,transcrib]'s ,notes3 ,e ef=t has be5 made to replicate ?is text z fai?fully z possible1 includ+ inconsi/5cies 9 spell+ & hyph5ation4 ,"s corrections ( spell+ & punctuation h be5 made4 ,!y are li/$ at ! end ( ! text4 ,italic text has be5 m>k$ ) und]scores4 ,greek text has be5 translit]at$ & m>k$ ) tildes4 ,,our ,,k ,,( ,,! ,,ext]nal ,,_w ,,z ,a ,,field ,,= ,,sci5tific ,,me?od ,,9 ,,philosophy ,,by ,,! ,,same ,,au?or ,,introduction ,,to ,,ma!matical ,,philosophy ,second ,edition4 ,demy #hvo1 #abs4 #f;d4 net4 ,,! ,,analysis ,,( ,,m9d ,demy #hvo1 #afs4 net4 ,,pr9ciples ,,( ,,social ,,recon/ruction ,sev5? ,impression4 ,cr4 #hvo1 #es4 net2 ,limp1 #cs4 #f;d4 net4 ,,roads ,,to ,,fre$om3 ,,socialism1 ,,an>*ism ,,& ,,syndicalism ,f\r? ,impression4 ,cr4 #hvo1 #es4 net2 ,limp1 #cs4 #f;d4 net4 ,,! ,,practice ,,& ,,!ory ,,( ,,bol%evism ,second ,impression4 ,cr4 #hvo1 #fs4 net4 ,,our ,,k ,,( ,,! ,,ext]nal ,,_w ,,z ,a ,,field ,,= ,,sci5tific ,,me?od ,,9 ,,philosophy ,,by ,,b]tr& ,,russell1 ,f4,r4,s ,,london3 ,,george ,,all5 ,,unw9 ,,ltd ,,rusk9 ,,h\se1 #dj ,,museum ,,/reet1 ,w4,c4 #a ,fir/ publi%$ 9 #aiad by ,! ,op5 ,c\rt ,publi%+ ,company ,reissu$ by ,george ,all5 ,unw9 ,ltd4 #aibb ,,preface ,! foll[+ lectures#a are an attempt to %[1 by means ( examples1 ! nature1 capacity1 & limitations ( ! logical-analytic me?od 9 philosophy4 ,?is me?od1 ( :i* ! fir/ complete example is to be f\nd 9 ! writ+s ( ,frege1 has gradually1 9 ! c\rse ( actual rese>*1 increas+ly =c$ itself ^u me z some?+ p]fectly def9ite1 capable ( embodim5t 9 maxims1 & adequate1 9 all bran*es ( philosophy1 to yield :atev] objective sci5tific k x is possible to obta94 ,mo/ ( ! me?ods hi!rto practis$ h pr(ess$ to lead to m ambiti\s results ?an any t logical analysis c claim to rea*1 b un=tunately ^! results h always be5 su* z _m compet5t philosoph]s consid]$ inadmissible4 ,reg>d$ m]ely z hypo!ses & z aids to imag9ation1 ! great sy/ems ( ! pa/ s]ve a v useful purpose1 & are abundantly wor?y ( /udy4 ,b some?+ diff]5t is requir$ if philosophy is to become a sci5ce1 & to aim at results indep5d5t ( ! ta/es & temp]am5t ( ! philosoph] :o advocates !m4 ,9 :at foll[s1 ,i h endeav\r$ to %[1 h[ev] imp]fectly1 ! way by :i* ,i believe t ?is desid]atum is to be f\nd4 #a ,deliv]$ z ,l[ell ,lectures 9 ,bo/on1 9 ,m>* & ,april #aiad4 ,! c5tral problem by :i* ,i h s\ght to illu/rate me?od is ! problem ( ! relation betwe5 ! crude data ( s5se & ! space1 "t1 & matt] ( ma!matical physics4 ,i h be5 made aw>e ( ! importance ( ?is problem by my fri5d & collaborator ,dr ,:itehead1 to :om are due almo/ all ! diff]5ces betwe5 ! views advocat$ "h & ^? sugge/$ 9 ,! ,problems ( ,philosophy4#b ,i owe to him ! def9ition ( po9ts1 ! sugge/ion = ! treatm5t ( in/ants & ?+s1 & ! :ole conception ( ! _w ( physics z a con/ruction r ?an an inf]5ce4 ,:at is said on ^! topics "h is1 9 fact1 a r\gh prelim9>y acc\nt ( ! m precise results :i* he is giv+ 9 ! f\r? volume ( our ,pr9cipia ,ma!matica4#c ,x w be se5 t if 8 way ( deal+ ) ^! topics is capable ( be+ successfully c>ri$ ?r\gh1 a :olly new light is ?r[n on ! "t-hon\r$ controv]sies ( reali/s & ideali/s1 & a me?od is obta9$ ( solv+ all t is soluble 9 _! problem4 #b ,london & ,new ,york1 #aiab 7,home ,univ]sity ,libr>y74 #c ,! fir/ volume 0 publi%$ at ,cambridge 9 #aiaj1 ! second 9 #aiab1 & ! ?ird 9 #aiac4 ,! speculations ( ! pa/ z to ! reality or unreality ( ! _w ( physics 7 baffl$1 at ! outset1 by ! abs5ce ( any satisfactory !ory ( ! ma!matical inf9ite4 ,?is difficulty has be5 remov$ by ! "w ( ,georg ,cantor4 ,b ! positive & detail$ solution ( ! problem by means ( ma!matical con/ructions bas$ ^u s5sible objects z data has only be5 r5d]$ possible by ! gr[? ( ma!matical logic1 )\t :i* x is practically impossible to manipulate ideas ( ! requisite ab/ractness & complexity4 ,?is aspect1 :i* is some:at obscur$ 9 a m]ely popul> outl9e su* z is conta9$ 9 ! foll[+ lectures1 w become pla9 z soon z ,dr ,:itehead's "w is publi%$4 ,9 pure logic1 :i*1 h[ev]1 w be v briefly discuss$ 9 ^! lectures1 ,i h _h ! b5efit ( vitally important discov]ies1 n yet publi%$1 by my fri5d ,mr ,ludwig ,wittg5/e94 ,s9ce my purpose 0 to illu/rate me?od1 ,i h includ$ mu* t is t5tative & incomplete1 = x is n by ! /udy ( f9i%$ /ructures alone t ! mann] ( con/ruction c be le>nt4 ,except 9 reg>d to su* matt]s z ,cantor's !ory ( inf9ity1 no f9ality is claim$ = ! !ories sugge/$2 b ,i believe t :]e !y are f\nd to require modification1 ?is w be discov]$ by sub/antially ! same me?od z t :i* at pres5t makes !m appe> probable1 & x is on ?is gr\nd t ,i ask ! read] to be tol]ant ( _! incomplet5ess4 ,cambridge1 ,june #aiad4 ,,cont5ts ,,lecture ,,page ,i4 ,curr5t ,t5d5cies #c ,,ii4 ,logic z ! ,ess5ce ( ,philosophy #cc ,,iii4 ,on our ,k ( ! ,ext]nal ,_w #fc ,,iv4 ,! ,_w ( ,physics & ! ,_w ( ,s5se #aja ,v4 ,! ,!ory ( ,cont9uity #abi ,,vi4 ,! ,problem ( ,inf9ity consid]$ ,hi/orically #aee ,,vii4 ,! ,positive ,!ory ( ,inf9ity #ahe ,,viii4 ,on ! ,notion ( ,cause1 ) ,applications to ! ,free-w ,problem #baa ,index #bdc ,,lecture ,i ,,curr5t ,,t5d5cies ,philosophy1 f ! e>lie/ times1 has made great] claims1 & a*iev$ few] results1 ?an any o!r bran* ( le>n+4 ,ev] s9ce ,?ales said t all is wat]1 philosoph]s h be5 ready ) glib ass]tions ab\t ! sum-total ( ?+s2 & equally glib d5ials h come f o!r philosoph]s ev] s9ce ,?ales 0 contradict$ by ,anaxim&]4 ,i believe t ! "t has n[ arriv$ :5 ?is unsatisfactory /ate ( ?+s c be br\ght to an end4 ,9 ! foll[+ c\rse ( lectures ,i %all try1 *iefly by tak+ c]ta9 special problems z examples1 to indicate :]e9 ! claims ( philosoph]s h be5 excessive1 & :y _! a*ievem5ts h n be5 great]4 ,! problems & ! me?od ( philosophy h1 ,i believe1 be5 misconceiv$ by all s*ools1 _m ( its traditional problems be+ insoluble ) our means ( k1 :ile o!r m neglect$ b n less important problems c1 by a m pati5t & m adequate me?od1 be solv$ ) all ! precision & c]ta9ty to :i* ! mo/ advanc$ sci5ces h atta9$4 ,among pres5t-day philosophies1 we may di/+ui% ?ree pr9cipal types1 (t5 comb9$ 9 v>y+ proportions by a s+le philosoph]1 b 9 ess5ce & t5d5cy di/9ct4 ,! fir/ ( ^!1 :i* ,i %all call ! classical tradition1 desc5ds 9 ! ma9 f ,kant & ,hegel2 x repres5ts ! attempt to adapt to pres5t ne$s ! me?ods & results ( ! great con/ructive philosoph]s f ,plato d[nw>ds4 ,! second type1 :i* may be call$ evolutionism1 d]iv$ its pr$om9ance f ,d>w91 & mu/ be reckon$ z hav+ _h ,h]b]t ,sp5c] = its fir/ philosophical repres5tative2 b 9 rec5t times x has become1 *iefly ?r\gh ,william ,james & ,m4 ,b]gson1 f> bold] & f> m se>*+ 9 its innovations ?an x 0 9 ! h&s ( ,h]b]t ,sp5c]4 ,! ?ird type1 :i* may be call$ logical atomism = want ( a bett] "n1 has gradually crept into philosophy ?r\gh ! critical scrut9y ( ma!matics4 ,?is type ( philosophy1 :i* is ! "o t ,i wi% to advocate1 has n z yet _m :ole-he>t$ adh]5ts1 b ! new realism :i* owes its inception to ,h>v>d is v l>gely impregnat$ ) its _s4 ,x repres5ts1 ,i believe1 ! same k9d ( advance z 0 introduc$ into physics by ,galileo3 ! sub/itution ( piecemeal1 detail$1 & v]ifiable results = l>ge unte/$ g5]alities recomm5d$ only by a c]ta9 appeal to imag9ation4 ,b be=e we c und]/& ! *anges advocat$ by ?is new philosophy1 we mu/ briefly exam9e & criticise ! o!r two types ) :i* x has to cont5d4 ,a4 ,! ,classical ,tradition ,tw5ty ye>s ago1 ! classical tradition1 hav+ vanqui%$ ! oppos+ tradition ( ! ,engli% empirici/s1 held almo/ unque/ion$ sway 9 all ,anglo-,saxon univ]sities4 ,at ! pres5t day1 ?\gh x is los+ gr\nd1 _m ( ! mo/ prom95t tea*]s /ill adh]e to x4 ,9 academic ,france1 9 spite ( ,m4 ,b]gson1 x is f> /rong] ?an all its oppon5ts comb9$2 & 9 ,g]many x has _m vigor\s advocates4 ,nev]!less1 x repres5ts on ! :ole a decay+ =ce1 & x has fail$ to adapt itself to ! temp] ( ! age4 ,its advocates are1 9 ! ma91 ^? ^: extra-philosophical k is lit]>y1 r ?an ^? :o h felt ! inspiration ( sci5ce4 ,!re are1 ap>t f reason$ argum5ts1 c]ta9 g5]al intellectual =ces aga9/ x--! same g5]al =ces :i* are break+ d[n ! o!r great syn!ses ( ! pa/1 & mak+ our age "o ( bewild]$ grop+ :]e our ance/ors walk$ 9 ! cle> daylight ( unque/ion+ c]ta9ty4 ,! orig9al impulse out ( :i* ! classical tradition develop$ 0 ! naive fai? ( ! ,greek philosoph]s 9 ! omnipot5ce ( reason+4 ,! discov]y ( geometry _h intoxicat$ !m1 & its a priori d$uctive me?od appe>$ capable ( univ]sal application4 ,!y w\ld prove1 = in/ance1 t all reality is "o1 t !re is no su* ?+ z *ange1 t ! _w ( s5se is a _w ( m]e illusion2 & ! /rang5ess ( _! results gave !m no qualms because !y believ$ 9 ! correctness ( _! reason+4 ,?us x came to be ?\ght t by m]e ?9k+ ! mo/ surpris+ & important tru?s conc]n+ ! :ole ( reality c\ld be e/abli%$ ) a c]ta9ty :i* no contr>y obs]vations c\ld %ake4 ,z ! vital impulse ( ! e>ly philosoph]s di$ away1 its place 0 tak5 by au?ority & tradition1 re9=c$1 9 ! ,middle ,ages & almo/ to our own day1 by sy/ematic !ology4 ,mod]n philosophy1 f ,desc>tes onw>ds1 ?\gh n b\nd by au?ority l t ( ! ,middle ,ages1 /ill accept$ m or less uncritically ! ,ari/otelian logic4 ,moreov]1 x /ill believ$1 except 9 ,great ,brita91 t a priori reason+ c\ld reveal o!rwise undiscov]able secrets ab\t ! univ]se1 & c\ld prove reality to be q diff]5t f :at1 to direct obs]vation1 x appe>s to be4 ,x is ?is belief1 r ?an any p>ticul> t5ets result+ f x1 t ,i reg>d z ! di/+ui%+ *>act]i/ic ( ! classical tradition1 & z hi!rto ! ma9 ob/acle to a sci5tific attitude 9 philosophy4 ,! nature ( ! philosophy embodi$ 9 ! classical tradition may be made cle>] by tak+ a p>ticul> expon5t z an illu/ration4 ,= ?is purpose1 let u consid] = a mom5t ! doctr9es ( ,mr ,bradley1 :o is probably ! mo/ di/+ui%$ liv+ repres5tative ( ?is s*ool4 ,mr ,bradley's ,appe>ance & ,reality is a book consi/+ ( two p>ts1 ! fir/ call$ ,appe>ance1 ! second ,reality4 ,! fir/ "p exam9es & condemns almo/ all t makes up our ev]yday _w3 ?+s & qualities1 relations1 space & "t1 *ange1 causation1 activity1 ! self4 ,all ^!1 ?\gh 9 "s s5se facts :i* qualify reality1 are n real z !y appe>4 ,:at is real is "o s+le1 indivisible1 timeless :ole1 call$ ! ,absolute1 :i* is 9 "s s5se spiritual1 b does n consi/ ( s\ls1 or ( ?\ght & w z we "k !m4 ,& all ?is is e/abli%$ by ab/ract logical reason+ pr(ess+ to f9d self-contradictions 9 ! categories condemn$ z m]e appe>ance1 & to leave no t5able alt]native to ! k9d ( ,absolute :i* is f9ally affirm$ to be real4 ,"o brief example may suffice to illu/rate ,mr ,bradley's me?od4 ,! _w appe>s to be full ( _m ?+s ) v>i\s relations to ea* o!r--"r & left1 be=e & aft]1 fa!r & son1 & s on4 ,b relations1 accord+ to ,mr ,bradley1 are f\nd on exam9ation to be self-contradictory & !re=e impossible4 ,he fir/ argues t1 if !re are relations1 !re mu/ be qualities betwe5 :i* !y hold4 ,?is "p ( 8 argum5t ne$ n deta9 u4 ,he !n proce$s3 ,b h[ ! relation c /& to ! qualities is1 on ! o!r side1 un9telligible4 ,if x is no?+ to ! qualities1 !n !y are n relat$ at all2 &1 if s1 z we saw1 !y h ceas$ to be qualities1 & _! relation is a non5tity4 ,b if x is to be some?+ to !m1 !n cle>ly we %all require a new connect+ relation4 ,= ! relation h>dly c be ! m]e adjective ( "o or bo? ( its t]ms2 or1 at lea/1 z su* x seems indef5sible4 ,&1 be+ some?+ itself1 if x does n itself be> a relation to ! t]ms1 9 :at intelligible way w x succe$ 9 be+ any?+ to !m8 ,b "h aga9 we are hurri$ (f into ! eddy ( a hopeless process1 s9ce we are =c$ to g on f9d+ new relations )\t end4 ,! l9ks are unit$ by a l9k1 & ?is bond ( union is a l9k :i* also has two ends2 & ^! require ea* a fre% l9k to connect !m ) ! old4 ,! problem is to f9d h[ ! relation c /& to its qualities1 & ?is problem is insoluble4#d #d ,appe>ance & ,reality1 pp4 #cb-cc4 ,i d n propose to exam9e ?is argum5t 9 detail1 or to %[ ! exact po9ts :]e1 9 my op9ion1 x is fallaci\s4 ,i h quot$ x only z an example ( me?od4 ,mo/ p w admit1 ,i ?9k1 t x is calculat$ to produce bewild]m5t r ?an conviction1 because !re is m likelihood ( error 9 a v subtle1 ab/ract1 & difficult argum5t ?an 9 s pat5t a fact z ! int]relat$ness ( ! ?+s 9 ! _w4 ,to ! e>ly ,greeks1 to :om geometry 0 practically ! only kn[n sci5ce1 x 0 possible to foll[ reason+ ) ass5t ev5 :5 x l$ to ! /range/ conclusions4 ,b to u1 ) our me?ods ( exp]im5t & obs]vation1 our k ( ! long hi/ory ( a priori errors refut$ by empirical sci5ce1 x has become natural to suspect a fallacy 9 any d$uction ( :i* ! conclusion appe>s to contradict pat5t facts4 ,x is easy to c>ry su* suspicion too f>1 & x is v desirable1 if possible1 actually to discov] ! exact nature ( ! error :5 x exi/s4 ,b !re is no d\bt t :at we may call ! empirical outlook has become "p ( mo/ educat$ p's habit ( m9d2 & x is ?is1 r ?an any def9ite argum5t1 t has dim9i%$ ! hold ( ! classical tradition ^u /ud5ts ( philosophy & ! in/ruct$ public g5]ally4 ,! function ( logic 9 philosophy1 z ,i %all try to %[ at a lat] /age1 is all-important2 b ,i d n ?9k its function is t :i* x has 9 ! classical tradition4 ,9 t tradition1 logic becomes con/ructive ?r\gh negation4 ,:]e a numb] ( alt]natives seem1 at fir/ sight1 to be equally possible1 logic is made to condemn all ( !m except "o1 & t "o is !n pron\nc$ to be realis$ 9 ! actual _w4 ,?us ! _w is con/ruct$ by means ( logic1 ) little or no appeal to concrete exp]i5ce4 ,! true function ( logic is1 9 my op9ion1 exactly ! opposite ( ?is4 ,z appli$ to matt]s ( exp]i5ce1 x is analytic r ?an con/ructive2 tak5 a priori1 x %[s ! possibility ( hi!rto unsuspect$ alt]natives m (t5 ?an ! impossibility ( alt]natives :i* seem$ prima facie possible4 ,?us1 :ile x lib]ates imag9ation z to :at ! _w may be1 x refuses to legislate z to :at ! _w is4 ,?is *ange1 :i* has be5 br\ght ab\t by an int]nal revolution 9 logic1 has swept away ! ambiti\s con/ructions ( traditional metaphysics1 ev5 = ^? ^: fai? 9 logic is greate/2 :ile to ! _m :o reg>d logic z a *im]a ! p>adoxical sy/ems to :i* x has giv5 rise d n seem wor?y ev5 ( refutation4 ,?us on all sides ^! sy/ems h ceas$ to attract1 & ev5 ! philosophical _w t5ds m & m to pass !m by4 ,"o or two ( ! fav\rite doctr9es ( ! s*ool we are consid]+ may be m5tion$ to illu/rate ! nature ( its claims4 ,! univ]se1 x tells u1 is an organic unity1 l an animal or a p]fect "w ( art4 ,by ?is x means1 r\ghly speak+1 t all ! diff]5t p>ts fit toge!r & co-op]ate1 & are :at !y are because ( _! place 9 ! :ole4 ,?is belief is sometimes advanc$ dogmatically1 :ile at o!r times x is def5d$ by c]ta9 logical argum5ts4 ,if x is true1 e "p ( ! univ]se is a microcosm1 a m9iature reflection ( ! :ole4 ,if we knew ourselves ?or\ghly1 accord+ to ?is doctr9e1 we %\ld "k ev]y?+4 ,common s5se w\ld naturally object t !re are p--say 9 ,*9a--) :om our relations are s indirect & trivial t we _c inf] any?+ important z to !m f any fact ab\t ourselves4 ,if !re are liv+ be+s 9 ,m>s or 9 m di/ant p>ts ( ! univ]se1 ! same argum5t becomes ev5 /rong]4 ,b fur!r1 p]haps ! :ole cont5ts ( ! space & "t 9 :i* we live =m only "o ( _m univ]ses1 ea* seem+ to itself complete4 ,& ?us ! conception ( ! necess>y unity ( all t is resolves itself into ! pov]ty ( imag9ation1 & a fre] logic emancipates u f ! /rait-wai/coat$ b5evol5t in/itution :i* idealism palms (f z ! totality ( be+4 ,ano!r v important doctr9e held by mo/1 ?\gh n all1 ( ! s*ool we are exam9+ is ! doctr9e t all reality is :at is call$ m5tal or spiritual1 or t1 at any rate1 all reality is dep5d5t = its exi/5ce ^u :at is m5tal4 ,?is view is (t5 p>ticul>is$ into ! =m :i* /ates t ! relation ( kn[] & kn[n is fundam5tal1 & t no?+ c exi/ unless x ei!r kn[s or is kn[n4 ,"h aga9 ! same legislative function is ascrib$ to a priori argum5tation3 x is ?\ght t !re are contradictions 9 an unkn[n reality4 ,aga91 if ,i am n mi/ak51 ! argum5t is fallaci\s1 & a bett] logic w %[ t no limits c be set to ! ext5t & nature ( ! unkn[n4 ,& :5 ,i speak ( ! unkn[n1 ,i d n mean m]ely :at we p]sonally d n "k1 b :at is n kn[n to any m9d4 ,"h z else:]e1 :ile ! old] logic %ut out possibilities & imprison$ imag9ation )9 ! walls ( ! famili>1 ! new] logic %[s r :at may happ51 & refuses to decide z to :at mu/ happ54 ,! classical tradition 9 philosophy is ! la/ surviv+ *ild ( two v div]se p>5ts3 ! ,greek belief 9 reason1 & ! m$iaeval belief 9 ! tid9ess ( ! univ]se4 ,to ! s*oolm51 :o liv$ amid w>s1 massacres1 & pe/il5ces1 no?+ appe>$ s delightful z safety & ord]4 ,9 _! idealis+ dreams1 x 0 safety & ord] t !y s\ght3 ! univ]se ( ,?omas ,aqu9as or ,dante is z small & neat z a ,dut* int]ior4 ,to u1 to :om safety has become monotony1 to :om ! primeval savag]ies ( nature are s remote z to become a m]e pleas+ condim5t to our ord]$ r\t9e1 ! _w ( dreams is v diff]5t f :at x 0 amid ! w>s ( ,guelf & ,ghibell9e4 ,h5ce ,william ,james's prote/ aga9/ :at he calls ! block univ]se ( ! classical tradition2 h5ce ,nietzs*e's wor%ip ( =ce2 h5ce ! v]bal blood?ir/9ess ( _m quiet lit]>y m54 ,! b>b>ic sub/ratum ( human nature1 unsatisfi$ 9 action1 f9ds an outlet 9 imag9ation4 ,9 philosophy1 z else:]e1 ?is t5d5cy is visible2 & x is ?is1 r ?an =mal argum5t1 t has ?ru/ aside ! classical tradition = a philosophy :i* fancies itself m virile & m vital4 ,b4 ,evolutionism ,evolutionism1 9 "o =m or ano!r1 is ! prevail+ cre$ ( our "t4 ,x dom9ates our politics1 our lit]ature1 & n lea/ our philosophy4 ,nietzs*e1 pragmatism1 ,b]gson1 are phases 9 its philosophic developm5t1 & _! popul>ity f> beyond ! circles ( pr(essional philosoph]s %[s its consonance ) ! _s ( ! age4 ,x believes itself firmly bas$ on sci5ce1 a lib]ator ( hopes1 an inspir] ( an invigorat+ fai? 9 human p[]1 a sure antidote to ! ratioc9ative au?ority ( ! ,greeks & ! dogmatic au?ority ( m$iaeval sy/ems4 ,aga9/ s fa%ionable & s agreeable a cre$ x may seem useless to raise a prote/2 & ) mu* ( its _s e mod]n man mu/ be 9 sympa?y4 ,b ,i ?9k t1 9 ! intoxication ( a quick success1 mu* t is important & vital to a true und]/&+ ( ! univ]se has be5 =gott54 ,some?+ ( ,hell5ism mu/ be comb9$ ) ! new _s be=e x c em]ge f ! ard\r ( y\? into ! wisdom ( manhood4 ,& x is "t to rememb] t biology is nei!r ! only sci5ce1 nor yet ! model to :i* all o!r sci5ces mu/ adapt !mselves4 ,evolutionism1 z ,i %all try to %[1 is n a truly sci5tific philosophy1 ei!r 9 its me?od or 9 ! problems :i* x consid]s4 ,! true sci5tific philosophy is some?+ m ardu\s & m alo(1 appeal+ to less mundane hopes1 & requir+ a sev]] discipl9e = its successful practice4 ,d>w9's ,orig9 ( ,species p]suad$ ! _w t ! diff]5ce betwe5 diff]5t species ( animals & plants is n ! fix$1 immutable diff]5ce t x appe>s to be4 ,! doctr9e ( natural k9ds1 :i* _h r5d]$ classification easy & def9ite1 :i* 0 en%r9$ 9 ! ,ari/otelian tradition1 & protect$ by its suppos$ necessity = or?odox dogma1 0 sudd5ly swept away = ev] out ( ! biological _w4 ,! diff]5ce betwe5 man & ! l[] animals1 :i* to our human conceit appe>s enorm\s1 0 %[n to be a gradual a*ievem5t1 involv+ int]m$iate be+s :o c\ld n ) c]ta9ty be plac$ ei!r )9 or )\t ! human family4 ,! sun & planets _h already be5 %[n by ,laplace to be v probably d]iv$ f a primitive m or less undiff]5tiat$ nebula4 ,?us ! old fix$ l&m>ks became wav]+ & indi/9ct1 & all %>p outl9es 7 blurr$4 ,?+s & species lo/ _! b\nd>ies1 & none c\ld say :]e !y began or :]e !y end$4 ,b if human conceit 0 /agg]$ = a mom5t by its k9%ip ) ! ape1 x soon f\nd a way to reass]t itself1 & t way is ! philosophy ( evolution4 ,a process :i* l$ f ! amoeba to man appe>$ to ! philosoph]s to be obvi\sly a progress--?\gh :e!r ! amoeba w\ld agree ) ?is op9ion is n kn[n4 ,h5ce ! cycle ( *anges :i* sci5ce _h %[n to be ! probable hi/ory ( ! pa/ 0 welcom$ z reveal+ a law ( developm5t t[>ds good 9 ! univ]se--an evolution or unfold+ ( an ideal sl[ly embody+ itself 9 ! actual4 ,b su* a view1 ?\gh x might satisfy ,sp5c] & ^? :om we may call ,hegelian evolutioni/s1 c\ld n be accept$ z adequate by ! m :ole-he>t$ vot>ies ( *ange4 ,an ideal to :i* ! _w cont9u\sly approa*es is1 to ^! m9ds1 too dead & /atic to be inspir+4 ,n only ! aspirations1 b ! ideal too1 mu/ *ange & develop ) ! c\rse ( evolution2 !re mu/ be no fix$ goal1 b a cont9ual fa%ion+ ( fre% ne$s by ! impulse :i* is life & :i* alone gives unity to ! process4 ,ev] s9ce ! sev5te5? c5tury1 ^? :om ,william ,james describ$ z ! t5d]-m9d$ h be5 engag$ 9 a desp]ate /ruggle ) ! me*anical view ( ! c\rse ( nature :i* physical sci5ce seems to impose4 ,a great "p ( ! attractiv5ess ( ! classical tradition 0 due to ! p>tial escape f me*anism :i* x provid$4 ,b n[1 ) ! influ5ce ( biology1 ! t5d]-m9d$ believe t a m radical escape is possible1 sweep+ aside n m]ely ! laws ( physics1 b ! :ole app>5tly immutable app>atus ( logic1 ) its fix$ concepts1 its g5]al pr9ciples1 & its reason+s :i* seem able to compel ev5 ! mo/ unwill+ ass5t4 ,! old] k9d ( teleology1 !re=e1 :i* reg>d$ ! ,end z a fix$ goal1 already p>tially visible1 t[>ds :i* we 7 gradually approa*+1 is reject$ by ,m4 ,b]gson z n all[+ en\gh = ! absolute dom9ion ( *ange4 ,aft] expla9+ :y he does n accept me*anism1 he proce$s3#e ,b radical f9alism is q z unacceptable1 & = ! same reason4 ,! doctr9e ( teleology1 9 its extreme =m1 z we f9d x 9 ,leibniz = example1 implies t ?+s & be+s m]ely realise a programme previ\sly arrang$4 ,b if !re is no?+ un=ese51 no inv5tion or creation 9 ! univ]se1 "t is useless aga94 ,z 9 ! me*ani/ic hypo!sis1 "h aga9 x is suppos$ t all is giv54 ,f9alism ?us und]/ood is only inv]t$ me*anism4 ,x spr+s f ! same po/ulate1 ) ?is sole diff]5ce1 t 9 ! movem5t ( our f9ite intellects along successive ?+s1 ^: successiv5ess is r$uc$ to a m]e appe>ance1 x holds 9 front ( u ! light ) :i* x claims to guide u1 in/ead ( putt+ x beh9d4 ,x sub/itutes ! attraction ( ! future = ! impulsion ( ! pa/4 ,b succession rema9s none ! less a m]e appe>ance1 z inde$ does movem5t itself4 ,9 ! doctr9e ( ,leibniz1 "t is r$uc$ to a confus$ p]ception1 relative to ! human /&po9t1 a p]ception :i* w\ld vani%1 l a ris+ mi/1 = a m9d seat$ at ! c5tre ( ?+s4 ,yet f9alism is n1 l me*anism1 a doctr9e ) fix$ rigid outl9es4 ,x admits ( z _m inflections z we l4 ,! me*ani/ic philosophy is to be tak5 or left3 x mu/ be left if ! lea/ gra9 ( du/1 by /ray+ f ! pa? =ese5 by me*anics1 %\ld %[ ! slighte/ trace ( spontaneity4 ,! doctr9e ( f9al causes1 on ! contr>y1 w nev] be def9itively refut$4 ,if "o =m ( x be put aside1 x w take ano!r4 ,its pr9ciple1 :i* is ess5tially psy*ological1 is v flexible4 ,x is s ext5sible1 & !reby s compreh5sive1 t "o accepts some?+ ( x z soon z "o rejects pure me*anism4 ,! !ory we %all put =w>d 9 ?is book w !re=e necess>ily p>take ( f9alism to a c]ta9 ext5t4 #e ,creative ,evolution1 ,engli% translation1 p4 #da4 ,m4 ,b]gson's =m ( f9alism dep5ds ^u 8 conception ( life4 ,life1 9 8 philosophy1 is a cont9u\s /ream1 9 :i* all divisions are artificial & unreal4 ,sep>ate ?+s1 beg9n+s & end+s1 are m]e conv5i5t fictions3 !re is only smoo?1 unbrok5 transition4 ,! beliefs ( to-day may c\nt z true to-day1 if !y c>ry u along ! /ream2 b to-morr[ !y w be false1 & mu/ be replac$ by new beliefs to meet ! new situation4 ,all our ?9k+ consi/s ( conv5i5t fictions1 imag9>y congeal+s ( ! /ream3 reality fl[s on 9 spite ( all our fictions1 & ?\gh x c be liv$1 x _c be conceiv$ 9 ?\ght4 ,someh[1 )\t explicit /atem5t1 ! assurance is slipp$ 9 t ! future1 ?\gh we _c =esee x1 w be bett] ?an ! pa/ or ! pres5t3 ! read] is l ! *ild :o expects a sweet because x has be5 told to op5 its m\? & %ut its eyes4 ,logic1 ma!matics1 physics disappe> 9 ?is philosophy1 because !y are too /atic2 :at is real is an impulse & movem5t t[>ds a goal :i*1 l ! ra9b[1 rec$es z we advance1 & makes e place diff]5t :5 we rea* x f :at x appe>$ to be at a di/ance4 ,n[ ,i d n propose at pres5t to ent] ^u a te*nical exam9ation ( ?is philosophy4 ,at pres5t ,i wi% to make only two criticisms ( x--fir/1 t its tru? does n foll[ f :at sci5ce has r5d]$ probable conc]n+ ! facts ( evolution1 & secondly1 t ! motives & int]e/s :i* inspire x are s exclusively practical1 & ! problems ) :i* x deals are s special1 t x c h>dly be reg>d$ z really t\*+ any ( ! que/ions t to my m9d con/itute g5u9e philosophy4 7#a7 ,:at biology has r5d]$ probable is t ! div]se species arose by adaptation f a less diff]5tiat$ ance/ry4 ,?is fact is 9 itself exce$+ly int]e/+1 b x is n ! k9d ( fact f :i* philosophical consequ5ces foll[4 ,philosophy is g5]al1 & takes an imp>tial int]e/ 9 all t exi/s4 ,! *anges suff]$ by m9ute portions ( matt] on ! e>?'s surface are v important to u z active s5ti5t be+s2 b to u z philosoph]s !y h no great] int]e/ ?an o!r *anges 9 portions ( matt] else:]e4 ,& if ! *anges on ! e>?'s surface dur+ ! la/ few millions ( ye>s appe> to our pres5t e?ical notions to be 9 ! nature ( a progress1 t gives no gr\nd = believ+ t progress is a g5]al law ( ! univ]se4 ,except "u ! influ5ce ( desire1 no "o w\ld admit = a mom5t s crude a g5]alisation f su* a t9y selection ( facts4 ,:at does result1 n specially f biology1 b f all ! sci5ces :i* deal ) :at exi/s1 is t we _c und]/& ! _w unless we c und]/& *ange & cont9uity4 ,?is is ev5 m evid5t 9 physics ?an x is 9 biology4 ,b ! analysis ( *ange & cont9uity is n a problem ^u :i* ei!r physics or biology ?r[s any light3 x is a problem ( a new k9d1 belong+ to a diff]5t k9d ( /udy4 ,! "q :e!r evolutionism (f]s a true or a false answ] to ?is problem is n1 !re=e1 a "q to be solv$ by appeals to p>ticul> facts1 su* z biology & physics reveal4 ,9 assum+ dogmatically a c]ta9 answ] to ?is "q1 evolutionism ceases to be sci5tific1 yet x is only 9 t\*+ on ?is "q t evolutionism rea*es ! subject-matt] ( philosophy4 ,evolutionism ?us consi/s ( two p>ts3 "o n philosophical1 b only a ha/y g5]alisation ( ! k9d :i* ! special sci5ces might h]eaft] confirm or confute2 ! o!r n sci5tific1 b a m]e unsupport$ dogma1 belong+ to philosophy by its subject-matt]1 b 9 no way d$ucible f ! facts ^u :i* evolution relies4 7#b7 ,! pr$om9ant int]e/ ( evolutionism is 9 ! "q ( human de/9y1 or at lea/ ( ! de/9y ( ,life4 ,x is m int]e/$ 9 morality & happ9ess ?an 9 k = its own sake4 ,x mu/ be admitt$ t ! same may be said ( _m o!r philosophies1 & t a desire = ! k9d ( k :i* philosophy really c give is v r>e4 ,b if philosophy is to become sci5tific--& x is our object to discov] h[ ?is c be a*iev$--x is necess>y fir/ & =emo/ t philosoph]s %\ld acquire ! dis9t]e/$ intellectual curiosity :i* *>act]ises ! g5u9e man ( sci5ce4 ,k conc]n+ ! future--:i* is ! k9d ( k t mu/ be s\ght if we are to "k ab\t human de/9y--is possible )9 c]ta9 n>r[ limits4 ,x is impossible to say h[ mu* ! limits may be enl>g$ ) ! progress ( sci5ce4 ,b :at is evid5t is t any proposition ab\t ! future belongs by its subject-matt] to "s p>ticul> sci5ce1 & is to be asc]ta9$1 if at all1 by ! me?ods ( t sci5ce4 ,philosophy is n a %ort cut to ! same k9d ( results z ^? ( ! o!r sci5ces3 if x is to be a g5u9e /udy1 x mu/ h a prov9ce ( its own1 & aim at results :i* ! o!r sci5ces c nei!r prove nor disprove4 ,! consid]ation t philosophy1 if !re is su* a /udy1 mu/ consi/ ( propositions :i* c\ld n occur 9 ! o!r sci5ces1 is "o :i* has v f>-rea*+ consequ5ces4 ,all ! que/ions :i* h :at is call$ a human int]e/--su*1 = example1 z ! "q ( a future life--belong1 at lea/ 9 !ory1 to special sci5ces1 & are capable1 at lea/ 9 !ory1 ( be+ decid$ by empirical evid5ce4 ,philosoph]s h too (t51 9 ! pa/1 p]mitt$ !mselves to pron\nce on empirical que/ions1 & f\nd !mselves1 z a result1 9 disa/r\s conflict ) well-atte/$ facts4 ,we mu/1 !re=e1 r5\nce ! hope t philosophy c promise satisfaction to our mundane desires4 ,:at x c d1 :5 x is purifi$ f all practical ta9t1 is to help u to und]/& ! g5]al aspects ( ! _w & ! logical analysis ( famili> b complex ?