc]ns ! g5]al pr9ciple ( deal+ ) discordant & errone\s results1 x mu/ be rememb]$ t ! famili> av]age is b "o out ( innum]able possible res\rces1 all ( :i* w\ld yield ! same sort ( help4 #ag4 ,once m4 ,we saw t a resort to ! av]age _h ! effect ( 'hump+ up' our curve m t[>ds ! c5tre1 expressive ( ! fact t ! errors ( av]ages are ( a bett]1 i4e4 small] k9d4 ,b x mu/ be notic$ t exactly ! same *>act]i/ics w foll[1 z a g5]al rule1 f any o!r su* mode ( deal+ ) ! individual errors4 ,no /rict pro( ( ?is fact c be giv5 "h1 b a ref]5ce to "o ( ! famili> results ( tak+ comb9ations ( ?+s w %[ :5ce ?is t5d5cy arises4 ,extreme results1 z yield$ by an av]age ( any k9d1 c only be got 9 "o way1 viz4 by repetitions ( extremes 9 ! individuals f :i* ! av]ages 7 obta9$4 ,b int]m$iate results c be got at 9 two ways1 viz4 ei!r by int]m$iate individuals1 or by comb9ations ( individuals 9 opposite directions4 ,9 ! case ( ! ,b9omial ,law ( ,error ?is t5d5cy to ?ick5 t[>ds ! c5tre 0 already /rongly pr$om9ant 9 ! individual values be=e we took !m 9 h& = our av]age2 b ow+ to ?is *>act]i/ic ( comb9ations we may lay x d[n 7broadly speak+7 t any sort ( av]age appli$ to any sort ( law ( di/ribution w give a result :i* be>s ! same g5]al relation to ! individual values t ! dott$ l9es above be> to ! black l9e4#f #ah4 ,?is be+ s1 ! speculative advantages ( "o me?od ( comb9+1 or av]ag+1 or r$uc+1 our obs]vations1 ov] ano!r me?od1--irrespective1 t is1 ( ! practical conv5i5ces 9 c>ry+ !m out1--w consi/ solely 9 ! degree ( rapidity ) :i* x t5ds ?us to clu/] ! result ab\t ! c5tre4 ,we %all h to subject ?is m]it to a some:at fur!r analysis1 b = ! pres5t purpose x w suffice to say t if "o k9d ( av]age gave ! high] dott$ l9e 9 ! figure on p4 #dgi & ano!r gave ! l[] dott$ l9e1 we %\ld say t ! =m] 0 ! bett] "o4 ,! advantage is ( ! same g5]al k9d z t :i* is furni%$ 9 algebraical calculation1 by a s]ies :i* conv]ges rapidly t[>ds ! true value z comp>$ ) "o :i* conv]ges sl[ly4 ,we c d ! "w soon] or lat] by ! aid ( ei!r2 b we get ne>] ! tru? by ! same am\nt ( lab\r1 or get z ne> by a less am\nt ( lab\r1 on "o plan ?an on ! o!r4 ,z we are "h consid]+ ! case 9 :i* ! individual obs]vations are suppos$ to be gr\p$ 9 accordance ) ! ,b9omial ,law1 x w suffice to say t 9 ?is case !re is no d\bt t ! ari?metical av]age is n only ! simple/ & easie/ to deal )1 b is also ! be/ 9 ! above s5se ( ! t]m4 ,& s9ce ?is ,b9omial ,law1 or some?+ approximat+ to x1 is ( v wide preval5ce1 a /rong prim facie case is made out = ! g5]al employm5t ( ! famili> av]age4 #ai4 ,! analysis ( a few pages back c>ri$ ! results ( ! av]ag+ process z f> z c\ld be conv5i5tly done by ! help ( m]e ari?metic4 ,to g fur!r we mu/ appeal to high] ma!matics1 b ! foll[+ indication ( ! sort ( results obta9$ w suffice = our pres5t purpose4 ,aft] all1 ! successive /eps1 ?\gh dem&+ intricate reason+ = _! pro(1 are no?+ m ?an g5]alizations ( processes :i* c\ld be e/abli%$ by simple ari?metic4#g ,briefly1 :at we d is ?is3-- 7#a7 ,we fir/ ext5d ! pro( f ! b9omial =m1 ) its f9ite numb] ( elem5ts1 to ! limit+ or expon5tial =m4 ,in/ead ( conf9+ ourselves to a small numb] ( discrete errors1 we !n recognize ! possibility ( any numb] ( errors ( any magnitude :atev]4 7#b7 ,9 ! next place1 in/ead ( conf9+ ourselves to ! consid]ation ( an av]age ( two or ?ree only1--already1 z we h se51 a t$i\s piece ( ari?metic1--we calculate ! result ( an av]age ( any numb]1 n4 ,! actual result is extremely simple4 ,if ! modulus ( ! s+le errors is c1 t ( ! av]age ( n ( ^! w be c sqrtn4 7#c7 ,f9ally we draw simil> conclusions 9 ref]5ce to ! sum or diff]5ce ( two av]ages ( any numb]s4 ,suppose1 = in/ance1 t m errors 7 fir/ tak5 & av]ag$1 & !n n simil>ly tak5 & av]ag$4 ,^! av]ages w be ne>ly1 b n q1 equal4 ,_! sum or diff]5ce1--^!1 ( c\rse1 are indi/+ui%able 9 ! end1 s9ce positive & negative errors are suppos$ to be equal & opposite1--w itself be an 'error'1 e magnitude ( :i* w h a c]ta9 assignable probability or facility ( occurr5ce4 ,:at we d is to assign ! modulus ( ^! errors4 ,! actual result aga9 is simple4 ,if c _h be5 ! modulus ( ! s+le errors1 t ( ! sum or diff]5ce ( ! av]ages ( m & n ( !m w be c sqrt#a_/m #a_/n4 #bj4 ,s f>1 ! problem "u inve/igation has be5 ( a direct k9d4 ,we h suppos$ t ! ultimate mean value or c5tral position has be5 giv5 to u2 ei!r priori 7z 9 _m games ( *ance71 or f m imm$iate physical consid]ations 7z 9 aim+ at a m>k71 or f ext5sive /ati/ics 7z 9 tables ( human /ature74 ,9 all su* cases !re=e ! ma9 desid]atum is already tak5 = grant$1 & x may reasonably be ask$ :at rema9s to be done4 ,! answ]s are v>i\s4 ,= "o ?