+s4 ,?r\gh ?is a*ievem5t1 by ! sugge/ion ( fruitful hypo!ses1 x may be indirectly useful 9 o!r sci5ces1 notably ma!matics1 physics1 & psy*ology4 ,b a g5u9ely sci5tific philosophy _c hope to appeal to any except ^? :o h ! wi% to und]/&1 to escape f intellectual bewild]m5t4 ,x (f]s1 9 its own doma91 ! k9d ( satisfaction :i* ! o!r sci5ces (f]4 ,b x does n (f]1 or attempt to (f]1 a solution ( ! problem ( human de/9y1 or ( ! de/9y ( ! univ]se4 ,evolutionism1 if :at has be5 said is true1 is to be reg>d$ z a ha/y g5]alisation f c]ta9 r special facts1 accompani$ by a dogmatic rejection ( all attempts at analysis1 & inspir$ by int]e/s :i* are practical r ?an !oretical4 ,9 spite1 !re=e1 ( its appeal to detail$ results 9 v>i\s sci5ces1 x _c be reg>d$ z any m g5u9ely sci5tific ?an ! classical tradition :i* x has replac$4 ,h[ philosophy is to be r5d]$ sci5tific1 & :at is ! true subject-matt] ( philosophy1 ,i %all try to %[ fir/ by examples ( c]ta9 a*iev$ results1 & !n m g5]ally4 ,we w beg9 ) ! problem ( ! physical conceptions ( space & "t & matt]1 :i*1 z we h se51 are *all5g$ by ! cont5tions ( ! evolutioni/s4 ,t ^! conceptions /& 9 ne$ ( recon/ruction w be admitt$1 & is inde$ increas+ly urg$ by physici/s !mselves4 ,x w also be admitt$ t ! recon/ruction mu/ take m acc\nt ( *ange & ! univ]sal flux ?an is done 9 ! old] me*anics ) its fundam5tal conception ( an inde/ructible matt]4 ,b ,i d n ?9k ! recon/ruction requir$ is on ,b]gsonian l9es1 nor d ,i ?9k t 8 rejection ( logic c be any?+ b h>mful4 ,i %all n1 h[ev]1 adopt ! me?od ( explicit controv]sy1 b r ! me?od ( indep5d5t inquiry1 />t+ f :at1 9 a pre-philosophic /age1 appe> to be facts1 & keep+ always z close to ^! initial data z ! requirem5ts ( consi/5cy w p]mit4 ,al?\gh explicit controv]sy is almo/ always fruitless 9 philosophy1 ow+ to ! fact t no two philosoph]s ev] und]/& "o ano!r1 yet x seems necess>y to say some?+ at ! outset 9 ju/ification ( ! sci5tific z aga9/ ! my/ical attitude4 ,metaphysics1 f ! fir/1 has be5 develop$ by ! union or ! conflict ( ^! two attitudes4 ,among ! e>lie/ ,greek philosoph]s1 ! ,ionians 7 m sci5tific & ! ,sicilians m my/ical4#f ,b among ! latt]1 ,py?agoras1 = example1 0 9 himself a curi\s mixture ( ! two t5d5cies3 ! sci5tific attitude l$ him to 8 proposition on "r-angl$ triangles1 :ile 8 my/ic insight %[$ him t x is wick$ to eat beans4 ,naturally en\gh1 8 foll[]s divid$ into two sects1 ! lov]s ( "r-angl$ triangles & ! abhorr]s ( beans2 b ! =m] sect di$ out1 leav+1 h[ev]1 a haunt+ flav\r ( my/icism ov] mu* ,greek ma!matical speculation1 & 9 p>ticul> ov] ,plato's views on ma!matics4 ,plato1 ( c\rse1 embodies bo? ! sci5tific & ! my/ical attitudes 9 a high] =m ?an 8 pr$ecessors1 b ! my/ical attitude is di/9ctly ! /rong] ( ! two1 & secures ultimate victory :5ev] ! conflict is %>p4 ,plato1 moreov]1 adopt$ f ! ,eleatics ! device ( us+ logic to defeat common s5se1 & ?us to leave ! field cle> = my/icism--a device /ill employ$ 9 our own day by ! adh]5ts ( ! classical tradition4 #f ,cf4 ,burnet1 ,e>ly ,greek ,philosophy1 pp4 #he ff4 ,! logic us$ 9 def5ce ( my/icism seems to me faulty z logic1 & 9 a lat] lecture ,i %all criticise x on ?is gr\nd4 ,b ! m ?or\gh-go+ my/ics d n employ logic1 :i* !y despise3 !y appeal in/ead directly to ! imm$iate deliv]ance ( _! insight4 ,n[1 al?\gh fully develop$ my/icism is r>e 9 ! ,we/1 "s t9cture ( x col\rs ! ?\ghts ( _m p1 p>ticul>ly z reg>ds matt]s on :i* !y h /rong convictions n bas$ on evid5ce4 ,9 all :o seek passionately = ! fugitive & difficult goods1 ! conviction is almo/ irresi/ible t !re is 9 ! _w some?+ deep]1 m significant1 ?an ! multiplicity ( little facts *ronicl$ & classifi$ by sci5ce4 ,beh9d ! veil ( ^! mundane ?+s1 !y feel1 some?+ q diff]5t obscurely %imm]s1 %9+ =? cle>ly 9 ! great mom5ts ( illum9ation1 :i* alone give any?+ wor?y to be call$ real k ( tru?4 ,to seek su* mom5ts1 !re=e1 is to !m ! way ( wisdom1 r ?an1 l ! man ( sci5ce1 to obs]ve coolly1 to analyse )\t emotion1 & to accept )\t "q ! equal reality ( ! trivial & ! important4 ,( ! reality or unreality ( ! my/ic's _w ,i "k no?+4 ,i h no wi% to d5y x1 nor ev5 to decl>e t ! insight :i* reveals x is n a g5u9e insight4 ,:at ,i d wi% to ma9ta9--& x is "h t ! sci5tific attitude becomes imp]ative--is t insight1 unte/$ & unsupport$1 is an insuffici5t gu>antee ( tru?1 9 spite ( ! fact t mu* ( ! mo/ important tru? is fir/ sugge/$ by its means4 ,x is common to speak ( an opposition betwe5 in/9ct & reason2 9 ! eighte5? c5tury1 ! opposition 0 drawn 9 fav\r ( reason1 b "u ! influ5ce ( ,r\sseau & ! romantic movem5t in/9ct 0 giv5 ! pref]5ce1 fir/ by ^? :o rebell$ aga9/ artificial =ms ( gov]nm5t & ?\ght1 & !n1 z ! purely rationali/ic def5ce ( traditional !ology became increas+ly difficult1 by all :o felt 9 sci5ce a m5ace to cre$s :i* !y associat$ ) a spiritual outlook on life & ! _w4 ,b]gson1 "u ! "n ( intuition1 has rais$ in/9ct to ! position ( sole arbit] ( metaphysical tru?4 ,b 9 fact ! opposition ( in/9ct & reason is ma9ly illusory4 ,in/9ct1 intuition1 or insight is :at fir/ leads to ! beliefs :i* subsequ5t reason confirms or confutes2 b ! confirmation1 :]e x is possible1 consi/s1 9 ! la/ analysis1 ( agreem5t ) o!r beliefs no less in/9ctive4 ,reason is a h>monis+1 controll+ =ce r ?an a creative "o4 ,ev5 9 ! mo/ purely logical realms1 x is insight t fir/ arrives at :at is new4 ,:]e in/9ct & reason d sometimes conflict is 9 reg>d to s+le beliefs1 held in/9ctively1 & held ) su* det]m9ation t no degree ( inconsi/5cy ) o!r beliefs leads to _! ab&onm5t4 ,in/9ct1 l all human faculties1 is liable to error4 ,^? 9 :om reason is weak are (t5 unwill+ to admit ?is z reg>ds !mselves1 ?\gh all admit x 9 reg>d to o!rs4 ,:]e in/9ct is lea/ liable to error is 9 practical matt]s z to :i* "r judgm5t is a help to survival2 fri5d%ip & ho/ility 9 o!rs1 = in/ance1 are (t5 felt ) extraord9>y discrim9ation ?r\gh v c>eful disguises4 ,b ev5 9 su* matt]s a wrong impression may be giv5 by res]ve or flatt]y2 & 9 matt]s less directly practical1 su* z philosophy deals )1 v /rong in/9ctive beliefs may be :olly mi/ak51 z we may come to "k ?r\gh _! p]ceiv$ inconsi/5cy ) o!r equally /rong beliefs4 ,x is su* consid]ations t necessitate ! h>monis+ m$iation ( reason1 :i* te/s our beliefs by _! mutual compatibility1 & exam9es1 9 d\btful cases1 ! possible s\rces ( error on ! "o side & on ! o!r4 ,9 ?is !re is no opposition to in/9ct z a :ole1 b only to bl9d reliance ^u "s "o int]e/+ aspect ( in/9ct to ! exclusion ( o!r m commonplace b n less tru/wor?y aspects4 ,x is su* onesid$ness1 n in/9ct itself1 t reason aims at correct+4 ,^! m or less trite maxims may be illu/rat$ by application to ,b]gson's advocacy ( intuition z aga9/ intellect4 ,!re are1 he says1 two pr(\ndly diff]5t ways ( kn[+ a ?+4 ,! fir/ implies t we move r\nd ! object2 ! second t we ent] into x4 ,! fir/ dep5ds on ! po9t ( view at :i* we are plac$ & on ! symbols by :i* we express ourselves4 ,! second nei!r dep5ds on a po9t ( view nor relies on any symbol4 ,! fir/ k9d ( k may be said to /op at ! relative2 ! second1 9 ^? cases :]e x is possible1 to atta9 ! absolute4#g ,! second ( ^!1 :i* is intuition1 is1 he says1 ! k9d ( intellectual sympa?y by :i* "o places oneself )9 an object 9 ord] to co9cide ) :at is unique 9 x & !re=e inexpressible 7p4 #f74 ,9 illu/ration1 he m5tions self-k3 !re is "o reality1 at lea/1 :i* we all seize f )91 by intuition & n by simple analysis4 ,x is our own p]sonality 9 its fl[+ ?r\gh "t--our self :i* endures 7p4 #h74 ,! re/ ( ,b]gson's philosophy consi/s 9 report+1 ?r\gh ! imp]fect m$ium ( words1 ! k ga9$ by intuition1 & ! consequ5t complete condemnation ( all ! pret5d$ k d]iv$ f sci5ce & common s5se4 #g ,introduction to ,metaphysics1 p4 #a4 ,?is proc$ure1 s9ce x takes sides 9 a conflict ( in/9ctive beliefs1 /&s 9 ne$ ( ju/ification by prov+ ! great] tru/wor?9ess ( ! beliefs on "o side ?an ( ^? on ! o!r4 ,b]gson attempts ?is ju/ification 9 two ways--fir/1 by expla9+ t intellect is a purely practical faculty design$ to secure biological success2 secondly1 by m5tion+ rem>kable feats ( in/9ct 9 animals1 & by po9t+ out *>act]i/ics ( ! _w :i*1 ?\gh intuition c appreh5d !m1 are baffl+ to intellect z he int]prets x4 ,( ,b]gson's !ory t intellect is a purely practical faculty develop$ 9 ! /ruggle = survival1 & n a s\rce ( true beliefs1 we may say1 fir/1 t x is only ?r\gh intellect t we "k ( ! /ruggle = survival & ( ! biological ance/ry ( man3 if ! intellect is mislead+1 ! :ole ( ?is m]ely inf]r$ hi/ory is presumably untrue4 ,if1 on ! o!r h&1 we agree ) ,m4 ,b]gson 9 ?9k+ t evolution took place z ,d>w9 believ$1 !n x is n only intellect1 b all our faculties1 t h be5 develop$ "u ! /ress ( practical utility4 ,intuition is se5 at its be/ :]e x is directly useful--= example1 9 reg>d to o!r p's *>act]s & dispositions4 ,b]gson app>5tly holds t capacity = ?is k9d ( k is less explicable by ! /ruggle = exi/5ce ?an1 = example1 capacity = pure ma!matics4 ,yet ! savage deceiv$ by false fri5d%ip is likely to pay = 8 mi/ake ) 8 life2 :]eas ev5 9 ! mo/ civilis$ societies m5 are n put to dea? = ma!matical incompet5ce4 ,all ! mo/ /rik+ ( 8 in/ances ( intuition 9 animals h a v direct survival value4 ,! fact is1 ( c\rse1 t bo? intuition & intellect h be5 develop$ because !y are useful1 & t1 speak+ broadly1 !y are useful :5 !y give tru? & become h>mful :5 !y give falsehood4 ,intellect1 9 civilis$ man1 l arti/ic capacity1 has occasionally be5 develop$ beyond ! po9t :]e x is useful to ! individual2 intuition1 on ! o!r h&1 seems on ! :ole to dim9i% z civilisation increases4 ,speak+ broadly1 x is great] 9 *ildr5 ?an 9 adults1 9 ! un$ucat$ ?an 9 ! educat$4 ,probably 9 dogs x exce$s any?+ to be f\nd 9 human be+s4 ,b ^? :o f9d 9 ^! facts a recomm5dation ( intuition ought to return to runn+ wild 9 ! woods1 dye+ !mselves ) woad & liv+ on hips & haws4 ,let u next exam9e :e!r intuition possesses any su* infallibility z ,b]gson claims = x4 ,! be/ in/ance ( x1 accord+ to him1 is our acqua9tance ) ourselves2 yet self-k is prov]bially r>e & difficult4 ,mo/ m51 = example1 h 9 _! nature meannesses1 vanities1 & envies ( :i* !y are q unconsci\s1 ?\gh ev5 _! be/ fri5ds c p]ceive !m )\t any difficulty4 ,x is true t intuition has a conv9c+ness :i* is lack+ to intellect3 :ile x is pres5t1 x is almo/ impossible to d\bt its tru?4 ,b if x %\ld appe>1 on exam9ation1 to be at lea/ z fallible z intellect1 its great] subjective c]ta9ty becomes a dem]it1 mak+ x only ! m irresi/ibly deceptive4 ,ap>t f self-k1 "o ( ! mo/ notable examples ( intuition is ! k p believe !mselves to possess ( ^? ) :om !y are 9 love3 ! wall betwe5 diff]5t p]sonalities seems to become transp>5t1 & p ?9k !y see into ano!r s\l z into _! own4 ,yet deception 9 su* cases is con/antly practis$ ) success2 & ev5 :]e !re is no int5tional deception1 exp]i5ce gradually proves1 z a rule1 t ! suppos$ insight 0 illusory1 & t ! sl[]1 m grop+ me?ods ( ! intellect are 9 ! long run m reliable4 ,b]gson ma9ta9s t intellect c only deal ) ?+s 9 s f> z !y resemble :at has be5 exp]i5c$ 9 ! pa/1 :ile intuition has ! p[] ( appreh5d+ ! uniqu5ess & novelty t always belong to ea* fre% mom5t4 ,t !re is some?+ unique & new at e mom5t1 is c]ta9ly true2 x is also true t ?is _c be fully express$ by means ( intellectual concepts4 ,only direct acqua9tance c give k ( :at is unique & new4 ,b direct acqua9tance ( ?is k9d is giv5 fully 9 s5sation1 & does n require1 s f> z ,i c see1 any special faculty ( intuition = its appreh5sion4 ,x is nei!r intellect nor intuition1 b s5sation1 t supplies new data2 b :5 ! data are new 9 any rem>kable mann]1 intellect is mu* m capable ( deal+ ) !m ?an intuition w\ld be4 ,! h5 ) a brood ( duckl+s no d\bt has intuitions :i* seem to place h] inside !m1 & n m]ely to "k !m analytically2 b :5 ! duckl+s take to ! wat]1 ! :ole app>5t intuition is se5 to be illusory1 & ! h5 is left helpless on ! %ore4 ,intuition1 9 fact1 is an aspect & developm5t ( in/9ct1 &1 l all in/9ct1 is admirable 9 ^? cu/om>y surr\nd+s :i* h m\ld$ ! habits ( ! animal 9 "q1 b totally incompet5t z soon z ! surr\nd+s are *ang$ 9 a way :i* dem&s "s non-habitual mode ( action4 ,! !oretical und]/&+ ( ! _w1 :i* is ! aim ( philosophy1 is n a matt] ( great practical importance to animals1 or to savages1 or ev5 to mo/ civilis$ m54 ,x is h>dly to be suppos$1 !re=e1 t ! rapid1 r\gh & ready me?ods ( in/9ct or intuition w f9d 9 ?is field a fav\rable gr\nd = _! application4 ,x is ! old] k9ds ( activity1 :i* br+ out our k9%ip ) remote g5]ations ( animal & semi-human ance/ors1 t %[ intuition at its be/4 ,9 su* matt]s z self-pres]vation & love1 intuition w act sometimes 7?\gh n always7 ) a swiftness & precision :i* are a/oni%+ to ! critical intellect4 ,b philosophy is n "o ( ! pursuits :i* illu/rate our aff9ity ) ! pa/3 x is a highly ref9$1 highly civilis$ pursuit1 dem&+1 = its success1 a c]ta9 lib]ation f ! life ( in/9ct1 & ev51 at times1 a c]ta9 alo(ness f all mundane hopes & fe>s4 ,x is n 9 philosophy1 !re=e1 t we c hope to see intuition at its be/4 ,on ! contr>y1 s9ce ! true objects ( philosophy1 & ! habits ( ?\ght dem&$ = _! appreh5sion1 are /range1 unusual1 & remote1 x is "h1 m almo/ ?an any:]e else1 t intellect proves sup]ior to intuition1 & t quick unanalys$ convictions are lea/ des]v+ ( uncritical acceptance4 ,be=e emb>k+ ^u ! some:at difficult & ab/ract discussions :i* lie be=e u1 x w be well to take a survey ( ! hopes we may reta9 & ! hopes we mu/ ab&on4 ,! hope ( satisfaction to our m human desires--! hope ( demon/rat+ t ! _w has ?is or t desirable e?ical *>act]i/ic--is n "o :i*1 s f> z ,i c see1 philosophy c d any?+ :atev] to satisfy4 ,! diff]5ce betwe5 a good _w & a bad "o is a diff]5ce 9 ! p>ticul> *>act]i/ics ( ! p>ticul> ?+s t exi/ 9 ^! worlds3 x is n a suffici5tly ab/ract diff]5ce to come )9 ! prov9ce ( philosophy4 ,love & hate1 = example1 are e?ical opposites1 b to philosophy !y are closely analog\s attitudes t[>ds objects4 ,! g5]al =m & /ructure ( ^? attitudes t[>ds objects :i* con/itute m5tal ph5om5a is a problem = philosophy2 b ! diff]5ce betwe5 love & hate is n a diff]5ce ( =m or /ructure1 & !re=e belongs r to ! special sci5ce ( psy*ology ?an to philosophy4 ,?us ! e?ical int]e/s :i* h (t5 inspir$ philosoph]s mu/ rema9 9 ! backgr\nd3 "s k9d ( e?ical int]e/ may inspire ! :ole /udy1 b none mu/ obtrude 9 ! detail or be expect$ 9 ! special results :i* are s\ght4 ,if ?is view seems at fir/ sight disappo9t+1 we may rem9d ourselves t a simil> *ange has be5 f\nd necess>y 9 all ! o!r sci5ces4 ,! physici/ or *emi/ is n n[ requir$ to prove ! e?ical importance ( 8 ions or atoms2 ! biologi/ is n expect$ to prove ! utility ( ! plants or animals :i* he dissects4 ,9 pre-sci5tific ages ?is 0 n ! case4 ,a/ronomy1 = example1 0 /udi$ because m5 believ$ 9 a/rology3 x 0 ?\ght t ! movem5ts ( ! planets _h ! mo/ direct & important be>+ ^u ! lives ( human be+s4 ,presumably1 :5 ?is belief decay$ & ! dis9t]e/$ /udy ( a/ronomy began1 _m :o _h f\nd a/rology absorb+ly int]e/+ decid$ t a/ronomy _h too little human int]e/ to be wor?y ( /udy4 ,physics1 z x appe>s 9 ,plato's ,timaeus = example1 is full ( e?ical notions3 x is an ess5tial "p ( its purpose to %[ t ! e>? is wor?y ( admiration4 ,! mod]n physici/1 on ! contr>y1 ?\gh he has no wi% to d5y t ! e>? is admirable1 is n conc]n$1 z physici/1 ) its e?ical attributes3 he is m]ely conc]n$ to f9d out facts1 n to consid] :e!r !y are good or bad4 ,9 psy*ology1 ! sci5tific attitude is ev5 m rec5t & m difficult ?an 9 ! physical sci5ces3 x is natural to consid] t human nature is ei!r good or bad1 & to suppose t ! diff]5ce betwe5 good & bad1 s all-important 9 practice1 mu/ be important 9 !ory also4 ,x is only dur+ ! la/ c5tury t an e?ically neutral sci5ce ( psy*ology has gr[n up2 & "h too e?ical neutrality has be5 ess5tial to sci5tific success4 ,9 philosophy1 hi!rto1 e?ical neutrality has be5 seldom s\ght & h>dly ev] a*iev$4 ,m5 h rememb]$ _! wi%es1 & h judg$ philosophies 9 relation to _! wi%es4 ,driv5 f ! p>ticul> sci5ces1 ! belief t ! notions ( good & evil mu/ af=d a key to ! und]/&+ ( ! _w has s\ght a refuge 9 philosophy4 ,b ev5 f ?is la/ refuge1 if philosophy is n to rema9 a set ( pleas+ dreams1 ?is belief mu/ be driv5 =?4 ,x is a commonplace t happ9ess is n be/ a*iev$ by ^? :o seek x directly2 & x w\ld seem t ! same is true ( ! good4 ,9 ?\ght1 at any rate1 ^? :o =get good & evil & seek only to "k ! facts are m likely to a*ieve good ?an ^? :o view ! _w ?r\gh ! di/ort+ m$ium ( _! own desires4 ,! imm5se ext5sion ( our k ( facts 9 rec5t times has _h1 z x _h 9 ! ,r5aissance1 two effects ^u ! g5]al intellectual outlook4 ,on ! "o h&1 x has made m5 di/ru/ful ( ! tru? ( wide1 ambiti\s sy/ems3 !ories come & g swiftly1 ea* s]v+1 = a mom5t1 to classify kn[n facts & promote ! se>* = new ones1 b ea* 9 turn prov+ inadequate to deal ) ! new facts :5 !y h be5 f\nd4 ,ev5 ^? :o inv5t ! !ories d n1 9 sci5ce1 reg>d !m z any?+ b a tempor>y make%ift4 ,! ideal ( an all-embrac+ syn!sis1 su* z ! ,middle ,ages believ$ !mselves to h atta9$1 rec$es fur!r & fur!r beyond ! limits ( :at seems feasible4 ,9 su* a _w1 z 9 ! _w ( ,montaigne1 no?+ seems wor? :ile except ! discov]y ( m & m facts1 ea* 9 turn ! dea?bl[ to "s *]i%$ !ory2 ! ord]+ intellect gr[s we>y1 & becomes slov5ly ?r\gh despair4 ,on ! o!r h&1 ! new facts h br\ght new p[]s2 man's physical control ov] natural =ces has be5 increas+ ) unexampl$ rapidity1 & promises to increase 9 ! future beyond all easily assignable limits4 ,?us alongside ( despair z reg>ds ultimate !ory !re is an imm5se optimism z reg>ds practice3 :at man c d seems almo/ b\ndless4 ,! old fix$ limits ( human p[]1 su* z dea?1 or ! dep5d5ce ( ! race on an equilibrium ( cosmic =ces1 are =gott51 & no h>d facts are all[$ to break 9 ^u ! dream ( omnipot5ce4 ,no philosophy is tol]at$ :i* sets b\nds to man's capacity ( gratify+ 8 wi%es2 & ?us ! v despair ( !ory is invok$ to sil5ce e :isp] ( d\bt z reg>ds ! possibilities ( practical a*ievem5t4 ,9 ! welcom+ ( new fact1 & 9 ! suspicion ( dogmatism z reg>ds ! univ]se at l>ge1 ! mod]n _s %\ld1 ,i ?9k1 be accept$ z :olly an advance4 ,b bo? 9 its practical pret5sions & 9 its !oretical despair x seems to me to g too f>4 ,mo/ ( :at is greate/ 9 man is call$ =? 9 response to ! ?w>t+ ( 8 hopes by immutable natural ob/acles2 by ! pret5ce ( omnipot5ce1 he becomes trivial & a little absurd4 ,& on ! !oretical side1 ultimate metaphysical tru?1 ?\gh less all-embrac+ & h>d] ( atta9m5t ?an x appe>$ to "s philosoph]s 9 ! pa/1 c1 ,i believe1 be discov]$ by ^? :o are will+ to comb9e ! hopefulness1 pati5ce1 & op5-m9d$ness ( sci5ce ) some?+ ( ! ,greek feel+ = beauty 9 ! ab/ract _w ( logic & = ! ultimate intr9sic value 9 ! contemplation ( tru?4 ,! philosophy1 !re=e1 :i* is to be g5u9ely inspir$ by ! sci5tific _s1 mu/ deal ) some:at dry & ab/ract matt]s1 & mu/ n hope to f9d an answ] to ! practical problems ( life4 ,to ^? :o wi% to und]/& mu* ( :at has 9 ! pa/ be5 mo/ difficult & obscure 9 ! con/itution ( ! univ]se1 x has great rew>ds to (f]--triumphs z notewor?y z ^? ( ,newton & ,d>w91 & z important 9 ! long run1 = ! m\ld+ ( our m5tal habits4 ,& x br+s ) x--z a new & p[]ful me?od ( inve/igation always does--a s5se ( p[] & a hope ( progress m reliable & bett] gr\nd$ ?an any t re/s on ha/y & fallaci\s g5]alisation z to ! nature ( ! univ]se at l>ge4 ,_m hopes :i* inspir$ philosoph]s 9 ! pa/ x _c claim to fulfil2 b o!r hopes1 m purely intellectual1 x c satisfy m fully ?an =m] ages c\ld h deem$ possible = human m9ds4 ,,lecture ,,ii ,,logic ,,z ,,! ,,ess5ce ,,( ,,philosophy ,! topics we discuss$ 9 our fir/ lecture1 & ! topics we %all discuss lat]1 all r$uce !mselves1 9 s f> z !y are g5u9ely philosophical1 to problems ( logic4 ,?is is n due to any accid5t1 b to ! fact t e philosophical problem1 :5 x is subject$ to ! necess>y analysis & purification1 is f\nd ei!r to be n really philosophical at all1 or else to be1 9 ! s5se 9 :i* we are us+ ! ^w1 logical4 ,b z ! ^w logic is nev] us$ 9 ! same s5se by two diff]5t philosoph]s1 "s explanation ( :at ,i mean by ! ^w is indisp5sable at ! outset4 ,logic1 9 ! ,middle ,ages1 & d[n to ! pres5t day 9 tea*+1 meant no m ?an a s*ola/ic collection ( te*nical t]ms & rules ( syllogi/ic inf]5ce4 ,ari/otle _h spok51 & x 0 ! "p ( humbl] m5 m]ely to repeat ! lesson aft] him4 ,! trivial nons5se embodi$ 9 ?is tradition is /ill set 9 exam9ations1 & def5d$ by em95t au?orities z an excell5t propa$eutic1 i4e4 a tra9+ 9 ^? habits ( solemn humbug :i* are s great a help 9 lat] life4 ,b x is n ?is t ,i mean to praise 9 say+ t all philosophy is logic4 ,ev] s9ce ! beg9n+ ( ! sev5te5? c5tury1 all vigor\s m9ds t h conc]n$ !mselves ) inf]5ce h ab&on$ ! m$iaeval tradition1 & 9 "o way or o!r h wid5$ ! scope ( logic4 ,! fir/ ext5sion 0 ! introduction ( ! inductive me?od by ,bacon & ,galileo--by ! =m] 9 a !oretical & l>gely mi/ak5 =m1 by ! latt] 9 actual use 9 e/abli%+ ! f\ndations ( mod]n physics & a/ronomy4 ,?is is probably ! only ext5sion ( ! old logic :i* has become famili> to ! g5]al educat$ public4 ,b induction1 important z x is :5 reg>d$ z a me?od ( inve/igation1 does n seem to rema9 :5 its "w is done3 9 ! f9al =m ( a p]fect$ sci5ce1 x w\ld seem t ev]y?+ ought to be d$uctive4 ,if induction rema9s at all1 :i* is a difficult "q1 x w rema9 m]ely z "o ( ! pr9ciples accord+ to :i* d$uctions are effect$4 ,?us ! ultimate result ( ! introduction ( ! inductive me?od seems n ! creation ( a new k9d ( non-d$uctive reason+1 b r ! wid5+ ( ! scope ( d$uction by po9t+ out a way ( d$uc+ :i* is c]ta9ly n syllogi/ic1 & does n fit into ! m$iaeval s*eme4 ,! "q ( ! scope & validity ( induction is ( great difficulty1 & ( great importance to our k4 ,take su* a "q z1 ,w ! sun rise to-morr[8 ,our fir/ in/9ctive feel+ is t we h abundant reason = say+ t x w1 because x has ris5 on s _m previ\s morn+s4 ,n[1 ,i d n myself "k :e!r ?is does af=d a gr\nd or n1 b ,i am will+ to suppose t x does4 ,! "q :i* !n arises is3 ,:at is ! pr9ciple ( inf]5ce by :i* we pass f pa/ sunrises to future ones8 ,! answ] giv5 by ,mill is t ! inf]5ce dep5ds ^u ! law ( causation4 ,let u suppose ?is to be true2 !n :at is ! reason = believ+ 9 ! law ( causation8 ,!re are broadly ?ree possible answ]s3 7#a7 t x is itself kn[n a priori2 7#b7 t x is a po/ulate2 7#c7 t x is an empirical g5]alisation f pa/ in/ances 9 :i* x has be5 f\nd to hold4 ,! !ory t causation is kn[n a priori _c be def9itely refut$1 b x c be r5d]$ v unplausible by ! m]e process ( =mulat+ ! law exactly1 & !reby %[+ t x is imm5sely m complicat$ & less obvi\s ?an is g5]ally suppos$4 ,! !ory t causation is a po/ulate1 i4e4 t x is some?+ :i* we *oose to ass]t al?\gh we "k t x is v likely false1 is also incapable ( refutation2 b x is pla9ly also incapable ( ju/ify+ any use ( ! law 9 inf]5ce4 ,we are ?us br\ght to ! !ory t ! law is an empirical g5]alisation1 :i* is ! view held by ,mill4 ,b if s1 h[ are empirical g5]alisations to be ju/ifi$8 ,! evid5ce 9 _! fav\r _c be empirical1 s9ce we wi% to argue f :at has be5 obs]v$ to :at has n be5 obs]v$1 :i* c only be done by means ( "s kn[n relation ( ! obs]v$ & ! unobs]v$2 b ! unobs]v$1 by def9ition1 is n kn[n empirically1 & !re=e its relation to ! obs]v$1 if kn[n at all1 mu/ be kn[n indep5d5tly ( empirical evid5ce4 ,let u see :at ,mill says on ?is subject4 ,accord+ to ,mill1 ! law ( causation is prov$ by an admitt$ly fallible process call$ induction by simple enum]ation4 ,?is process1 he says1 consi/s 9 ascrib+ ! nature ( g5]al tru?s to all propositions :i* are true 9 e in/ance t we happ5 to "k (4#h ,z reg>ds its fallibility1 he ass]ts t ! prec>i\sness ( ! me?od ( simple enum]ation is 9 an inv]se ratio to ! l>g5ess ( ! g5]alisation4 ,! process is delusive & insuffici5t1 exactly 9 proportion z ! subject-matt] ( ! obs]vation is special & limit$ 9 ext5t4 ,z ! sph]e wid5s1 ?is unsci5tific me?od becomes less & less liable to mislead2 & ! mo/ univ]sal class ( tru?s1 ! law ( causation = in/ance1 & ! pr9ciples ( numb] & ( geometry1 are duly & satisfactorily prov$ by t me?od alone1 nor are !y susceptible ( any o!r pro(4#i #h ,logic1 book iii41 *apt] iii41 ,sec4 #b4 #i ,book iii41 *apt] xxi41 ,sec4 #c4 ,9 ! above /atem5t1 !re are two obvi\s lacunae3 7#a7 ,h[ is ! me?od ( simple enum]ation itself ju/ifi$8 7#b7 ,:at logical pr9ciple1 if any1 cov]s ! same gr\nd z ?is me?od1 )\t be+ liable to its failures8 ,let u take ! second "q fir/4 ,a me?od ( pro( :i*1 :5 us$ z direct$1 gives sometimes tru? & sometimes falsehood--z ! me?od ( simple enum]ation does--is obvi\sly n a valid me?od1 = validity dem&s inv>iable tru?4 ,?us1 if simple enum]ation is to be r5d]$ valid1 x mu/ n be /at$ z ,mill /ates x4 ,we %all h to say1 at mo/1 t ! data r5d] ! result probable4 ,causation holds1 we %all say1 9 e in/ance we h be5 able to te/2 !re=e x probably holds 9 unte/$ in/ances4 ,!re are t]rible difficulties 9 ! notion ( probability1 b we may ignore !m at pres5t4 ,we ?us h :at at lea/ may be a logical pr9ciple1 s9ce x is )\t exception4 ,if a proposition is true 9 e in/ance t we happ5 to "k (1 & if ! in/ances are v num]\s1 !n1 we %all say1 x becomes v probable1 on ! data1 t x w be true 9 any fur!r in/ance4 ,?is is n refut$ by ! fact t :at we decl>e to be probable does n always happ51 = an ev5t may be probable on ! data & yet n occur4 ,x is1 h[ev]1 obvi\sly capable ( fur!r analysis1 & ( m exact /atem5t4 ,we %all h to say some?+ l ?is3 t e in/ance ( a proposition#aj be+ true increases ! probability ( its be+ true 9 a fre% in/ance1 & t a suffici5t numb] ( fav\rable in/ances w1 9 ! abs5ce ( in/ances to ! contr>y1 make ! probability ( ! tru? ( a fre% in/ance approa* indef9itely ne> to c]ta9ty4 ,"s su* pr9ciple z ?is is requir$ if ! me?od ( simple enum]ation is to be valid4 #aj ,or r a propositional function4 ,b ?is br+s u to our o!r "q1 namely1 h[ is our pr9ciple kn[n to be true8 ,obvi\sly1 s9ce x is requir$ to ju/ify induction1 x _c be prov$ by induction2 s9ce x goes beyond ! empirical data1 x _c be prov$ by !m alone2 s9ce x is requir$ to ju/ify all inf]5ces f empirical data to :at goes beyond !m1 x _c itself be ev5 r5d]$ 9 any degree probable by su* data4 ,h5ce1 if x is kn[n1 x is n kn[n by exp]i5ce1 b indep5d5tly ( exp]i5ce4 ,i d n say t any su* pr9ciple is kn[n3 ,i only say t x is requir$ to ju/ify ! inf]5ces f exp]i5ce :i* empirici/s all[1 & t x _c itself be ju/ifi$ empirically4#aa #aa ,! subject ( causality & induction w be discuss$ aga9 9 ,lecture ,,viii4 ,a simil> conclusion c be prov$ by simil> argum5ts conc]n+ any o!r logical pr9ciple4 ,?us logical k is n d]ivable f exp]i5ce alone1 & ! empirici/'s philosophy c !re=e n be accept$ 9 its entirety1 9 spite ( its excell5ce 9 _m matt]s :i* lie outside logic4 ,hegel & 8 foll[]s wid5$ ! scope ( logic 9 q a diff]5t way--a way :i* ,i believe to be fallaci\s1 b :i* requires discussion if only to %[ h[ _! conception ( logic diff]s f ! conception :i* ,i wi% to advocate4 ,9 _! writ+s1 logic is practically id5tical ) metaphysics4 ,9 broad outl9e1 ! way ?is came ab\t is z foll[s4 ,hegel believ$ t1 by means ( a priori reason+1 x c\ld be %[n t ! _w mu/ h v>i\s important & int]e/+ *>act]i/ics1 s9ce any _w )\t ^! *>act]i/ics w\ld be impossible & self-contradictory4 ,?us :at he calls logic is an inve/igation ( ! nature ( ! univ]se1 9 s f> z ?is c be inf]r$ m]ely f ! pr9ciple t ! univ]se mu/ be logically self-consi/5t4 ,i d n myself believe t f ?is pr9ciple alone any?+ ( importance c be inf]r$ z reg>ds ! exi/+ univ]se4 ,b1 h[ev] t may be1 ,i %\ld n reg>d ,hegel's reason+1 ev5 if x 7 valid1 z prop]ly belong+ to logic3 x w\ld r be an application ( logic to ! actual _w4 ,logic itself w\ld be conc]n$ r ) su* que/ions z :at self-consi/5cy is1 :i* ,hegel1 s f> z ,i "k1 does n discuss4 ,& ?\gh he criticises ! traditional logic1 & pr(esses to replace x by an improv$ logic ( 8 own1 !re is "s s5se 9 :i* ! traditional logic1 ) all its faults1 is uncritically & unconsci\sly assum$ ?r\gh\t 8 reason+4 ,x is n 9 ! direction advocat$ by him1 x seems to me1 t ! re=m ( logic is to be s\ght1 b by a m fundam5tal1 m pati5t1 & less ambiti\s inve/igation into ! presuppositions :i* 8 sy/em %>es ) ^? ( mo/ o!r philosoph]s4 ,! way 9 :i*1 z x seems to me1 ,hegel's sy/em assumes ! ord9>y logic :i* x subsequ5tly criticises1 is exemplifi$ by ! g5]al conception ( categories ) :i* he op]ates ?r\gh\t4 ,?is conception is1 ,i ?9k1 ess5tially a product ( logical confusion1 b x seems 9 "s way to /& = ! conception ( qualities ( ,reality z a :ole4 ,mr ,bradley has work$ out a !ory accord+ to :i*1 9 all judgm5t1 we are ascrib+ a pr$icate to ,reality z a :ole2 & ?is !ory is d]iv$ f ,hegel4 ,n[ ! traditional logic holds t e proposition ascribes a pr$icate to a subject1 & f ?is x easily foll[s t !re c be only "o subject1 ! ,absolute1 = if !re 7 two1 ! proposition t !re 7 two w\ld n ascribe a pr$icate to ei!r4 ,?us ,hegel's doctr9e1 t philosophical propositions mu/ be ( ! =m1 ! ,absolute is su*-&-su*1 dep5ds ^u ! traditional belief 9 ! univ]sality ( ! subject-pr$icate =m4 ,?is belief1 be+ traditional1 sc>cely self-consci\s1 & n suppos$ to be important1 op]ates und]gr\nd1 & is assum$ 9 argum5ts :i*1 l ! refutation ( relations1 appe> at fir/ sight su* z to e/abli% its tru?4 ,?is is ! mo/ important respect 9 :i* ,hegel uncritically assumes ! traditional logic4 ,o!r less important respects--?\gh important en\gh to be ! s\rce ( su* ess5tially ,hegelian conceptions z ! concrete univ]sal & ! union ( id5tity 9 diff]5ce--w be f\nd :]e he explicitly deals ) =mal logic4#ab #ab ,see ! translation by ,h4 ,s4 ,macran1 ,hegel's ,doctr9e ( ,=mal ,logic1 ,ox=d1 #aiab4 ,hegel's argum5t 9 ?is portion ( 8 ,logic dep5ds ?r\gh\t ^u confus+ ! is ( pr$ication1 z 9 ,socrates is mortal1 ) ! is ( id5tity1 z 9 ,socrates is ! philosoph] :o drank ! hemlock4 ,ow+ to ?is confusion1 he ?9ks t ,socrates & mortal mu/ be id5tical4 ,see+ t !y are diff]5t1 he does n inf]1 z o!rs w\ld1 t !re is a mi/ake some:]e1 b t !y exhibit id5tity 9 diff]5ce4 ,aga91 ,socrates is p>ticul>1 mortal is univ]sal4 ,!re=e1 he says1 s9ce ,socrates is mortal1 x foll[s t ! p>ticul> is ! univ]sal--tak+ ! is to be ?r\gh\t expressive ( id5tity4 ,b to say ! p>ticul> is ! univ]sal is self-contradictory4 ,aga9 ,hegel does n suspect a mi/ake b proce$s to syn!sise p>ticul> & univ]sal 9 ! individual1 or concrete univ]sal4 ,?is is an example ( h[1 = want ( c>e at ! />t1 va/ & impos+ sy/ems ( philosophy are built ^u /upid & trivial confusions1 :i*1 b = ! almo/ incr$ible fact t !y are un9t5tional1 "o w\ld be tempt$ to *>act]ise z puns4 ,!re is q ano!r direction 9 :i* a l>ge te*nical developm5t ( logic has tak5 place3 ,i mean ! direction ( :at is call$ logi/ic or ma!matical logic4 ,?is k9d ( logic is ma!matical 9 two diff]5t s5ses3 x is itself a bran* ( ma!matics1 & x is ! logic :i* is specially applicable to o!r m traditional bran*es ( ma!matics4 ,hi/orically1 x began z m]ely a bran* ( ma!matics3 its special applicability to o!r bran*es is a m rec5t developm5t4 ,9 bo? respects1 x is ! fulfilm5t ( a hope :i* ,leibniz *]i%$ ?r\gh\t 8 life1 & pursu$ ) all ! ard\r ( 8 amaz+ intellectual en]gy4 ,mu* ( 8 "w on ?is subject has be5 publi%$ rec5tly1 s9ce 8 discov]ies h be5 remade by o!rs2 b none 0 publi%$ by him1 because 8 results p]si/$ 9 contradict+ c]ta9 po9ts 9 ! traditional doctr9e ( ! syllogism4 ,we n[ "k t on ^! po9ts ! traditional doctr9e is wrong1 b respect = ,ari/otle prev5t$ ,leibniz f realis+ t ?is 0 possible4#ac #ac ,cf4 ,c\turat1 ,la ,logique de ,leibniz1 pp4 #cfa1 #chf4 ,! mod]n developm5t ( ma!matical logic dates f ,boole's ,laws ( ,?\ght 7#ahed74 ,b 9 him & 8 successors1 be=e ,peano & ,frege1 ! only ?+ really a*iev$1 ap>t f c]ta9 details1 0 ! inv5tion ( a ma!matical symbolism = d$uc+ consequ5ces f ! premisses :i* ! new] me?ods %>$ ) ^? ( ,ari/otle4 ,?is subject has consid]able int]e/ z an indep5d5t bran* ( ma!matics1 b x has v little to d ) real logic4 ,! fir/ s]i\s advance 9 real logic s9ce ! "t ( ! ,greeks 0 made indep5d5tly by ,peano & ,frege--bo? ma!maticians4 ,!y bo? arriv$ at _! logical results by an analysis ( ma!matics4 ,traditional logic reg>d$ ! two propositions1 ,socrates is mortal & ,all m5 are mortal1 z be+ ( ! same =m2#ad ,peano & ,frege %[$ t !y are utt]ly diff]5t 9 =m4 ,! philosophical importance ( logic may be illu/rat$ by ! fact t ?is confusion--:i* is /ill committ$ by mo/ writ]s--obscur$ n only ! :ole /udy ( ! =ms ( judgm5t & inf]5ce1 b also ! relations ( ?+s to _! qualities1 ( concrete exi/5ce to ab/ract concepts1 & ( ! _w ( s5se to ! _w ( ,platonic ideas4 ,peano & ,frege1 :o po9t$ out ! error1 did s = te*nical reasons1 & appli$ _! logic ma9ly to te*nical developm5ts2 b ! philosophical importance ( ! advance :i* !y made is impossible to exagg]ate4 #ad ,x 0 (t5 recognis$ t !re 0 "s diff]5ce betwe5 !m1 b x 0 n recognis$ t ! diff]5ce is fundam5tal1 & ( v great importance4 ,ma!matical logic1 ev5 9 its mo/ mod]n =m1 is n directly ( philosophical importance except 9 its beg9n+s4 ,aft] ! beg9n+s1 x belongs r to ma!matics ?an to philosophy4 ,( its beg9n+s1 :i* are ! only "p ( x t c prop]ly be call$ philosophical logic1 ,i %all speak %ortly4 ,b ev5 ! lat] developm5ts1 ?\gh n directly philosophical1 w be f\nd ( great indirect use 9 philosophis+4 ,!y enable u to deal easily ) m ab/ract conceptions ?an m]ely v]bal reason+ c enum]ate2 !y sugge/ fruitful hypo!ses :i* o!rwise c\ld h>dly be ?\ght (2 & !y enable u to see quickly :at is ! smalle/ /ore ( mat]ials ) :i* a giv5 logical or sci5tific edifice c be con/ruct$4 ,n only ,frege's !ory ( numb]1 :i* we %all deal ) 9 ,lecture ,,vii41 b ! :ole !ory ( physical concepts :i* w be outl9$ 9 our next two lectures1 is inspir$ by ma!matical logic1 & c\ld nev] h be5 imag9$ )\t x4 ,9 bo? ^! cases1 & 9 _m o!rs1 we %all appeal to a c]ta9 pr9ciple call$ ! pr9ciple ( ab/raction4 ,?is pr9ciple1 :i* might equally well be call$ ! pr9ciple :i* disp5ses ) ab/raction1 & is "o :i* cle>s away incr$ible accumulations ( metaphysical lumb]1 0 directly sugge/$ by ma!matical logic1 & c\ld h>dly h be5 prov$ or practically us$ )\t its help4 ,! pr9ciple w be expla9$ 9 our f\r? lecture1 b its use may be briefly indicat$ 9 advance4 ,:5 a gr\p ( objects h t k9d ( simil>ity :i* we are incl9$ to attribute to possession ( a common quality1 ! pr9ciple 9 "q %[s t memb]%ip ( ! gr\p w s]ve all ! purposes ( ! suppos$ common quality1 & t !re=e1 unless "s common quality is actually kn[n1 ! gr\p or class ( simil> objects may be us$ to replace ! common quality1 :i* ne$ n be assum$ to exi/4 ,9 ?is & o!r ways1 ! indirect uses ( ev5 ! lat] p>ts ( ma!matical logic are v great2 b x is n[ "t to turn our att5tion to its philosophical f\ndations4 ,9 e proposition & 9 e inf]5ce !re is1 besides ! p>ticul> subject-matt] conc]n$1 a c]ta9 =m1 a way 9 :i* ! con/itu5ts ( ! proposition or inf]5ce are put toge!r4 ,if ,i say1 ,socrates is mortal1 ,jones is angry1 ,! sun is hot1 !re is some?+ 9 common 9 ^! ?ree cases1 some?+ indicat$ by ! ^w is4 ,:at is 9 common is ! =m ( ! proposition1 n an actual con/itu5t4 ,if ,i say a numb] ( ?+s ab\t ,socrates--t he 0 an ,a!nian1 t he m>ri$ ,xantippe1 t he drank ! hemlock--!re is a common con/itu5t1 namely ,socrates1 9 all ! propositions ,i enunciate1 b !y h div]se =ms4 ,if1 on ! o!r h&1 ,i take any "o ( ^! propositions & replace its con/itu5ts1 "o at a "t1 by o!r con/itu5ts1 ! =m rema9s con/ant1 b no con/itu5t rema9s4 ,take 7say7 ! s]ies ( propositions1 ,socrates drank ! hemlock1 ,col]idge drank ! hemlock1 ,col]idge drank opium1 ,col]idge ate opium4 ,! =m rema9s un*ang$ ?r\gh\t ?is s]ies1 b all ! con/itu5ts are alt]$4 ,?us =m is n ano!r con/itu5t1 b is ! way ! con/itu5ts are put toge!r4 ,x is =ms1 9 ?is s5se1 t are ! prop] object ( philosophical logic4 ,x is obvi\s t ! k ( logical =ms is some?+ q diff]5t f k ( exi/+ ?+s4 ,! =m ( ,socrates drank ! hemlock is n an exi/+ ?+ l ,socrates or ! hemlock1 nor does x ev5 h t close relation to exi/+ ?+s t dr9k+ has4 ,x is some?+ altoge!r m ab/ract & remote4 ,we might und]/& all ! sep>ate words ( a s5t5ce )\t und]/&+ ! s5t5ce3 if a s5t5ce is long & complicat$1 ?is is apt to happ54 ,9 su* a case we h k ( ! con/itu5ts1 b n ( ! =m4 ,we may also h k ( ! =m )\t hav+ k ( ! con/itu5ts4 ,if ,i say1 ,ror>ius drank ! hemlock1 ^? among y :o h nev] he>d ( ,ror>ius 7suppos+ !re are any7 w und]/& ! =m1 )\t hav+ k ( all ! con/itu5ts4 ,9 ord] to und]/& a s5t5ce1 x is necess>y to h k bo? ( ! con/itu5ts & ( ! p>ticul> in/ance ( ! =m4 ,x is 9 ?is way t a s5t5ce conveys in=mation1 s9ce x tells u t c]ta9 kn[n objects are relat$ accord+ to a c]ta9 kn[n =m4 ,?us "s k9d ( k ( logical =ms1 ?\gh ) mo/ p x is n explicit1 is involv$ 9 all und]/&+ ( disc\rse4 ,x is ! bus9ess ( philosophical logic to extract ?is k f its concrete integum5ts1 & to r5d] x explicit & pure4 ,9 all inf]5ce1 =m alone is ess5tial3 ! p>ticul> subject-matt] is irrelevant except z secur+ ! tru? ( ! premisses4 ,?is is "o reason = ! great importance ( logical =m4 ,:5 ,i say1 ,socrates 0 a man1 all m5 are mortal1 !re=e ,socrates 0 mortal1 ! connection ( premisses & conclusion does n 9 any way dep5d ^u its be+ ,socrates & man & mortality t ,i am m5tion+4 ,! g5]al =m ( ! inf]5ce may be express$ 9 "s su* words z1 ,if a ?+ has a c]ta9 prop]ty1 & :atev] has ?is prop]ty has a c]ta9 o!r prop]ty1 !n ! ?+ 9 "q also has t o!r prop]ty4 ,"h no p>ticul> ?+s or prop]ties are m5tion$3 ! proposition is absolutely g5]al4 ,all inf]5ces1 :5 /at$ fully1 are in/ances ( propositions hav+ ?is k9d ( g5]ality4 ,if !y seem to dep5d ^u ! subject-matt] o!rwise ?an z reg>ds ! tru? ( ! premisses1 t is because ! premisses h n be5 all explicitly /at$4 ,9 logic1 x is a wa/e ( "t to deal ) inf]5ces conc]n+ p>ticul> cases3 we deal ?r\gh\t ) completely g5]al & purely =mal implications1 leav+ x to o!r sci5ces to discov] :5 ! hypo!ses are v]ifi$ & :5 !y are n4 ,b ! =ms ( propositions giv+ rise to inf]5ces are n ! simple/ =ms3 !y are always hypo!tical1 /at+ t if "o proposition is true1 !n s is ano!r4 ,be=e consid]+ inf]5ce1 !re=e1 logic mu/ consid] ^? simpl] =ms :i* inf]5ce presupposes4 ,"h ! traditional logic fail$ completely3 x believ$ t !re 0 only "o =m ( simple proposition 7i4e4 ( proposition n /at+ a relation betwe5 two or m o!r propositions71 namely1 ! =m :i* ascribes a pr$icate to a subject4 ,?is is ! appropriate =m 9 assign+ ! qualities ( a giv5 ?+--we may say ?is ?+ is r\nd1 & r$1 & s on4 ,gramm> fav\rs ?is =m1 b philosophically x is s f> f univ]sal t x is n ev5 v common4 ,if we say ?is ?+ is bigg] ?an t1 we are n assign+ a m]e quality ( ?is1 b a relation ( ?is & t4 ,we might express ! same fact by say+ t ?+ is small] ?an ?is1 :]e grammatically ! subject is *ang$4 ,?us propositions /at+ t two ?+s h a c]ta9 relation h a diff]5t =m f subject-pr$icate propositions1 & ! failure to p]ceive ?is diff]5ce or to all[ = x has be5 ! s\rce ( _m errors 9 traditional metaphysics4 ,! belief or unconsci\s conviction t all propositions are ( ! subject-pr$icate =m--9 o!r words1 t e fact consi/s 9 "s ?+ hav+ "s quality--has r5d]$ mo/ philosoph]s incapable ( giv+ any acc\nt ( ! _w ( sci5ce & daily life4 ,if !y _h be5 hone/ly anxi\s to give su* an acc\nt1 !y w\ld probably h discov]$ _! error v quickly2 b mo/ ( !m 7 less anxi\s to und]/& ! _w ( sci5ce & daily life1 ?an to convict x ( unreality 9 ! int]e/s ( a sup]-s5sible real _w4 ,belief 9 ! unreality ( ! _w ( s5se arises ) irresi/ible =ce 9 c]ta9 moods--moods :i*1 ,i imag9e1 h "s simple physiological basis1 b are none ! less p[]fully p]suasive4 ,! conviction born ( ^! moods is ! s\rce ( mo/ my/icism & ( mo/ metaphysics4 ,:5 ! emotional int5sity ( su* a mood subsides1 a man :o is 9 ! habit ( reason+ w se>* = logical reasons 9 fav\r ( ! belief :i* he f9ds 9 himself4 ,b s9ce ! belief already exi/s1 he w be v hospitable to any reason t sugge/s itself4 ,! p>adoxes app>5tly prov$ by 8 logic are really ! p>adoxes ( my/icism1 & are ! goal :i* he feels 8 logic mu/ rea* if x is to be 9 accordance ) insight4 ,x is 9 ?is way t logic has be5 pursu$ by ^? ( ! great philosoph]s :o 7 my/ics--notably ,plato1 ,sp9oza1 & ,hegel4 ,b s9ce !y usually took = grant$ ! suppos$ insight ( ! my/ic emotion1 _! logical doctr9es 7 pres5t$ ) a c]ta9 dryness1 & 7 believ$ by _! disciples to be q indep5d5t ( ! sudd5 illum9ation f :i* !y sprang4 ,nev]!less _! orig9 clung to !m1 & !y rema9$--to borr[ a useful ^w f ,mr ,santayana--malici\s 9 reg>d to ! _w ( sci5ce & common s5se4 ,x is only s t we c acc\nt = ! complac5cy ) :i* philosoph]s h accept$ ! inconsi/5cy ( _! doctr9es ) all ! common & sci5tific facts :i* seem be/ e/abli%$ & mo/ wor?y ( belief4 ,! logic ( my/icism %[s1 z is natural1 ! defects :i* are inh]5t 9 any?+ malici\s4 ,:ile ! my/ic mood is dom9ant1 ! ne$ ( logic is n felt2 z ! mood fades1 ! impulse to logic reass]ts itself1 b ) a desire to reta9 ! vani%+ insight1 or at lea/ to prove t x 0 insight1 & t :at seems to contradict x is illusion4 ,! logic :i* ?us arises is n q dis9t]e/$ or c&id1 & is inspir$ by a c]ta9 hatr$ ( ! daily _w to :i* x is to be appli$4 ,su* an attitude naturally does n t5d to ! be/ results4 ,ev]yone kn[s t to read an au?or simply 9 ord] to refute him is n ! way to und]/& him2 & to read ! book ( ,nature ) a conviction t x is all illusion is j z unlikely to lead to und]/&+4 ,if our logic is to f9d ! common _w intelligible1 x mu/ n be ho/ile1 b mu/ be inspir$ by a g5u9e acceptance su* z is n usually to be f\nd among metaphysicians4 ,traditional logic1 s9ce x holds t all propositions h ! subject-pr$icate =m1 is unable to admit ! reality ( relations3 all relations1 x ma9ta9s1 mu/ be r$uc$ to prop]ties ( ! app>5tly relat$ t]ms4 ,!re are _m ways ( refut+ ?is op9ion2 "o ( ! easie/ is d]iv$ f ! consid]ation ( :at are call$ asymmetrical relations4 ,9 ord] to expla9 ?is1 ,i w fir/ expla9 two indep5d5t ways ( classify+ relations4 ,"s relations1 :5 !y hold betwe5 ,a & ,b1 also hold betwe5 ,b & ,a4 ,su*1 = example1 is ! relation bro!r or si/]4 ,if ,a is a bro!r or si/] ( ,b1 !n ,b is a bro!r or si/] ( ,a4 ,su* aga9 is any k9d ( simil>ity1 say simil>ity ( col\r4 ,any k9d ( dissimil>ity is also ( ?is k9d3 if ! col\r ( ,a is unlike ! col\r ( ,b1 !n ! col\r ( ,b is unlike ! col\r ( ,a4 ,relations ( ?is sort are call$ symmetrical4 ,?us a relation is symmetrical if1 :5ev] x holds betwe5 ,a & ,b1 x also holds betwe5 ,b & ,a4 ,all relations t are n symmetrical are call$ non-symmetrical4 ,?us bro!r is non-symmetrical1 because1 if ,a is a bro!r ( ,b1 x may happ5 t ,b is a si/] ( ,a4 ,a relation is call$ asymmetrical :51 if x holds betwe5 ,a & ,b1 x nev] holds betwe5 ,b & ,a4 ,?us husb&1 fa!r1 gr&fa!r1 etc41 are asymmetrical relations4 ,s are be=e1 aft]1 great]1 above1 to ! "r (1 etc4 ,all ! relations t give rise to s]ies are ( ?is k9d4 ,classification into symmetrical1 asymmetrical1 & m]ely non-symmetrical relations is ! fir/ ( ! two classifications we _h to consid]4 ,! second is into transitive1 intransitive1 & m]ely non-transitive relations1 :i* are def9$ z foll[s4 ,a relation is said to be transitive1 if1 :5ev] x holds betwe5 ,a & ,b & also betwe5 ,b & ,c1 x holds betwe5 ,a & ,c4 ,?us be=e1 aft]1 great]1 above are transitive4 ,all relations giv+ rise to s]ies are transitive1 b s are _m o!rs4 ,! transitive relations j m5tion$ 7 asymmetrical1 b _m transitive relations are symmetrical--= in/ance1 equality 9 any respect1 exact id5tity ( col\r1 be+ equally num]\s 7z appli$ to collections71 & s on4 ,a relation is said to be non-transitive :5ev] x is n transitive4 ,?us bro!r is non-transitive1 because a bro!r ( "o's bro!r may be oneself4 ,all k9ds ( dissimil>ity are non-transitive4 ,a relation is said to be intransitive :51 if ,a has ! relation to ,b1 & ,b to ,c1 ,a nev] has x to ,c4 ,?us fa!r is intransitive4 ,s is su* a relation z "o in* tall] or "o ye> lat]4 ,let u n[1 9 ! light ( ?is classification1 return to ! "q :e!r all relations c be r$uc$ to pr$ications4 ,9 ! case ( symmetrical relations--i4e4 relations :i*1 if !y hold betwe5 ,a & ,b1 also hold betwe5 ,b & ,a--"s k9d ( plausibility c be giv5 to ?is doctr9e4 ,a symmetrical relation :i* is transitive1 su* z equality1 c be reg>d$ z express+ possession ( "s common prop]ty1 :ile "o :i* is n transitive1 su* z inequality1 c be reg>d$ z express+ possession ( diff]5t prop]ties4 ,b :5 we come to asymmetrical relations1 su* z be=e & aft]1 great] & less1 etc41 ! attempt to r$uce !m to prop]ties becomes obvi\sly impossible4 ,:51 = example1 two ?+s are m]ely kn[n to be unequal1 )\t our kn[+ :i* is great]1 we may say t ! inequality results f _! hav+ diff]5t magnitudes1 because inequality is a symmetrical relation2 b to say t :5 "o ?+ is great] ?an ano!r1 & n m]ely unequal to x1 t means t !y h diff]5t magnitudes1 is =mally incapable ( expla9+ ! facts4 ,= if ! o!r ?+ _h be5 great] ?an ! "o1 ! magnitudes w\ld also h be5 diff]5t1 ?\gh ! fact to be expla9$ w\ld n h be5 ! same4 ,?us m]e diff]5ce ( magnitude is n all t is involv$1 s9ce1 if x 71 !re w\ld be no diff]5ce betwe5 "o ?+ be+ great] ?an ano!r1 & ! o!r be+ great] ?an ! "o4 ,we %all h to say t ! "o magnitude is great] ?an ! o!r1 & ?us we %all h fail$ to get rid ( ! relation great]4 ,9 %ort1 bo? possession ( ! same prop]ty & possession ( diff]5t prop]ties are symmetrical relations1 & !re=e _c acc\nt = ! exi/5ce ( asymmetrical relations4 ,asymmetrical relations are involv$ 9 all s]ies--9 space & "t1 great] & less1 :ole & "p1 & _m o!rs ( ! mo/ important *>act]i/ics ( ! actual _w4 ,all ^! aspects1 !re=e1 ! logic :i* r$uces ev]y?+ to subjects & pr$icates is compell$ to condemn z error & m]e appe>ance4 ,to ^? ^: logic is n malici\s1 su* a :olesale condemnation appe>s impossible4 ,& 9 fact !re is no reason except prejudice1 s f> z ,i c discov]1 = d5y+ ! reality ( relations4 ,:5 once _! reality is admitt$1 all logical gr\nds = suppos+ ! _w ( s5se to be illusory disappe>4 ,if ?is is to be suppos$1 x mu/ be frankly & simply on ! gr\nd ( my/ic insight unsupport$ by argum5t4 ,x is impossible to argue aga9/ :at pr(esses to be insight1 s long z x does n argue 9 its own fav\r4 ,z logicians1 !re=e1 we may admit ! possibility ( ! my/ic's _w1 :ile yet1 s long z we d n h 8 insight1 we mu/ cont9ue to /udy ! ev]yday _w ) :i* we are famili>4 ,b :5 he cont5ds t our _w is impossible1 !n our logic is ready to repel 8 attack4 ,& ! fir/ /ep 9 creat+ ! logic :i* is to p]=m ?is s]vice is ! recognition ( ! reality ( relations4 ,relations :i* h two t]ms are only "o k9d ( relations4 ,a relation may h ?ree t]ms1 or f\r1 or any numb]4 ,relations ( two t]ms1 be+ ! simple/1 h receiv$ m att5tion ?an ! o!rs1 & h g5]ally be5 alone consid]$ by philosoph]s1 bo? ^? :o accept$ & ^? :o d5i$ ! reality ( relations4 ,b o!r relations h _! importance1 & are indisp5sable 9 ! solution ( c]ta9 problems4 ,jeal\sy1 = example1 is a relation betwe5 ?ree p4 ,pr(essor ,royce m5tions ! relation giv+3 :5 ,a gives ,b to ,c1 t is a relation ( ?ree t]ms4#ae ,:5 a man says to 8 wife3 ,my de>1 ,i wi% y c\ld induce ,angel9a to accept ,edw91 8 wi% con/itutes a relation betwe5 f\r p1 himself1 8 wife1 ,angel9a1 & ,edw94 ,?us su* relations are by no means recondite or r>e4 ,b 9 ord] to expla9 exactly h[ !y diff] f relations ( two t]ms1 we mu/ emb>k ^u a classification ( ! logical =ms ( facts1 :i* is ! fir/ bus9ess ( logic1 & ! bus9ess 9 :i* ! traditional logic has be5 mo/ defici5t4 #ae ,encyclopa$ia ( ! ,philosophical ,sci5ces1 vol4 i4 p4 #ig4 ,! exi/+ _w consi/s ( _m ?+s ) _m qualities & relations4 ,a complete description ( ! exi/+ _w w\ld require n only a catalogue ( ! ?+s1 b also a m5tion ( all _! qualities & relations4 ,we %\ld h to "k n only ?is1 t1 & ! o!r ?+1 b also :i* 0 r$1 :i* yell[1 :i* 0 e>li] ?an :i*1 :i* 0 betwe5 :i* two o!rs1 & s on4 ,:5 ,i speak ( a fact1 ,i d n mean "o ( ! simple ?+s 9 ! _w2 ,i mean t a c]ta9 ?+ has a c]ta9 quality1 or t c]ta9 ?+s h a c]ta9 relation4 ,?us1 = example1 ,i %\ld n call ,napoleon a fact1 b ,i %\ld call x a fact t he 0 ambiti\s1 or t he m>ri$ ,joseph9e4 ,n[ a fact1 9 ?is s5se1 is nev] simple1 b always has two or m con/itu5ts4 ,:5 x simply assigns a quality to a ?+1 x has only two con/itu5ts1 ! ?+ & ! quality4 ,:5 x consi/s ( a relation betwe5 two ?+s1 x has ?ree con/itu5ts1 ! ?+s & ! relation4 ,:5 x consi/s ( a relation betwe5 ?ree ?+s1 x has f\r con/itu5ts1 & s on4 ,! con/itu5ts ( facts1 9 ! s5se 9 :i* we are us+ ! ^w fact1 are n o!r facts1 b are ?+s & qualities or relations4 ,:5 we say t !re are relations ( m ?an two t]ms1 we mean t !re are s+le facts consi/+ ( a s+le relation & m ?an two ?+s4 ,i d n mean t "o relation ( two t]ms may hold betwe5 ,a & ,b1 & also betwe5 ,a & ,c1 z1 = example1 a man is ! son ( 8 fa!r & also ! son ( 8 "m4 ,?is con/itutes two di/9ct facts3 if we *oose to treat x z "o fact1 x is a fact :i* has facts = its con/itu5ts4 ,b ! facts ,i am speak+ ( h no facts among _! con/itu5ts1 b only ?+s & relations4 ,= example1 :5 ,a is jeal\s ( ,b on acc\nt ( ,c1 !re is only "o fact1 involv+ ?ree p2 !re are n two in/ances ( jeal\sy1 b only "o4 ,x is 9 su* cases t ,i speak ( a relation ( ?ree t]ms1 :]e ! simple/ possible fact 9 :i* ! relation occurs is "o involv+ ?ree ?+s 9 addition to ! relation4 ,& ! same applies to relations ( f\r t]ms or five or any o!r numb]4 ,all su* relations mu/ be admitt$ 9 our inv5tory ( ! logical =ms ( facts3 two facts involv+ ! same numb] ( ?+s h ! same =m1 & two :i* involve diff]5t numb]s ( ?+s h diff]5t =ms4 ,giv5 any fact1 !re is an ass]tion :i* expresses ! fact4 ,! fact itself is objective1 & indep5d5t ( our ?\ght or op9ion ab\t x2 b ! ass]tion is some?+ :i* involves ?\ght1 & may be ei!r true or false4 ,an ass]tion may be positive or negative3 we may ass]t t ,*>les ,i4 0 execut$1 or t he did n die 9 8 b$4 ,a negative ass]tion may be said to be a d5ial4 ,giv5 a =m ( words :i* mu/ be ei!r true or false1 su* z ,*>les ,i4 di$ 9 8 b$1 we may ei!r ass]t or d5y ?is =m ( words3 9 ! "o case we h a positive ass]tion1 9 ! o!r a negative "o4 ,a =m ( words :i* mu/ be ei!r true or false ,i %all call a proposition4 ,?us a proposition is ! same z :at may be significantly ass]t$ or d5i$4 ,a proposition :i* expresses :at we h call$ a fact1 i4e4 :i*1 :5 ass]t$1 ass]ts t a c]ta9 ?+ has a c]ta9 quality1 or t c]ta9 ?+s h a c]ta9 relation1 w be call$ an atomic proposition1 because1 z we %all see imm$iately1 !re are o!r propositions into :i* atomic propositions ent] 9 a way analog\s to t 9 :i* atoms ent] into molecules4 ,atomic propositions1 al?\gh1 l facts1 !y may h any "o ( an inf9ite numb] ( =ms1 are only "o k9d ( propositions4 ,all o!r k9ds are m complicat$4 ,9 ord] to pres]ve ! p>allelism 9 language z reg>ds facts & propositions1 we %all give ! "n atomic facts to ! facts we h hi!rto be5 consid]+4 ,?us atomic facts are :at det]m9e :e!r atomic propositions are to be ass]t$ or d5i$4 ,:e!r an atomic proposition1 su* z ?is is r$1 or ?is is be=e t1 is to be ass]t$ or d5i$ c only be kn[n empirically4 ,p]haps "o atomic fact may sometimes be capable ( be+ inf]r$ f ano!r1 ?\gh ?is seems v d\btful2 b 9 any case x _c be inf]r$ f premisses no "o ( :i* is an atomic fact4 ,x foll[s t1 if atomic facts are to be kn[n at all1 "s at lea/ mu/ be kn[n )\t inf]5ce4 ,! atomic facts :i* we come to "k 9 ?is way are ! facts ( s5se-p]ception2 at any rate1 ! facts ( s5se-p]ception are ^? :i* we mo/ obvi\sly & c]ta9ly come to "k 9 ?is way4 ,if we knew all atomic facts1 & also knew t !re 7 none except ^? we knew1 we %\ld1 !oretically1 be able to inf] all tru?s ( :atev] =m4#af ,?us logic w\ld !n supply u ) ! :ole ( ! app>atus requir$4 ,b 9 ! fir/ acquisition ( k conc]n+ atomic facts1 logic is useless4 ,9 pure logic1 no atomic fact is ev] m5tion$3 we conf9e ourselves :olly to =ms1 )\t ask+ ourselves :at objects c fill ! =ms4 ,?us pure logic is indep5d5t ( atomic facts2 b conv]sely1 !y are1 9 a s5se1 indep5d5t ( logic4 ,pure logic & atomic facts are ! two poles1 ! :olly a priori & ! :olly empirical4 ,b betwe5 ! two lies a va/ int]m$iate region1 :i* we mu/ n[ briefly explore4 #af ,?is p]haps requires modification 9 ord] to include su* facts z beliefs & wi%es1 s9ce su* facts app>5tly conta9 propositions z compon5ts4 ,su* facts1 ?\gh n /rictly atomic1 mu/ be suppos$ includ$ if ! /atem5t 9 ! text is to be true4 ,molecul> propositions are su* z conta9 conjunctions--if1 or1 &1 unless1 etc4--& su* words are ! m>ks ( a molecul> proposition4 ,consid] su* an ass]tion z1 ,if x ra9s1 ,i %all br+ my umbrella4 ,?is ass]tion is j z capable ( tru? or falsehood z ! ass]tion ( an atomic proposition1 b x is obvi\s t ei!r ! correspond+ fact1 or ! nature ( ! correspond5ce ) fact1 mu/ be q diff]5t f :at x is 9 ! case ( an atomic proposition4 ,:e!r x ra9s1 & :e!r ,i br+ my umbrella1 are ea* sev]ally matt]s ( atomic fact1 asc]ta9able by obs]vation4 ,b ! connection ( ! two involv$ 9 say+ t if ! "o happ5s1 !n ! o!r w happ51 is some?+ radically diff]5t f ei!r ( ! two sep>ately4 ,x does n require = its tru? t x %\ld actually ra91 or t ,i %\ld actually br+ my umbrella2 ev5 if ! wea!r is cl\dless1 x may /ill be true t ,i %\ld h br\ght my umbrella if ! wea!r _h be5 diff]5t4 ,?us we h "h a connection ( two propositions1 :i* does n dep5d ^u :e!r !y are to be ass]t$ or d5i$1 b only ^u ! second be+ inf]able f ! fir/4 ,su* propositions1 !re=e1 h a =m :i* is diff]5t f t ( any atomic proposition4 ,su* propositions are important to logic1 because all inf]5ce dep5ds ^u !m4 ,if ,i h told y t if x ra9s ,i %all br+ my umbrella1 & if y see t !re is a /eady d[np\r1 y c inf] t ,i %all br+ my umbrella4 ,!re c be no inf]5ce except :]e propositions are connect$ 9 "s su* way1 s t f ! tru? or falsehood ( ! "o some?+ foll[s z to ! tru? or falsehood ( ! o!r4 ,x seems to be ! case t we c sometimes "k molecul> propositions1 z 9 ! above in/ance ( ! umbrella1 :5 we d n "k :e!r ! compon5t atomic propositions are true or false4 ,! practical utility ( inf]5ce re/s ^u ?is fact4 ,! next k9d ( propositions we h to consid] are g5]al propositions1 su* z all m5 are mortal1 all equilat]al triangles are equiangul>4 ,& ) ^! belong propositions 9 :i* ! ^w "s occurs1 su* z "s m5 are philosoph]s or "s philosoph]s are n wise4 ,^! are ! d5ials ( g5]al propositions1 namely 79 ! above in/ances71 ( all m5 are non-philosoph]s & all philosoph]s are wise4 ,we w call propositions conta9+ ! ^w "s negative g5]al propositions1 & ^? conta9+ ! ^w all positive g5]al propositions4 ,^! propositions1 x w be se51 beg9 to h ! appe>ance ( ! propositions 9 logical text-books4 ,b _! peculi>ity & complexity are n kn[n to ! text-books1 & ! problems :i* !y raise are only discuss$ 9 ! mo/ sup]ficial mann]4 ,:5 we 7 discuss+ atomic facts1 we saw t we %\ld be able1 !oretically1 to inf] all o!r tru?s by logic if we knew all atomic facts & also knew t !re 7 no o!r atomic facts besides ^? we knew4 ,! k t !re are no o!r atomic facts is positive g5]al k2 x is ! k t all atomic facts are kn[n to me1 or at lea/ all atomic facts are 9 ?is collection--h[ev] ! collection may be giv54 ,x is easy to see t g5]al propositions1 su* z all m5 are mortal1 _c be kn[n by inf]5ce f atomic facts alone4 ,if we c\ld "k ea* individual man1 & "k t he 0 mortal1 t w\ld n enable u to "k t all m5 are mortal1 unless we knew t ^? 7 all ! m5 !re are1 :i* is a g5]al proposition4 ,if we knew e o!r exi/+ ?+ ?r\gh\t ! univ]se1 & knew t ea* sep>ate ?+ 0 n an immortal man1 t w\ld n give u our result unless we knew t we _h explor$ ! :ole univ]se1 i4e4 unless we knew all ?+s belong to ?is collection ( ?