+ we may want to e/imate ! value ( an av]age ( _m :5 comp>$ ) an av]age ( a few4 ,suppose t "o man has collect$ /ati/ics includ+ #ajjj in/ances1 & ano!r has collect$ #djjj simil> in/ances4 ,common s5se c recognize t ! latt] are bett] ?an ! =m]2 b x has no idea h[ mu* bett] !y are4 ,"h1 z else:]e1 quantitative precision is ! privilege ( sci5ce4 ,! answ] we receive f ?is qu>t] is t1 9 ! long run1 ! modulus1--& ) ?is ! probable error1 ! mean error1 & ! error ( mean squ>e1 :i* all v>y 9 proportion1--dim9i%es inv]sely z ! squ>e root ( ! numb] ( measurem5ts or obs]vations4 7,?is foll[s f ! second ( ! above =mul47 ,accord+ly ! probable error ( ! m ext5sive /ati/ics "h is "o half t ( ! less ext5sive4 ,take ano!r in/ance4 ,obs]vation %[s t ! mean height ( #b1cae crim9als diff]s f ! mean height ( #h1ehe memb]s ( ! g5]al adult population by ab\t two in*es 7v4 ,edgewor?1 ,me?ods ( ,/ati/ics3 ,/at4 ,soc4 ,j\rn4 #ahhe74 ,z be=e1 common s5se w\ld feel little d\bt t su* a diff]5ce 0 significant1 b x c\ld give no num]ical e/imate ( ! significance4 ,appeal+ to sci5ce1 we see t ?is is an illu/ration ( ! ?ird ( ! above =mul4 ,:at we really want to "k is ! odds aga9/ ! av]ages ( two l>ge bat*es diff]+ by an assign$ am\nt3 9 ?is case by an am\nt equall+ tw5ty-five times ! modulus ( ! v>iable quantity4 ,! odds aga9/ ?is are _m billions to "o4 #ba4 ,! numb] ( direct problems :i* w ?us admit ( solution is v great1 b we mu/ conf9e ourselves "h to ! ma9 inv]se problem to :i* ! =ego+ discussion is a prelim9>y4 ,x is ?is4 ,giv5 a few only ( "o ( ^! gr\ps ( measurem5ts or obs]vations2 :at c we d ) ^!1 9 ! way ( det]m9+ t mean ab\t :i* !y w\ld ultimately be f\nd to clu/]8 ,giv5 a l>ge numb] ( !m1 !y w\ld betray ! position ( _! ultimate c5tre ) con/antly increas+ c]ta9ty3 b we are n[ suppos+ t !re are only a few ( !m at h&1 say half a doz51 & t we h no p[] at pres5t to add to ! numb]4 ,9 o!r words1--express+ ourselves by ! aid ( graphical illu/ration1 :i* is p]haps ! be/ me?od = ! novice & = ! logical /ud5t1--9 ! direct problem we m]ely h to draw ! curve ( frequ5cy f a k ( its det]m9+ elem5ts2 viz4 ! position ( ! c5tre1 & ! num]ical value ( ! modulus4 ,9 ! inv]se problem1 on ! o!r h&1 we h ?ree elem5ts at lea/1 to det]m9e4 ,= n only mu/ we1 7#a71 z be=e1 det]m9e :]eab\ts ! c5tre may be assum$ to lie2 & 7#b71 z be=e1 det]m9e ! value ( ! modulus or degree ( disp]sion ab\t ?is c5tre4 ,?is does n complete our k4 ,s9ce nei!r ( ^! two elem5ts is assign$ ) c]ta9ty1 we want :at is always requir$ 9 ! ,!ory ( ,*ances1 viz4 "s e/imate ( _! probable tru?4 ,t is1 aft] mak+ ! be/ assignm5t we c z to ! value ( ^! elem5ts1 we want also to assign num]ically ! 'probable error' committ$ 9 su* assignm5t4 ,no?+ m ?an ?is c be atta9$ 9 ,probability1 b no?+ less ?an ?is %\ld be set be=e u4 #bb4 7#a7 ,z reg>ds ! fir/ ( ^! que/ions1 ! answ] is v simple4 ,:e!r ! numb] ( measurem5ts or obs]vations be few or _m1 we mu/ make ! assumption t _! av]age is ! po9t we want2 t is1 t ! av]age ( ! few w co9cide ) ! ultimate av]age4 ,?is is ! be/1 9 fact ! only assumption we c make4 ,we %\ld adopt ?is plan1 ( c\rse1 9 ! extreme case ( !re be+ only "o value be=e u1 by j tak+ t "o2 & our confid5ce increases sl[ly ) ! numb] ( values be=e u4 ,! only diff]5ce !re=e "h betwe5 k re/+ ^u su* data1 & k re/+ ^u complete data1 lies n 9 ! result obta9$ b 9 ! confid5ce ) :i* we ent]ta9 x4 #bc4 7#b7 ,z reg>ds ! second "q1 viz4 ! det]m9ation ( ! modulus or degree ( disp]sion ab\t ! mean1 mu* ! same may be said4 ,t is1 we adopt ! same rule = ! det]m9ation ( ! ,e4,m4,s4 7error ( mean squ>e7 by :i* ! modulus is assign$1 z we %\ld adopt if we possess$ full ,in=mation4 ,or r we are conf9$ to "o ( ! rules giv5 on p4 #dgc1 viz4 ! second1 = by supposition we h nei!r ! priori k :i* w\ld be able to supply ! fir/1 nor a suffici5t numb] ( obs]vations to ju/ify ! ?ird4 ,t is1 we reckon ! errors1 measur$ f ! av]age1 & calculate _! mean squ>e3 twice ?is is equal to ! squ>e ( ! modulus ( ! probable curve ( facility4#h #bd4 7#c7 ,! ?ird "q dem&s = its solution some:at advanc$ ma!matics2 b ! results c be indicat$ )\t mu* difficulty4 ,a popul> way ( /at+ our requirem5t w\ld be to say t we want to "k h[ likely x is t ! mean ( ! few1 :i* we h ?us accept$1 %all co9cide ) ! true mean4 ,b ?is w\ld be to speak loosely1 = ! *ances are ( c\rse indef9itely great aga9/ su* precise co9cid5ce4 ,:at we really d is to assign ! 'probable error'2 t is1 to assign a limit :i* x is z likely z n t ! discrepancy betwe5 ! inf]r$ mean & ! true mean %\ld exce$4#i ,to take a num]ical example3 suppose we _h made sev]al measurem5ts ( a wall ) a tape1 & t ! av]age ( ^! 0 #aej feet4 ,! scrupul\s surveyor w\ld give u ?is result1 ) "s su* correction z ?is add$1--'probable error #c in*es'4 ,all t ?is means is t we may assume t ! true value is #aej feet1 ) a confid5ce t 9 half ! cases 7( ?is description7 9 :i* we did s1 we %\ld really be )9 ?ree in*es ( ! tru?4 ,! expression = ?is probable error is a simple multiple ( ! modulus3 x is ! modulus multipli$ by #j4dgfi4444 ,t x %\ld be "s function ( ! modulus1 or ,e4,m4,s41 seems plausible en\gh2 = ! great] ! errors1--9 o!r words ! wid] ! obs]v$ discrepancy among/ our measurem5ts1--! less mu/ be ! confid5ce we c feel 9 ! accuracy ( our det]m9ation ( ! mean4 ,b1 ( c\rse1 )\t ma!matics we %\ld be q unable to attempt any num]ical assignm5t4 #be4 ,! g5]al conclusion !re=e is t ! det]m9ation ( ! curve ( facility1--& !re=e ultimately ( e conclusion :i* re/s ^u a k ( ?is curve1--:]e only a few obs]vations are available1 is ( j ! same k9d z :]e an inf9ity are available4 ,! rules = obta9+ x are ! same1 b ! confid5ce ) :i* x c be accept$ is less4 ,! k1 !re=e1 obta9able by an av]age ( a small numb] ( measurem5ts ( any k9d1 h>dly diff]s except 9 degree f t :i* w\ld be atta9able by an indef9itely ext5sive s]ies ( !m4 ,we "k ! same sort ( facts1 only we are less c]ta9 ab\t !m4 ,b1 on ! o!r h&1 ! k yield$ by an av]age ev5 ( a small numb] diff]s 9 k9d f t :i* is yield$ by a s+le measurem5t4 ,rev]t to our m>ksman1 ^: bullseye is suppos$ to h be5 aft]w>ds remov$4 ,if he _h fir$ only a s+le %ot1 n only %\ld we be less c]ta9 ( ! po9t he _h aim$ at1 b we %\ld h no means :atev] ( guess+ at ! quality ( 8 %oot+1 or ( inf]r+ 9 consequ5ce any?