+s ,i h exam9$4 ,?us g5]al tru?s _c be inf]r$ f p>ticul> tru?s alone1 b mu/1 if !y are to be kn[n1 be ei!r self-evid5t1 or inf]r$ f premisses ( :i* at lea/ "o is a g5]al tru?4 ,b all empirical evid5ce is ( p>ticul> tru?s4 ,h5ce1 if !re is any k ( g5]al tru?s at all1 !re mu/ be "s k ( g5]al tru?s :i* is indep5d5t ( empirical evid5ce1 i4e4 does n dep5d ^u ! data ( s5se4 ,! above conclusion1 ( :i* we _h an in/ance 9 ! case ( ! inductive pr9ciple1 is important1 s9ce x af=ds a refutation ( ! old] empirici/s4 ,!y believ$ t all our k is d]iv$ f ! s5ses & dep5d5t ^u !m4 ,we see t1 if ?is view is to be ma9ta9$1 we mu/ refuse to admit t we "k any g5]al propositions4 ,x is p]fectly possible logically t ?is %\ld be ! case1 b x does n appe> to be s 9 fact1 & inde$ no "o w\ld dream ( ma9ta9+ su* a view except a !ori/ at ! la/ extremity4 ,we mu/ !re=e admit t !re is g5]al k n d]iv$ f s5se1 & t "s ( ?is k is n obta9$ by inf]5ce b is primitive4 ,su* g5]al k is to be f\nd 9 logic4 ,:e!r !re is any su* k n d]iv$ f logic1 ,i d n "k2 b 9 logic1 at any rate1 we h su* k4 ,x w be rememb]$ t we exclud$ f pure logic su* propositions z1 ,socrates is a man1 all m5 are mortal1 !re=e ,socrates is mortal1 because ,socrates & man & mortal are empirical t]ms1 only to be und]/ood ?r\gh p>ticul> exp]i5ce4 ,! correspond+ proposition 9 pure logic is3 ,if any?+ has a c]ta9 prop]ty1 & :atev] has ?is prop]ty has a c]ta9 o!r prop]ty1 !n ! ?+ 9 "q has ! o!r prop]ty4 ,?is proposition is absolutely g5]al3 x applies to all ?+s & all prop]ties4 ,& x is q self-evid5t4 ,?us 9 su* propositions ( pure logic we h ! self-evid5t g5]al propositions ( :i* we 7 9 se>*4 ,a proposition su* z1 ,if ,socrates is a man1 & all m5 are mortal1 !n ,socrates is mortal1 is true 9 virtue ( its =m alone4 ,its tru?1 9 ?is hypo!tical =m1 does n dep5d ^u :e!r ,socrates actually is a man1 nor ^u :e!r 9 fact all m5 are mortal2 ?us x is equally true :5 we sub/itute o!r t]ms = ,socrates & man & mortal4 ,! g5]al tru? ( :i* x is an in/ance is purely =mal1 & belongs to logic4 ,s9ce x does n m5tion any p>ticul> ?+1 or ev5 any p>ticul> quality or relation1 x is :olly indep5d5t ( ! accid5tal facts ( ! exi/5t _w1 & c be kn[n1 !oretically1 )\t any exp]i5ce ( p>ticul> ?+s or _! qualities & relations4 ,logic1 we may say1 consi/s ( two p>ts4 ,! fir/ "p inve/igates :at propositions are & :at =ms !y may h2 ?is "p enum]ates ! diff]5t k9ds ( atomic propositions1 ( molecul> propositions1 ( g5]al propositions1 & s on4 ,! second "p consi/s ( c]ta9 supremely g5]al propositions1 :i* ass]t ! tru? ( all propositions ( c]ta9 =ms4 ,?is second "p m]ges into pure ma!matics1 ^: propositions all turn out1 on analysis1 to be su* g5]al =mal tru?s4 ,! fir/ "p1 :i* m]ely enum]ates =ms1 is ! m difficult1 & philosophically ! m important2 & x is ! rec5t progress 9 ?is fir/ "p1 m ?an any?+ else1 t has r5d]$ a truly sci5tific discussion ( _m philosophical problems possible4 ,! problem ( ! nature ( judgm5t or belief may be tak5 z an example ( a problem ^: solution dep5ds ^u an adequate inv5tory ( logical =ms4 ,we h already se5 h[ ! suppos$ univ]sality ( ! subject-pr$icate =m made x impossible to give a "r analysis ( s]ial ord]1 & !re=e made space & "t un9telligible4 ,b 9 ?is case x 0 only necess>y to admit relations ( two t]ms4 ,! case ( judgm5t dem&s ! admission ( m complicat$ =ms4 ,if all judgm5ts 7 true1 we might suppose t a judgm5t consi/$ 9 appreh5sion ( a fact1 & t ! appreh5sion 0 a relation ( a m9d to ! fact4 ,f pov]ty 9 ! logical inv5tory1 ?is view has (t5 be5 held4 ,b x leads to absolutely insoluble difficulties 9 ! case ( error4 ,suppose ,i believe t ,*>les ,i4 di$ 9 8 b$4 ,!re is no objective fact ,*>les ,i4's dea? 9 8 b$ to :i* ,i c h a relation ( appreh5sion4 ,*>les ,i4 & dea? & 8 b$ are objective1 b !y are n1 except 9 my ?\ght1 put toge!r z my false belief supposes4 ,x is !re=e necess>y1 9 analys+ a belief1 to look = "s o!r logical =m ?an a two-t]m relation4 ,failure to realise ?is necessity has1 9 my op9ion1 vitiat$ almo/ ev]y?+ t has hi!rto be5 writt5 on ! !ory ( k1 mak+ ! problem ( error insoluble & ! diff]5ce betwe5 belief & p]ception inexplicable4 ,mod]n logic1 z ,i hope is n[ evid5t1 has ! effect ( enl>g+ our ab/ract imag9ation1 & provid+ an inf9ite numb] ( possible hypo!ses to be appli$ 9 ! analysis ( any complex fact4 ,9 ?is respect x is ! exact opposite ( ! logic practis$ by ! classical tradition4 ,9 t logic1 hypo!ses :i* seem prima facie possible are pr(ess$ly prov$ impossible1 & x is decre$ 9 advance t reality mu/ h a c]ta9 special "*4 ,9 mod]n logic1 on ! contr>y1 :ile ! prima facie hypo!ses z a rule rema9 admissible1 o!rs1 :i* only logic w\ld h sugge/$1 are add$ to our /ock1 & are v (t5 f\nd to be indisp5sable if a "r analysis ( ! facts is to be obta9$4 ,! old logic put ?\ght 9 fett]s1 :ile ! new logic gives x w+s4 ,x has1 9 my op9ion1 introduc$ ! same k9d ( advance into philosophy z ,galileo introduc$ into physics1 mak+ x possible at la/ to see :at k9ds ( problems may be capable ( solution1 & :at k9ds mu/ be ab&on$ z beyond human p[]s4 ,& :]e a solution appe>s possible1 ! new logic provides a me?od :i* enables u to obta9 results t d n m]ely embody p]sonal idiosyncrasies1 b mu/ comm& ! ass5t ( all :o are compet5t to =m an op9ion4 ,,lecture ,,iii ,,on ,,our ,,k ,,( ,,! ,,ext]nal ,,_w ,philosophy may be approa*$ by _m roads1 b "o ( ! olde/ & mo/ travell$ is ! road :i* leads ?r\gh d\bt z to ! reality ( ! _w ( s5se4 ,9 ,indian my/icism1 9 ,greek & mod]n moni/ic philosophy f ,p>m5ides onw>d1 9 ,b]keley1 9 mod]n physics1 we f9d s5sible appe>ance criticis$ & condemn$ = a bewild]+ v>iety ( motives4 ,! my/ic condemns x on ! gr\nd ( imm$iate k ( a m real & significant _w beh9d ! veil2 ,p>m5ides & ,plato condemn x because its cont9ual flux is ?\ght inconsi/5t ) ! un*ang+ nature ( ! ab/ract entities reveal$ by logical analysis2 ,b]keley br+s sev]al weapons1 b 8 *ief is ! subjectivity ( s5se-data1 _! dep5d5ce ^u ! organisation & po9t ( view ( ! spectator2 :ile mod]n physics1 on ! basis ( s5sible evid5ce itself1 ma9ta9s a mad dance ( electrons :i* has1 sup]ficially at lea/1 v little resemblance to ! imm$iate objects ( sight or t\*4 ,e "o ( ^! l9es ( attack raises vital & int]e/+ problems4 ,! my/ic1 s long z he m]ely reports a positive revelation1 _c be refut$2 b :5 he d5ies reality to objects ( s5se1 he may be que/ion$ z to :at he means by reality1 & may be ask$ h[ _! unreality foll[s f ! suppos$ reality ( 8 sup]-s5sible _w4 ,9 answ]+ ^! que/ions1 he is l$ to a logic :i* m]ges into t ( ,p>m5ides & ,plato & ! ideali/ tradition4 ,! logic ( ! ideali/ tradition has gradually gr[n v complex & v ab/ruse1 z may be se5 f ! ,bradleian sample consid]$ 9 our fir/ lecture4 ,if we attempt$ to deal fully ) ?is logic1 we %\ld n h "t to rea* any o!r aspect ( our subject2 we w !re=e1 :ile ackn[l$g+ t x des]ves a long discussion1 pass by its c5tral doctr9es ) only su* occasional criticism z may s]ve to exemplify o!r topics1 & conc5trate our att5tion on su* matt]s z its objections to ! cont9uity ( motion & ! inf9ity ( space & "t--objections :i* h be5 fully answ]$ by mod]n ma!maticians 9 a mann] con/itut+ an abid+ triumph = ! me?od ( logical analysis 9 philosophy4 ,^! objections & ! mod]n answ]s to !m w occupy our fif?1 six?1 & sev5? lectures4 ,b]keley's attack1 z re9=c$ by ! physiology ( ! s5se-organs & n]ves & bra91 is v p[]ful4 ,i ?9k x mu/ be admitt$ z probable t ! imm$iate objects ( s5se dep5d = _! exi/5ce ^u physiological conditions 9 ourselves1 & t1 = example1 ! col\r$ surfaces :i* we see cease to exi/ :5 we %ut our eyes4 ,b x w\ld be a mi/ake to inf] t !y are dep5d5t ^u m9d1 n real :ile we see !m1 or n ! sole basis = our k ( ! ext]nal _w4 ,?is l9e ( argum5t w be develop$ 9 ! pres5t lecture4 ,! discrepancy betwe5 ! _w ( physics & ! _w ( s5se1 :i* we %all consid] 9 our f\r? lecture1 w be f\nd to be m app>5t ?an real1 & x w be %[n t :atev] !re is reason to believe 9 physics c probably be int]pret$ 9 t]ms ( s5se4 ,! in/rum5t ( discov]y ?r\gh\t is mod]n logic1 a v diff]5t sci5ce f ! logic ( ! text-books & also f ! logic ( idealism4 ,our second lecture has giv5 a %ort acc\nt ( mod]n logic & ( its po9ts ( div]g5ce f ! v>i\s traditional k9ds ( logic4 ,9 our la/ lecture1 aft] a discussion ( causality & free w1 we %all try to rea* a g5]al acc\nt ( ! logical-analytic me?od ( sci5tific philosophy1 & a t5tative e/imate ( ! hopes ( philosophical progress :i* x all[s u to ent]ta94 ,9 ?is lecture1 ,i wi% to apply ! logical-analytic me?od to "o ( ! olde/ problems ( philosophy1 namely1 ! problem ( our k ( ! ext]nal _w4 ,:at ,i h to say on ?is problem does n am\nt to an answ] ( a def9ite & dogmatic k9d2 x am\nts only to an analysis & /atem5t ( ! que/ions involv$1 ) an indication ( ! directions 9 :i* evid5ce may be s\ght4 ,b al?\gh n yet a def9ite solution1 :at c be said at pres5t seems to me to ?r[ a completely new light on ! problem1 & to be indisp5sable1 n only 9 seek+ ! answ]1 b also 9 ! prelim9>y "q z to :at p>ts ( our problem may possibly h an asc]ta9able answ]4 ,9 e philosophical problem1 our inve/igation />ts f :at may be call$ data1 by :i* ,i mean matt]s ( common k1 vague1 complex1 inexact1 z common k always is1 b yet someh[ comm&+ our ass5t z on ! :ole & 9 "s int]pretation pretty c]ta9ly true4 ,9 ! case ( our pres5t problem1 ! common k involv$ is ( v>i\s k9ds4 ,!re is fir/ our acqua9tance ) p>ticul> objects ( daily life--furniture1 h\ses1 t[ns1 o!r p1 & s on4 ,!n !re is ! ext5sion ( su* p>ticul> k to p>ticul> ?+s outside our p]sonal exp]i5ce1 ?r\gh hi/ory & geography1 newspap]s1 etc4 ,& la/ly1 !re is ! sy/ematisation ( all ?is k ( p>ticul>s by means ( physical sci5ce1 :i* d]ives imm5se p]suasive =ce f its a/oni%+ p[] ( =etell+ ! future4 ,we are q will+ to admit t !re may be errors ( detail 9 ?is k1 b we believe !m to be discov]able & corrigible by ! me?ods :i* h giv5 rise to our beliefs1 & we d n1 z practical m51 ent]ta9 = a mom5t ! hypo!sis t ! :ole edifice may be built on insecure f\ndations4 ,9 ! ma91 !re=e1 & )\t absolute dogmatism z to ?is or t special portion1 we may accept ?is mass ( common k z af=d+ data = our philosophical analysis4 ,x may be said--& ?is is an objection :i* mu/ be met at ! outset--t x is ! duty ( ! philosoph] to call 9 "q ! admitt$ly fallible beliefs ( daily life1 & to replace !m by some?+ m solid & irrefragable4 ,9 a s5se ?is is true1 & 9 a s5se x is effect$ 9 ! c\rse ( analysis4 ,b 9 ano!r s5se1 & a v important "o1 x is q impossible4 ,:ile admitt+ t d\bt is possible ) reg>d to all our common k1 we mu/ nev]!less accept t k 9 ! ma9 if philosophy is to be possible at all4 ,!re is n any sup]f9e br& ( k1 obta9able by ! philosoph]1 :i* c give u a /&po9t f :i* to criticise ! :ole ( ! k ( daily life4 ,! mo/ t c be done is to exam9e & purify our common k by an int]nal scrut9y1 assum+ ! canons by :i* x has be5 obta9$1 & apply+ !m ) m c>e & ) m precision4 ,philosophy _c boa/ ( hav+ a*iev$ su* a degree ( c]ta9ty t x c h au?ority to condemn ! facts ( exp]i5ce & ! laws ( sci5ce4 ,! philosophic scrut9y1 !re=e1 ?\gh sceptical 9 reg>d to e detail1 is n sceptical z reg>ds ! :ole4 ,t is to say1 its criticism ( details w only be bas$ ^u _! relation to o!r details1 n ^u "s ext]nal crit]ion :i* c be appli$ to all ! details equally4 ,! reason = ?is ab/5tion f a univ]sal criticism is n any dogmatic confid5ce1 b its exact opposite2 x is n t common k mu/ be true1 b t we possess no radically diff]5t k9d ( k d]iv$ f "s o!r s\rce4 ,univ]sal scepticism1 ?\gh logically irrefutable1 is practically b>r52 x c only1 !re=e1 give a c]ta9 flav\r ( hesitancy to our beliefs1 & _c be us$ to sub/itute o!r beliefs = !m4 ,al?\gh data c only be criticis$ by o!r data1 n by an outside /&>d1 yet we may di/+ui% diff]5t grades ( c]ta9ty 9 ! diff]5t k9ds ( common k :i* we enum]at$ j n[4 ,:at does n g beyond our own p]sonal s5sible acqua9tance mu/ be = u ! mo/ c]ta93 ! evid5ce ( ! s5ses is prov]bially ! lea/ op5 to "q4 ,:at dep5ds on te/imony1 l ! facts ( hi/ory & geography :i* are le>nt f books1 has v>y+ degrees ( c]ta9ty accord+ to ! nature & ext5t ( ! te/imony4 ,d\bts z to ! exi/5ce ( ,napoleon c only be ma9ta9$ = a joke1 :]eas ! hi/oricity ( ,agamemnon is a legitimate subject ( debate4 ,9 sci5ce1 aga91 we f9d all grades ( c]ta9ty %ort ( ! highe/4 ,! law ( gravitation1 at lea/ z an approximate tru?1 has acquir$ by ?is "t ! same k9d ( c]ta9ty z ! exi/5ce ( ,napoleon1 :]eas ! late/ speculations conc]n+ ! con/itution ( matt] w\ld be univ]sally ackn[l$g$ to h z yet only a r slight probability 9 _! fav\r4 ,^! v>y+ degrees ( c]ta9ty atta*+ to diff]5t data may be reg>d$ z !mselves =m+ "p ( our data2 !y1 along ) ! o!r data1 lie )9 ! vague1 complex1 inexact body ( k :i* x is ! bus9ess ( ! philosoph] to analyse4 ,! fir/ ?+ t appe>s :5 we beg9 to analyse our common k is t "s ( x is d]ivative1 :ile "s is primitive2 t is to say1 !re is "s t we only believe because ( some?+ else f :i* x has be5 inf]r$ 9 "s s5se1 ?\gh n necess>ily 9 a /rict logical s5se1 :ile o!r p>ts are believ$ on _! own acc\nt1 )\t ! support ( any outside evid5ce4 ,x is obvi\s t ! s5ses give k ( ! latt] k9d3 ! imm$iate facts p]ceiv$ by sight or t\* or he>+ d n ne$ to be prov$ by argum5t1 b are completely self-evid5t4 ,psy*ologi/s1 h[ev]1 h made u aw>e t :at is actually giv5 9 s5se is mu* less ?an mo/ p w\ld naturally suppose1 & t mu* ( :at at fir/ sight seems to be giv5 is really inf]r$4 ,?is applies especially 9 reg>d to our space-p]ceptions4 ,= in/ance1 we in/9ctively inf] ! real size & %ape ( a visible object f its app>5t size & %ape1 accord+ to its di/ance & our po9t ( view4 ,:5 we he> a p]son speak+1 our actual s5sations usually miss a great deal ( :at he says1 & we supply its place by unconsci\s inf]5ce2 9 a =eign language1 :]e ?is process is m difficult1 we f9d ourselves app>5tly gr[n deaf1 requir+1 = example1 to be mu* ne>] ! /age at a !atre ?an w\ld be necess>y 9 our own c\ntry4 ,?us ! fir/ /ep 9 ! analysis ( data1 namely1 ! discov]y ( :at is really giv5 9 s5se1 is full ( difficulty4 ,we w1 h[ev]1 n l+] on ?is po9t2 s long z its exi/5ce is realis$1 ! exact outcome does n make any v great diff]5ce 9 our ma9 problem4 ,! next /ep 9 our analysis mu/ be ! consid]ation ( h[ ! d]ivative p>ts ( our common k arise4 ,"h we become involv$ 9 a some:at puzzl+ entanglem5t ( logic & psy*ology4 ,psy*ologically1 a belief may be call$ d]ivative :5ev] x is caus$ by "o or m o!r beliefs1 or by "s fact ( s5se :i* is n simply :at ! belief ass]ts4 ,d]ivative beliefs 9 ?is s5se con/antly arise )\t any process ( logical inf]5ce1 m]ely by association ( ideas or "s equally extra-logical process4 ,f ! expression ( a man's face we judge z to :at he is feel+3 we say we see t he is angry1 :5 9 fact we only see a fr[n4 ,we d n judge z to 8 /ate ( m9d by any logical process3 ! judgm5t gr[s up1 (t5 )\t our be+ able to say :at physical m>k ( emotion we actually saw4 ,9 su* a case1 ! k is d]ivative psy*ologically2 b logically x is 9 a s5se primitive1 s9ce x is n ! result ( any logical d$uction4 ,!re may or may n be a possible d$uction lead+ to ! same result1 b :e!r !re is or n1 we c]ta9ly d n employ x4 ,if we call a belief logically primitive :5 x is n actually arriv$ at by a logical inf]5ce1 !n innum]able beliefs are logically primitive :i* psy*ologically are d]ivative4 ,! sep>ation ( ^! two k9ds ( primitiv5ess is vitally important to our pres5t discussion4 ,:5 we reflect ^u ! beliefs :i* are logically b n psy*ologically primitive1 we f9d t1 unless !y c on reflection be d$uc$ by a logical process f beliefs :i* are also psy*ologically primitive1 our confid5ce 9 _! tru? t5ds to dim9i% ! m we ?9k ab\t !m4 ,we naturally believe1 = example1 t tables & *airs1 trees & m\nta9s1 are /ill !re :5 we turn our backs ^u !m4 ,i d n wi% = a mom5t to ma9ta9 t ?is is c]ta9ly n ! case1 b ,i d ma9ta9 t ! "q :e!r x is ! case is n to be settl$ (f-h& on any suppos$ gr\nd ( obvi\sness4 ,! belief t !y p]si/ is1 9 all m5 except a few philosoph]s1 logically primitive1 b x is n psy*ologically primitive2 psy*ologically1 x arises only ?r\gh our hav+ se5 ^? tables & *airs1 trees & m\nta9s4 ,z soon z ! "q is s]i\sly rais$ :e!r1 because we h se5 !m1 we h a "r to suppose t !y are !re /ill1 we feel t "s k9d ( argum5t mu/ be produc$1 & t if none is =?com+1 our belief c be no m ?an a pi\s op9ion4 ,we d n feel ?is z reg>ds ! imm$iate objects ( s5se3 !re !y are1 & z f> z _! mom5t>y exi/5ce is conc]n$1 no fur!r argum5t is requir$4 ,!re is accord+ly m ne$ ( ju/ify+ our psy*ologically d]ivative beliefs ?an ( ju/ify+ ^? t are primitive4 ,we are ?us l$ to a some:at vague di/9ction betwe5 :at we may call h>d data & s(t data4 ,?is di/9ction is a matt] ( degree1 & mu/ n be press$2 b if n tak5 too s]i\sly x may help to make ! situation cle>4 ,i mean by h>d data ^? :i* resi/ ! solv5t influ5ce ( critical reflection1 & by s(t data ^? :i*1 "u ! op]ation ( ?is process1 become to our m9ds m or less d\btful4 ,! h>de/ ( h>d data are ( two sorts3 ! p>ticul> facts ( s5se1 & ! g5]al tru?s ( logic4 ,! m we reflect ^u ^!1 ! m we realise exactly :at !y are1 & exactly :at a d\bt conc]n+ !m really means1 ! m lum9\sly c]ta9 d !y become4 ,v]bal d\bt conc]n+ ev5 ^! is possible1 b v]bal d\bt may occur :5 :at is nom9ally be+ d\bt$ is n really 9 our ?\ghts1 & only words are actually pres5t to our m9ds4 ,real d\bt1 9 ^! two cases1 w\ld1 ,i ?9k1 be pa?ological4 ,at any rate1 to me !y seem q c]ta91 & ,i %all assume t y agree ) me 9 ?is4 ,)\t ?is assumption1 we are 9 dang] ( fall+ into t univ]sal scepticism :i*1 z we saw1 is z b>r5 z x is irrefutable4 ,if we are to cont9ue philosophis+1 we mu/ make our b[ to ! sceptical hypo!sis1 &1 :ile admitt+ ! elegant t]s5ess ( its philosophy1 proce$ to ! consid]ation ( o!r hypo!ses :i*1 ?\gh p]haps n c]ta91 h at lea/ z good a "r to our respect z ! hypo!sis ( ! sceptic4 ,apply+ our di/9ction ( h>d & s(t data to psy*ologically d]ivative b logically primitive beliefs1 we %all f9d t mo/1 if n all1 are to be class$ z s(t data4 ,!y may be f\nd1 on reflection1 to be capable ( logical pro(1 & !y !n aga9 become believ$1 b no long] z data4 ,z data1 ?\gh entitl$ to a c]ta9 limit$ respect1 !y _c be plac$ on a level ) ! facts ( s5se or ! laws ( logic4 ,! k9d ( respect :i* !y des]ve seems to me su* z to w>rant u 9 hop+1 ?\gh n too confid5tly1 t ! h>d data may prove !m to be at lea/ probable4 ,also1 if ! h>d data are f\nd to ?r[ no light :atev] ^u _! tru? or falsehood1 we are ju/ifi$1 ,i ?9k1 9 giv+ r m weight to ! hypo!sis ( _! tru? ?an to ! hypo!sis ( _! falsehood4 ,= ! pres5t1 h[ev]1 let u conf9e ourselves to ! h>d data1 ) a view to discov]+ :at sort ( _w c be con/ruct$ by _! means alone4 ,our data n[ are prim>ily ! facts ( s5se 7i4e4 ( our own s5se-data7 & ! laws ( logic4 ,b ev5 ! sev]e/ scrut9y w all[ "s additions to ?is sl5d] /ock4 ,"s facts ( memory--especially ( rec5t memory--seem to h ! highe/ degree ( c]ta9ty4 ,"s introspective facts are z c]ta9 z any facts ( s5se4 ,& facts ( s5se !mselves mu/1 = our pres5t purposes1 be int]pret$ ) a c]ta9 latitude4 ,spatial & temporal relations mu/ sometimes be includ$1 = example 9 ! case ( a swift motion fall+ :olly )9 ! speci\s pres5t4 ,& "s facts ( comp>ison1 su* z ! lik5ess or unlik5ess ( two %ades ( col\r1 are c]ta9ly to be includ$ among h>d data4 ,also we mu/ rememb] t ! di/9ction ( h>d & s(t data is psy*ological & subjective1 s t1 if !re are o!r m9ds ?an our own--:i* at our pres5t /age mu/ be held d\btful--! catalogue ( h>d data may be diff]5t = !m f :at x is = u4 ,c]ta9 common beliefs are und\bt$ly exclud$ f h>d data4 ,su* is ! belief :i* l$ u to introduce ! di/9ction1 namely1 t s5sible objects 9 g5]al p]si/ :5 we are n p]ceiv+ !m4 ,su* also is ! belief 9 o!r p's m9ds3 ?is belief is obvi\sly d]ivative f our p]ception ( _! bodies1 & is felt to dem& logical ju/ification z soon z we become aw>e ( its d]ivativ5ess4 ,belief 9 :at is report$ by ! te/imony ( o!rs1 includ+ all t we le>n f books1 is ( c\rse involv$ 9 ! d\bt z to :e!r o!r p h m9ds at all4 ,?us ! _w f :i* our recon/ruction is to beg9 is v fragm5t>y4 ,! be/ we c say = x is t x is slightly m ext5sive ?an ! _w at :i* ,desc>tes arriv$ by a simil> process1 s9ce t _w conta9$ no?+ except himself & 8 ?\ghts4 ,we are n[ 9 a position to und]/& & /ate ! problem ( our k ( ! ext]nal _w1 & to remove v>i\s misund]/&+s :i* h obscur$ ! mean+ ( ! problem4 ,! problem really is3 ,c ! exi/5ce ( any?+ o!r ?an our own h>d data be inf]r$ f ! exi/5ce ( ^? data8 ,b be=e consid]+ ?is problem1 let u briefly consid] :at ! problem is n4 ,:5 we speak ( ! ext]nal _w 9 ?is discussion1 we mu/ n mean spatially ext]nal1 unless space is int]pret$ 9 a peculi> & recondite mann]4 ,! imm$iate objects ( sight1 ! col\r$ surfaces :i* make up ! visible _w1 are spatially ext]nal 9 ! natural mean+ ( ?is phrase4 ,we feel !m to be !re z oppos$ to "h2 )\t mak+ any assumption ( an exi/5ce o!r ?an h>d data1 we c m or less e/imate ! di/ance ( a col\r$ surface4 ,x seems probable t di/ances1 provid$ !y are n too great1 are actually giv5 m or less r\ghly 9 sight2 b :e!r ?is is ! case or n1 ord9>y di/ances c c]ta9ly be e/imat$ approximately by means ( ! data ( s5se alone4 ,! imm$iately giv5 _w is spatial1 & is fur!r n :olly conta9$ )9 our own bodies4 ,?us our k ( :at is ext]nal 9 ?is s5se is n op5 to d\bt4 ,ano!r =m 9 :i* ! "q is (t5 put is3 ,c we "k ( ! exi/5ce ( any reality :i* is indep5d5t ( ourselves8 ,?is =m ( ! "q suff]s f ! ambiguity ( ! two words indep5d5t & self4 ,to take ! ,self fir/3 ! "q z to :at is to be reckon$ "p ( ! ,self & :at is n1 is a v difficult "o4 ,among _m o!r ?+s :i* we may mean by ! ,self1 two may be select$ z specially important1 namely1 7#a7 ! b>e subject :i* ?9ks & is aw>e ( objects1 7#b7 ! :ole assemblage ( ?+s t w\ld necess>ily cease to exi/ if our lives came to an end4 ,! b>e subject1 if x exi/s at all1 is an inf]5ce1 & is n "p ( ! data2 !re=e ?is mean+ ( ,self may be ignor$ 9 our pres5t inquiry4 ,! second mean+ is difficult to make precise1 s9ce we h>dly "k :at ?+s dep5d ^u our lives = _! exi/5ce4 ,& 9 ?is =m1 ! def9ition ( ,self introduces ! ^w dep5d1 :i* raises ! same que/ions z are rais$ by ! ^w indep5d5t4 ,let u !re=e take up ! ^w indep5d5t1 & return to ! ,self lat]4 ,:5 we say t "o ?+ is indep5d5t ( ano!r1 we may mean ei!r t x is logically possible = ! "o to exi/ )\t ! o!r1 or t !re is no causal relation betwe5 ! two su* t ! "o only occurs z ! effect ( ! o!r4 ,! only way1 s f> z ,i "k1 9 :i* "o ?+ c be logically dep5d5t ^u ano!r is :5 ! o!r is "p ( ! "o4 ,! exi/5ce ( a book1 = example1 is logically dep5d5t ^u t ( its pages3 )\t ! pages !re w\ld be no book4 ,?us 9 ?is s5se ! "q1 ,c we "k ( ! exi/5ce ( any reality :i* is indep5d5t ( ourselves8 r$uces to ! "q1 ,c we "k ( ! exi/5ce ( any reality ( :i* our ,self is n "p8 ,9 ?is =m1 ! "q br+s u back to ! problem ( def9+ ! ,self2 b ,i ?9k1 h[ev] ! ,self may be def9$1 ev5 :5 x is tak5 z ! b>e subject1 x _c be suppos$ to be "p ( ! imm$iate object ( s5se2 ?us 9 ?is =m ( ! "q we mu/ admit t we c "k ( ! exi/5ce ( realities indep5d5t ( ourselves4 ,! "q ( causal dep5d5ce is mu* m difficult4 ,to "k t "o k9d ( ?+ is causally indep5d5t ( ano!r1 we mu/ "k t x actually occurs )\t ! o!r4 ,n[ x is fairly obvi\s t1 :atev] legitimate mean+ we give to ! ,self1 our ?\ghts & feel+s are causally dep5d5t ^u ourselves1 i4e4 d n occur :5 !re is no ,self = !m to belong to4 ,b 9 ! case ( objects ( s5se ?is is n obvi\s2 inde$1 z we saw1 ! common-s5se view is t su* objects p]si/ 9 ! abs5ce ( any p]cipi5t4 ,if ?is is ! case1 !n !y are causally indep5d5t ( ourselves2 if n1 n4 ,?us 9 ?is =m ! "q r$uces to ! "q :e!r we c "k t objects ( s5se1 or any o!r objects n our own ?\ghts & feel+s1 exi/ at times :5 we are n p]ceiv+ !m4 ,?is =m1 9 :i* ! difficult ^w indep5d5t no long] occurs1 is ! =m 9 :i* we /at$ ! problem a m9ute ago4 ,our "q 9 ! above =m raises two di/9ct problems1 :i* x is important to keep sep>ate4 ,fir/1 c we "k t objects ( s5se1 or v simil> objects1 exi/ at times :5 we are n p]ceiv+ !m8 ,secondly1 if ?is _c be kn[n1 c we "k t o!r objects1 inf]able f objects ( s5se b n necess>ily resembl+ !m1 exi/ ei!r :5 we are p]ceiv+ ! objects ( s5se or at any o!r "t8 ,?is latt] problem arises 9 philosophy z ! problem ( ! ?+ 9 itself1 & 9 sci5ce z ! problem ( matt] z assum$ 9 physics4 ,we w consid] ?is latt] problem fir/4 ,ow+ to ! fact t we feel passive 9 s5sation1 we naturally suppose t our s5sations h outside causes4 ,n[ x is necess>y "h fir/ ( all to di/+ui% betwe5 7#a7 our s5sation1 :i* is a m5tal ev5t consi/+ 9 our be+ aw>e ( a s5sible object1 & 7#b7 ! s5sible object ( :i* we are aw>e 9 s5sation4 ,:5 ,i speak ( ! s5sible object1 x mu/ be und]/ood t ,i d n mean su* a ?+ z a table1 :i* is bo? visible & tangible1 c be se5 by _m p at once1 & is m or less p]man5t4 ,:at ,i mean is j t pat* ( col\r :i* is mom5t>ily se5 :5 we look at ! table1 or j t p>ticul> h>dness :i* is felt :5 we press x1 or j t p>ticul> s\nd :i* is he>d :5 we rap x4 ,ea* ( ^! ,i call a s5sible object1 & our aw>5ess ( x ,i call a s5sation4 ,n[ our s5se ( passivity1 if x really af=d$ any argum5t1 w\ld only t5d to %[ t ! s5sation has an outside cause2 ?is cause we %\ld naturally seek 9 ! s5sible object4 ,?us !re is no good reason1 s f>1 = suppos+ t s5sible objects mu/ h outside causes4 ,b bo? ! ?+-9-itself ( philosophy & ! matt] ( physics pres5t !mselves z outside causes ( ! s5sible object z mu* z ( ! s5sation4 ,:at are ! gr\nds = ?is common op9ion8 ,9 ea* case1 ,i ?9k1 ! op9ion has result$ f ! comb9ation ( a belief t some?+ :i* c p]si/ indep5d5tly ( our consci\sness makes itself kn[n 9 s5sation1 ) ! fact t our s5sations (t5 *ange 9 ways :i* seem to dep5d ^u u r ?an ^u any?+ :i* w\ld be suppos$ to p]si/ indep5d5tly ( u4 ,at fir/1 we believe unreflect+ly t ev]y?+ is z x seems to be1 & t1 if we %ut our eyes1 ! objects we _h be5 see+ rema9 z !y 7 ?\gh we no long] see !m4 ,b !re are argum5ts aga9/ ?is view1 :i* h g5]ally be5 ?\ght conclusive4 ,x is extraord9>ily difficult to see j :at ! argum5ts prove2 b if we are to make any progress ) ! problem ( ! ext]nal _w1 we mu/ try to make up our m9ds z to ^! argum5ts4 ,a table view$ f "o place pres5ts a diff]5t appe>ance f t :i* x pres5ts f ano!r place4 ,?is is ! language ( common s5se1 b ?is language already assumes t !re is a real table ( :i* we see ! appe>ances4 ,let u try to /ate :at is kn[n 9 t]ms ( s5sible objects alone1 )\t any elem5t ( hypo!sis4 ,we f9d t z we walk r\nd ! table1 we p]ceive a s]ies ( gradually *ang+ visible objects4 ,b 9 speak+ ( walk+ r\nd ! table1 we h /ill reta9$ ! hypo!sis t !re is a s+le table connect$ ) all ! appe>ances4 ,:at we ought to say is t1 :ile we h ^? muscul> & o!r s5sations :i* make u say we are walk+1 our visual s5sations *ange 9 a cont9u\s way1 s t1 = example1 a /rik+ pat* ( col\r is n sudd5ly replac$ by some?+ :olly diff]5t1 b is replac$ by an ins5sible gradation ( slightly diff]5t col\rs ) slightly diff]5t %apes4 ,?is is :at we really "k by exp]i5ce1 :5 we h fre$ our m9ds f ! assumption ( p]man5t ?+s ) *ang+ appe>ances4 ,:at is really kn[n is a correlation ( muscul> & o!r bodily s5sations ) *anges 9 visual s5sations4 ,b walk+ r\nd ! table is n ! only way ( alt]+ its appe>ance4 ,we c %ut "o eye1 or put on blue spectacles1 or look ?r\gh a microscope4 ,all ^! op]ations1 9 v>i\s ways1 alt] ! visual appe>ance :i* we call t ( ! table4 ,m di/ant objects w also alt] _! appe>ance if 7z we say7 ! /ate ( ! atmosph]e *anges--if !re is fog or ra9 or sun%9e4 ,physiological *anges also alt] ! appe>ances ( ?+s4 ,if we assume ! _w ( common s5se1 all ^! *anges1 includ+ ^? attribut$ to physiological causes1 are *anges 9 ! int]v5+ m$ium4 ,x is n q s easy z 9 ! =m] case to r$uce ?is set ( facts to a =m 9 :i* no?+ is assum$ beyond s5sible objects4 ,any?+ int]v5+ betwe5 ourselves & :at we see mu/ be invisible3 our view 9 e direction is b\nd$ by ! ne>e/ visible object4 ,x might be object$ t a dirty pane ( glass1 = example1 is visible al?\gh we c see ?+s ?r\gh x4 ,b 9 ?is case we really see a spott$ pat*work3 ! dirti] specks 9 ! glass are visible1 :ile ! clean] p>ts are invisible & all[ u to see :at is beyond4 ,?us ! discov]y t ! int]v5+ m$ium affects ! appe>ances ( ?+s _c be made by means ( ! s5se ( sight alone4 ,let u take ! case ( ! blue spectacles1 :i* is ! simple/1 b may s]ve z a type = ! o!rs4 ,! frame ( ! spectacles is ( c\rse visible1 b ! blue glass1 if x is clean1 is n visible4 ,! blu5ess1 :i* we say is 9 ! glass1 appe>s z be+ 9 ! objects se5 ?r\gh ! glass4 ,! glass itself is kn[n by means ( ! s5se ( t\*4 ,9 ord] to "k t x is betwe5 u & ! objects se5 ?r\gh x1 we mu/ "k h[ to correlate ! space ( t\* ) ! space ( sight4 ,?is correlation itself1 :5 /at$ 9 t]ms ( ! data ( s5se alone1 is by no means a simple matt]4 ,b x pres5ts no difficulties ( pr9ciple1 & may !re=e be suppos$ accompli%$4 ,:5 x has be5 accompli%$1 x becomes possible to atta* a mean+ to ! /atem5t t ! blue glass1 :i* we c t\*1 is betwe5 u & ! object se51 z we say1 ?r\gh x4 ,b we h /ill n r$uc$ our /atem5t completely to :at is actually giv5 9 s5se4 ,we h fall5 into ! assumption t ! object ( :i* we are consci\s :5 we t\* ! blue spectacles /ill exi/s aft] we h ceas$ to t\* !m4 ,s long z we are t\*+ !m1 no?+ except our f+] c be se5 ?r\gh ! "p t\*$1 :i* is ! only "p :]e we imm$iately "k t !re is some?+4 ,if we are to acc\nt = ! blue appe>ance ( objects o!r ?an ! spectacles1 :5 se5 ?r\gh !m1 x might seem z if we mu/ assume t ! spectacles /ill exi/ :5 we are n t\*+ !m2 & if ?is assumption really is necess>y1 our ma9 problem is answ]$3 we h means ( kn[+ ( ! pres5t exi/5ce ( objects n giv5 9 s5se1 ?\gh ( ! same k9d z objects =m]ly giv5 9 s5se4 ,x may be que/ion$1 h[ev]1 :e!r ?is assumption is actually unavoidable1 ?\gh x is unque/ionably ! mo/ natural "o to make4 ,we may say t ! object ( :i* we become aw>e :5 we t\* ! spectacles cont9ues to h effects aft]w>ds1 ?\gh p]haps x no long] exi/s4 ,9 ?is view1 ! suppos$ cont9u$ exi/5ce ( s5sible objects aft] !y h ceas$ to be s5sible w be a fallaci\s inf]5ce f ! fact t !y /ill h effects4 ,x is (t5 suppos$ t no?+ :i* has ceas$ to exi/ c cont9ue to h effects1 b ?is is a m]e prejudice1 due to a wrong conception ( causality4 ,we _c1 !re=e1 dismiss our pres5t hypo!sis on ! gr\nd ( a priori impossibility1 b mu/ exam9e fur!r :e!r x c really acc\nt = ! facts4 ,x may be said t our hypo!sis is useless 9 ! case :5 ! blue glass is nev] t\*$ at all4 ,h[1 9 t case1 are we to acc\nt = ! blue appe>ance ( objects8 ,& m g5]ally1 :at are we to make ( ! hypo!tical s5sations ( t\* :i* we associate ) unt\*$ visible objects1 :i* we "k w\ld be v]ifi$ if we *ose1 ?\gh 9 fact we d n v]ify !m8 ,mu/ n ^! be attribut$ to p]man5t possession1 by ! objects1 ( ! prop]ties :i* t\* w\ld reveal8 ,let u consid] ! m g5]al "q fir/4 ,exp]i5ce has taught u t :]e we see c]ta9 k9ds ( col\r$ surfaces we c1 by t\*1 obta9 c]ta9 expect$ s5sations ( h>dness or s(tness1 tactile %ape1 & s on4 ,?is leads u to believe t :at is se5 is usually tangible1 & t x has1 :e!r we t\* x or n1 ! h>dness or s(tness :i* we %\ld expect to feel if we t\*$ x4 ,b ! m]e fact t we are able to inf] :at our tactile s5sations w\ld be %[s t x is n logically necess>y to assume tactile qualities be=e !y are felt4 ,all t is really kn[n is t ! visual appe>ance 9 "q1 toge!r ) t\*1 w lead to c]ta9 s5sations1 :i* c necess>ily be det]m9$ 9 t]ms ( ! visual appe>ance1 s9ce o!rwise !y c\ld n be inf]r$ f x4 ,we c n[ give a /atem5t ( ! exp]i5c$ facts conc]n+ ! blue spectacles1 :i* w supply an int]pretation ( common-s5se beliefs )\t assum+ any?+ beyond ! exi/5ce ( s5sible objects at ! times :5 !y are s5sible4 ,by exp]i5ce ( ! correlation ( t\* & sight s5sations1 we become able to associate a c]ta9 place 9 t\*-space ) a c]ta9 correspond+ place 9 sight-space4 ,sometimes1 namely 9 ! case ( transp>5t ?+s1 we f9d t !re is a tangible object 9 a t\*-place )\t !re be+ any visible object 9 ! correspond+ sight-place4 ,b 9 su* a case z t ( ! blue spectacles1 we f9d t :atev] object is visible beyond ! empty sight-place 9 ! same l9e ( sight has a diff]5t col\r f :at x has :5 !re is no tangible object 9 ! int]v5+ t\*-place2 & z we move ! tangible object 9 t\*-space1 ! blue pat* moves 9 sight-space4 ,if n[ we f9d a blue pat* mov+ 9 ?is way 9 sight-space1 :5 we h no s5sible exp]i5ce ( an int]v5+ tangible object1 we nev]!less inf] t1 if we put our h& at a c]ta9 place 9 t\*-space1 we %\ld exp]i5ce a c]ta9 t\*-s5sation4 ,if we are to avoid non-s5sible objects1 ?is mu/ be tak5 z ! :ole ( our mean+ :5 we say t ! blue spectacles are 9 a c]ta9 place1 ?\gh we h n t\*$ !m1 & h only se5 o!r ?+s r5d]$ blue by _! int]position4 ,i ?9k x may be laid d[n q g5]ally t1 9 s f> z physics or common s5se is v]ifiable1 x mu/ be capable ( int]pretation 9 t]ms ( actual s5se-data alone4 ,! reason = ?is is simple4 ,v]ification consi/s always 9 ! occurr5ce ( an expect$ s5se-datum4 ,a/ronom]s tell u !re w be an eclipse ( ! moon3 we look at ! moon1 & f9d ! e>?'s %ad[ bit+ into x1 t is to say1 we see an appe>ance q diff]5t f t ( ! usual full moon4 ,n[ if an expect$ s5se-datum con/itutes a v]ification1 :at 0 ass]t$ mu/ h be5 ab\t s5se-data2 or1 at any rate1 if "p ( :at 0 ass]t$ 0 n ab\t s5se-data1 !n only ! o!r "p has be5 v]ifi$4 ,!re is 9 fact a c]ta9 regul>ity or con=mity to law ab\t ! occurr5ce ( s5se-data1 b ! s5se-data t occur at "o "t are (t5 causally connect$ ) ^? t occur at q o!r times1 & n1 or at lea/ n v closely1 ) ^? t occur at neighb\r+ times4 ,if ,i look at ! moon & imm$iately aft]w>ds he> a tra9 com+1 !re is no v close causal connection betwe5 my two s5se-data2 b if ,i look at ! moon on two nights a week ap>t1 !re is a v close causal connection betwe5 ! two s5se-data4 ,! simple/1 or at lea/ ! easie/1 /atem5t ( ! connection is obta9$ by imag9+ a real moon :i* goes on :e!r ,i look at x or n1 provid+ a s]ies ( possible s5se-data ( :i* only ^? are actual :i* belong to mom5ts :5 ,i *oose to look at ! moon4 ,b ! degree ( v]ification obta9able 9 ?is way is v small4 ,x mu/ be rememb]$ t1 at our pres5t level ( d\bt1 we are n at lib]ty to accept te/imony4 ,:5 we he> c]ta9 noises1 :i* are ^? we %\ld utt] if we wi%$ to express a c]ta9 ?\ght1 we assume t t ?\ght1 or "o v l x1 has be5 9 ano!r m9d1 & has giv5 rise to ! expression :i* we he>4 ,if at ! same "t we see a body resembl+ our own1 mov+ its lips z we move ours :5 we speak1 we _c resi/ ! belief t x is alive1 & t ! feel+s inside x cont9ue :5 we are n look+ at x4 ,:5 we see our fri5d drop a weight ^u 8 toe1 & he> him say--:at we %\ld say 9 simil> circum/ances1 ! ph5om5a c no d\bt be expla9$ )\t assum+ t he is any?+ b a s]ies ( %apes & noises se5 & he>d by u1 b practically no man is s infect$ ) philosophy z n to be q c]ta9 t 8 fri5d has felt ! same k9d ( pa9 z he himself w\ld feel4 ,we w consid] ! legitimacy ( ?is belief pres5tly2 = ! mom5t1 ,i only wi% to po9t out t x ne$s ! same k9d ( ju/ification z our belief t ! moon exi/s :5 we d n see x1 & t1 )\t x1 te/imony he>d or read is r$uc$ to noises & %apes1 & _c be reg>d$ z evid5ce ( ! facts :i* x reports4 ,! v]ification ( physics :i* is possible at our pres5t level is1 !re=e1 only t degree ( v]ification :i* is possible by "o man's unaid$ obs]vations1 :i* w n c>ry u v f> t[>ds ! e/abli%m5t ( a :ole sci5ce4 ,be=e proce$+ fur!r1 let u summ>ise ! argum5t s f> z x has gone4 ,! problem is3 ,c ! exi/5ce ( any?+ o!r ?an our own h>d data be inf]r$ f ^! data8 ,x is a mi/ake to /ate ! problem 9 ! =m3 ,c we "k ( ! exi/5ce ( any?+ o!r ?an ourselves & our /ates8 or3 ,c we "k ( ! exi/5ce ( any?+ indep5d5t ( ourselves8 because ( ! extreme difficulty ( def9+ self & indep5d5t precisely4 ,! felt passivity ( s5sation is irrelevant1 s9ce1 ev5 if x prov$ any?+1 x c\ld only prove t s5sations are caus$ by s5sible objects4 ,! natural naive belief is t ?+s se5 p]si/1 :5 unse51 exactly or approximately z !y appe>$ :5 se52 b ?is belief t5ds to be dispell$ by ! fact t :at common s5se reg>ds z ! appe>ance ( "o object *anges ) :at common s5se reg>ds z *anges 9 ! po9t ( view & 9 ! int]v5+ m$ium1 includ+ 9 ! latt] our own s5se-organs & n]ves & bra94 ,?is fact1 z j /at$1 assumes1 h[ev]1 ! common-s5se _w ( /able objects :i* x pr(esses to call 9 "q2 h5ce1 be=e we c discov] its precise be>+ on our problem1 we mu/ f9d a way ( /at+ x :i* does n involve any ( ! assumptions :i* x is design$ to r5d] d\btful4 ,:at we !n f9d1 z ! b>e outcome ( exp]i5ce1 is t gradual *anges 9 c]ta9 s5se-data are correlat$ ) gradual *anges 9 c]ta9 o!rs1 or 79 ! case ( bodily motions7 ) ! o!r s5se-data !mselves4 ,! assumption t s5sible objects p]si/ aft] !y h ceas$ to be s5sible--= example1 t ! h>dness ( a visible body1 :i* has be5 discov]$ by t\*1 cont9ues :5 ! body is no long] t\*$--may be replac$ by ! /atem5t t ! effects ( s5sible objects p]si/1 i4e4 t :at happ5s n[ c only be acc\nt$ =1 9 _m cases1 by tak+ acc\nt ( :at happ5$ at an e>li] "t4 ,ev]y?+ t "o man1 by 8 own p]sonal exp]i5ce1 c v]ify 9 ! acc\nt ( ! _w giv5 by common s5se & physics1 w be explicable by "s su* means1 s9ce v]ification consi/s m]ely 9 ! occurr5ce ( an expect$ s5se-datum4 ,b :at dep5ds ^u te/imony1 :e!r he>d or read1 _c be expla9$ 9 ?is way1 s9ce te/imony dep5ds ^u ! exi/5ce ( m9ds o!r ?an our own1 & ?us requires a k ( some?+ n giv5 9 s5se4 ,b be=e exam9+ ! "q ( our k ( o!r m9ds1 let u return to ! "q ( ! ?+-9-itself1 namely1 to ! !ory t :at exi/s at times :5 we are n p]ceiv+ a giv5 s5sible object is some?+ q unlike t object1 some?+ :i*1 toge!r ) u & our s5se-organs1 causes our s5sations1 b is nev] itself giv5 9 s5sation4 ,! ?+-9-itself1 :5 we />t f common-s5se assumptions1 is a fairly natural outcome ( ! difficulties due to ! *ang+ appe>ances ( :at is suppos$ to be "o object4 ,x is suppos$ t ! table 7= example7 causes our s5se-data ( sight & t\*1 b mu/1 s9ce ^! are alt]$ by ! po9t ( view & ! int]v5+ m$ium1 be q diff]5t f ! s5se-data to :i* x gives rise4 ,!re is1 9 ?is !ory1 a t5d5cy to a confusion f :i* x d]ives "s ( its plausibility1 namely1 ! confusion betwe5 a s5sation z a psy*ical occurr5ce & its object4 ,a pat* ( col\r1 ev5 if x only exi/s :5 x is se51 is /ill some?+ q diff]5t f ! see+ ( x3 ! see+ ( x is m5tal1 b ! pat* ( col\r is n4 ,?is confusion1 h[ev]1 c be avoid$ )\t our necess>ily ab&on+ ! !ory we are exam9+4 ,! objection to x1 ,i ?9k1 lies 9 its failure to realise ! radical nature ( ! recon/ruction dem&$ by ! difficulties to :i* x po9ts4 ,we _c speak legitimately ( *anges 9 ! po9t ( view & ! int]v5+ m$ium until we h already con/ruct$ "s _w m /able ?an t ( mom5t>y s5sation4 ,our discussion ( ! blue spectacles & ! walk r\nd ! table has1 ,i hope1 made ?is cle>4 ,b :at rema9s f> f cle> is ! nature ( ! recon/ruction requir$4 ,al?\gh we _c re/ cont5t ) ! above !ory1 9 ! t]ms 9 :i* x is /at$1 we mu/ nev]!less treat x ) a c]ta9 respect1 = x is 9 outl9e ! !ory ^u :i* physical sci5ce & physiology are built1 & x mu/1 !re=e1 be susceptible ( a true int]pretation4 ,let u see h[ ?is is to be done4 ,! fir/ ?+ to realise is t !re are no su* ?+s z illusions ( s5se4 ,objects ( s5se1 ev5 :5 !y occur 9 dreams1 are ! mo/ indubitably real objects kn[n to u4 ,:at1 !n1 makes u call !m unreal 9 dreams8 ,m]ely ! unusual nature ( _! connection ) o!r objects ( s5se4 ,i dream t ,i am 9 ,am]ica1 b ,i wake up & f9d myself 9 ,engl& )\t ^? int]v5+ days on ! ,atlantic :i*1 alas6 are insep>ably connect$ ) a real visit to ,am]ica4 ,objects ( s5se are call$ real :5 !y h ! k9d ( connection ) o!r objects ( s5se :i* exp]i5ce has l$ u to reg>d z normal2 :5 !y fail 9 ?is1 !y are call$ illusions4 ,b :at is illusory is only ! inf]5ces to :i* !y give rise2 9 !mselves1 !y are e bit z real z ! objects ( wak+ life4 ,& conv]sely1 ! s5sible objects ( wak+ life mu/ n be expect$ to h any m intr9sic reality ?an ^? ( dreams4 ,dreams & wak+ life1 9 our fir/ ef=ts at con/ruction1 mu/ be treat$ ) equal respect2 x is only by "s reality n m]ely s5sible t dreams c be condemn$4 ,accept+ ! indubitable mom5t>y reality ( objects ( s5se1 ! next ?+ to notice is ! confusion und]ly+ objections d]iv$ f _! *angeabl5ess4 ,z we walk r\nd ! table1 its aspect *anges2 b x is ?\ght impossible to ma9ta9 ei!r t ! table *anges1 or t its v>i\s aspects c all really exi/ 9 ! same place4 ,if we press "o eyeball1 we %all see two tables2 b x is ?\ght prepo/]\s to ma9ta9 t !re are really two tables4 ,su* argum5ts1 h[ev]1 seem to involve ! assumption t !re c be some?+ m real ?an objects ( s5se4 ,if we see two tables1 !n !re are two visual tables4 ,x is p]fectly true t1 at ! same mom5t1 we may discov] by t\* t !re is only "o tactile table4 ,?is makes u decl>e ! two visual tables an illusion1 because usually "o visual object corresponds to "o tactile object4 ,b all t we are w>rant$ 9 say+ is t1 9 ?is case1 ! mann] ( correlation ( t\* & sight is unusual4 ,aga91 :5 ! aspect ( ! table *anges z we walk r\nd x1 & we are told !re _c be s _m diff]5t aspects 9 ! same place1 ! answ] is simple3 :at does ! critic ( ! table mean by ! same place8 ,! use ( su* a phrase presupposes t all our difficulties h be5 solv$2 z yet1 we h no "r to speak ( a place except ) ref]5ce to "o giv5 set ( mom5t>y s5se-data4 ,:5 all are *ang$ by a bodily movem5t1 no place rema9s ! same z x 04 ,?us ! difficulty1 if x exi/s1 has at lea/ n be5 rightly /at$4 ,we w n[ make a new />t1 adopt+ a diff]5t me?od4 ,in/ead ( inquir+ :at is ! m9imum ( assumption by :i* we c expla9 ! _w ( s5se1 we w1 9 ord] to h a model hypo!sis z a help = ! imag9ation1 con/ruct "o possible 7n necess>y7 explanation ( ! facts4 ,x may p]haps !n be possible to p>e away :at is sup]flu\s 9 our hypo!sis1 leav+ a residue :i* may be reg>d$ z ! ab/ract answ] to our problem4 ,let u imag9e t ea* m9d looks out ^u ! _w1 z 9 ,leibniz's monadology1 f a po9t ( view peculi> to itself2 & = ! sake ( simplicity let u conf9e ourselves to ! s5se ( sight1 ignor+ m9ds :i* are devoid ( ?is s5se4 ,ea* m9d sees at ea* mom5t an imm5sely complex ?ree-dim5sional _w2 b !re is absolutely no?+ :i* is se5 by two m9ds simultane\sly4 ,:5 we say t two p see ! same ?+1 we always f9d t1 ow+ to diff]5ce ( po9t ( view1 !re are diff]5ces1 h[ev] slight1 betwe5 _! imm$iate s5sible objects4 7,i am "h assum+ ! validity ( te/imony1 b z we are only con/ruct+ a possible !ory1 t is a legitimate assumption47 ,! ?ree-dim5sional _w se5 by "o m9d !re=e conta9s no place 9 common ) t se5 by ano!r1 = places c only be con/itut$ by ! ?+s 9 or ar\nd !m4 ,h5ce we may suppose1 9 spite ( ! diff]5ces betwe5 ! diff]5t worlds1 t ea* exi/s entire exactly z x is p]ceiv$1 & might be exactly z x is ev5 if x 7 n p]ceiv$4 ,we may fur!r suppose t !re are an inf9ite numb] ( su* worlds :i* are 9 fact unp]ceiv$4 ,if two m5 are sitt+ 9 a room1 two some:at simil> worlds are p]ceiv$ by !m2 if a ?ird man ent]s & sits betwe5 !m1 a ?ird _w1 int]m$iate betwe5 ! two previ\s worlds1 beg9s to be p]ceiv$4 ,x is true t we _c reasonably suppose j ?is _w to h exi/$ be=e1 because x is condition$ by ! s5se-organs1 n]ves1 & bra9 ( ! newly arriv$ man2 b we c reasonably suppose t "s aspect ( ! univ]se exi/$ f t po9t ( view1 ?\gh no "o 0 p]ceiv+ x4 ,! sy/em consi/+ ( all views ( ! univ]se p]ceiv$ & unp]ceiv$1 ,i %all call ! sy/em ( p]spectives2 ,i %all conf9e ! expression private worlds to su* views ( ! univ]se z are actually p]ceiv$4 ,?us a private _w is a p]ceiv$ p]spective2 b !re may be any numb] ( unp]ceiv$ p]spectives4 ,two m5 are sometimes f\nd to p]ceive v simil> p]spectives1 s simil> t !y c use ! same words to describe !m4 ,!y say !y see ! same table1 because ! diff]5ces betwe5 ! two tables !y see are slight & n practically important4 ,?us x is possible1 sometimes1 to e/abli% a correlation by simil>ity betwe5 a great _m ( ! ?+s ( "o p]spective1 & a great _m ( ! ?+s ( ano!r4 ,9 case ! simil>ity is v great1 we say ! po9ts ( view ( ! two p]spectives are ne> toge!r 9 space2 b ?is space 9 :i* !y are ne> toge!r is totally diff]5t f ! spaces inside ! two p]spectives4 ,x is a relation betwe5 ! p]spectives1 & is n 9 ei!r ( !m2 no "o c p]ceive x1 & if x is to be kn[n x c be only by inf]5ce4 ,betwe5 two p]ceiv$ p]spectives :i* are simil>1 we c imag9e a :ole s]ies ( o!r p]spectives1 "s at lea/ unp]ceiv$1 & su* t betwe5 any two1 h[ev] simil>1 !re are o!rs /ill m simil>4 ,9 ?is way ! space :i* consi/s ( relations betwe5 p]spectives c be r5d]$ cont9u\s1 & 7if we *oose7 ?ree-dim5sional4 ,we c n[ def9e ! mom5t>y common-s5se ?+1 z oppos$ to its mom5t>y appe>ances4 ,by ! simil>ity ( neighb\r+ p]spectives1 _m objects 9 ! "o c be correlat$ ) objects 9 ! o!r1 namely1 ) ! simil> objects4 ,giv5 an object 9 "o p]spective1 =m ! sy/em ( all ! objects correlat$ ) x 9 all ! p]spectives2 t sy/em may be id5tifi$ ) ! mom5t>y common-s5se ?+4 ,?us an aspect ( a ?+ is a memb] ( ! sy/em ( aspects :i* is ! ?+ at t mom5t4 7,! correlation ( ! times ( diff]5t p]spectives raises c]ta9 complications1 ( ! k9d consid]$ 9 ! !ory ( relativity2 b we may ignore ^! at pres5t47 ,all ! aspects ( a ?+ are real1 :]eas ! ?+ is a m]e logical con/ruction4 ,x has1 h[ev]1 ! m]it ( be+ neutral z betwe5 diff]5t po9ts ( view1 & ( be+ visible to m ?an "o p]son1 9 ! only s5se 9 :i* x c ev] be visible1 namely1 9 ! s5se t ea* sees "o ( its aspects4 ,x w be obs]v$ t1 :ile ea* p]spective conta9s its own space1 !re is only "o space 9 :i* ! p]spectives !mselves are ! elem5ts4 ,!re are z _m private spaces z !re are p]spectives2 !re are !re=e at lea/ z _m z !re are p]cipi5ts1 & !re may be any numb] ( o!rs :i* h a m]ely mat]ial exi/5ce & are n se5 by anyone4 ,b !re is only "o p]spective-space1 ^: elem5ts are s+le p]spectives1 ea* ) its own private space4 ,we h n[ to expla9 h[ ! private space ( a s+le p]spective is correlat$ ) "p ( ! "o all-embrac+ p]spective space4 ,p]spective space is ! sy/em ( po9ts ( view ( private spaces 7p]spectives71 or1 s9ce po9ts ( view h n be5 def9$1 we may say x is ! sy/em ( ! private spaces !mselves4 ,^! private spaces w ea* c\nt z "o po9t1 or at any rate z "o elem5t1 9 p]spective space4 ,!y are ord]$ by means ( _! simil>ities4 ,suppose1 = example1 t we />t f "o :i* conta9s ! appe>ance ( a circul> disc1 su* z w\ld be call$ a p5ny1 & suppose ?is appe>ance1 9 ! p]spective 9 "q1 is circul>1 n elliptic4 ,we c !n =m a :ole s]ies ( p]spectives conta9+ a graduat$ s]ies ( circul> aspects ( v>y+ sizes3 = ?is purpose we only h to move 7z we say7 t[>ds ! p5ny or away f x4 ,! p]spectives 9 :i* ! p5ny looks circul> w be said to lie on a /raight l9e 9 p]spective space1 & _! ord] on ?is l9e w be t ( ! sizes ( ! circul> aspects4 ,moreov]--?\gh ?is /atem5t mu/ be notic$ & subsequ5tly exam9$--! p]spectives 9 :i* ! p5ny looks big w be said to be ne>] to ! p5ny ?an ^? 9 :i* x looks small4 ,x is to be rem>k$ also t any o!r ?+ ?an our p5ny might h be5 *os5 to def9e ! relations ( our p]spectives 9 p]spective space1 & t exp]i5ce %[s t ! same spatial ord] ( p]spectives w\ld h result$4 ,9 ord] to expla9 ! correlation ( private spaces ) p]spective space1 we h fir/ to expla9 :at is meant by ! place 79 p]spective space7 :]e a ?+ is4 ,= ?is purpose1 let u aga9 consid] ! p5ny :i* appe>s 9 _m p]spectives4 ,we =m$ a /raight l9e ( p]spectives 9 :i* ! p5ny look$ circul>1 & we agre$ t ^? 9 :i* x look$ l>g] 7 to be consid]$ z ne>] to ! p5ny4 ,we c =m ano!r /raight l9e ( p]spectives 9 :i* ! p5ny is se5 end-on & looks l a /raight l9e ( a c]ta9 ?ickness4 ,^! two l9es w meet 9 a c]ta9 place 9 p]spective space1 i4e4 9 a c]ta9 p]spective1 :i* may be def9$ z ! place 79 p]spective space7 :]e ! p5ny is4 ,x is true t1 9 ord] to prolong our l9es until !y rea* ?is place1 we %all h to make use ( o!r ?+s besides ! p5ny1 because1 s f> z exp]i5ce goes1 ! p5ny ceases to pres5t any appe>ance aft] we h come s ne> to x t x t\*es ! eye4 ,b ?is raises no real difficulty1 because ! spatial ord] ( p]spectives is f\nd empirically to be indep5d5t ( ! p>ticul> ?+s *os5 = def9+ ! ord]4 ,we c1 = example1 remove our p5ny & prolong ea* ( our two /raight l9es up to _! int]section by plac+ o!r p5nies fur!r (f 9 su* a way t ! aspects ( ! "o are circul> :]e ^? ( our orig9al p5ny 7 circul>1 & ! aspects ( ! o!r are /raight :]e ^? ( our orig9al p5ny 7 /raight4 ,!re w !n be j "o p]spective 9 :i* "o ( ! new p5nies looks circul> & ! o!r /raight4 ,?is w be1 by def9ition1 ! place :]e ! orig9al p5ny 0 9 p]spective space4 ,! above is1 ( c\rse1 only a fir/ r\gh sket* ( ! way 9 :i* our def9ition is to be rea*$4 ,x neglects ! size ( ! p5ny1 & x assumes t we c remove ! p5ny )\t be+ di/urb$ by any simultane\s *anges 9 ! positions ( o!r ?+s4 ,b x is pla9 t su* niceties _c affect ! pr9ciple1 & c only introduce complications 9 its application4 ,hav+ n[ def9$ ! p]spective :i* is ! place :]e a giv5 ?+ is1 we c und]/& :at is meant by say+ t ! p]spectives 9 :i* a ?+ looks l>ge are ne>] to ! ?+ ?an ^? 9 :i* x looks small3 !y are1 9 fact1 ne>] to ! p]spective :i* is ! place :]e ! ?+ is4 ,we c n[ also expla9 ! correlation betwe5 a private space & p>ts ( p]spective space4 ,if !re is an aspect ( a giv5 ?+ 9 a c]ta9 private space1 !n we correlate ! place :]e ?is aspect is 9 ! private space ) ! place :]e ! ?+ is 9 p]spective space4 ,we may def9e "h z ! place1 9 p]spective space1 :i* is occupi$ by our private _w4 ,?us we c n[ und]/& :at is meant by speak+ ( a ?+ z ne> to or f> f "h4 ,a ?+ is ne> to "h if ! place :]e x is is ne> to my private _w4 ,we c also und]/& :at is meant by say+ t our private _w is inside our head2 = our private _w is a place 9 p]spective space1 & may be "p ( ! place :]e our head is4 ,x w be obs]v$ t two places 9 p]spective space are associat$ ) e aspect ( a ?+3 namely1 ! place :]e ! ?+ is1 & ! place :i* is ! p]spective ( :i* ! aspect 9 "q =ms "p4 ,e aspect ( a ?+ is a memb] ( two diff]5t classes ( aspects1 namely3 7#a7 ! v>i\s aspects ( ! ?+1 ( :i* at mo/ "o appe>s 9 any giv5 p]spective2 7#b7 ! p]spective ( :i* ! giv5 aspect is a memb]1 i4e4 t 9 :i* ! ?+ has ! giv5 aspect4 ,! physici/ naturally classifies aspects 9 ! fir/ way1 ! psy*ologi/ 9 ! second4 ,! two places associat$ ) a s+le aspect correspond to ! two ways ( classify+ x4 ,we may di/+ui% ! two places z t at :i*1 & t f :i*1 ! aspect appe>s4 ,! place at :i* is ! place ( ! ?+ to :i* ! aspect belongs2 ! place f :i* is ! place ( ! p]spective to :i* ! aspect belongs4 ,let u n[ endeav\r to /ate ! fact t ! aspect :i* a ?+ pres5ts at a giv5 place is affect$ by ! int]v5+ m$ium4 ,! aspects ( a ?+ 9 diff]5t p]spectives are to be conceiv$ z spread+ outw>ds f ! place :]e ! ?+ is1 & und]go+ v>i\s *anges z !y get fur!r away f ?is place4 ,! laws accord+ to :i* !y *ange _c be /at$ if we only take acc\nt ( ! aspects t are ne> ! ?+1 b require t we %\ld also take acc\nt ( ! ?+s t are at ! places f :i* ^! aspects appe>4 ,?is empirical fact c1 !re=e1 be int]pret$ 9 t]ms ( our con/ruction4 ,we h n[ con/ruct$ a l>gely hypo!tical picture ( ! _w1 :i* conta9s & places ! exp]i5c$ facts1 includ+ ^? d]iv$ f te/imony4 ,! _w we h con/ruct$ c1 ) a c]ta9 am\nt ( tr\ble1 be us$ to int]pret ! crude facts ( s5se1 ! facts ( physics1 & ! facts ( physiology4 ,x is !re=e a _w :i* may be actual4 ,x fits ! facts1 & !re is no empirical evid5ce aga9/ x2 x also is free f logical impossibilities4 ,b h we any good reason to suppose t x is real8 ,?is br+s u back to our orig9al problem1 z to ! gr\nds = believ+ 9 ! exi/5ce ( any?+ outside my private _w4 ,:at we h d]iv$ f our hypo!tical con/ruction is t !re are no gr\nds aga9/ ! tru? ( ?is belief1 b we h n d]iv$ any positive gr\nds 9 its fav\r4 ,we w resume ?is inquiry by tak+ up aga9 ! "q ( te/imony & ! evid5ce = ! exi/5ce ( o!r m9ds4 ,x mu/ be conc$$ to beg9 ) t ! argum5t 9 fav\r ( ! exi/5ce ( o!r p's m9ds _c be conclusive4 ,a phantasm ( our dreams w appe> to h a m9d--a m9d to be annoy+1 z a rule4 ,x w give unexpect$ answ]s1 refuse to con=m to our desires1 & %[ all ^? o!r signs ( intellig5ce to :i* we are accu/om$ 9 ! acqua9tances ( our wak+ h\rs4 ,& yet1 :5 we are awake1 we d n believe t ! phantasm 01 l ! appe>ances ( p 9 wak+ life1 repres5tative ( a private _w to :i* we h no direct access4 ,if we are to believe ?is ( ! p we meet :5 we are awake1 x mu/ be on "s gr\nd %ort ( demon/ration1 s9ce x is obvi\sly possible t :at we call wak+ life may be only an unusually p]si/5t & recurr5t nightm>e4 ,x may be t our imag9ation br+s =? all t o!r p seem to say to u1 all t we read 9 books1 all ! daily1 weekly1 mon?ly1 & qu>t]ly j\rnals t di/ract our ?\ghts1 all ! adv]tisem5ts ( soap & all ! spee*es ( politicians4 ,?is may be true1 s9ce x _c be %[n to be false1 yet no "o c really believe x4 ,is !re any logical gr\nd = reg>d+ ?is possibility z improbable8 ,or is !re no?+ beyond habit & prejudice8 ,! m9ds ( o!r p are among our data1 9 ! v wide s5se 9 :i* we us$ ! ^w at fir/4 ,t is to say1 :5 we fir/ beg9 to reflect1 we f9d ourselves already believ+ 9 !m1 n because ( any argum5t1 b because ! belief is natural to u4 ,x is1 h[ev]1 a psy*ologically d]ivative belief1 s9ce x results f obs]vation ( p's bodies2 & along ) o!r su* beliefs1 x does n belong to ! h>de/ ( h>d data1 b becomes1 "u ! influ5ce ( philosophic reflection1 j suffici5tly que/ionable to make u desire "s argum5t connect+ x ) ! facts ( s5se4 ,! obvi\s argum5t is1 ( c\rse1 d]iv$ f analogy4 ,o!r p's bodies behave z ours d :5 we h c]ta9 ?\ghts & feel+s2 h5ce1 by analogy1 x is natural to suppose t su* behavi\r is connect$ ) ?\ghts & feel+s l our own4 ,someone says1 ,look out6 & we f9d we are on ! po9t ( be+ kill$ by a motor-c>2 we !re=e attribute ! words we he>d to ! p]son 9 "q hav+ se5 ! motor-c> fir/1 9 :i* case !re are exi/+ ?+s ( :i* we are n directly consci\s4 ,b ?is :ole sc5e1 ) our inf]5ce1 may occur 9 a dream1 9 :i* case ! inf]5ce is g5]ally consid]$ to be mi/ak54 ,is !re any?+ to make ! argum5t f analogy m cog5t :5 we are 7z we ?9k7 awake8 ,! analogy 9 wak+ life is only to be pref]r$ to t 9 dreams on ! gr\nd ( its great] ext5t & consi/5cy4 ,if a man 7 to dream e night ab\t a set ( p :om he nev] met by day1 :o _h consi/5t *>act]s & grew old] ) ! lapse ( ye>s1 he might1 l ! man 9 ,cald]on's play1 f9d x difficult to decide :i* 0 ! dream-_w & :i* 0 ! s-call$ real _w4 ,x is only ! failure ( our dreams to =m a consi/5t :ole ei!r ) ea* o!r or ) wak+ life t makes u condemn !m4 ,c]ta9 uni=mities are obs]v$ 9 wak+ life1 :ile dreams seem q erratic4 ,! natural hypo!sis w\ld be t demons & ! spirits ( ! dead visit u :ile we sleep2 b ! mod]n m9d1 z a rule1 refuses to ent]ta9 ?is view1 ?\gh x is h>d to see :at c\ld be said aga9/ x4 ,on ! o!r h&1 ! my/ic1 9 mom5ts ( illum9ation1 seems to awak5 f a sleep :i* has fill$ all 8 mundane life3 ! :ole _w ( s5se becomes phantasmal1 & he sees1 ) ! cl>ity & conv9c+ness t belongs to our morn+ realisation aft] dreams1 a _w utt]ly diff]5t f t ( our daily c>es & tr\bles4 ,:o %all condemn him8 ,:o %all ju/ify him8 ,or :o %all ju/ify ! seem+ solidity ( ! common objects among :i* we suppose ourselves to live8 ,! hypo!sis t o!r p h m9ds mu/1 ,i ?9k1 be all[$ to be n susceptible ( any v /rong support f ! analogical argum5t4 ,at ! same "t1 x is a hypo!sis :i* sy/ematises a va/ body ( facts & nev] leads to any consequ5ces :i* !re is reason to ?9k false4 ,!re is !re=e no?