+ ab\t ! probable remot5ess ( ! next %ot f t :i* _h gone be=e4 ,b directly we h a plurality ( %ots be=e u1 we n m]ely feel m confid5t z to :]eab\ts ! c5tre ( aim 01 b we also ga9 "s k z to h[ ! future %ots w clu/] ab\t ! spot ?us indicat$4 ,! quality ( 8 %oot+ beg9s at once to be betray$ by ! results4 #bf4 ,?us f> we h be5 suppos+ ! ,law ( ,facility to be ( ! ,b9omial type4 ,!re are sev]al reasons = discuss+ ?is at su* comp>ative l5g?4 ,= "o ?+ x is ! only type :i*1--or some?+ approximately resembl+ :i*1--is actually preval5t ov] a wide range ( ph5om5a4 ,!n aga91 9 spite ( its app>5t intricacy1 x is really "o ( ! simple/ to deal )2 ow+ to ! fact t e curve ( facility d]iv$ f x by tak+ av]ages simply repeats ! same type aga94 ,! curve ( ! av]age only diff]s f t ( ! s+le elem5ts 9 hav+ a small] modulus2 & its modulus is small] 9 a ratio :i* is exce$+ly easy to give4 ,if t ( ! "o is c1 t ( ! o!r 7d]iv$ by av]ag+ n s+le elem5ts7 is c_/sqrtn4 ,b = und]/&+ ! !ory ( av]ages we mu/ consid] o!r cases z well4 ,take !n "o :i* is intr9sically z simple z x possibly c be1 viz4 t 9 :i* all values )9 c]ta9 assign$ limits are equally probable4 ,?is is a case famili> en\gh 9 ab/ract ,probability1 ?\gh1 z j rem>k$1 n s common 9 natural ph5om5a4 ,x is ! /ate ( ?+s :5 we act at r&om directly ^u ! objects ( *oice2#aj z :51 = in/ance1 we *oose digits at r&om out ( a table ( log>i?ms4 ,! read] :o likes to d s c )\t mu* lab\r "w out ! result ( tak+ an av]age ( two or ?ree results by proce$+ 9 exactly ! same way :i* we adopt$ on p4 #dgf4 ,! 'curve ( facility' ) :i* we h to />t 9 ?is case has become ( c\rse simply a f9ite /raight l9e4 ,treat+ ! "q z "o ( simple comb9ations1 we may divide ! l9e into a numb] ( equal p>ts1 by equidi/ant po9ts2 & !n proce$ to take ^! two & two toge!r 9 e possible way1 z we did 9 ! case discuss$ "s pages back4 ,if we did s1 :at we %\ld f9d w\ld be ?is4 ,:5 an av]age ( two is tak51 ! 'curve ( facility' ( ! av]age becomes a triangle ) ! initial /raight l9e = base2 s t ! ultimate mean or c5tral po9t becomes ! likelie/ result ev5 ) ?is comm5cem5t ( ! av]ag+ process4 ,if we 7 to take av]ages ( ?ree1 f\r1 & s on1 :at we %\ld f9d w\ld be t ! ,b9omial law beg9s to display itself "h4 ,! famili> bell %ape ( ! expon5tial curve w\ld be m & m closely approximat$ to1 until we obta9$ some?+ q indi/+ui%able f x4 #bg4 ,! conclusion !re=e is t :5 we are deal+ ) av]ages involv+ a consid]able numb] x is n necess>y1 9 g5]al1 to presuppose ! b9omial law ( di/ribution 9 our orig9al data4 ,! law ( arrangem5t ( :at we may call ! d]iv$ curve1 viz4 t correspond+ to ! av]ages1 w n be appreciably affect$ !reby4 ,accord+ly we seem to be ju/ifi$ 9 br++ to be> all ! same app>atus ( calculation z 9 ! =m] case4 ,we take ! initial av]age z ! probable position ( ! true c5tre or ultimate av]age3 we e/imate ! probability t we are )9 an assignable di/ance ( ! tru? 9 s do+ by calculat+ ! 'error ( mean squ>e'2 & we appeal to ?is same elem5t to det]m9e ! modulus1 i4e4 ! am\nt ( contraction or disp]sion1 ( our d]iv$ curve ( facility4 ,! same g5]al consid]ations w apply to mo/ o!r k9ds ( ,law ( ,facility4 ,broadly speak+1--we %all come to ! exam9ation ( c]ta9 exceptions imm$iately1--:atev] may h be5 ! primitive arrangem5t 7i4e4 t ( ! s+le results7 ! arrangem5t ( ! d]iv$ results 7i4e4 t ( ! av]ages7 w be m cr[d$ up t[>ds ! c5tre4 ,?is foll[s f ! *>act]i/ic ( comb9ations already notic$1 viz4 t extreme values c only be got at by a repetition ( sev]al extremes1 :]eas int]m$iate values c be got at ei!r by repetition ( int]m$iates or ?r\gh ! c\nt]action ( opposite extremes4 ,provid$ ! orig9al di/ribution be symmetrical ab\t ! c5tre1 & provid$ ! limits ( possible error be f9ite1 or if inf9ite1 t ! fall+ (f ( frequ5cy z we rec$e f ! mean be v rapid1 !n ! results ( tak+ av]ages w be bett] ?an ^? ( tru/+ to s+le results4 #bh4 ,we w n[ take notice ( an exceptional case4 ,we %all d s1 n because x is "o :i* c (t5 actually occur1 b because ! consid]ation ( x w =ce u to ask ourselves ) "s m9ut5ess :at we mean 9 ! above in/ances by call+ ! results ( ! av]ages 'bett]' ?an ^? ( ! individual values4 ,a diagram w br+ home to u ! po9t ( ! difficulty bett] ?an any v]bal or symbolic description4 ,figure3 ,di/ribution = two samples f a non-,gaussian di/ribution4 ,! black l9e repres5ts a ,law ( ,error easily /at$ 9 words1 & "o :i*1 z we %all subsequ5tly see1 c be conceiv$ z occurr+ 9 practice4 ,x repres5ts a /ate ( ?