+ to be said aga9/ its tru?1 & good reason to use x z a work+ hypo!sis4 ,:5 once x is admitt$1 x enables u to ext5d our k ( ! s5sible _w by te/imony1 & ?us leads to ! sy/em ( private worlds :i* we assum$ 9 our hypo!tical con/ruction4 ,9 actual fact1 :atev] we may try to ?9k z philosoph]s1 we _c help believ+ 9 ! m9ds ( o!r p1 s t ! "q :e!r our belief is ju/ifi$ has a m]ely speculative int]e/4 ,& if x is ju/ifi$1 !n !re is no fur!r difficulty ( pr9ciple 9 t va/ ext5sion ( our k1 beyond our own private data1 :i* we f9d 9 sci5ce & common s5se4 ,?is some:at meagre conclusion mu/ n be reg>d$ z ! :ole outcome ( our long discussion4 ,! problem ( ! connection ( s5se ) objective reality has commonly be5 dealt ) f a /&po9t :i* did n c>ry initial d\bt s f> z we h c>ri$ x2 mo/ writ]s1 consci\sly or unconsci\sly1 h assum$ t ! te/imony ( o!rs is to be admitt$1 & !re=e 7at lea/ by implication7 t o!rs h m9ds4 ,_! difficulties h aris5 aft] ?is admission1 f ! diff]5ces 9 ! appe>ance :i* "o physical object pres5ts to two p at ! same "t1 or to "o p]son at two times betwe5 :i* x _c be suppos$ to h *ang$4 ,su* difficulties h made p d\btful h[ f> objective reality c\ld be kn[n by s5se at all1 & h made !m suppose t !re 7 positive argum5ts aga9/ ! view t x c be s kn[n4 ,our hypo!tical con/ruction meets ^! argum5ts1 & %[s t ! acc\nt ( ! _w giv5 by common s5se & physical sci5ce c be int]pret$ 9 a way :i* is logically unobjectionable1 & f9ds a place = all ! data1 bo? h>d & s(t4 ,x is ?is hypo!tical con/ruction1 ) its reconciliation ( psy*ology & physics1 :i* is ! *ief outcome ( our discussion4 ,probably ! con/ruction is only 9 "p necess>y z an initial assumption1 & c be obta9$ f m sl5d] mat]ials by ! logical me?ods ( :i* we %all h an example 9 ! def9itions ( po9ts1 in/ants1 & p>ticles2 b ,i d n yet "k to :at l5g?s ?is dim9ution 9 our initial assumptions c be c>ri$4 ,,lecture ,,iv ,,! ,,_w ,,( ,,physics ,,& ,,! ,,_w ,,( ,,s5se ,among ! objections to ! reality ( objects ( s5se1 !re is "o :i* is d]iv$ f ! app>5t diff]5ce betwe5 matt] z x appe>s 9 physics & ?+s z !y appe> 9 s5sation4 ,m5 ( sci5ce1 = ! mo/ "p1 are will+ to condemn imm$iate data z m]ely subjective1 :ile yet ma9ta9+ ! tru? ( ! physics inf]r$ f ^? data4 ,b su* an attitude1 ?\gh x may be capable ( ju/ification1 obvi\sly /&s 9 ne$ ( x2 & ! only ju/ification possible mu/ be "o :i* exhibits matt] z a logical con/ruction f s5se-data--unless1 inde$1 !re 7 "s :olly a priori pr9ciple by :i* unkn[n entities c\ld be inf]r$ f su* z are kn[n4 ,x is !re=e necess>y to f9d "s way ( bridg+ ! gulf betwe5 ! _w ( physics & ! _w ( s5se1 & x is ?is problem :i* w occupy u 9 ! pres5t lecture4 ,physici/s appe> to be unconsci\s ( ! gulf1 :ile psy*ologi/s1 :o are consci\s ( x1 h n ! ma!matical k requir$ = spann+ x4 ,! problem is difficult1 & ,i d n "k its solution 9 detail4 ,all t ,i c hope to d is to make ! problem felt1 & to indicate ! k9d ( me?ods by :i* a solution is to be s\ght4 ,let u beg9 by a brief description ( ! two contra/$ worlds4 ,we w take fir/ ! _w ( physics1 =1 ?\gh ! o!r _w is giv5 :ile ! physical _w is inf]r$1 to u n[ ! _w ( physics is ! m famili>1 ! _w ( pure s5se hav+ become /range & difficult to r$iscov]4 ,physics />t$ f ! common-s5se belief 9 fairly p]man5t & fairly rigid bodies--tables & *airs1 /ones1 m\nta9s1 ! e>? & moon & sun4 ,?is common-s5se belief1 x %\ld be notic$1 is a piece ( audaci\s metaphysical !oris+2 objects are n cont9ually pres5t to s5sation1 & x may be d\bt$ :e!r !y are !re :5 !y are n se5 or felt4 ,?is problem1 :i* has be5 acute s9ce ! "t ( ,b]keley1 is ignor$ by common s5se1 & has !re=e hi!rto be5 ignor$ by physici/s4 ,we h ?us "h a fir/ dep>ture f ! imm$iate data ( s5sation1 ?\gh x is a dep>ture m]ely by way ( ext5sion1 & 0 probably made by our savage ance/ors 9 "s v remote prehi/oric epo*4 ,b tables & *airs1 /ones & m\nta9s1 are n q p]man5t or q rigid4 ,tables & *airs lose _! legs1 /ones are split by fro/1 & m\nta9s are cleft by e>?quakes & eruptions4 ,!n !re are o!r ?+s1 :i* seem mat]ial1 & yet pres5t almo/ no p]man5ce or rigidity4 ,brea?1 smoke1 cl\ds1 are examples ( su* ?+s--s1 9 a less] degree1 are ice & sn[2 & riv]s & seas1 ?\gh fairly p]man5t1 are n 9 any degree rigid4 ,brea?1 smoke1 cl\ds1 & g5]ally ?+s t c be se5 b n t\*$1 7 ?\ght to be h>dly real2 to ?is day ! usual m>k ( a gho/ is t x c be se5 b n t\*$4 ,su* objects 7 peculi> 9 ! fact t !y seem$ to disappe> completely1 n m]ely to be trans=m$ into some?+ else4 ,ice & sn[1 :5 !y disappe>1 are replac$ by wat]2 & x requir$ no great !oretical ef=t to inv5t ! hypo!sis t ! wat] 0 ! same ?+ z ! ice & sn[1 b 9 a new =m4 ,solid bodies1 :5 !y break1 break into p>ts :i* are practically ! same 9 %ape & size z !y 7 be=e4 ,a /one c be hamm]$ into a p[d]1 b ! p[d] consi/s ( gra9s :i* reta9 ! "* !y _h be=e ! p\nd+4 ,?us ! ideal ( absolutely rigid & absolutely p]man5t bodies1 :i* e>ly physici/s pursu$ ?r\gh\t ! *ang+ appe>ances1 seem$ atta9able by suppos+ ord9>y bodies to be compos$ ( a va/ numb] ( t9y atoms4 ,?is billi>d-ball view ( matt] dom9at$ ! imag9ation ( physici/s until q mod]n times1 until1 9 fact1 x 0 replac$ by ! electromagnetic !ory1 :i* 9 its turn is develop+ into a new atomism4 ,ap>t f ! special =m ( ! atomic !ory :i* 0 inv5t$ = ! ne$s ( *emi/ry1 "s k9d ( atomism dom9at$ ! :ole ( traditional dynamics1 & 0 impli$ 9 e /atem5t ( its laws & axioms4 ,! pictorial acc\nts :i* physici/s give ( ! mat]ial _w z !y conceive x und]go viol5t *anges "u ! influ5ce ( modifications 9 !ory :i* are mu* slight] ?an ! layman might suppose f ! alt]ations ( ! description4 ,c]ta9 features1 h[ev]1 h rema9$ fairly /able4 ,x is always assum$ t !re is some?+ inde/ructible :i* is capable ( motion 9 space2 :at is inde/ructible is always v small1 b does n always occupy a m]e po9t 9 space4 ,!re is suppos$ to be "o all-embrac+ space 9 :i* ! motion takes place1 & until lately we might h assum$ "o all-embrac+ "t also4 ,b ! pr9ciple ( relativity has giv5 prom95ce to ! conception ( local "t1 & has some:at dim9i%$ m5's confid5ce 9 ! "o ev5-fl[+ /ream ( "t4 ,)\t dogmatis+ z to ! ultimate outcome ( ! pr9ciple ( relativity1 h[ev]1 we may safely say1 ,i ?9k1 t x does n de/roy ! possibility ( correlat+ diff]5t local times1 & does n !re=e h su* f>-rea*+ philosophical consequ5ces z is sometimes suppos$4 ,9 fact1 9 spite ( difficulties z to measurem5t1 ! "o all-embrac+ "t /ill1 ,i ?9k1 und]lies all t physics has to say ab\t motion4 ,we ?us h /ill 9 physics1 z we _h 9 ,newton's "t1 a set ( inde/ructible entities :i* may be call$ p>ticles1 mov+ relatively to ea* o!r 9 a s+le space & a s+le "t4 ,! _w ( imm$iate data is q diff]5t f ?is4 ,no?+ is p]man5t2 ev5 ! ?+s t we ?9k are fairly p]man5t1 su* z m\nta9s1 only become data :5 we see !m1 & are n imm$iately giv5 z exi/+ at o!r mom5ts4 ,s f> f "o all-embrac+ space be+ giv51 !re are sev]al spaces = ea* p]son1 accord+ to ! diff]5t s5ses :i* give relations t may be call$ spatial4 ,exp]i5ce tea*es u to obta9 "o space f ^! by correlation1 & exp]i5ce1 toge!r ) in/9ctive !oris+1 tea*es u to correlate our spaces ) ^? :i* we believe to exi/ 9 ! s5sible worlds ( o!r p4 ,! con/ruction ( a s+le "t (f]s less difficulty s long z we conf9e ourselves to "o p]son's private _w1 b ! correlation ( "o private "t ) ano!r is a matt] ( great difficulty4 ,?us1 ap>t f any ( ! fluctuat+ hypo!ses ( physics1 ?ree ma9 problems arise 9 connect+ ! _w ( physics ) ! _w ( s5se1 namely 7#a7 ! con/ruction ( p]man5t ?+s1 7#b7 ! con/ruction ( a s+le space1 & 7#c7 ! con/ruction ( a s+le "t4 ,we w consid] ^! ?ree problems 9 succession4 7#a7 ,! belief 9 inde/ructible ?+s v e>ly took ! =m ( atomism4 ,! und]ly+ motive 9 atomism 0 n1 ,i ?9k1 any empirical success 9 int]pret+ ph5om5a1 b r an in/9ctive belief t b5ea? all ! *anges ( ! s5sible _w !re mu/ be some?+ p]man5t & un*ang+4 ,?is belief 01 no d\bt1 fo/]$ & n\ri%$ by its practical successes1 culm9at+ 9 ! cons]vation ( mass2 b x 0 n produc$ by ^! successes4 ,on ! contr>y1 !y 7 produc$ by x4 ,philosophical writ]s on physics sometimes speak z ?\gh ! cons]vation ( some?+ or o!r 7 ess5tial to ! possibility ( sci5ce1 b ?is1 ,i believe1 is an entirely errone\s op9ion4 ,if ! a priori belief 9 p]man5ce _h n exi/$1 ! same laws :i* are n[ =mulat$ 9 t]ms ( ?is belief might j z well h be5 =mulat$ )\t x4 ,:y %\ld we suppose t1 :5 ice melts1 ! wat] :i* replaces x is ! same ?+ 9 a new =m8 ,m]ely because ?is supposition enables u to /ate ! ph5om5a 9 a way :i* is consonant ) our prejudices4 ,:at we really "k is t1 "u c]ta9 conditions ( temp]ature1 ! appe>ance we call ice is replac$ by ! appe>ance we call wat]4 ,we c give laws accord+ to :i* ! "o appe>ance w be succe$$ by ! o!r1 b !re is no reason except prejudice = reg>d+ bo? z appe>ances ( ! same sub/ance4 ,"o task1 if :at has j be5 said is correct1 :i* confronts u 9 try+ to connect ! _w ( s5se ) ! _w ( physics1 is ! task ( recon/ruct+ ! conception ( matt] )\t ! a priori beliefs :i* hi/orically gave rise to x4 ,9 spite ( ! revolution>y results ( mod]n physics1 ! empirical successes ( ! conception ( matt] %[ t !re mu/ be "s legitimate conception :i* fulfils r\ghly ! same functions4 ,! "t has h>dly come :5 we c /ate precisely :at ?is legitimate conception is1 b we c see 9 a g5]al way :at x mu/ be l4 ,= ?is purpose1 x is only necess>y to take our ord9>y common-s5se /atem5ts & reword !m )\t ! assumption ( p]man5t sub/ance4 ,we say1 = example1 t ?+s *ange gradually--sometimes v quickly1 b n )\t pass+ ?r\gh a cont9u\s s]ies ( int]m$iate /ates4 ,:at ?is means is t1 giv5 any s5sible appe>ance1 !re w usually be1 if we wat*1 a cont9u\s s]ies ( appe>ances connect$ ) ! giv5 "o1 lead+ on by imp]ceptible gradations to ! new appe>ances :i* common-s5se reg>ds z ^? ( ! same ?+4 ,?us a ?+ may be def9$ z a c]ta9 s]ies ( appe>ances1 connect$ ) ea* o!r by cont9uity & by c]ta9 causal laws4 ,9 ! case ( sl[ly *ang+ ?+s1 ?is is easily se54 ,consid]1 say1 a wall-pap] :i* fades 9 ! c\rse ( ye>s4 ,x is an ef=t n to conceive ( x z "o ?+ ^: col\r is slightly diff]5t at "o "t f :at x is at ano!r4 ,b :at d we really "k ab\t x8 ,we "k t "u suitable circum/ances--i4e4 :5 we are1 z is said1 9 ! room--we p]ceive c]ta9 col\rs 9 a c]ta9 patt]n3 n always precisely ! same col\rs1 b suffici5tly simil> to feel famili>4 ,if we c /ate ! laws accord+ to :i* ! col\r v>ies1 we c /ate all t is empirically v]ifiable2 ! assumption t !re is a con/ant entity1 ! wall-pap]1 :i* has ^! v>i\s col\rs at v>i\s times1 is a piece ( gratuit\s metaphysics4 ,we may1 if we l1 def9e ! wall-pap] z ! s]ies ( its aspects4 ,^! are collect$ toge!r by ! same motives :i* l$ u to reg>d ! wall-pap] z "o ?+1 namely a comb9ation ( s5sible cont9uity & causal connection4 ,m g5]ally1 a ?+ w be def9$ z a c]ta9 s]ies ( aspects1 namely ^? :i* w\ld commonly be said to be ( ! ?+4 ,to say t a c]ta9 aspect is an aspect ( a c]ta9 ?+ w m]ely mean t x is "o ( ^? :i*1 tak5 s]ially1 are ! ?+4 ,ev]y?+ w !n proce$ z be=e3 :atev] 0 v]ifiable is un*ang$1 b our language is s int]pret$ z to avoid an unnecess>y metaphysical assumption ( p]man5ce4 ,! above extrusion ( p]man5t ?+s af=ds an example ( ! maxim :i* inspires all sci5tific philosophis+1 namely ,occam's razor3 ,entities are n to be multipli$ )\t necessity4 ,9 o!r words1 9 deal+ ) any subject-matt]1 f9d out :at entities are und5iably involv$1 & /ate ev]y?+ 9 t]ms ( ^! entities4 ,v (t5 ! result+ /atem5t is m complicat$ & difficult ?an "o :i*1 l common s5se & mo/ philosophy1 assumes hypo!tical entities ^: exi/5ce !re is no good reason to believe 94 ,we f9d x easi] to imag9e a wall-pap] ) *ang+ col\rs ?an to ?9k m]ely ( ! s]ies ( col\rs2 b x is a mi/ake to suppose t :at is easy & natural 9 ?\ght is :at is mo/ free f unw>rantable assumptions1 z ! case ( ?+s v aptly illu/rates4 ,! above summ>y acc\nt ( ! g5esis ( ?+s1 ?\gh x may be correct 9 outl9e1 has omitt$ "s s]i\s difficulties :i* x is necess>y briefly to consid]4 ,/>t+ f a _w ( helt]-skelt] s5se-data1 we wi% to collect !m into s]ies1 ea* ( :i* c be reg>d$ z consi/+ ( ! successive appe>ances ( "o ?+4 ,!re is1 to beg9 )1 "s conflict betwe5 :at common s5se reg>ds z "o ?+1 & :at physics reg>ds an un*ang+ collection ( p>ticles4 ,to common s5se1 a human body is "o ?+1 b to sci5ce ! matt] compos+ x is cont9ually *ang+4 ,?is conflict1 h[ev]1 is n v s]i\s1 & may1 = our r\gh prelim9>y purpose1 be l>gely ignor$4 ,! problem is3 by :at pr9ciples %all we select c]ta9 data f ! *aos1 & call !m all appe>ances ( ! same ?+8 ,a r\gh & approximate answ] to ?is "q is n v difficult4 ,!re are c]ta9 fairly /able collections ( appe>ances1 su* z l&scapes1 ! furniture ( rooms1 ! faces ( acqua9tances4 ,9 ^! cases1 we h little hesitation 9 reg>d+ !m on successive occasions z appe>ances ( "o ?+ or collection ( ?+s4 ,b1 z ! ,com$y ( ,errors illu/rates1 we may be l$ a/ray if we judge by m]e resemblance4 ,?is %[s t some?+ m is involv$1 = two diff]5t ?+s may h any degree ( lik5ess up to exact simil>ity4 ,ano!r insuffici5t crit]ion ( "o ?+ is cont9uity4 ,z we h already se51 if we wat* :at we reg>d z "o *ang+ ?+1 we usually f9d its *anges to be cont9u\s s f> z our s5ses c p]ceive4 ,we are ?us l$ to assume t1 if we see two f9itely diff]5t appe>ances at two diff]5t times1 & if we h reason to reg>d !m z belong+ to ! same ?+1 !n !re 0 a cont9u\s s]ies ( int]m$iate /ates ( t ?+ dur+ ! "t :5 we 7 n obs]v+ x4 ,& s x comes to be ?\ght t cont9uity ( *ange is necess>y & suffici5t to con/itute "o ?+4 ,b 9 fact x is nei!r4 ,x is n necess>y1 because ! unobs]v$ /ates1 9 ! case :]e our att5tion has n be5 conc5trat$ on ! ?+ ?r\gh\t1 are purely hypo!tical1 & _c possibly be our gr\nd = suppos+ ! e>li] & lat] appe>ances to belong to ! same ?+2 on ! contr>y1 x is because we suppose ?is t we assume int]m$iate unobs]v$ /ates4 ,cont9uity is also n suffici5t1 s9ce we c1 = example1 pass by s5sibly cont9u\s gradations f any "o drop ( ! sea to any o!r drop4 ,! utmo/ we c say is t discont9uity dur+ un9t]rupt$ obs]vation is z a rule a m>k ( diff]5ce betwe5 ?+s1 ?\gh ev5 ?is _c be said 9 su* cases z sudd5 explosions4 ,! assumption ( cont9uity is1 h[ev]1 successfully made 9 physics4 ,?is proves some?+1 ?\gh n any?+ ( v obvi\s utility to our pres5t problem3 x proves t no?+ 9 ! kn[n _w is inconsi/5t ) ! hypo!sis t all *anges are really cont9u\s1 ?\gh f too great rapidity or f our lack ( obs]vation !y may n always appe> cont9u\s4 ,9 ?is hypo!tical s5se1 cont9uity may be all[$ to be a necess>y condition if two appe>ances are to be class$ z appe>ances ( ! same ?+4 ,b x is n a suffici5t condition1 z appe>s f ! in/ance ( ! drops 9 ! sea4 ,?us some?+ m mu/ be s\ght be=e we c give ev5 ! r\ghe/ def9ition ( a ?+4 ,:at is want$ fur!r seems to be some?+ 9 ! nature ( fulfilm5t ( causal laws4 ,?is /atem5t1 z x /&s1 is v vague1 b we w endeav\r to give x precision4 ,:5 ,i speak ( causal laws1 ,i mean any laws :i* connect ev5ts at diff]5t times1 or ev51 z a limit+ case1 ev5ts at ! same "t provid$ ! connection is n logically demon/rable4 ,9 ?is v g5]al s5se1 ! laws ( dynamics are causal laws1 & s are ! laws correlat+ ! simultane\s appe>ances ( "o ?+ to diff]5t s5ses4 ,! "q is3 ,h[ d su* laws help 9 ! def9ition ( a ?+8 ,to answ] ?is "q1 we mu/ consid] :at x is t is prov$ by ! empirical success ( physics4 ,:at is prov$ is t its hypo!ses1 ?\gh unv]ifiable :]e !y g beyond s5se-data1 are at no po9t 9 contradiction ) s5se-data1 b1 on ! contr>y1 are ideally su* z to r5d] all s5se-data calculable f a suffici5t collection ( data all belong+ to a giv5 p]iod ( "t4 ,n[ physics has f\nd x empirically possible to collect s5se-data into s]ies1 ea* s]ies be+ reg>d$ z belong+ to "o ?+1 & behav+1 ) reg>d to ! laws ( physics1 9 a way 9 :i* s]ies n belong+ to "o ?+ w\ld 9 g5]al n behave4 ,if x is to be unambigu\s :e!r two appe>ances belong to ! same ?+ or n1 !re mu/ be only "o way ( gr\p+ appe>ances s t ! result+ ?+s obey ! laws ( physics4 ,x w\ld be v difficult to prove t ?is is ! case1 b = our pres5t purposes we may let ?is po9t pass1 & assume t !re is only "o way4 ,we mu/ include 9 our def9ition ( a ?+ ^? ( its aspects1 if any1 :i* are n obs]v$4 ,?us we may lay d[n ! foll[+ def9ition3 ,?+s are ^? s]ies ( aspects :i* obey ! laws ( physics4 ,t su* s]ies exi/ is an empirical fact1 :i* con/itutes ! v]ifiability ( physics4 ,x may /ill be object$ t ! matt] ( physics is some?+ o!r ?an s]ies ( s5se-data4 ,s5se-data1 x may be said1 belong to psy*ology & are1 at any rate 9 "s s5se1 subjective1 :]eas physics is q indep5d5t ( psy*ological consid]ations1 & does n assume t its matt] only exi/s :5 x is p]ceiv$4 ,to ?is objection !re are two answ]s1 bo? ( "s importance4 7a7 ,we h be5 consid]+1 9 ! above acc\nt1 ! "q ( ! v]ifiability ( physics4 ,n[ v]ifiability is by no means ! same ?+ z tru?2 x is1 9 fact1 some?+ f> m subjective & psy*ological4 ,= a proposition to be v]ifiable1 x is n en\gh t x %\ld be true1 b x mu/ also be su* z we c discov] to be true4 ,?us v]ifiability dep5ds ^u our capacity = acquir+ k1 & n only ^u ! objective tru?4 ,9 physics1 z ord9>ily set =?1 !re is mu* t is unv]ifiable3 !re are hypo!ses z to 7,a7 h[ ?+s w\ld appe> to a spectator 9 a place :]e1 z x happ5s1 !re is no spectator2 7,b7 h[ ?+s w\ld appe> at times :51 9 fact1 !y are n appe>+ to anyone2 7,c7 ?+s :i* nev] appe> at all4 ,all ^! are introduc$ to simplify ! /atem5t ( ! causal laws1 b none ( !m =m an integral "p ( :at is kn[n to be true 9 physics4 ,?is br+s u to our second answ]4 7b7 ,if physics is to consi/ :olly ( propositions kn[n to be true1 or at lea/ capable ( be+ prov$ or disprov$1 ! ?ree k9ds ( hypo!tical entities we h j enum]at$ mu/ all be capable ( be+ exhibit$ z logical functions ( s5se-data4 ,9 ord] to %[ h[ ?is might possibly be done1 let u recall ! hypo!tical ,leibnizian univ]se ( ,lecture ,,iii4 ,9 t univ]se1 we _h a numb] ( p]spectives1 two ( :i* nev] _h any entity 9 common1 b (t5 conta9$ entities :i* c\ld be suffici5tly correlat$ to be reg>d$ z belong+ to ! same ?+4 ,we w call "o ( ^! an actual private _w :5 !re is an actual spectator to :i* x appe>s1 & ideal :5 x is m]ely con/ruct$ on pr9ciples ( cont9uity4 ,a physical ?+ consi/s1 at ea* in/ant1 ( ! :ole set ( its aspects at t in/ant1 9 all ! diff]5t worlds2 ?us a mom5t>y /ate ( a ?+ is a :ole set ( aspects4 ,an ideal appe>ance w be an aspect m]ely calculat$1 b n actually p]ceiv$ by any spectator4 ,an ideal /ate ( a ?+ w be a /ate at a mom5t :5 all its appe>ances are ideal4 ,an ideal ?+ w be "o ^: /ates at all times are ideal4 ,ideal appe>ances1 /ates1 & ?+s1 s9ce !y are calculat$1 mu/ be functions ( actual appe>ances1 /ates1 & ?+s2 9 fact1 ultimately1 !y mu/ be functions ( actual appe>ances4 ,?us x is unnecess>y1 = ! enunciation ( ! laws ( physics1 to assign any reality to ideal elem5ts3 x is en\gh to accept !m z logical con/ructions1 provid$ we h means ( kn[+ h[ to det]m9e :5 !y become actual4 ,?is1 9 fact1 we h ) "s degree ( approximation2 ! />ry heav51 = in/ance1 becomes actual :5ev] we *oose to look at x4 ,x is op5 to u to believe t ! ideal elem5ts exi/1 & !re c be no reason = disbeliev+ ?is2 b unless 9 virtue ( "s a priori law we _c "k x1 = empirical k is conf9$ to :at we actually obs]ve4 7#b7 ,! ?ree ma9 conceptions ( physics are space1 "t1 & matt]4 ,"s ( ! problems rais$ by ! conception ( matt] h be5 indicat$ 9 ! above discussion ( ?+s4 ,b space & "t also raise difficult problems ( mu* ! same k9d1 namely1 difficulties 9 r$uc+ ! haphaz>d untidy _w ( imm$iate s5sation to ! smoo? ord]ly _w ( geometry & k9ematics4 ,let u beg9 ) ! consid]ation ( space4 ,p :o h nev] read any psy*ology seldom realise h[ mu* m5tal lab\r has gone into ! con/ruction ( ! "o all-embrac+ space into :i* all s5sible objects are suppos$ to fit4 ,kant1 :o 0 unusually ignorant ( psy*ology1 describ$ space z an inf9ite giv5 :ole1 :]eas a mom5t's psy*ological reflection %[s t a space :i* is inf9ite is n giv51 :ile a space :i* c be call$ giv5 is n inf9ite4 ,:at ! nature ( giv5 space really is1 is a difficult "q1 ^u :i* psy*ologi/s are by no means agre$4 ,b "s g5]al rem>ks may be made1 :i* w suffice to %[ ! problems1 )\t tak+ sides on any psy*ological issue /ill 9 debate4 ,! fir/ ?+ to notice is t diff]5t s5ses h diff]5t spaces4 ,! space ( sight is q diff]5t f ! space ( t\*3 x is only by exp]i5ce 9 infancy t we le>n to correlate !m4 ,9 lat] life1 :5 we see an object )9 rea*1 we "k h[ to t\* x1 & m or less :at x w feel l2 if we t\* an object ) our eyes %ut1 we "k :]e we %\ld h to look = x1 & m or less :at x w\ld look l4 ,b ?is k is d]iv$ f e>ly exp]i5ce ( ! correlation ( c]ta9 k9ds ( t\*-s5sations ) c]ta9 k9ds ( sight-s5sations4 ,! "o space into :i* bo? k9ds ( s5sations fit is an intellectual con/ruction1 n a datum4 ,& besides t\* & sight1 !re are o!r k9ds ( s5sation :i* give o!r1 ?\gh less important spaces3 ^! also h to be fitt$ into ! "o space by means ( exp]i5c$ correlations4 ,& z 9 ! case ( ?+s1 s "h3 ! "o all-embrac+ space1 ?\gh conv5i5t z a way ( speak+1 ne$ n be suppos$ really to exi/4 ,all t exp]i5ce makes c]ta9 is ! sev]al spaces ( ! sev]al s5ses1 correlat$ by empirically discov]$ laws4 ,! "o space may turn out to be valid z a logical con/ruction1 comp\nd$ ( ! sev]al spaces1 b !re is no good reason to assume its indep5d5t metaphysical reality4 ,ano!r respect 9 :i* ! spaces ( imm$iate exp]i5ce diff] f ! space ( geometry & physics is 9 reg>d to po9ts4 ,! space ( geometry & physics consi/s ( an inf9ite numb] ( po9ts1 b no "o has ev] se5 or t\*$ a po9t4 ,if !re are po9ts 9 a s5sible space1 !y mu/ be an inf]5ce4 ,x is n easy to see any way 9 :i*1 z indep5d5t entities1 !y c\ld be validly inf]r$ f ! data2 ?us "h aga91 we %all h1 if possible1 to f9d "s logical con/ruction1 "s complex assemblage ( imm$iately giv5 objects1 :i* w h ! geometrical prop]ties requir$ ( po9ts4 ,x is cu/om>y to ?9k ( po9ts z simple & inf9itely small1 b geometry 9 no way dem&s t we %\ld ?9k ( !m 9 ?is way4 ,all t is necess>y = geometry is t !y %\ld h mutual relations possess+ c]ta9 enum]at$ ab/ract prop]ties1 & x may be t an assemblage ( data ( s5sation w s]ve ?is purpose4 ,exactly h[ ?is is to be done1 ,i d n yet "k1 b x seems fairly c]ta9 t x c be done4 ,! foll[+ illu/rative me?od1 simplifi$ s z to be easily manipulat$1 has be5 inv5t$ by ,dr ,:itehead = ! purpose ( %[+ h[ po9ts might be manufactur$ f s5se-data4 ,we h fir/ ( all to obs]ve t !re are no inf9itesimal s5se-data3 any surface we c see1 = example1 mu/ be ( "s f9ite ext5t4 ,b :at at fir/ appe>s z "o undivid$ :ole is (t5 f\nd1 "u ! influ5ce ( att5tion1 to split up into p>ts conta9$ )9 ! :ole4 ,?us "o spatial object may be conta9$ )9 ano!r1 & entirely enclos$ by ! o!r4 ,?is relation ( enclosure1 by ! help ( "s v natural hypo!ses1 w enable u to def9e a po9t z a c]ta9 class ( spatial objects1 namely all ^? 7z x w turn out 9 ! end7 :i* w\ld naturally be said to conta9 ! po9t4 ,9 ord] to obta9 a def9ition ( a po9t 9 ?is way1 we proce$ z foll[s3 ,giv5 any set ( volumes or surfaces1 !y w n 9 g5]al conv]ge into "o po9t4 ,b if !y get small] & small]1 :ile ( any two ( ! set !re is always "o t encloses ! o!r1 !n we beg9 to h ! k9d ( conditions :i* w\ld enable u to treat !m z hav+ a po9t = _! limit4 ,! hypo!ses requir$ = ! relation ( enclosure are t 7#a7 x mu/ be transitive2 7#b7 ( two diff]5t spatial objects1 x is impossible = ea* to enclose ! o!r1 b a s+le spatial object always encloses itself2 7#c7 any set ( spatial objects su* t !re is at lea/ "o spatial object enclos$ by !m all has a l[] limit or m9imum1 i4e4 an object enclos$ by all ( !m & enclos+ all objects :i* are enclos$ by all ( !m2 7#d7 to prev5t trivial exceptions1 we mu/ add t !re are to be in/ances ( enclosure1 i4e4 !re are really to be objects ( :i* "o encloses ! o!r4 ,:5 an enclosure-relation has ^! prop]ties1 we w call x a po9t-produc]4 ,giv5 any relation ( enclosure1 we w call a set ( objects an enclosure-s]ies if1 ( any two ( !m1 "o is conta9$ 9 ! o!r4 ,we require a condition :i* %all secure t an enclosure-s]ies conv]ges to a po9t1 & ?is is obta9$ z foll[s3 ,let our enclosure-s]ies be su* t1 giv5 any o!r enclosure-s]ies ( :i* !re are memb]s enclos$ 9 any arbitr>ily *os5 memb] ( our fir/ s]ies1 !n !re are memb]s ( our fir/ s]ies enclos$ 9 any arbitr>ily *os5 memb] ( our second s]ies4 ,9 ?is case1 our fir/ enclosure-s]ies may be call$ a punctual enclosure-s]ies4 ,!n a po9t is all ! objects :i* enclose memb]s ( a giv5 punctual enclosure-s]ies4 ,9 ord] to ensure inf9ite divisibility1 we require "o fur!r prop]ty to be add$ to ^? def9+ po9t-produc]s1 namely t any object :i* encloses itself also encloses an object o!r ?an itself4 ,! po9ts g5]at$ by po9t-produc]s ) ?is prop]ty w be f\nd to be su* z geometry requires4 7#c7 ,! "q ( "t1 s long z we conf9e ourselves to "o private _w1 is r less complicat$ ?an t ( space1 & we c see pretty cle>ly h[ x might be dealt ) by su* me?ods z we h be5 consid]+4 ,ev5ts ( :i* we are consci\s d n la/ m]ely = a ma!matical in/ant1 b always = "s f9ite "t1 h[ev] %ort4 ,ev5 if !re be a physical _w su* z ! ma!matical !ory ( motion supposes1 impressions on our s5se-organs produce s5sations :i* are n m]ely & /rictly in/antane\s1 & !re=e ! objects ( s5se ( :i* we are imm$iately consci\s are n /rictly in/antane\s4 ,in/ants1 !re=e1 are n among ! data ( exp]i5ce1 &1 if legitimate1 mu/ be ei!r inf]r$ or con/ruct$4 ,x is difficult to see h[ !y c be validly inf]r$2 ?us we are left ) ! alt]native t !y mu/ be con/ruct$4 ,h[ is ?is to be done8 ,imm$iate exp]i5ce provides u ) two "t-relations among ev5ts3 !y may be simultane\s1 or "o may be e>li] & ! o!r lat]4 ,^! two are bo? "p ( ! crude data2 x is n ! case t only ! ev5ts are giv51 & _! "t-ord] is add$ by our subjective activity4 ,! "t-ord]1 )9 c]ta9 limits1 is z mu* giv5 z ! ev5ts4 ,9 any /ory ( adv5ture y w f9d su* passages z ! foll[+3 ,) a cynical smile he po9t$ ! revolv] at ! brea/ ( ! dauntless y\?4 ',at ! ^w ?ree ,i %all fire1' he said4 ,! words "o & two _h already be5 spok5 ) a cool & delib]ate di/9ctness4 ,! ^w ?ree 0 =m+ on 8 lips4 ,at ?is mom5t a bl9d+ fla% ( lightn+ r5t ! air4 ,"h we h simultaneity--n due1 z ,kant w\ld h u believe1 to ! subjective m5tal app>atus ( ! dauntless y\?1 b giv5 z objectively z ! revolv] & ! lightn+4 ,& x is equally giv5 9 imm$iate exp]i5ce t ! words "o & two come e>li] ?an ! fla%4 ,^! "t-relations hold betwe5 ev5ts :i* are n /rictly in/antane\s4 ,?us "o ev5t may beg9 soon] ?an ano!r1 & !re=e be be=e x1 b may cont9ue aft] ! o!r has begun1 & !re=e be also simultane\s ) x4 ,if x p]si/s aft] ! o!r is ov]1 x w also be lat] ?an ! o!r4 ,e>li]1 simultane\s1 & lat]1 are n inconsi/5t ) ea* o!r :5 we are conc]n$ ) ev5ts :i* la/ = a f9ite "t1 h[ev] %ort2 !y only become inconsi/5t :5 we are deal+ ) some?+ in/antane\s4 ,x is to be obs]v$ t we _c give :at may be call$ absolute dates1 b only dates det]m9$ by ev5ts4 ,we _c po9t to a "t itself1 b only to "s ev5t occurr+ at t "t4 ,!re is !re=e no reason 9 exp]i5ce to suppose t !re are times z oppos$ to ev5ts3 ! ev5ts1 ord]$ by ! relations ( simultaneity & succession1 are all t exp]i5ce provides4 ,h5ce1 unless we are to introduce sup]flu\s metaphysical entities1 we mu/1 9 def9+ :at ma!matical physics c reg>d z an in/ant1 proce$ by means ( "s con/ruction :i* assumes no?+ beyond ev5ts & _! temporal relations4 ,if we wi% to assign a date exactly by means ( ev5ts1 h[ %all we proce$8 ,if we take any "o ev5t1 we _c assign our date exactly1 because ! ev5t is n in/antane\s1 t is to say1 x may be simultane\s ) two ev5ts :i* are n simultane\s ) ea* o!r4 ,9 ord] to assign a date exactly1 we mu/ be able1 !oretically1 to det]m9e :e!r any giv5 ev5t is be=e1 at1 or aft] ?is date1 & we mu/ "k t any o!r date is ei!r be=e or aft] ?is date1 b n simultane\s ) x4 ,suppose1 n[1 in/ead ( tak+ "o ev5t ,a1 we take two ev5ts ,a & ,b1 & suppose ,a & ,b p>tly ov]lap1 b ,b ends be=e ,a ends4 ,!n an ev5t :i* is simultane\s ) bo? ,a & ,b mu/ exi/ dur+ ! "t :5 ,a & ,b ov]lap2 ?us we h come r ne>] to a precise date ?an :5 we consid]$ ,a & ,b alone4 ,let ,c be an ev5t :i* is simultane\s ) bo? ,a & ,b1 b :i* ends be=e ei!r ,a or ,b has end$4 ,!n an ev5t :i* is simultane\s ) ,a & ,b & ,c mu/ exi/ dur+ ! "t :5 all ?ree ov]lap1 :i* is a /ill %ort] "t4 ,proce$+ 9 ?is way1 by tak+ m & m ev5ts1 a new ev5t :i* is dat$ z simultane\s ) all ( !m becomes gradually m & m accurately dat$4 ,?is sugge/s a way by :i* a completely accurate date c be def9$4 ,a ,b ,c ,let u take a gr\p ( ev5ts ( :i* any two ov]lap1 s t !re is "s "t1 h[ev] %ort1 :5 !y all exi/4 ,if !re is any o!r ev5t :i* is simultane\s ) all ( ^!1 let u add x to ! gr\p2 let u g on until we h con/ruct$ a gr\p su* t no ev5t outside ! gr\p is simultane\s ) all ( !m1 b all ! ev5ts inside ! gr\p are simultane\s ) ea* o!r4 ,let u def9e ?is :ole gr\p z an in/ant ( "t4 ,x rema9s to %[ t x has ! prop]ties we expect ( an in/ant4 ,:at are ! prop]ties we expect ( in/ants8 ,fir/1 !y mu/ =m a s]ies3 ( any two1 "o mu/ be be=e ! o!r1 & ! o!r mu/ be n be=e ! "o2 if "o is be=e ano!r1 & ! o!r be=e a ?ird1 ! fir/ mu/ be be=e ! ?ird4 ,secondly1 e ev5t mu/ be at a c]ta9 numb] ( in/ants2 two ev5ts are simultane\s if !y are at ! same in/ant1 & "o is be=e ! o!r if !re is an in/ant1 at :i* ! "o is1 :i* is e>li] ?an "s in/ant at :i* ! o!r is4 ,?irdly1 if we assume t !re is always "s *ange go+ on some:]e dur+ ! "t :5 any giv5 ev5t p]si/s1 ! s]ies ( in/ants ought to be compact1 i4e4 giv5 any two in/ants1 !re ought to be o!r in/ants betwe5 !m4 ,d in/ants1 z we h def9$ !m1 h ^! prop]ties8 ,we %all say t an ev5t is at an in/ant :5 x is a memb] ( ! gr\p by :i* ! in/ant is con/itut$2 & we %all say t "o in/ant is be=e ano!r if ! gr\p :i* is ! "o in/ant conta9s an ev5t :i* is e>li] ?an1 b n simultane\s )1 "s ev5t 9 ! gr\p :i* is ! o!r in/ant4 ,:5 "o ev5t is e>li] ?an1 b n simultane\s ) ano!r1 we %all say t x :olly prec$es ! o!r4 ,n[ we "k t ( two ev5ts :i* are n simultane\s1 !re mu/ be "o :i* :olly prec$es ! o!r1 & 9 t case ! o!r _c also :olly prec$e ! "o2 we also "k t1 if "o ev5t :olly prec$es ano!r1 & ! o!r :olly prec$es a ?ird1 !n ! fir/ :olly prec$es ! ?ird4 ,f ^! facts x is easy to d$uce t ! in/ants z we h def9$ !m =m a s]ies4 ,we h next to %[ t e ev5t is at at lea/ "o in/ant1 i4e4 t1 giv5 any ev5t1 !re is at lea/ "o class1 su* z we us$ 9 def9+ in/ants1 ( :i* x is a memb]4 ,= ?is purpose1 consid] all ! ev5ts :i* are simultane\s ) a giv5 ev5t1 & d n beg9 lat]1 i4e4 are n :olly aft] any?+ simultane\s ) x4 ,we w call ^! ! initial contempor>ies ( ! giv5 ev5t4 ,x w be f\nd t ?is class ( ev5ts is ! fir/ in/ant at :i* ! giv5 ev5t exi/s1 provid$ e ev5t :olly aft] "s contempor>y ( ! giv5 ev5t is :olly aft] "s initial contempor>y ( x4 ,f9ally1 ! s]ies ( in/ants w be compact if1 giv5 any two ev5ts ( :i* "o :olly prec$es ! o!r1 !re are ev5ts :olly aft] ! "o & simultane\s ) some?+ :olly be=e ! o!r4 ,:e!r ?is is ! case or n1 is an empirical "q2 b if x is n1 !re is no reason to expect ! "t-s]ies to be compact4#ag #ag ,! assumptions made conc]n+ "t-relations 9 ! above are z foll[s3-- ,i4 ,9 ord] to secure t in/ants =m a s]ies1 we assume3 7a7 ,no ev5t :olly prec$es itself4 7,an ev5t is def9$ z :atev] is simultane\s ) some?+ or o!r47 7b7 ,if "o ev5t :olly prec$es ano!r1 & ! o!r :olly prec$es a ?ird1 !n ! fir/ :olly prec$es ! ?ird4 7c7 ,if "o ev5t :olly prec$es ano!r1 x is n simultane\s ) x4 7d7 ,( two ev5ts :i* are n simultane\s1 "o mu/ :olly prec$e ! o!r4 ,,ii4 ,9 ord] to secure t ! initial contempor>ies ( a giv5 ev5t %\ld =m an in/ant1 we assume3 7e7 ,an ev5t :olly aft] "s contempor>y ( a giv5 ev5t is :olly aft] "s initial contempor>y ( ! giv5 ev5t4 ,,iii4 ,9 ord] to secure t ! s]ies ( in/ants %all be compact1 we assume3 7f7 ,if "o ev5t :olly prec$es ano!r1 !re is an ev5t :olly aft] ! "o & simultane\s ) some?+ :olly be=e ! o!r4 ,?is assumption entails ! consequ5ce t if "o ev5t cov]s ! :ole ( a /ret* ( "t imm$iately prec$+ ano!r ev5t1 !n x mu/ h at lea/ "o in/ant 9 common ) ! o!r ev5t2 i4e4 x is impossible = "o ev5t to cease j be=e ano!r beg9s4 ,i d n "k :e!r ?is %\ld be reg>d$ z inadmissible4 ,= a ma!matico-logical treatm5t ( ! above topics1 cf4 ,n4 ,wiln]1 ,a ,contribution to ! ,!ory ( ,relative ,position1 ,proc4 ,camb4 ,phil4 ,soc41 xvii4 #e1 pp4 #dda-ddi4 ,?us our def9ition ( in/ants secures all t ma!matics requires1 )\t hav+ to assume ! exi/5ce ( any disputable metaphysical entities4 ,in/ants may also be def9$ by means ( ! enclosure-relation1 exactly z 0 done 9 ! case ( po9ts4 ,"o object w be temporally enclos$ by ano!r :5 x is simultane\s ) ! o!r1 b n be=e or aft] x4 ,:atev] encloses temporally or is enclos$ temporally we %all call an ev5t4 ,9 ord] t ! relation ( temporal enclosure may be a po9t-produc]1 we require 7#a7 t x %\ld be transitive1 i4e4 t if "o ev5t encloses ano!r1 & ! o!r a ?ird1 !n ! fir/ encloses ! ?ird2 7#b7 t e ev5t encloses itself1 b if "o ev5t encloses ano!r diff]5t ev5t1 !n ! o!r does n enclose ! "o2 7#c7 t giv5 any set ( ev5ts su* t !re is at lea/ "o ev5t enclos$ by all ( !m1 !n !re is an ev5t enclos+ all t !y all enclose1 & itself enclos$ by all ( !m2 7#d7 t !re is at lea/ "o ev5t4 ,to ensure inf9ite divisibility1 we require also t e ev5t %\ld enclose ev5ts o!r ?an itself4 ,assum+ ^! *>act]i/ics1 temporal enclosure is an inf9itely divisible po9t-produc]4 ,we c n[ =m an enclosure-s]ies ( ev5ts1 by *oos+ a gr\p ( ev5ts su* t ( any two !re is "o :i* encloses ! o!r2 ?is w be a punctual enclosure-s]ies if1 giv5 any o!r enclosure-s]ies su* t e memb] ( our fir/ s]ies encloses "s memb] ( our second1 !n e memb] ( our second s]ies encloses "s memb] ( our fir/4 ,!n an in/ant is ! class ( all ev5ts :i* enclose memb]s ( a giv5 punctual enclosure-s]ies4 ,! correlation ( ! times ( diff]5t private worlds s z to produce ! "o all-embrac+ "t ( physics is a m difficult matt]4 ,we saw1 9 ,lecture ,,iii41 t diff]5t private worlds (t5 conta9 correlat$ appe>ances1 su* z common s5se w\ld reg>d z appe>ances ( ! same ?+4 ,:5 two appe>ances 9 diff]5t worlds are s correlat$ z to belong to "o mom5t>y /ate ( a ?+1 x w\ld be natural to reg>d !m z simultane\s1 & z ?us af=d+ a simple means ( correlat+ diff]5t private times4 ,b ?is c only be reg>d$ z a fir/ approximation4 ,:at we call "o s\nd w be he>d soon] by p ne> ! s\rce ( ! s\nd ?an by p fur!r f x1 & ! same applies1 ?\gh 9 a less degree1 to light4 ,?us two correlat$ appe>ances 9 diff]5t worlds are n necess>ily to be reg>d$ z occurr+ at ! same date 9 physical "t1 ?\gh !y w be p>ts ( "o mom5t>y /ate ( a ?+4 ,! correlation ( diff]5t private times is regulat$ by ! desire to secure ! simple/ possible /atem5t ( ! laws ( physics1 & ?us raises r complicat$ te*nical problems2 b f ! po9t ( view ( philosophical !ory1 !re is no v s]i\s difficulty ( pr9ciple involv$4 ,! above brief outl9e mu/ n be reg>d$ z m ?an t5tative & sugge/ive4 ,x is int5d$ m]ely to %[ ! k9d ( way 9 :i*1 giv5 a _w ) ! k9d ( prop]ties t psy*ologi/s f9d 9 ! _w ( s5se1 x may be possible1 by means ( purely logical con/ructions1 to make x am5able to ma!matical treatm5t by def9+ s]ies or classes ( s5se-data :i* c be call$ respectively p>ticles1 po9ts1 & in/ants4 ,if su* con/ructions are possible1 !n ma!matical physics is applicable to ! real _w1 9 spite ( ! fact t its p>ticles1 po9ts1 & in/ants are n to be f\nd among actually exi/+ entities4 ,! problem :i* ! above consid]ations are int5d$ to elucidate is "o ^: importance & ev5 exi/5ce has be5 conceal$ by ! un=tunate sep>ation ( diff]5t /udies :i* prevails ?r\gh\t ! civilis$ _w4 ,physici/s1 ignorant & contemptu\s ( philosophy1 h be5 cont5t to assume _! p>ticles1 po9ts1 & in/ants 9 practice1 :ile conc$+1 ) ironical polit5ess1 t _! concepts laid no claim to metaphysical validity4 ,metaphysicians1 obsess$ by ! ideali/ic op9ion t only m9d is real1 & ! ,p>m5idean belief t ! real is un*ang+1 repeat$ "o aft] ano!r ! suppos$ contradictions 9 ! notions ( matt]1 space1 & "t1 & !re=e naturally made no endeav\r to inv5t a t5able !ory ( p>ticles1 po9ts1 & in/ants4 ,psy*ologi/s1 :o h done invaluable "w 9 br++ to light ! *aotic nature ( ! crude mat]ials suppli$ by unmanipulat$ s5sation1 h be5 ignorant ( ma!matics & mod]n logic1 & h !re=e be5 cont5t to say t matt]1 space1 & "t are intellectual con/ructions1 )\t mak+ any attempt to %[ 9 detail ei!r h[ ! intellect c con/ruct !m1 or :at secures ! practical validity :i* physics %[s !m to possess4 ,philosoph]s1 x is to be hop$1 w come to recognise t !y _c a*ieve any solid success 9 su* problems )\t "s slight k ( logic1 ma!matics1 & physics2 mean:ile1 = want ( /ud5ts ) ! necess>y equipm5t1 ?is vital problem rema9s unattempt$ & unkn[n4 ,!re are1 x is true1 two au?ors1 bo? physici/s1 :o h done some?+1 ?\gh n mu*1 to br+ ab\t a recognition ( ! problem z "o dem&+ /udy4 ,^! two au?ors are ,po9c>e & ,ma*1 ,po9c>e especially 9 8 ,sci5ce & ,hypo!sis1 ,ma* especially 9 8 ,analysis ( ,s5sations4 ,bo? ( !m1 h[ev]1 admirable z _! "w is1 seem to me to suff] f a g5]al philosophical bias4 ,po9c>e is ,kantian1 :ile ,ma* is ultra-empirici/2 ) ,po9c>e almo/ all ! ma!matical "p ( physics is m]ely conv5tional1 :ile ) ,ma* ! s5sation z a m5tal ev5t is id5tifi$ ) its object z a "p ( ! physical _w4 ,nev]!less1 bo? ^! au?ors1 & especially ,ma*1 des]ve m5tion z hav+ made s]i\s contributions to ! consid]ation ( our problem4 ,:5 a po9t or an in/ant is def9$ z a class ( s5sible qualities1 ! fir/ impression produc$ is likely to be "o ( wild & wilful p>adox4 ,c]ta9 consid]ations apply "h1 h[ev]1 :i* w aga9 be relevant :5 we come to ! def9ition ( numb]s4 ,!re is a :ole type ( problems :i* c be solv$ by su* def9itions1 & almo/ always !re w be at fir/ an effect ( p>adox4 ,giv5 a set ( objects any two ( :i* h a relation ( ! sort call$ symmetrical & transitive1 x is almo/ c]ta9 t we %all come to reg>d !m z all hav+ "s common quality1 or z all hav+ ! same relation to "s "o object outside ! set4 ,?is k9d ( case is important1 & ,i %all !re=e try to make x cle> ev5 at ! co/ ( "s repetition ( previ\s def9itions4 ,a relation is said to be symmetrical :51 if "o t]m has ?is relation to ano!r1 !n ! o!r also has x to ! "o4 ,?us bro!r or si/] is a symmetrical relation3 if "o p]son is a bro!r or a si/] ( ano!r1 !n ! o!r is a bro!r or si/] ( ! "o4 ,simultaneity1 aga91 is a symmetrical relation2 s is equality 9 size4 ,a relation is said to be transitive :51 if "o t]m has ?is relation to ano!r1 & ! o!r to a ?ird1 !n ! "o has x to ! ?ird4 ,! symmetrical relations m5tion$ j n[ are also transitive--provid$1 9 ! case ( bro!r or si/]1 we all[ a p]son to be c\nt$ z 8 or h] own bro!r or si/]1 & provid$1 9 ! case ( simultaneity1 we mean complete simultaneity1 i4e4 beg9n+ & end+ toge!r4 ,b _m relations are transitive )\t be+ symmetrical--= in/ance1 su* relations z great]1 e>li]1 to ! "r (1 ance/or (1 9 fact all su* relations z give rise to s]ies4 ,o!r relations are symmetrical )\t be+ transitive--= example1 diff]5ce 9 any respect4 ,if ,a is ( a diff]5t age f ,b1 & ,b ( a diff]5t age f ,c1 x does n foll[ t ,a is ( a diff]5t age f ,c4 ,simultaneity1 aga91 9 ! case ( ev5ts :i* la/ = a f9ite "t1 w n necess>ily be transitive if x only means t ! times ( ! two ev5ts ov]lap4 ,if ,a ends j aft] ,b has begun1 & ,b ends j aft] ,c has begun1 ,a & ,b w be simultane\s 9 ?is s5se1 & s w ,b & ,c1 b ,a & ,c may well n be simultane\s4 ,all ! relations :i* c naturally be repres5t$ z equality 9 any respect1 or z possession ( a common prop]ty1 are transitive & symmetrical--?is applies1 = example1 to su* relations z be+ ( ! same height or weight or col\r4 ,ow+ to ! fact t possession ( a common prop]ty gives rise to a transitive symmetrical relation1 we come to imag9e t :]ev] su* a relation occurs x mu/ be due to a common prop]ty4 ,be+ equally num]\s is a transitive symmetrical relation ( two collections2 h5ce we imag9e t bo? h a common prop]ty1 call$ _! numb]4 ,exi/+ at a giv5 in/ant 79 ! s5se 9 :i* we def9$ an in/ant7 is a transitive symmetrical relation2 h5ce we come to ?9k t !re really is an in/ant :i* conf]s a common prop]ty on all ! ?+s exi/+ at t in/ant4 ,be+ /ates ( a giv5 ?+ is a transitive symmetrical relation2 h5ce we come to imag9e t !re really is a ?+1 o!r ?an ! s]ies ( /ates1 :i* acc\nts = ! transitive symmetrical relation4 ,9 all su* cases1 ! class ( t]ms t h ! giv5 transitive symmetrical relation to a giv5 t]m w fulfil all ! =mal requisites ( a common prop]ty ( all ! memb]s ( ! class4 ,s9ce !re c]ta9ly is ! class1 :ile any o!r common prop]ty may be illusory1 x is prud5t1 9 ord] to avoid ne$less assumptions1 to sub/itute ! class = ! common prop]ty :i* w\ld be ord9>ily assum$4 ,?is is ! reason = ! def9itions we h adopt$1 & ?is is ! s\rce ( ! app>5t p>adoxes4 ,no h>m is done if !re are su* common prop]ties z language assumes1 s9ce we d n d5y !m1 b m]ely ab/a9 f ass]t+ !m4 ,b if !re are n su* common prop]ties 9 any giv5 case1 !n our me?od has secur$ u aga9/ error4 ,9 ! abs5ce ( special k1 !re=e1 ! me?od we h adopt$ is ! only "o :i* is safe1 & :i* avoids ! risk ( introduc+ fictiti\s metaphysical entities4 ,,lecture ,v ,,! ,,!ory ,,( ,,cont9uity ,! !ory ( cont9uity1 ) :i* we %all be occupi$ 9 ! pres5t lecture1 is1 9 mo/ ( its ref9em5ts & developm5ts1 a purely ma!matical subject--v beautiful1 v important1 & v delightful1 b n1 /rictly speak+1 a "p ( philosophy4 ,! logical basis ( ! !ory alone belongs to philosophy1 & alone w occupy u to-night4 ,! way ! problem ( cont9uity ent]s into philosophy is1 broadly speak+1 ! foll[+3 ,space & "t are treat$ by ma!maticians z consi/+ ( po9ts & in/ants1 b !y also h a prop]ty1 easi] to feel ?an to def9e1 :i* is call$ cont9uity1 & is ?\ght by _m philosoph]s to be de/roy$ :5 !y are resolv$ into po9ts & in/ants4 ,z5o1 z we %all see1 prov$ t analysis into po9ts & in/ants 0 impossible if we adh]$ to ! view t ! numb] ( po9ts or in/ants 9 a f9ite space or "t mu/ be f9ite4 ,lat] philosoph]s1 believ+ inf9ite numb] to be self-contradictory1 h f\nd "h an ant9omy3 ,spaces & times c\ld n consi/ ( a f9ite numb] ( po9ts & in/ants1 = su* reasons z ,z5o's2 !y c\ld n consi/ ( an inf9ite numb] ( po9ts & in/ants1 because inf9ite numb]s 7 suppos$ to be self-contradictory4 ,!re=e spaces & times1 if real at all1 mu/ n be reg>d$ z compos$ ( po9ts & in/ants4 ,b ev5 :5 po9ts & in/ants1 z indep5d5t entities1 are disc>d$1 z !y 7 by ! !ory advocat$ 9 our la/ lecture1 ! problems ( cont9uity1 z ,i %all try to %[ pres5tly1 rema91 9 a practically un*ang$ =m4 ,let u !re=e1 to beg9 )1 admit po9ts & in/ants1 & consid] ! problems 9 connection ) ?is simpl] or at lea/ m famili> hypo!sis4 ,! argum5t aga9/ cont9uity1 9 s f> z x re/s ^u ! suppos$ difficulties ( inf9ite numb]s1 has be5 dispos$ ( by ! positive !ory ( ! inf9ite1 :i* w be consid]$ 9 ,lecture ,,vii4 ,b !re rema9s a feel+--( ! k9d t l$ ,z5o to ! cont5tion t ! arr[ 9 its flight is at re/--:i* sugge/s t po9ts & in/ants1 ev5 if !y are inf9itely num]\s1 c only give a j]ky motion1 a succession ( diff]5t immobilities1 n ! smoo? transitions ) :i* ! s5ses h made u famili>4 ,?is feel+ is due1 ,i believe1 to a failure to realise imag9atively1 z well z ab/ractly1 ! nature ( cont9u\s s]ies z !y appe> 9 ma!matics4 ,:5 a !ory has be5 appreh5d$ logically1 !re is (t5 a long & s]i\s lab\r /ill requir$ 9 ord] to feel x3 x is necess>y to dwell ^u x1 to ?ru/ out f ! m9d1 "o by "o1 ! mislead+ sugge/ions ( false b m famili> !ories1 to acquire ! k9d ( intimacy :i*1 9 ! case ( a =eign language1 w\ld enable u to ?9k & dream 9 x1 n m]ely to con/ruct labori\s s5t5ces by ! help ( gramm> & diction>y4 ,x is1 ,i believe1 ! abs5ce ( ?is k9d ( intimacy :i* makes _m philosoph]s reg>d ! ma!matical doctr9e ( cont9uity z an inadequate explanation ( ! cont9uity :i* we exp]i5ce 9 ! _w ( s5se4 ,9 ! pres5t lecture1 ,i %all fir/ try to expla9 9 outl9e :at ! ma!matical !ory ( cont9uity is 9 its philosophically important ess5tials4 ,! application to actual space & "t w n be 9 "q to beg9 )4 ,i d n see any reason to suppose t ! po9ts & in/ants :i* ma!maticians introduce 9 deal+ ) space & "t are actual physically exi/+ entities1 b ,i d see reason to suppose t ! cont9uity ( actual space & "t may be m or less analog\s to ma!matical cont9uity4 ,! !ory ( ma!matical cont9uity is an ab/ract logical !ory1 n dep5d5t = its validity ^u any prop]ties ( actual space & "t4 ,:at is claim$ = x is t1 :5 x is und]/ood1 c]ta9 *>act]i/ics ( space & "t1 previ\sly v h>d to analyse1 are f\nd n to pres5t any logical difficulty4 ,:at we "k empirically ab\t space & "t is insuffici5t to enable u to decide betwe5 v>i\s ma!matically possible alt]natives1 b ^! alt]natives are all fully intelligible & fully adequate to ! obs]v$ facts4 ,= ! pres5t1 h[ev]1 x w be well to =get space & "t & ! cont9uity ( s5sible *ange1 9 ord] to return to ^! topics equipp$ ) ! weapons provid$ by ! ab/ract !ory ( cont9uity4 ,cont9uity1 9 ma!matics1 is a prop]ty only possible to a s]ies ( t]ms1 i4e4 to t]ms arrang$ 9 an ord]1 s t we c say ( any two t "o comes be=e ! o!r4 ,numb]s 9 ord] ( magnitude1 ! po9ts on a l9e f left to "r1 ! mom5ts ( "t f e>li] to lat]1 are in/ances ( s]ies4 ,! notion ( ord]1 :i* is "h introduc$1 is "o :i* is n requir$ 9 ! !ory ( c>d9al numb]4 ,x is possible to "k t two classes h ! same numb] ( t]ms )\t kn[+ any ord] 9 :i* !y are to be tak54 ,we h an in/ance ( ?is 9 su* a case z ,engli% husb&s & ,engli% wives3 we c see t !re mu/ be ! same numb] ( husb&s z ( wives1 )\t hav+ to arrange !m 9 a s]ies4 ,b cont9uity1 :i* we are n[ to consid]1 is ess5tially a prop]ty ( an ord]3 x does n belong to a set ( t]ms 9 !mselves1 b only to a set 9 a c]ta9 ord]4 ,a set ( t]ms :i* c be arrang$ 9 "o ord] c always also be arrang$ 9 o!r ord]s1 & a set ( t]ms :i* c be arrang$ 9 a cont9u\s ord] c always also be arrang$ 9 ord]s :i* are n cont9u\s4 ,?us ! ess5ce ( cont9uity mu/ n be s\ght 9 ! nature ( ! set ( t]ms1 b 9 ! nature ( _! arrangem5t 9 a s]ies4 ,ma!maticians h di/+ui%$ diff]5t degrees ( cont9uity1 & h conf9$ ! ^w cont9u\s1 = te*nical purposes1 to s]ies hav+ a c]ta9 high degree ( cont9uity4 ,b = philosophical purposes1 all t is important 9 cont9uity is introduc$ by ! l[e/ degree ( cont9uity1 :i* is call$ compactness4 ,a s]ies is call$ compact :5 no two t]ms are consecutive1 b betwe5 any two !re are o!rs4 ,"o ( ! simple/ examples ( a compact s]ies is ! s]ies ( fractions 9 ord] ( magnitude4 ,giv5 any two fractions1 h[ev] ne> toge!r1 !re are o!r fractions great] ?an ! "o & small] ?an ! o!r1 & !re=e no two fractions are consecutive4 ,!re is no fraction1 = example1 :i* is next aft] #a_/b3 if we *oose "s fraction :i* is v little great] ?an #a_/b1 say #ea_/ajj we c f9d o!rs1 su* z #aja_/bjj1 :i* are ne>] to #a_/b4 ,?us betwe5 any two fractions1 h[ev] little !y diff]1 !re are an inf9ite numb] ( o!r fractions4 ,ma!matical space & "t also h ?is prop]ty ( compactness1 ?\gh :e!r actual space & "t h x is a fur!r "q1 dep5d5t ^u empirical evid5ce1 & probably incapable ( be+ answ]$ ) c]ta9ty4 ,9 ! case ( ab/ract objects su* z fractions1 x is p]haps n v difficult to realise ! logical possibility ( _! =m+ a compact s]ies4 ,! difficulties t might be felt are ^? ( inf9ity1 = 9 a compact s]ies ! numb] ( t]ms betwe5 any two giv5 t]ms mu/ be inf9ite4 ,b :5 ^! difficulties h be5 solv$1 ! m]e compactness 9 itself (f]s no great ob/acle to ! imag9ation4 ,9 m concrete cases1 h[ev]1 su* z motion1 compactness becomes mu* m repugnant to our habits ( ?\ght4 ,x w !re=e be desirable to consid] explicitly ! ma!matical acc\nt ( motion1 ) a view to mak+ its logical possibility felt4 ,! ma!matical acc\nt ( motion is p]haps artificially simplifi$ :5 reg>d$ z describ+ :at actually occurs 9 ! physical _w2 b :at actually occurs mu/ be capable1 by a c]ta9 am\nt ( logical manipulation1 ( be+ br\ght )9 ! scope ( ! ma!matical acc\nt1 & mu/1 9 its analysis1 raise j su* problems z are rais$ 9 _! simple/ =m by ?is acc\nt4 ,neglect+1 !re=e1 = ! pres5t1 ! "q ( its physical adequacy1 let u devote ourselves m]ely to consid]+ its possibility z a =mal /atem5t ( ! nature ( motion4 ,9 ord] to simplify our problem z mu* z possible1 let u imag9e a t9y speck ( light mov+ along a scale4 ,:at d we mean by say+ t ! motion is cont9u\s8 ,x is n necess>y = our purposes to consid] ! :ole ( :at ! ma!matician means by ?is /atem5t3 only "p ( :at he means is philosophically important4 ,"o "p ( :at he means is t1 if we consid] any two positions ( ! speck occupi$ at any two in/ants1 !re w be o!r int]m$iate positions occupi$ at int]m$iate in/ants4 ,h[ev] ne> toge!r we take ! two positions1 ! speck w n jump sudd5ly f ! "o to ! o!r1 b w pass ?r\gh an inf9ite numb] ( o!r positions on ! way4 ,e di/ance1 h[ev] small1 is trav]s$ by pass+ ?r\gh all ! inf9ite s]ies ( positions betwe5 ! two ends ( ! di/ance4 ,b at ?is po9t imag9ation sugge/s t we may describe ! cont9uity ( motion by say+ t ! speck always passes f "o position at "o in/ant to ! next position at ! next in/ant4 ,z soon z we say ?is or imag9e x1 we fall into error1 because !re is no next po9t or next in/ant4 ,if !re 71 we %\ld f9d ,z5o's p>adoxes1 9 "s =m1 unavoidable1 z w appe> 9 our next lecture4 ,"o simple p>adox may s]ve z an illu/ration4 ,if our speck is 9 motion along ! scale ?r\gh\t ! :ole ( a c]ta9 "t1 x _c be at ! same po9t at two consecutive in/ants4 ,b x _c1 f "o in/ant to ! next1 travel fur!r ?an f "o po9t to ! next1 = if x did1 !re w\ld be no in/ant at :i* x 0 9 ! positions int]m$iate betwe5 t at ! fir/ in/ant & t at ! next1 & we agre$ t ! cont9uity ( motion excludes ! possibility ( su* sudd5 jumps4 ,x foll[s t our speck mu/1 s long z x moves1 pass f "o po9t at "o in/ant to ! next po9t at ! next in/ant4 ,?us !re w be j "o p]fectly def9ite velocity ) :i* all motions mu/ take place3 no motion c be fa/] ?an ?is1 & no motion c be sl[]4 ,s9ce ?is conclusion is false1 we mu/ reject ! hypo!sis ^u :i* x is bas$1 namely t !re are consecutive po9ts & in/ants4#ah ,h5ce ! cont9uity ( motion mu/ n be suppos$ to consi/ 9 a body's occupy+ consecutive positions at consecutive times4 #ah ,! above p>adox is ess5tially ! same z ,z5o's argum5t ( ! /adium :i* w be consid]$ 9 our next lecture4 ,! difficulty to imag9ation lies *iefly1 ,i ?9k1 9 keep+ out ! sugge/ion ( inf9itesimal di/ances & times4 ,suppose we halve a giv5 di/ance1 & !n halve ! half1 & s on1 we c cont9ue ! process z long z we please1 & ! long] we cont9ue x1 ! small] ! result+ di/ance becomes4 ,?is inf9ite divisibility seems1 at fir/ sight1 to imply t !re are inf9itesimal di/ances1 i4e4 di/ances s small t any f9ite fraction ( an in* w\ld be great]4 ,?is1 h[ev]1 is an error4 ,! cont9u$ bisection ( our di/ance1 ?\gh x gives u cont9ually small] di/ances1 gives u always f9ite di/ances4 ,if our orig9al di/ance 0 an in*1 we rea* successively half an in*1 a qu>t] ( an in*1 an eigh?1 a sixte5?1 & s on2 b e "o ( ?is inf9ite s]ies ( dim9i%+ di/ances is f9ite4 ,b1 x may be said1 9 ! end ! di/ance w gr[ inf9itesimal4 ,no1 because !re is no end4 ,! process ( bisection is "o :i* c1 !oretically1 be c>ri$ on = ev]1 )\t any la/ t]m be+ atta9$4 ,?us inf9ite divisibility ( di/ances1 :i* mu/ be admitt$1 does n imply t !re are di/ances s small t any f9ite di/ance w\ld be l>g]4 ,x is easy1 9 ?is k9d ( "q1 to fall into an elem5t>y logical blund]4 ,giv5 any f9ite di/ance1 we c f9d a small] di/ance2 ?is may be express$ 9 ! ambigu\s =m !re is a di/ance small] ?an any f9ite di/ance4 ,b if ?is is !n int]pret$ z mean+ !re is a di/ance su* t1 :atev] f9ite di/ance may be *os51 ! di/ance 9 "q is small]1 !n ! /atem5t is false4 ,common language is ill adapt$ to express+ matt]s ( ?is k9d1 & philosoph]s :o h be5 dep5d5t on x h frequ5tly be5 misl$ by x4 ,9 a cont9u\s motion1 !n1 we %all say t at any giv5 in/ant ! mov+ body occupies a c]ta9 position1 & at o!r in/ants x occupies o!r positions2 ! int]val betwe5 any two in/ants & betwe5 any two positions is always f9ite1 b ! cont9uity ( ! motion is %[n 9 ! fact t1 h[ev] ne> toge!r we take ! two positions & ! two in/ants1 !re are an inf9ite numb] ( positions /ill ne>] toge!r1 :i* are occupi$ at in/ants t are also /ill ne>] toge!r4 ,! mov+ body nev] jumps f "o position to ano!r1 b always passes by a gradual transition ?r\gh an inf9ite numb] ( int]m$i>ies4 ,at a giv5 in/ant1 x is :]e x is1 l ,z5o's arr[2#ai b we _c say t x is at re/ at ! in/ant1 s9ce ! in/ant does n la/ = a f9ite "t1 & !re is n a beg9n+ & end ( ! in/ant ) an int]val betwe5 !m4 ,re/ consi/s 9 be+ 9 ! same position at all ! in/ants ?r\gh\t a c]ta9 f9ite p]iod1 h[ev] %ort2 x does n consi/ simply 9 a body's be+ :]e x is at a giv5 in/ant4 ,?is :ole !ory1 z is obvi\s1 dep5ds ^u ! nature ( compact s]ies1 & dem&s1 = its full compreh5sion1 t compact s]ies %\ld h become famili> & easy to ! imag9ation z well z to delib]ate ?\ght4 #ai ,see next lecture4 ,:at is requir$ may be express$ 9 ma!matical language by say+ t ! position ( a mov+ body mu/ be a cont9u\s function ( ! "t4 ,to def9e accurately :at ?is means1 we proce$ z foll[s4 ,consid] a p>ticle :i*1 at ! mom5t t1 is at ! po9t ,p4 ,*oose n[ any small portion ,p#a,p#b ( ! pa? ( ! p>ticle1 ?is portion be+ "o :i* conta9s ,p4 ,we say !n t1 if ! motion ( ! p>ticle is cont9u\s at ! "t t1 x mu/ be possible to f9d two in/ants t#a1 t#b1 "o e>li] ?an t & "o lat]1 su* t ?r\gh\t ! :ole "t f t#a to t#b 7bo? includ$71 ! p>ticle lies betwe5 ,p#a & ,p#b4 ,& we say t ?is mu/ /ill hold h[ev] small we make ! portion ,p#a,p#b4 ,:5 ?is is ! case1 we say t ! motion is cont9u\s at ! "t t2 & :5 ! motion is cont9u\s at all times1 we say t ! motion z a :ole is cont9u\s4 ,x is obvi\s t if ! p>ticle 7 to jump sudd5ly f ,p to "s o!r po9t ,q1 our def9ition w\ld fail = all int]vals ,p#a,p#b :i* 7 too small to include ,q4 ,?us our def9ition af=ds an analysis ( ! cont9uity ( motion1 :ile admitt+ po9ts & in/ants & d5y+ inf9itesimal di/ances 9 space or p]iods 9 "t4 ,p#a ,p ,p#b ,q ------------------------ ,philosoph]s1 mo/ly 9 ignorance ( ! ma!matician's analysis1 h adopt$ o!r & m h]oic me?ods ( deal+ ) ! prima facie difficulties ( cont9u\s motion4 ,a typical & rec5t example ( philosophic !ories ( motion is af=d$ by ,b]gson1 ^: views on ?is subject ,i h exam9$ else:]e4#bj #bj ,moni/1 ,july #aiab1 pp4 #ccg-cda4 ,ap>t f def9ite argum5ts1 !re are c]ta9 feel+s1 r ?an reasons1 :i* /& 9 ! way ( an acceptance ( ! ma!matical acc\nt ( motion4 ,to beg9 )1 if a body is mov+ at all fa/1 we see its motion j z we see its col\r4 ,a sl[ motion1 l t ( ! h\r-h& ( a wat*1 is only kn[n 9 ! way :i* ma!matics w\ld lead u to expect1 namely by obs]v+ a *ange ( position aft] a lapse ( "t2 b1 :5 we obs]ve ! motion ( ! second-h&1 we d n m]ely see fir/ "o position & !n ano!r--we see some?+ z directly s5sible z col\r4 ,:at is ?is some?+ t we see1 & t we call visible motion8 ,:atev] x is1 x is n ! successive occupation ( successive positions3 some?+ beyond ! ma!matical !ory ( motion is requir$ to acc\nt = x4 ,oppon5ts ( ! ma!matical !ory emphasise ?is fact4 ,y\r !ory1 !y say1 may be v logical1 & might apply admirably to "s o!r _w2 b 9 ?is actual _w1 actual motions are q diff]5t f :at y\r !ory w\ld decl>e !m to be1 & require1 !re=e1 "s diff]5t philosophy f y\rs = _! adequate explanation4 ,! objection ?us rais$ is "o :i* ,i h no wi% to und]rate1 b ,i believe x c be fully answ]$ )\t dep>t+ f ! me?ods & ! outlook :i* h l$ to ! ma!matical !ory ( motion4 ,let u1 h[ev]1 fir/ try to /ate ! objection m fully4 ,if ! ma!matical !ory is adequate1 no?+ happ5s :5 a body moves except t x is 9 diff]5t places at diff]5t times4 ,b 9 ?is s5se ! h\r-h& & ! second-h& are equally 9 motion1 yet 9 ! second-h& !re is some?+ p]ceptible to our s5ses :i* is abs5t 9 ! h\r-h&4 ,we c see1 at ea* mom5t1 t ! second-h& is mov+1 :i* is diff]5t f see+ x fir/ 9 "o place & !n 9 ano!r4 ,?is seems to involve our see+ x simultane\sly 9 a numb] ( places1 al?