+s "u :i* up to a c]ta9 di/ance f ,o1 on ea* side1 viz4 to ,a & ,b1 ! probability ( an error dim9i%es uni=mly ) ! di/ance f ,o2 :il/ beyond ^! po9ts1 up to ,e & ,f1 ! probability ( error rema9s con/ant4 ,! dott$ l9e repres5ts ! resultant ,law ( ,error obta9$ by tak+ ! av]age ( ! =m] two & two toge!r4 ,n[ is ! latt] 'bett]' ?an ! =m]8 ,"u x1 c]ta9ly1 great errors are less frequ5t & int]m$iate ones m frequ5t2 b !n on ! o!r h& ! small errors are less frequ5t3 is ?is /ate ( ?+s on ! :ole an improvem5t or n8 ,?is requires u to reconsid] ! :ole "q4 #bi4 ,9 all ! cases discuss$ 9 ! previ\s sections ! sup]iority ( ! curve ( av]ages ov] t ( ! s+le results %[$ itself at e po9t4 ,! big errors 7 sc>c] & ! small errors 7 common]2 x 0 only j at "o int]m$iate po9t t ! two 7 on t]ms ( equality1 & ?is po9t 0 n suppos$ to possess any p>ticul> significance or importance4 ,accord+ly we _h no occasion to analyse ! v>i\s cases includ$ "u ! g5]al relation4 ,x 0 en\gh to say t "o 0 bett] ?an ! o!r1 & x 0 suffici5t = all purposes to take ! 'modulus' z ! measure ( ?is sup]iority4 ,9 fact we are q safe 9 simply say+ t ! av]age ( ^? av]age results is bett] ?an t ( ! individual ones4 ,:5 h[ev] we proce$ 9 :at ,hume calls ! sift+ hum\r1 & enquire :y x is suffici5t ?us to tru/ to ! av]age2 we f9d1 9 addition to ! consid]ations hi!rto advanc$1 t "s po/ulate 0 requir$ z to ! consequ5ces ( ! errors we incur4 ,x involv$ an e/imate ( :at is sometimes call$ ! 'detrim5t' ( an error4 ,x seem$ to take = grant$ t l>ge & small errors all /& ^u ! same g5]al foot+ ( be+ mis*iev\s 9 _! consequ5ces1 b t _! evil effects increase 9 a great] ratio ?an t ( _! own magnitude4 #cj4 ,suppose1 = comp>ison1 a case 9 :i* ! importance ( an error is directly proportional to its magnitude 7( c\rse we suppose positive & negative errors to balance ea* o!r 9 ! long run73 x does n appe> t any advantage w\ld be ga9$ by tak+ av]ages4 ,some?+ ( ?is sort may be consid]$ to prevail 9 cases ( m]e pur*ase & sale4 ,suppose t any "o _h to buy a v l>ge numb] ( y>ds ( clo? at a con/ant price p] y>d3 t he _h to d ?is1 say1 five times a day = _m days 9 succession4 ,& conceive t ! measurem5t ( ! clo? 0 r\ghly e/imat$ on ea* sep>ate occasion1 ) resultant errors :i* are z likely to be 9 excess z 9 defect4 ,w\ld x make ! slighte/ diff]5ce to him :e!r he paid sep>ately = ea* piece2 or :e!r ! five e/imat$ l5g?s 7 add$ toge!r1 _! av]age tak51 & he 7 *>g$ ) ?is av]age price = ea* piece8 ,9 ! latt] case ! errors :i* w be made 9 ! e/imation ( ea* piece w ( c\rse be less 9 ! long run ?an !y w\ld be 9 ! =m]3 w ?is be ( any consequ5ce8 ,! answ] surely is t x w n make ! slighte/ diff]5ce to ei!r p>ty 9 ! b>ga94 ,9 ! long run1 s9ce ! same p>ties are conc]n$1 x w n matt] :e!r ! int]m$iate errors h be5 small or l>ge4 ,( c\rse no?+ ( ?is sort c be reg>d$ z ! g5]al rule4 ,9 almo/ e case 9 :i* we h to make measurem5ts we %all f9d t l>ge errors are mu* m mis*iev\s ?an small ones1 t is1 mis*iev\s 9 a great] ratio ?an t ( _! m]e magnitude4 ,ev5 9 pur*ase & sale1 :]e diff]5t pur*as]s are conc]n$1 ?is mu/ be s1 = ! pleasure ( him :o is ov]s]v$ w h>dly equal ! pa9 ( him :o is und]s]v$4 ,& 9 _m cases ( sci5tific measurem5t l>ge errors may be simply fatal1 9 ! s5se t if !re 7 no reasonable prospect ( avoid+ !m we %\ld n c>e to und]take ! measurem5t at all4 #ca4 ,if we 7 only conc]n$ ) practical consid]ations we might /op at ?is po9t2 b if we want to realize ! full logical import ( av]age-tak+ z a means to ?is p>ticul> end1 viz4 ( e/imat+ "s assign$ magnitude1 we mu/ look m closely into su* an exceptional case z t :i* 0 indicat$ 9 ! figure on p4 #dic4 ,:at we !re assum$ 0 a /ate ( ?+s 9 ref]5ce to :i* extremely small errors 7 v frequ5t1 b t :5 once we got beyond a c]ta9 small range all o!r errors1 )9 consid]able limits1 7 equally likely4 ,x is n difficult to imag9e an example :i* w aptly illu/rate ! case 9 po9t3 at wor/ x may seem a little f>-fet*$4 ,conceive !n t "s firm 9 ,engl& receiv$ a hurri$ ord] to supply a portion ( a ma*9e1 say a /eam-eng9e1 to cu/om]s at a di/ant place2 & t x 0 absolutely ess5tial t ! "w %\ld be true to ! t5? ( an in* = x to be ( any use4 ,b conceive also t two specifications _h be5 s5t1 re/+ on diff]5t measurem5ts1 9 "o ( :i* ! l5g? ( ! requisite piece 0 describ$ z sixty & 9 ! o!r sixty-"o in*es4 ,on ! assumption ( any ord9>y law ( error1 :e!r ( ! b9omial type or n1 !re c be no d\bt t ! firm w\ld make ! be/ ( a v bad job by con/ruct+ a piece ( #fj in*es & a half3 i4e4 !y w\ld h a bett] *ance ( be+ )9 ! requisite t5? ( an in* by s do+1 ?an by tak+ ei!r ( ! two specifications at r&om & con/ruct+ x accurately to ?is4 ,b if ! law 7 ( ! k9d indicat$ 9 our diagram1#aa !n x seems equally c]ta9 t !y w\ld be less likely to be )9 ! requisite n>r[ m>g9 by s do+4 ,z a m]e "q ( probability1--t is1 if su* e/imates 7 act$ ^u aga9 & aga91--!re w\ld be few] failures enc\nt]$ by simply *oos+ "o ( ! conflict+ measurem5ts at r&om & work+ exactly to ?is1 ?an by tru/+ to ! av]age ( ! two4 ,?is sugge/s "s fur!r reflections z to ! tak+ ( av]ages4 ,we w turn n[ to ano!r exceptional case1 b "o involv+ some:at diff]5t consid]ations ?an ^? :i* h be5 j discuss$4 ,z be=e1 x may be mo/ conv5i5tly introduc$ by comm5c+ ) an example4 #cb4 ,suppose !n t two sc\ts 7 s5t to take ! calibre ( a gun 9 a ho/ile =t1--we may conceive t ! =t 0 to be occupi$ next day1 & us$ aga9/ ! enemy1 & t x 0 important to h a supply ( %ot or %ell1--& t ! result is t "o ( !m reports ! calibre to be #h in*es & ! o!r #i4 ,w\ld x be wise to assume t ! mean ( ^! two1 viz4 #h-a_/b in*es1 0 a likeli] value ?an ei!r sep>ately8 ,! answ] seems to be ?is4 ,if we h reason to suppose t ! possible calibres p>take ( ! nature ( a cont9u\s magnitude1--i4e4 t all values1 ) c]ta9 limits1 are to be consid]$ z admissible1 7an assumption :i* we always make 9 our ord9>y inv]se /ep f an obs]vation or magnitude to ! ?+ obs]v$ or measur$7--!n we %\ld be ju/ifi$ 9 select+ ! av]age z ! likeli] value4 ,b if1 on ! o!r h&1 we _h reason to suppose t :ole in*es are always or g5]ally pref]r$1 z is 9 fact ! case n[ ) heavy guns1 we %\ld d bett] to take1 ev5 at haz>d1 "o ( ! two e/imates set be=e u1 & tru/ ?is alone in/ead ( tak+ an av]age ( ! two4 #cc4 ,! pr9ciple ^u :i* we act "h may be /at$ ?us4 ,j z 9 ! direct process ( calculat+ or display+ ! 'errors'1 :e!r 9 an algebraic =mula or 9 a diagram1 we g5]ally assume t _! possibility is cont9u\s1 i4e4 t all int]m$iate values are possible2 s1 9 ! inv]se process ( det]m9+ ! probable position ( ! orig9al f ! kn[n value ( two or m errors1 we assume t t position is capable ( fall+ at any po9t :atev] betwe5 c]ta9 limits4 ,9 su* an example z ! above1 :]e we "k or suspect a discont9uity ( t possibility ( position1 ! value ( ! av]age may be entirely de/roy$4 ,9 ! above example we 7 suppos$ to "k t ! calibre ( ! guns 0 likely to run 9 ,engli% in*es or 9 "s o!r recogniz$ units4 ,b if ! batt]y 7 9 ,*9a or ,japan1 & we knew no?+ ( ! /&>ds ( l5g? 9 use !re1 we c\ld no long] appeal to ?is pr9ciple4 ,x is d\btless highly probable t ^? calibres are n ( ! nature ( cont9u\sly v>y+ magnitudes2 b 9 an entire ignorance ( ! /&>ds actually adopt$1 we are to all int5ts & purposes 9 ! same position z if !y 7 ( t cont9u\s nature4 ,:5 ?is is s ! objections to tru/+ to ! av]age w\ld no long] hold good1 & if we _h only "o opportunity1 or a v few opportunities1 we %\ld d be/ to adh]e to ! cu/om>y practice4 #cd4 ,:5 h[ev] we are able to collect & comp>e a l>ge numb] ( measurem5ts ( v>i\s objects1 ?is consid]ation ( ! probable discont9uity ( ! objects we ?us measure1--t is1 _! t5d5cy to assume "s "o or o!r ( a f9ite numb] ( di/9ct magnitudes1 in/ead ( %[+ an equal read9ess to adapt !mselves to all int]m$iate values1--aga9 assumes importance4 ,9 fact1 giv5 a suffici5t numb] ( measurable objects1 we c actually d$uce ) mu* probability ! /&>d accord+ to :i* ! ?+s 9 "q 7 made4 ,?is is ! problem :i* ,mr ,fl9d]s ,petrie has attack$ ) s mu* acut5ess & indu/ry 9 8 "w on ,inductive ,metrology1 a "w :i*1 m]ely on ! gr\nd ( its speculative int]e/1 may well be comm5d$ to ! /ud5t ( ,probability4 ,! ma9 pr9ciples on :i* ! reason+ is bas$ are ^! two3--7#a7 t all artific]s are prone to con/ruct _! works accord+ to r\nd numb]s1 or simple fractions1 ( _! units ( measurem5t2 & 7#b7 t1 aim+ to secure ?is1 !y w /ray f x 9 tol]able accordance ) ! law ( error4 ,! result ( ^! two assumptions is t if we collect a v l>ge numb] ( measurem5ts ( ! diff]5t p>ts & proportions ( "s anci5t build+1--say an ,egyptian temple1--:il/ no assignable l5g? is likely to be p]man5tly unrepres5t$1 yet we f9d a m>k$ t5d5cy = ! measurem5ts to clu/] ab\t c]ta9 det]m9ate po9ts 9 our own1 or any o!r /&>d scale ( measurem5t4 ,^! po9ts m>k ! l5g? ( ! /&>d1 or ( "s multiple or submultiple ( ! /&>d1 employ$ by ! old build]s4 ,x ne$ h>dly be said t !re are a multitude ( practical consid]ations to be tak5 into acc\nt be=e ?is me?od c be expect$ to give tru/wor?y results1 b ! lead+ pr9ciples ^u :i* x re/s are comp>atively simple4 #ce4 ,! case j consid]$ is really no?+ else ?an ! recurr5ce1 "u a diff]5t application1 ( "o :i* occupi$ our att5tion at a v e>ly /age4 ,we notic$ 7,*ap4 ,,ii47 ! possibility ( a curve ( facility :i* in/ead ( hav+ a s+le v]tex l t correspond+ to ! common law ( error1 %\ld display two humps or v]tices4 ,x c readily be %[n t ?is problem ( ! measurem5ts ( anci5t build+s1 is no?+ m ?an ! reop5+ ( ! same "q1 9 a slightly m complex =m1 9 ref]5ce to ! "q ( ! functions ( an av]age4 ,take a simple example4 ,suppose an in/ance 9 :i* great errors1 ( a c]ta9 approximate magnitude1 are di/9ctly m likely to be committ$ ?an small ones1 s t ! curve ( facility1 in/ead ( ris+ into "o peak t[>ds ! c5tre1 z 9 t ( ! famili> law ( error1 %[s a depression or valley !re4 ,imag9e1 9 fact1 two b9omial curves1 ) a %ort int]val betwe5 _! c5tres4 ,n[ if we 7 to calculate ! result ( tak+ av]ages "h we %\ld f9d t ?is at once t5ds to fill up ! valley2 & if we w5t on long en\gh1 t is1 if we kept on tak+ av]ages ( suffici5tly l>ge numb]s1 a peak w\ld beg9 to arise 9 ! c5tre4 ,9 fact ! famili> s+le b9omial curve w\ld beg9 to make its appe>ance4 #cf4 ,! "q !n at once sugge/s itself1 ought we to d ?is8 ,%all we give ! av]age free play to p]=m its allott$ function ( ?us cr[d+ ?+s up t[>ds ! c5tre8 ,to answ] ?is "q we mu/ introduce a di/9ction4 ,if t peculi> d\ble-peak$ curve _h be51 z x conceivably might1 a true error-curve1--t is1 if x _h repres5t$ ! div]g5ces actually made 9 aim+ at ! real c5tre1--! result w\ld be j :at we %\ld want4 ,x w\ld furni% an in/ance ( ! advantages to be ga9$ by tak+ av]ages ev5 9 circum/ances :i* 7 orig9ally unfav\rable4 ,x is n difficult to sugge/ an appropriate illu/ration4 ,suppose a man fir+ at a m>k f "s %elt]$ spot1 b su* t ! range cross$ a broad expos$ valley up or d[n :i* a /rong w9d 0 g5]ally bl[+4 ,if ! %ot-m>ks 7 obs]v$ we %\ld f9d !m clu/]+ ab\t two c5tres to ! "r & left ( ! bullseye4 ,& if ! results 7 plott$ out 9 a curve !y w\ld yield su* a d\ble-peak$ curve z we h describ$4 ,b if ! w9ds 7 equally /rong & preval5t 9 opposite directions1 we %\ld f9d t ! av]ag+ process r$ress$ ! consequ5t di/urbance4 ,if h[ev] ! curve repres5t$1 z x is decid$ly m likely to d1 "s outcome ( natural ph5om5a 9 :i* !re 01 s to say1 a real d\ble aim on ! "p ( nature1 x w\ld be o!rwise4 ,take1 = in/ance1 ! results ( measur+ a l>ge numb] ( p :o belong$ to two v het]og5e\s races4 ,! curve ( facility w\ld "h be ( ! k9d indicat$ on p4 #de1 & if ! numb]s ( ! two comm+l$ races 7 equal x w\ld display a pair ( tw9 peaks4 ,aga9 ! "q arises1 'ought' we to involve ! :ole range )9 ! scope ( a s+le av]age8 ,! answ] is t ! obligation dep5ds ^u ! purpose we h 9 view4 ,if we want to comp>e t het]og5e\s race1 z a :ole1 ) "s o!r1 or ) itself at "s o!r "t1 we %all d well to av]age )\t analysis4 ,all /ati/ics ( population1 z we h already se5 7v4 p4 #dg71 are =c$ to neglect a multitude ( discrim9at+ *>act]i/ics ( ! k9d 9 "q4 ,b if our object 7 to int]pret ! causes ( ?is abnormal error-curve we %\ld d well to break up ! /ati/ics into correspond+ p>ts1 & subject ^! to analysis sep>ately4 ,simil>ly ) ! measurem5ts ( ! anci5t build+s4 ,9 ?is case if all our v>i\s 'errors' 7 ?r[n toge!r into "o gr\p ( /ati/ics we %\ld f9d t ! resultant curve ( facility display$1 n two peaks only1 b a succession ( !m2 & ^! ( v>i\s magnitudes1 correspond+ to ! frequ5cy ( occurr5ce ( ea* p>ticul> measurem5t4 ,we might take an av]age ( ! :ole1 b h>dly any rational purpose c\ld be subs]v$ 9 s do+2 :]eas ea* sep>ate po9t ( maximum frequ5cy ( occurr5ce has some?+ significant to tea* u4 #cg4 ,"o o!r peculi> case may be notic$ 9 conclusion4 ,suppose a di/9ctly asymmetrical1 or lop-sid$ curve ( facility1 su* z ?is3-- ,figure3 ,an asymmetric 7lop-sid$7 di/ribution4 ,laws ( error1 ( :i* ?is is a graphical repres5tation1 are1 ,i appreh5d1 f> f uncommon4 ,! curve 9 "q1 is1 9 fact1 b a slight exagg]ation ( t ( b>ometrical heights z ref]r$ to 9 ! la/ *apt]2 :5 x 0 expla9$ t 9 su* cases ! mean1 ! m$ian1 & ! maximum ord9ate w\ld %[ a mutual div]g5ce4 ,! d\bt "h is n1 z 9 ! prec$+ in/ances1 :e!r or n a s+le av]age %\ld be tak51 b r :at k9d ( av]age %\ld be select$4 ,z be=e1 ! answ] mu/ dep5d ^u ! special purpose we h 9 view4 ,= all ord9>y purposes ( comp>ison betwe5 "o "t or place & ano!r1 any av]age w answ]1 & we %\ld !re=e naturally take ! ari?metical1 z ! mo/ famili>1 or ! m$ian1 z ! simple/4 #ch4 ,cases might h[ev] arise "u :i* o!r k9ds ( av]age c\ld ju/ify !mselves1 ) a mom5t>y notice ( :i* we may n[ conclude4 ,suppose1 = in/ance1 t ! "q involv$ "h 7 "o ( desirability ( climate4 ,! ord9>y mean1 dep5d+ z x does s l>gely ^u ! numb] & magnitude ( extreme values1 might v reasonably be consid]$ a less appropriate te/ ?an t ( judg+ simply by ! relatively mo/ frequ5t value3 9 o!r words1 by ! maximum ord9ate4 ,& v>i\s o!r po9ts ( view c be sugge/$ 9 respect ( :i* ?is p>ticul> value w\ld be ! mo/ suitable & significant4 ,9 ! =ego+ case1 viz4 t ( ! wea!r curve1 !re 0 no objective or 'true' value aim$ at4 ,b a curve closely resembl+ ?is w\ld be repres5tative ( t p>ticul> class ( e/imates indicat$ by ,mr ,galton1 & = :i*1 z he has po9t$ out1 ! geometrical mean becomes ! only appropriate "o4 ,9 ?is case ! curve ( facility ends abruptly at ,o3 x resembles a mu* =e%ort5$ modification ( ! common expon5tial =m4 ,its *>act]i/ics h be5 discuss$ 9 ! pap] by ,dr ,macali/] already ref]r$ to1 b any attempt to exam9e its prop]ties "h w\ld lead u into f> too intricate details4 #ci4 ,! g5]al conclusion f all ?is seems q 9 accordance ) ! nature & functions ( an av]age z po9t$ out 9 ! la/ *apt]4 ,e av]age1 x 0 urg$1 is b a s+le repres5tative int]m$iate value sub/itut$ = a plurality ( actual values4 ,x mu/ accord+ly let slip ! bulk ( ! in=mation involv$ 9 ^! latt]4 ,occasionally1 z 9 mo/ ord9>y measurem5ts1 ! "o ?+ :i* x repres5ts is obvi\sly ! ?+ we are 9 want (2 & !n ! only "q c be1 :i* mean w mo/ accord ) ! 'true' value we are seek+4 ,b :51 z may happ5 9 mo/ ( ! common applications ( /ati/ics1 !re is really no 'true value' ( an objective k9d beh9d ! ph5om5a1 ! problem may bran* out 9 v>i\s directions4 ,we may h a v>iety ( purposes to "w out1 & ^! may dem& "s discrim9ation z reg>ds ! av]age mo/ appropriate = !m4 ,:5ev] !re=e we h any d\bt :e!r ! famili> ari?metical av]age is suitable = ! purpose 9 h& we mu/ fir/ decide precisely :at t purpose is4 #a4 ,mr ,mansfield ,m]riman publi%$ 9 #ahgg 7,trans4 ( ! ,connecticut ,acad47 a li/ ( #djh writ+s on ! subject ( ,lea/ ,squ>es4 #b4 ,9 o!r words1 we are to take ! c5tre ( gravity ( ! %ot-m>ks1 reg>d+ !m z all ( equal weight4 ,?is is1 9 reality1 ! 'av]age' ( all ! m>ks1 z ! elem5t>y geometrical con/ruction = obta9+ ! c5tre ( gravity ( a sy/em ( po9ts w %[2 b x is n famili>ly s reg>d$4 ,( c\rse1 :5 we are deal+ ) su* cases z occur 9 ,m5suration1 :]e we h to comb9e or reconcile ?ree or m inconsi/5t equations1 "s su* rule z t ( ,lea/ ,squ>es becomes imp]ative4 ,no tak+ ( an av]age w get u out ( ! difficulty4 #c4 ,! only reason = suppos+ ?is exceptional %ape is to secure simplicity4 ,! ord9>y t>get1 all[+ errors 9 two dim5sions1 w\ld yield slightly m complicat$ results4 #d4 ,:5 fir/ ref]r$ to1 ! g5]al =m ( ?is equation 0 giv5 7v4 p4 #bi74 ,! special =m "h assign$1 9 :i* 7h_/sqrt7 is sub/itut$ = ,a1 is commonly employ$ 9 ,probability1 because ! integral ( y dx1 betwe5 inf9ity & -inf9ity1 becomes equal to unity4 ,t is1 ! sum ( all ! mutually exclusive possibilities is repres5t$1 z usual1 by unity4 ,9 ?is =m ( expression h is a quantity ( ! ord] x-#a2 = hx is to be a num]ical quantity1 /&+ z x does z an index4 ,! modulus1 be+ ! reciprocal ( ?is1 is ( ! same ord] ( quantities z ! errors !mselves4 ,9 fact1 if we multiply x by #j4dgfi444 we h ! s-call$ 'probable error4' #e4 ,see1 = ! explanation ( ?is1 & ( ! graphical me?od ( illu/rat+ x1 ! note on p4 #bi4 #f4 ,broadly speak+1 we may say t ! above rem>ks hold good ( any law ( frequ5cy ( error 9 :i* !re are actual limits1 h[ev] wide1 to ! possible magnitude ( an error4 ,if !re are no limits to ! possible errors1 ?is *>act]i/ic ( an av]age to heap its results up t[>ds ! c5tre w dep5d ^u circum/ances4 ,:51 z 9 ! expon5tial curve1 ! approximation to ! base1 z asymptote1 is exce$+ly rapid1--t is1 :5 ! extreme errors are relatively v few1--x /ill holds good4 ,b if we 7 to take z our law ( facility su* an equation z y _/7#a x#b71 7z h9t$ by ,de ,morgan & not$ by ,mr ,edgewor?3 ,camb4 ,phil4 ,trans4 vol4 ,x4 p4 #ahd1 & vol4 ,,xiv4 p4 #afj7 x does n hold good4 ,! result ( av]ag+ is to dim9i% ! t5d5cy to clu/] t[>ds ! c5tre4 #g4 ,! read] w f9d ! pro(s ( ^! & o!r simil> =mul 9 ,gall[ay on ,probability1 & 9 ,airy on ,errors4 #h4 ,! =mula commonly us$ = ! ,e4,m4,s4 9 ?is case is 7sum e#b7_/7n - #a7 & n 7sum e#b7_/n4 ,! diff]5ce is trifl+1 unless n be small2 ! ju/ification has be5 (f]$ = x t s9ce ! sum ( ! squ>es measur$ f ! true c5tre is a m9imum 7t c5tre be+ ! ultimate ari?metical mean7 ! sum ( ! squ>es measur$ f ! some:at incorrectly assign$ c5tre w be some:at l>g]4 #i4 ,x appe>s to me t 9 /rict logical propriety we %\ld l to "k ! probable error committ$ 9 bo? ! assignm5ts ( ! prec$+ two sections4 ,b ! pr(\nd ma!maticians :o h discuss$ ?is "q1 & :o alone are compet5t to treat x1 h mo/ly writt5 ) ! practical wants ( ,a/ronomy 9 view2 & = ?is purpose x is suffici5t to take acc\nt ( ! "o great desid]atum1 viz4 ! true values s\ght4 ,accord+ly ! only rules commonly giv5 ref] to ! probable error ( ! mean4 #aj4 i4e4 z di/+ui%$ f act+ ^u !m indirectly4 ,?is latt] proce$+1 z expla9$ 9 ! *apt] on ,r&omness1 may result 9 giv+ a non-uni=m di/ribution4 #aa4 ,!re is no difficulty 9 conceiv+ circum/ances "u :i* a law v closely resembl+ ?is w\ld prevail4 ,suppose1 e4g41 t "o ( ! two measurem5ts _h be5 made by a c>eful & skill$ me*anic1 & ! o!r by a man :o to save himself tr\ble _h put 9 ! e/imate at r&om 7)9 c]ta9 limits71--! firm hav+ a k ( ?is fact b be+ ( c\rse unable to assign ! two to _! au?ors1--we %\ld get v mu* su* a ,law ( ,error z is suppos$ above4 ,,index4 ,accid5ts #cdb ,airy1 ,g4 ,b4 #ddg1 #dhd ,anticipations1 tacit #bhg ,arbu?nott #beh ,ari/otle #bje1 #cjg ,av]age ari?metical #dcg geometrical #dci m$ian #ddb consequ5ces ( #dhb necess>y results ( #deg uses ( #dci1 #dhi ,babbage #cdc ,bags & balls #ahj1 #daa ,belief correctness ( #abe1 #aca1 #agh gradations ( #aci gr[? ( #aii language ( #adc measurem5t ( #aai1 #abe1 #adf quantity ( #acc te/ ( #adj1 #adi1 #bid undue #abi vagu5ess ( #abg ,b5?am #cai1 #cbc ,b]n\lli #ia1 #aag1 #chi ,b]tillon #dce ,bir?s1 male & female #ij1 #beh1 #bfc ,boat race1 ,ox=d & ,cambridge #cci ,boole #ahc ,buckle #bcg ,buffon #aec1 #bje1 #ceb1 #chi ,burg]sdyck #caa ,butl] #bji1 #bha1 #ccc1 #cff ,c>lisle ,tables #afi ,casual1 mean+ ( #bde ,causation ne$ ( #bcg pro( ( #bdd ,c5tre ( gravity #dfg ,c]ta9ty1 9 ,law #cbd reasonable #cbg hypo!tical #baj ,*ance & ,causation #bdd ,creation #beh ,design #bef ,g5ius #cec neglect ( small #cfc selections #cch ,*auv5et #ceb ,classification1 num]ical s*eme ( #dh ,co9cid5ces #bde ,comb9ations & ,p]mutations #hg ,communism #cge1 #cib ,conceptualism #bge ,conflict ( *ances #dah ,consumptives1 insurance ( #bbg ,c\rnot #bde1 #bee1 #cch ,crackan?orpe #cab1 #cbj ,craig1 ,j4 #aib ,cr(ton1 ,m4 ,w4 #fa1 #aja1 #ajd ,dante #bhe ,deflection causes ( #eg f aim #ch ,de ,morgan #hc1 #ajf1 #aai1 #abb1 #ace1 #agg1 #agi1 #aig1 #bcf1 #bdg1 #bif1 #cjh1 #cej1 #cgi1 #chb1 #dhc ,de ,ros trial #bee ,digits1 r&om #aaa1 #aad ,discont9uity #aaf ,di/ribution1 r&om #ajf ,diagrams #bi1 #de1 #aah1 #ddc1 #dgf1 #dha1 #dic1 #eja ,dialectic #cjb1 #cbj ,donk9 #abc1 #ahh1 #bhc ,duration ( life #ae1 #dda ,ds+ #bei ,ebb+haus #aii ,edgewor?1 ,f4 ,y4 #cd1 #aai1 #bef1 #cci1 #cic1 #dce1 #dhc ,ellis1 ,l4 #i ,epidemics #fb ,error1 law ( #bi asymmetrical #cd1 #dda1 #ddc b9omial #cg1 #deg1 #dfi1 #dhj geometrical #cd1 #ejb het]og5e\s #de production ( #cf ,error mean #ddf probable #ddf1 #dgb1 #dhh ( mean squ>e #ddg1 #dhh ,escapes1 n>r[ #cda ,expectation1 moral #chh ,exp]i5ce & probability #gd ,expon5tial curve #bi ,extraord9>y s5se ( #aei1 #dbc /ories #djg1 #dba ,fallacies 9 ,logic & ,probability #cfg ,fatalism #bdc ,fe*n] #cd1 #chi1 #dce1 #dda ,fluctuation #ddh unlimit$ #gc ,=bes1 ,j4 ,d4 #ahh1 #bfb ,=mal ,logic #abc ,=mal & ,mat]ial treatm5t #hf ,free w #bdj ,gall[ay #bdh1 #ddh1 #dhd ,galton1 ,f4 #cc1 #ej1 #gj1 #cah1 #ddb1 #dea1 #dgc1 #ejb ,gambl+ & ,insurance #cgj disadvantage ( #chd f9al results ( #che1 #cia ,godfray1 ,h4 #ii ,grote1 ,g4 #cjg ,guy #f ,hamilton1 ,w4 #bff1 #big ,happ9ess1 human #chb ,heads & ,tails #gg ,h]$ity #ej1 #ceg ,h]s*el #cj1 #dff ,h\d9 #cfa ,hume #bcf1 #dai1 #dcc ,hypo!ses #bfh ,imm$iate inf]5ces #aba ,indep5d5t ev5ts #age1 #bdf ,induction & ,probability #aid1 #bja1 #bjh1 #bcc1 #ceh difficulty ( #bac pure #bjj ,inequality ( weal? #chb ,inf]5ce1 rules ( #afg ,inoculation #cgd ,insurance ju/ification ( #adi difficulties ( #bba life #aea peculi> case #bbd !ory ( #cgb v>ieties ( #cgd ,inv]se probability #agi1 #aif1 #bdi ,irregul>ity1 absolute & relative #f ,jacobs1 ,j4 #aii ,jackson1 ,j4 ,g4 #bec ,jevons #cg1 #hc1 #acf1 #aih1 #bja1 #bji1 #bdg ,kant #caj1 #cag ,keck]mann #bih1 #caf ,k9ds1 natural #ee ,krug #cbd ,lamb]t #cji ,language ( ,*ance #aei ,laplace #hi1 #abj1 #aig1 #bcg1 #dbd ,law abs5ce ( #aja empirical #afj ( causation #bjf ,lea/ squ>es #da1 #dfg ,leibnitz #cji1 #cbj ,lett]s lo/ #afb1 #cfh misdirect$ #fg1 #bcg1 #bda ,lexis1 ,w4 #bfc1 #dda ,limit conception ( #ah1 #aji1 #afd ( possible fluctuation #cb ,l9es1 r&om #aac ,li/]'s me?od #ahg ,lott]ies #abh ,lunn1 ,j4 ,r4 #bdh ,likely1 equally #gg1 #ahc ,mc,alister1 ,d4 #cd1 #ahg1 #ejb ,mansel1 ,h4 ,l4 #bii1 #cja1 #cbj ,m>t+ale #cdc ,mat]ial & ,=mal ,logic #bfe ,maximum ord9ate #dda1 #dee ,measurem5t ( ,belief #aai ,memory #aib ,m5tal qualities1 measurem5t ( #di ,m]riman1 ,m4 #ceb1 #ddh1 #dfj1 #dfe ,mill1 ,j4 ,s4 #aca1 #bjg1 #bff1 #bhb1 #djb ,milton1 *ance production ( #cec ,miracles #dbh ,mi*ell1 ,j4 #bfj ,modality #bie divisions ( #cjg false #big =mal #bih 9 ,law #cai ,modulus #dfd1 #dgb1 #dhd ,monro1 ,c4 ,j4 #cbe1 #daf ,names1 ref]5ce ( #bgj ,nations1 comp>ison ( #ea ,natural ,k9ds #ee1 #fc1 #ga ,necess>y & impossible matt] #caj ,objects & ag5cies #ec ,occam #cad ,paley #dcc ,p5ny1 tosses ( #add ,petrie1 ,f4 #dih ,pet]sburg ,problem #ai1 #aed ,poisson #dje ,prantl #caa ,presumption1 legal #cbi ,prvo/ #cdh ,probability def9ition ( #afe relative #bij integral #dfc ,probable facts #bfi value #dda error #ddf1 #dgb ,problem1 ,?ree po9t #ajd ,proctor1 ,r4 ,a4 #bfb1 #cgh ,prophecies1 suicidal #bbf ,provid5ce #hi1 #dca ,propositions1 proportional #b ,psy*ical rese>* #bef ,pyramid1 ! great #bea 1 digits 9 #aaa1 #bdg ,qu>tiles #ddf ,quetelet #bc1 #cj1 #dc1 #ia1 #bei1 #ccj1 #cdh1 #ded ,r&omness etymology ( #if 9 fir+ #ih pro( ( #ajg ,r>e ev5ts #cdi ,realism #ib ,reason1 suffici5t #hb ,residuals #dfj ,rob]ts1 ,c4 #be ,rod brok5 at r&om #ih ?r[n at r&om #ajc ,rules ,inductive & ,d$uctive #agf ( ,succession #aia conflict ( #bbb plurality ( #bag ,s]ies def9ite proportions 9 #aa fix$ & v>iable #af ideal #ie peculi> #ab ,%anks #bdh ,skeat1 ,w4 ,w4 #if ,smiglecius #cjf1 #caf ,smy?1 ,p4 #bea ,socialism #cib ,spiritualism #cfe ,/>s1 r&om arrangem5t ( #ajh1 #bfj ,/ati/ics by ,int]comp>ison #dgc unconsci\s appeal to #djj ,/ati/ical ,j\rnal #f ,/ature human #be1 #dga ,fr5* & ,engli% #dd ,/eph51 ,j4 ,f4 #bhb1 #cbc1 #cbf ,/ew>t1 ,d4 #bji1 #bcg ,subjective & objective t]ms #afj ,succession long #cfj ,rule ( #aij1 #cfb ,suffield1 ,g4 #bdh ,suicides #fg1 #bcg ,surnames1 ext9ction ( #chg ,surprise1 emotion ( #aeg ,syllogisms1 pure & modal #caf ,taylor #cbi ,te/imony s+le #daa comb9$ #dbf two k9ds ( #dji wor?less #daf ,?omson1 ,w4 #aec1 #cad1 #dai ,"t influ5ce ( #aia 9 ,probability #bgi ,todhunt] #dae ,tont9es #chj ,triangle1 r&om #ajc ,tuck]1 ,a4 #abg ,types exi/5ce ( #db1 #fj1 #dec fix$ & fluctuat+ #fd1 #ic ,ueb]weg #caa ,unc]ta9ty 9 life #cgj ,uni=mity #bdj ,units ( calculation #dfd ,volunt>y ag5cy #fe1 #fh1 #he ,wat=d #cgd ,wallis1 ,j4 #cab ,watson1 ,h4 ,w4 #chg ,:ately #big1 #cjg ,:i/ #dja ,:itwor?1 ,w4 ,a4 #hg1 #ahc1 #chd ,wilson1 ,j4 ,m4 #ajd ,witnesses1 indep5d5t #dje ,wolf #cji ,woolh\se #aja ,,cambridge3 ,,pr9t$ ,,by ,c4,j4 ,,clay1 ,m4,a4 ,,& ,,sons1 ,,at ,,! ,,univ]sity ,,press4