\gh x mu/ also involve our see+ t x is 9 "s ( ^! places e>li] ?an 9 o!rs4 ,if1 = example1 ,i move my h& quickly f left to "r1 y seem to see ! :ole movem5t at once1 9 spite ( ! fact t y "k x beg9s at ! left & ends at ! "r4 ,x is ?is k9d ( consid]ation1 ,i ?9k1 :i* leads ,b]gson & _m o!rs to reg>d a movem5t z really "o indivisible :ole1 n ! s]ies ( sep>ate /ates imag9$ by ! ma!matician4 ,to ?is objection !re are ?ree supplem5t>y answ]s1 physiological1 psy*ological1 & logical4 ,we w consid] !m successively4 7#a7 ,! physiological answ] m]ely %[s t1 if ! physical _w is :at ! ma!matician supposes1 its s5sible appe>ance may nev]!less be expect$ to be :at x is4 ,! aim ( ?is answ] is ?us ! mode/ "o ( %[+ t ! ma!matical acc\nt is n impossible z appli$ to ! physical _w2 x does n ev5 attempt to %[ t ?is acc\nt is necess>y1 or t an analog\s acc\nt applies 9 psy*ology4 ,:5 any n]ve is /imulat$1 s z to cause a s5sation1 ! s5sation does n cease in/antane\sly ) ! cessation ( ! /imulus1 b dies away 9 a %ort f9ite "t4 ,a fla% ( lightn+1 brief z x is to our sight1 is brief] /ill z a physical ph5om5on3 we cont9ue to see x = a few mom5ts aft] ! light-waves h ceas$ to /rike ! eye4 ,?us 9 ! case ( a physical motion1 if x is suffici5tly swift1 we %all actually at "o in/ant see ! mov+ body ?r\gh\t a f9ite portion ( its c\rse1 & n only at ! exact spot :]e x is at t in/ant4 ,s5sations1 h[ev]1 z !y die away1 gr[ gradually fa9t]2 ?us ! s5sation due to a /imulus :i* is rec5tly pa/ is n exactly l ! s5sation due to a pres5t /imulus4 ,x foll[s f ?is t1 :5 we see a rapid motion1 we %all n only see a numb] ( positions ( ! mov+ body simultane\sly1 b we %all see !m ) diff]5t degrees ( int5sity--! pres5t position mo/ vividly1 & ! o!rs ) dim9i%+ vividness1 until s5sation fades away into imm$iate memory4 ,?is /ate ( ?+s acc\nts fully = ! p]ception ( motion4 ,a motion is p]ceiv$1 n m]ely inf]r$1 :5 x is suffici5tly swift = _m positions to be s5sible at "o "t2 & ! e>li] & lat] p>ts ( "o p]ceiv$ motion are di/+ui%$ by ! less & great] vividness ( ! s5sations4 ,?is answ] %[s t physiology c acc\nt = our p]ception ( motion4 ,b physiology1 9 speak+ ( /imulus & s5se-organs & a physical motion di/9ct f ! imm$iate object ( s5se1 is assum+ ! tru? ( physics1 & is ?us only capable ( %[+ ! physical acc\nt to be possible1 n ( %[+ x to be necess>y4 ,?is consid]ation br+s u to ! psy*ological answ]4 7#b7 ,! psy*ological answ] to our difficulty ab\t motion is "p ( a va/ !ory1 n yet work$ out1 & only capable1 at pres5t1 ( be+ vaguely outl9$4 ,we consid]$ ?is !ory 9 ! ?ird & f\r? lectures2 = ! pres5t1 a m]e sket* ( its application to our pres5t problem mu/ suffice4 ,! _w ( physics1 :i* 0 assum$ 9 ! physiological answ]1 is obvi\sly inf]r$ f :at is giv5 9 s5sation2 yet z soon z we s]i\sly consid] :at is actually giv5 9 s5sation1 we f9d x app>5tly v diff]5t f ! _w ( physics4 ,! "q is ?us =c$ ^u u3 ,is ! inf]5ce f s5se to physics a valid "o8 ,i believe ! answ] to be affirmative1 = reasons :i* ,i sugge/$ 9 ! ?ird & f\r? lectures2 b ! answ] _c be ei!r %ort or easy4 ,x consi/s1 broadly speak+1 9 %[+ t1 al?\gh ! p>ticles1 po9ts1 & in/ants ) :i* physics op]ates are n !mselves giv5 9 exp]i5ce1 & are v likely n actually exi/+ ?+s1 yet1 out ( ! mat]ials provid$ 9 s5sation1 x is possible to make logical con/ructions hav+ ! ma!matical prop]ties :i* physics assigns to p>ticles1 po9ts1 & in/ants4 ,if ?is c be done1 !n all ! propositions ( physics c be translat$1 by a sort ( diction>y1 into propositions ab\t ! k9ds ( objects :i* are giv5 9 s5sation4 ,apply+ ^! g5]al consid]ations to ! case ( motion1 we f9d t1 ev5 )9 ! sph]e ( imm$iate s5se-data1 x is necess>y1 or at any rate m consonant ) ! facts ?an any o!r equally simple view1 to di/+ui% in/antane\s /ates ( objects1 & to reg>d su* /ates z =m+ a compact s]ies4 ,let u consid] a body :i* is mov+ swiftly en\gh = its motion to be p]ceptible1 & long en\gh = its motion to be n :olly compris$ 9 "o s5sation4 ,!n1 9 spite ( ! fact t we see a f9ite ext5t ( ! motion at "o in/ant1 ! ext5t :i* we see at "o in/ant is diff]5t f t :i* we see at ano!r4 ,?us we are br\ght back1 aft] all1 to a s]ies ( mom5t>y views ( ! mov+ body1 & ?is s]ies w be compact1 l ! =m] physical s]ies ( po9ts4 ,9 fact1 ?\gh ! t]ms ( ! s]ies seem diff]5t1 ! ma!matical "* ( ! s]ies is un*ang$1 & ! :ole ma!matical !ory ( motion w apply to x v]batim4 ,:5 we are consid]+ ! actual data ( s5sation 9 ?is connection1 x is important to realise t two s5se-data may be1 & mu/ sometimes be1 really diff]5t :5 we _c p]ceive any diff]5ce betwe5 !m4 ,an old b conclusive reason = believ+ ?is 0 emphasis$ by ,po9c>e4#ba ,9 all cases ( s5se-data capable ( gradual *ange1 we may f9d "o s5se-datum indi/+ui%able f ano!r1 & t o!r indi/+ui%able f a ?ird1 :ile yet ! fir/ & ?ird are q easily di/+ui%able4 ,suppose1 = example1 a p]son ) 8 eyes %ut is hold+ a weight 9 8 h&1 & someone noiselessly adds a small extra weight4 ,if ! extra weight is small en\gh1 no diff]5ce w be p]ceiv$ 9 ! s5sation4 ,aft] a "t1 ano!r small extra weight may be add$1 & /ill no *ange w be p]ceiv$2 b if bo? extra weights _h be5 add$ at once1 x may be t ! *ange w\ld be q easily p]ceptible4 ,or1 aga91 take %ades ( col\r4 ,x w\ld be easy to f9d ?ree /uffs ( su* closely simil> %ades t no diff]5ce c\ld be p]ceiv$ betwe5 ! fir/ & second1 nor yet betwe5 ! second & ?ird1 :ile yet ! fir/ & ?ird w\ld be di/+ui%able4 ,9 su* a case1 ! second %ade _c be ! same z ! fir/1 or x w\ld be di/+ui%able f ! ?ird2 nor ! same z ! ?ird1 or x w\ld be di/+ui%able f ! fir/4 ,x mu/1 !re=e1 ?\gh indi/+ui%able f bo?1 be really int]m$iate betwe5 !m4 #ba ,le cont9u ma!matique1 ,revue de ,metaphysique et de ,morale1 vol4 i4 p4 #bi4 ,su* consid]ations z ! above %[ t1 al?\gh we _c di/+ui% s5se-data unless !y diff] by m ?an a c]ta9 am\nt1 x is p]fectly reasonable to suppose t s5se-data ( a giv5 k9d1 su* z weights or col\rs1 really =m a compact s]ies4 ,! objections :i* may be br\ght f a psy*ological po9t ( view aga9/ ! ma!matical !ory ( motion are n1 !re=e1 objections to ?is !ory prop]ly und]/ood1 b only to a q unnecess>y assumption ( simplicity 9 ! mom5t>y object ( s5se4 ,( ! imm$iate object ( s5se1 9 ! case ( a visible motion1 we may say t at ea* in/ant x is 9 all ! positions :i* rema9 s5sible at t in/ant2 b ?is set ( positions *anges cont9u\sly f mom5t to mom5t1 & is am5able to exactly ! same ma!matical treatm5t z if x 7 a m]e po9t4 ,:5 we ass]t t "s ma!matical acc\nt ( ph5om5a is correct1 all t we prim>ily ass]t is t some?+ def9able 9 t]ms ( ! crude ph5om5a satisfies our =mulae2 & 9 ?is s5se ! ma!matical !ory ( motion is applicable to ! data ( s5sation z well z to ! suppos$ p>ticles ( ab/ract physics4 ,!re are a numb] ( di/9ct que/ions :i* are apt to be confus$ :5 ! ma!matical cont9uum is said to be inadequate to ! facts ( s5se4 ,we may /ate ^!1 9 ord] ( dim9i%+ g5]ality1 z foll[s3-- 7a7 ,are s]ies possess+ ma!matical cont9uity logically possible8 7b7 ,assum+ t !y are possible logically1 are !y n impossible z appli$ to actual s5se-data1 because1 among actual s5se-data1 !re are no su* fix$ mutually ext]nal t]ms z are to be f\nd1 e4g41 9 ! s]ies ( fractions8 7c7 ,does n ! assumption ( po9ts & in/ants make ! :ole ma!matical acc\nt fictiti\s8 7d7 ,f9ally1 assum+ t all ^! objections h be5 answ]$1 is !re1 9 actual empirical fact1 any suffici5t reason to believe ! _w ( s5se cont9u\s8 ,let u consid] ^! que/ions 9 succession4 7a7 ,! "q ( ! logical possibility ( ! ma!matical cont9uum turns p>tly on ! elem5t>y misund]/&+s we consid]$ at ! beg9n+ ( ! pres5t lecture1 p>tly on ! possibility ( ! ma!matical inf9ite1 :i* w occupy our next two lectures1 & p>tly on ! logical =m ( ! answ] to ! ,b]gsonian objection :i* we /at$ a few m9utes ago4 ,i %all say no m on ?is topic at pres5t1 s9ce x is desirable fir/ to complete ! psy*ological answ]4 7b7 ,! "q :e!r s5se-data are compos$ ( mutually ext]nal units is n "o :i* c be decid$ by empirical evid5ce4 ,x is (t5 urg$ t1 z a matt] ( imm$iate exp]i5ce1 ! s5sible flux is devoid ( divisions1 & is falsifi$ by ! dissections ( ! intellect4 ,n[ ,i h no wi% to argue t ?is view is contr>y to imm$iate exp]i5ce3 ,i wi% only to ma9ta9 t x is ess5tially incapable ( be+ prov$ by imm$iate exp]i5ce4 ,z we saw1 !re mu/ be among s5se-data diff]5ces s slight z to be imp]ceptible3 ! fact t s5se-data are imm$iately giv5 does n mean t _! diff]5ces also mu/ be imm$iately giv5 7?\gh !y may be74 ,suppose1 = example1 a col\r$ surface on :i* ! col\r *anges gradually--s gradually t ! diff]5ce ( col\r 9 two v neighb\r+ portions is imp]ceptible1 :ile ! diff]5ce betwe5 m widely sep>at$ portions is q noticeable4 ,! effect produc$1 9 su* a case1 w be precisely t ( int]p5etration1 ( transition :i* is n a matt] ( discrete units4 ,& s9ce x t5ds to be suppos$ t ! col\rs1 be+ imm$iate data1 mu/ appe> diff]5t if !y are diff]5t1 x seems easily to foll[ t int]p5etration mu/ be ! ultimately "r acc\nt4 ,b ?is does n foll[4 ,x is unconsci\sly assum$1 z a premiss = a r$uctio ad absurdum ( ! analytic view1 t1 if ,a & ,b are imm$iate data1 & ,a diff]s f ,b1 !n ! fact t !y diff] mu/ also be an imm$iate datum4 ,x is difficult to say h[ ?is assumption arose1 b ,i ?9k x is to be connect$ ) ! confusion betwe5 acqua9tance & k ab\t4 ,acqua9tance1 :i* is :at we d]ive f s5se1 does n1 !oretically at lea/1 imply ev5 ! smalle/ k ab\t1 i4e4 x does n imply k ( any proposition conc]n+ ! object ) :i* we are acqua9t$4 ,x is a mi/ake to speak z if acqua9tance _h degrees3 !re is m]ely acqua9tance & non-acqua9tance4 ,:5 we speak ( becom+ bett] acqua9t$1 z = in/ance ) a p]son1 :at we mu/ mean is1 becom+ acqua9t$ ) m p>ts ( a c]ta9 :ole2 b ! acqua9tance ) ea* "p is ei!r complete or nonexi/5t4 ,?us x is a mi/ake to say t if we 7 p]fectly acqua9t$ ) an object we %\ld "k all ab\t x4 ,k ab\t is k ( propositions1 :i* is n involv$ necess>ily 9 acqua9tance ) ! con/itu5ts ( ! propositions4 ,to "k t two %ades ( col\r are diff]5t is k ab\t !m2 h5ce acqua9tance ) ! two %ades does n 9 any way necessitate ! k t !y are diff]5t4 ,f :at has j be5 said x foll[s t ! nature ( s5se-data _c be validly us$ to prove t !y are n compos$ ( mutually ext]nal units4 ,x may be admitt$1 on ! o!r h&1 t no?+ 9 _! empirical "* specially necessitates ! view t !y are compos$ ( mutually ext]nal units4 ,?is view1 if x is held1 mu/ be held on logical1 n on empirical1 gr\nds4 ,i believe t ! logical gr\nds are adequate to ! conclusion4 ,!y re/1 at bottom1 ^u ! impossibility ( expla9+ complexity )\t assum+ con/itu5ts4 ,x is und5iable t ! visual field1 = example1 is complex2 & s f> z ,i c see1 !re is always self-contradiction 9 ! !ories :i*1 :ile admitt+ ?is complexity1 attempt to d5y t x results f a comb9ation ( mutually ext]nal units4 ,b to pursue ?is topic w\ld lead u too f> f our !me1 & ,i %all !re=e say no m ab\t x at pres5t4 7c7 ,x is sometimes urg$ t ! ma!matical acc\nt ( motion is r5d]$ fictiti\s by its assumption ( po9ts & in/ants4 ,n[ !re are "h two diff]5t que/ions to be di/+ui%$4 ,!re is ! "q ( absolute or relative space & "t1 & !re is ! "q :e!r :at occupies space & "t mu/ be compos$ ( elem5ts :i* h no ext5sion or duration4 ,& ea* ( ^! que/ions 9 turn may take two =ms1 namely3 7,a7 is ! hypo!sis consi/5t ) ! facts & ) logic8 7,b7 is x necessitat$ by ! facts or by logic8 ,i wi% to answ]1 9 ea* case1 yes to ! fir/ =m ( ! "q1 & no to ! second4 ,b 9 any case ! ma!matical acc\nt ( motion w n be fictiti\s1 provid$ a "r int]pretation is giv5 to ! words po9t & in/ant4 ,a few words on ea* alt]native w s]ve to make ?is cle>4 ,=mally1 ma!matics adopts an absolute !ory ( space & "t1 i4e4 x assumes t1 besides ! ?+s :i* are 9 space & "t1 !re are also entities1 call$ po9ts & in/ants1 :i* are occupi$ by ?+s4 ,?is view1 h[ev]1 ?\gh advocat$ by ,newton1 has long be5 reg>d$ by ma!maticians z m]ely a conv5i5t fiction4 ,!re is1 s f> z ,i c see1 no conceivable evid5ce ei!r = or aga9/ x4 ,x is logically possible1 & x is consi/5t ) ! facts4 ,b ! facts are also consi/5t ) ! d5ial ( spatial & temporal entities ov] & above ?+s ) spatial & temporal relations4 ,h5ce1 9 accordance ) ,occam's razor1 we %all d well to ab/a9 f ei!r assum+ or d5y+ po9ts & in/ants4 ,?is means1 s f> z practical work+ out is conc]n$1 t we adopt ! relational !ory2 = 9 practice ! refusal to assume po9ts & in/ants has ! same effect z ! d5ial ( !m4 ,b 9 /rict !ory ! two are q diff]5t1 s9ce ! d5ial introduces an elem5t ( unv]ifiable dogma :i* is :olly abs5t :5 we m]ely refra9 f ! ass]tion4 ,?us1 al?\gh we %all d]ive po9ts & in/ants f ?+s1 we %all leave ! b>e possibility op5 t !y may also h an indep5d5t exi/5ce z simple entities4 ,we come n[ to ! "q :e!r ! ?+s 9 space & "t are to be conceiv$ z compos$ ( elem5ts )\t ext5sion or duration1 i4e4 ( elem5ts :i* only occupy a po9t & an in/ant4 ,physics1 =mally1 assumes 9 its diff]5tial equations t ?+s consi/ ( elem5ts :i* occupy only a po9t at ea* in/ant1 b p]si/ ?r\gh\t "t4 ,= reasons expla9$ 9 ,lecture ,,iv41 ! p]si/5ce ( ?+s ?r\gh "t is to be reg>d$ z ! =mal result ( a logical con/ruction1 n z necess>ily imply+ any actual p]si/5ce4 ,! same motives1 9 fact1 :i* lead to ! division ( ?+s into po9t-p>ticles1 ought presumably to lead to _! division into in/ant-p>ticles1 s t ! ultimate =mal con/itu5t ( ! matt] 9 physics w be a po9t-in/ant-p>ticle4 ,b su* objects1 z well z ! p>ticles ( physics1 are n data4 ,! same economy ( hypo!sis1 :i* dictates ! practical adoption ( a relative r ?an an absolute space & "t1 also dictates ! practical adoption ( mat]ial elem5ts :i* h a f9ite ext5sion & duration4 ,s9ce1 z we saw 9 ,lecture ,,iv41 po9ts & in/ants c be con/ruct$ z logical functions ( su* elem5ts1 ! ma!matical acc\nt ( motion1 9 :i* a p>ticle passes cont9u\sly ?r\gh a cont9u\s s]ies ( po9ts1 c be int]pret$ 9 a =m :i* assumes only elem5ts :i* agree ) our actual data 9 hav+ a f9ite ext5sion & duration4 ,?us1 s f> z ! use ( po9ts & in/ants is conc]n$1 ! ma!matical acc\nt ( motion c be fre$ f ! *>ge ( employ+ fictions4 7d7 ,b we mu/ n[ face ! "q3 ,is !re1 9 actual empirical fact1 any suffici5t reason to believe ! _w ( s5se cont9u\s8 ,! answ] "h mu/1 ,i ?9k1 be 9 ! negative4 ,we may say t ! hypo!sis ( cont9uity is p]fectly consi/5t ) ! facts & ) logic1 & t x is te*nically simpl] ?an any o!r t5able hypo!sis4 ,b s9ce our p[]s ( discrim9ation among v simil> s5sible objects are n inf9itely precise1 x is q impossible to decide betwe5 diff]5t !ories :i* only diff] 9 reg>d to :at is bel[ ! m>g9 ( discrim9ation4 ,if1 = example1 a col\r$ surface :i* we see consi/s ( a f9ite numb] ( v small surfaces1 & if a motion :i* we see consi/s1 l a c9ematograph1 ( a l>ge f9ite numb] ( successive positions1 !re w be no?+ empirically discov]able to %[ t objects ( s5se are n cont9u\s4 ,9 :at is call$ exp]i5c$ cont9uity1 su* z is said to be giv5 9 s5se1 !re is a l>ge negative elem5t3 abs5ce ( p]ception ( diff]5ce occurs 9 cases :i* are ?\ght to give p]ception ( abs5ce ( diff]5ce4 ,:51 = example1 we _c di/+ui% a col\r ,a f a col\r ,b1 nor a col\r ,b f a col\r ,c1 b c di/+ui% ,a f ,c1 ! indi/+ui%ability is a purely negative fact1 namely1 t we d n p]ceive a diff]5ce4 ,ev5 9 reg>d to imm$iate data1 ?is is no reason = d5y+ t !re is a diff]5ce4 ,?us1 if we see a col\r$ surface ^: col\r *anges gradually1 its s5sible appe>ance if ! *ange is cont9u\s w be indi/+ui%able f :at x w\ld be if ! *ange 7 by small f9ite jumps4 ,if ?is is true1 z x seems to be1 x foll[s t !re c nev] be any empirical evid5ce to demon/rate t ! s5sible _w is cont9u\s1 & n a collection ( a v l>ge f9ite numb] ( elem5ts ( :i* ea* diff]s f its neighb\r 9 a f9ite ?\gh v small degree4 ,! cont9uity ( space & "t1 ! inf9ite numb] ( diff]5t %ades 9 ! spectrum1 & s on1 are all 9 ! nature ( unv]ifiable hypo!ses--p]fectly possible logically1 p]fectly consi/5t ) ! kn[n facts1 & simpl] te*nically ?an any o!r t5able hypo!ses1 b n ! sole hypo!ses :i* are logically & empirically adequate4 ,if a relational !ory ( in/ants is con/ruct$1 9 :i* an in/ant is def9$ z a gr\p ( ev5ts simultane\s ) ea* o!r & n all simultane\s ) any ev5t outside ! gr\p1 !n if our result+ s]ies ( in/ants is to be compact1 x mu/ be possible1 if x :olly prec$es y1 to f9d an ev5t z1 simultane\s ) "p ( x1 :i* :olly prec$es "s ev5t :i* :olly prec$es y4 ,n[ ?is requires t ! numb] ( ev5ts conc]n$ %\ld be inf9ite 9 any f9ite p]iod ( "t4 ,if ?is is to be ! case 9 ! _w ( "o man's s5se-data1 & if ea* s5se-datum is to h n less ?an a c]ta9 f9ite temporal ext5sion1 x w be necess>y to assume t we always h an inf9ite numb] ( s5se-data simultane\s ) any giv5 s5se-datum4 ,apply+ simil> consid]ations to space1 & assum+ t s5se-data are to h n less ?an a c]ta9 spatial ext5sion1 x w be necess>y to suppose t an inf9ite numb] ( s5se-data ov]lap spatially ) any giv5 s5se-datum4 ,?is hypo!sis is possible1 if we suppose a s+le s5se-datum1 e4g4 9 sight1 to be a f9ite surface1 enclos+ o!r surfaces :i* are also s+le s5se-data4 ,b !re are difficulties 9 su* a hypo!sis1 & ,i d n "k :e!r ^! difficulties c\ld be successfully met4 ,if !y _c1 we mu/ d "o ( two ?+s3 ei!r decl>e t ! _w ( "o man's s5se-data is n cont9u\s1 or else refuse to admit t !re is any l[] limit to ! duration & ext5sion ( a s+le s5se-datum4 ,i d n "k :at is ! "r c\rse to adopt z reg>ds ^! alt]natives4 ,! logical analysis we h be5 consid]+ provides ! app>atus = deal+ ) ! v>i\s hypo!ses1 & ! empirical decision betwe5 !m is a problem = ! psy*ologi/4 7#c7 ,we h n[ to consid] ! logical answ] to ! alleg$ difficulties ( ! ma!matical !ory ( motion1 or r to ! positive !ory :i* is urg$ on ! o!r side4 ,! view urg$ explicitly by ,b]gson1 & impli$ 9 ! doctr9es ( _m philosoph]s1 is1 t a motion is some?+ indivisible1 n validly analysable into a s]ies ( /ates4 ,?is is "p ( a mu* m g5]al doctr9e1 :i* holds t analysis always falsifies1 because ! p>ts ( a complex :ole are diff]5t1 z comb9$ 9 t :ole1 f :at !y w\ld o!rwise be4 ,x is v difficult to /ate ?is doctr9e 9 any =m :i* has a precise mean+4 ,(t5 argum5ts are us$ :i* h no be>+ :atev] ^u ! "q4 ,x is urg$1 = example1 t :5 a man becomes a fa!r1 8 nature is alt]$ by ! new relation 9 :i* he f9ds himself1 s t he is n /rictly id5tical ) ! man :o 0 previ\sly n a fa!r4 ,?is may be true1 b x is a causal psy*ological fact1 n a logical fact4 ,! doctr9e w\ld require t a man :o is a fa!r _c be /rictly id5tical ) a man :o is a son1 because he is modifi$ 9 "o way by ! relation ( fa!rhood & 9 ano!r by t ( son%ip4 ,9 fact1 we may give a precise /atem5t ( ! doctr9e we are combat+ 9 ! =m3 ,!re c nev] be two facts conc]n+ ! same ?+4 ,a fact conc]n+ a ?+ always is or involves a relation to "o or m entities2 ?us two facts conc]n+ ! same ?+ w\ld involve two relations ( ! same ?+4 ,b ! doctr9e 9 "q holds t a ?+ is s modifi$ by its relations t x _c be ! same 9 "o relation z 9 ano!r4 ,h5ce1 if ?is doctr9e is true1 !re c nev] be m ?an "o fact conc]n+ any "o ?+4 ,i d n ?9k ! philosoph]s 9 "q h realis$ t ?is is ! precise /atem5t ( ! view !y advocate1 because 9 ?is =m ! view is s contr>y to pla9 tru? t its falsehood is evid5t z soon z x is /at$4 ,! discussion ( ?is "q1 h[ev]1 involves s _m logical subtleties1 & is s beset ) difficulties1 t ,i %all n pursue x fur!r at pres5t4 ,:5 once ! above g5]al doctr9e is reject$1 x is obvi\s t1 :]e !re is *ange1 !re mu/ be a succession ( /ates4 ,!re _c be *ange--& motion is only a p>ticul> case ( *ange--unless !re is some?+ diff]5t at "o "t f :at !re is at "s o!r "t4 ,*ange1 !re=e1 mu/ involve relations & complexity1 & mu/ dem& analysis4 ,s long z our analysis has only gone z f> z o!r small] *anges1 x is n complete2 if x is to be complete1 x mu/ end ) t]ms t are n *anges1 b are relat$ by a relation ( e>li] & lat]4 ,9 ! case ( *anges :i* appe> cont9u\s1 su* z motions1 x seems to be impossible to f9d any?+ o!r ?an *ange s long z we deal ) f9ite p]iods ( "t1 h[ev] %ort4 ,we are ?us driv5 back1 by ! logical necessities ( ! case1 to ! conception ( in/ants )\t duration1 or at any rate )\t any duration :i* ev5 ! mo/ delicate in/rum5ts c reveal4 ,?is conception1 ?\gh x c be made to seem difficult1 is really easi] ?an any o!r t ! facts all[4 ,x is a k9d ( logical framework into :i* any t5able !ory mu/ fit--n necess>ily itself ! /atem5t ( ! crude facts1 b a =m 9 :i* /atem5ts :i* are true ( ! crude facts c be made by a suitable int]pretation4 ,! direct consid]ation ( ! crude facts ( ! physical _w has be5 und]tak5 9 e>li] lectures2 9 ! pres5t lecture1 we h only be5 conc]n$ to %[ t no?+ 9 ! crude facts is inconsi/5t ) ! ma!matical doctr9e ( cont9uity1 or dem&s a cont9uity ( a radically diff]5t k9d f t ( ma!matical motion4 ,,lecture ,,vi ,,! ,,problem ,,( ,,inf9ity ,,consid]$ ,,hi/orically ,x w be rememb]$ t1 :5 we enum]at$ ! gr\nds ^u :i* ! reality ( ! s5sible _w has be5 que/ion$1 "o ( ^? m5tion$ 0 ! suppos$ impossibility ( inf9ity & cont9uity4 ,9 view ( our e>li] discussion ( physics1 x w\ld seem t no conclusive empirical evid5ce exi/s 9 fav\r ( inf9ity or cont9uity 9 objects ( s5se or 9 matt]4 ,nev]!less1 ! explanation :i* assumes inf9ity & cont9uity rema9s incomp>ably easi] & m natural1 f a sci5tific po9t ( view1 ?an any o!r1 & s9ce ,georg ,cantor has %[n t ! suppos$ contradictions are illusory1 !re is no long] any reason to /ruggle aft] a f9iti/ explanation ( ! _w4 ,! suppos$ difficulties ( cont9uity all h _! s\rce 9 ! fact t a cont9u\s s]ies mu/ h an inf9ite numb] ( t]ms1 & are 9 fact difficulties conc]n+ inf9ity4 ,h5ce1 9 free+ ! inf9ite f contradiction1 we are at ! same "t %[+ ! logical possibility ( cont9uity z assum$ 9 sci5ce4 ,! k9d ( way 9 :i* inf9ity has be5 us$ to discr$it ! _w ( s5se may be illu/rat$ by ,kant's fir/ two ant9omies4 ,9 ! fir/1 ! !sis /ates3 ,! _w has a beg9n+ 9 "t1 & z reg>ds space is enclos$ )9 limits2 ! anti!sis /ates3 ,! _w has no beg9n+ & no limits 9 space1 b is inf9ite 9 respect ( bo? "t & space4 ,kant pr(esses to prove bo? ^! propositions1 :]eas1 if :at we h said on mod]n logic has any tru?1 x mu/ be impossible to prove ei!r4 ,9 ord]1 h[ev]1 to rescue ! _w ( s5se1 x is en\gh to de/roy ! pro( ( "o ( ! two4 ,= our pres5t purpose1 x is ! pro( t ! _w is f9ite t int]e/s u4 ,kant's argum5t z reg>ds space "h re/s ^u 8 argum5t z reg>ds "t4 ,we ne$ !re=e only exam9e ! argum5t z reg>ds "t4 ,:at he says is z foll[s3 ,= let u assume t ! _w has no beg9n+ z reg>ds "t1 s t up to e giv5 in/ant an et]nity has elaps$1 & !re=e an inf9ite s]ies ( successive /ates ( ! ?+s 9 ! _w has pass$ by4 ,b ! inf9ity ( a s]ies consi/s j 9 ?is1 t x c nev] be complet$ by successive syn!sis4 ,!re=e an inf9ite pa/ _w-s]ies is impossible1 & accord+ly a beg9n+ ( ! _w is a necess>y condition ( its exi/5ce2 :i* 0 ! fir/ ?+ to be prov$4 ,_m diff]5t criticisms might be pass$ on ?is argum5t1 b we w cont5t ourselves ) a b>e m9imum4 ,to beg9 )1 x is a mi/ake to def9e ! inf9ity ( a s]ies z impossibility ( completion by successive syn!sis4 ,! notion ( inf9ity1 z we %all see 9 ! next lecture1 is prim>ily a prop]ty ( classes1 & only d]ivatively applicable to s]ies2 classes :i* are inf9ite are giv5 all at once by ! def9+ prop]ty ( _! memb]s1 s t !re is no "q ( completion or ( successive syn!sis4 ,& ! ^w syn!sis1 by sugge/+ ! m5tal activity ( syn!sis+1 introduces1 m or less surreptiti\sly1 t ref]5ce to m9d by :i* all ,kant's philosophy 0 infect$4 ,9 ! second place1 :5 ,kant says t an inf9ite s]ies c nev] be complet$ by successive syn!sis1 all t he has ev5 conceivably a "r to say is t x _c be complet$ 9 a f9ite "t4 ,?us :at he really proves is1 at mo/1 t if ! _w _h no beg9n+1 x mu/ h already exi/$ = an inf9ite "t4 ,?is1 h[ev]1 is a v poor conclusion1 by no means suitable = 8 purposes4 ,& ) ?is result we might1 if we *ose1 take leave ( ! fir/ ant9omy4 ,x is wor? :ile1 h[ev]1 to consid] h[ ,kant came to make su* an elem5t>y blund]4 ,:at happ5$ 9 8 imag9ation 0 obvi\sly some?+ l ?is3 ,/>t+ f ! pres5t & go+ backw>ds 9 "t1 we h1 if ! _w _h no beg9n+1 an inf9ite s]ies ( ev5ts4 ,z we see f ! ^w syn!sis1 he imag9$ a m9d try+ to grasp ^! successively1 9 ! rev]se ord] to t 9 :i* !y _h occurr$1 i4e4 go+ f ! pres5t backw>ds4 ,?is s]ies is obvi\sly "o :i* has no end4 ,b ! s]ies ( ev5ts up to ! pres5t has an end1 s9ce x ends ) ! pres5t4 ,ow+ to ! invet]ate subjectivism ( 8 m5tal habits1 he fail$ to notice t he _h rev]s$ ! s5se ( ! s]ies by sub/itut+ backw>d syn!sis = =w>d happ5+1 & ?us he suppos$ t x 0 necess>y to id5tify ! m5tal s]ies1 :i* _h no end1 ) ! physical s]ies1 :i* _h an end b no beg9n+4 ,x 0 ?is mi/ake1 ,i ?9k1 :i*1 op]at+ unconsci\sly1 l$ him to attribute validity to a s+ul>ly flimsy piece ( fallaci\s reason+4 ,! second ant9omy illu/rates ! dep5d5ce ( ! problem ( cont9uity ^u t ( inf9ity4 ,! !sis /ates3 ,e complex sub/ance 9 ! _w consi/s ( simple p>ts1 & !re exi/s ev]y:]e no?+ b ! simple or :at is compos$ ( x4 ,! anti!sis /ates3 ,no complex ?+ 9 ! _w consi/s ( simple p>ts1 & ev]y:]e 9 x !re exi/s no?+ simple4 ,"h1 z be=e1 ! pro(s ( bo? !sis & anti!sis are op5 to criticism1 b = ! purpose ( v9dicat+ physics & ! _w ( s5se x is en\gh to f9d a fallacy 9 "o ( ! pro(s4 ,we w *oose = ?is purpose ! pro( ( ! anti!sis1 :i* beg9s z foll[s3 ,assume t a complex ?+ 7z sub/ance7 consi/s ( simple p>ts4 ,s9ce all ext]nal relation1 & !re=e all composition out ( sub/ances1 is only possible 9 space1 ! space occupi$ by a complex ?+ mu/ consi/ ( z _m p>ts z ! ?+ consi/s (4 ,n[ space does n consi/ ( simple p>ts1 b ( spaces4 ,! re/ ( 8 argum5t ne$ n conc]n u1 = ! n]ve ( ! pro( lies 9 ! "o /atem5t3 ,space does n consi/ ( simple p>ts1 b ( spaces4 ,?is is l ,b]gson's objection to ! absurd proposition t motion is made up ( immobilities4 ,kant does n tell u :y he holds t a space mu/ consi/ ( spaces r ?an ( simple p>ts4 ,geometry reg>ds space z made up ( po9ts1 :i* are simple2 & al?\gh1 z we h se51 ?is view is n sci5tifically or logically necess>y1 x rema9s prima facie possible1 & its m]e possibility is en\gh to vitiate ,kant's argum5t4 ,=1 if 8 pro( ( ! !sis ( ! ant9omy 7 valid1 & if ! anti!sis c\ld only be avoid$ by assum+ po9ts1 !n ! ant9omy itself w\ld af=d a conclusive reason 9 fav\r ( po9ts4 ,:y1 !n1 did ,kant ?9k x impossible t space %\ld be compos$ ( po9ts8 ,i ?9k two consid]ations probably influ5c$ him4 ,9 ! fir/ place1 ! ess5tial ?+ ab\t space is spatial ord]1 & m]e po9ts1 by !mselves1 w n acc\nt = spatial ord]4 ,x is obvi\s t 8 argum5t assumes absolute space2 b x is spatial relations t are alone important1 & !y _c be r$uc$ to po9ts4 ,?is gr\nd = 8 view dep5ds1 !re=e1 ^u 8 ignorance ( ! logical !ory ( ord] & 8 oscillations betwe5 absolute & relative space4 ,b !re is also ano!r gr\nd = 8 op9ion1 :i* is m relevant to our pres5t topic4 ,?is is ! gr\nd d]iv$ f inf9ite divisibility4 ,a space may be halv$1 & !n halv$ aga91 & s on ad inf9itum1 & at e /age ( ! process ! p>ts are /ill spaces1 n po9ts4 ,9 ord] to rea* po9ts by su* a me?od1 x w\ld be necess>y to come to ! end ( an un5d+ process1 :i* is impossible4 ,b j z an inf9ite class c be giv5 all at once by its def9+ concept1 ?\gh x _c be rea*$ by successive enum]ation1 s an inf9ite set ( po9ts c be giv5 all at once z mak+ up a l9e or area or volume1 ?\gh !y c nev] be rea*$ by ! process ( successive division4 ,?us ! inf9ite divisibility ( space gives no gr\nd = d5y+ t space is compos$ ( po9ts4 ,kant does n give 8 gr\nds = ?is d5ial1 & we c !re=e only conjecture :at !y 74 ,b ! above two gr\nds1 :i* we h se5 to be fallaci\s1 seem suffici5t to acc\nt = 8 op9ion1 & we may !re=e conclude t ! anti!sis ( ! second ant9omy is unprov$4 ,! above illu/ration ( ,kant's ant9omies has only be5 introduc$ 9 ord] to %[ ! relevance ( ! problem ( inf9ity to ! problem ( ! reality ( objects ( s5se4 ,9 ! rema9d] ( ! pres5t lecture1 ,i wi% to /ate & expla9 ! problem ( inf9ity1 to %[ h[ x arose1 & to %[ ! irrelevance ( all ! solutions propos$ by philosoph]s4 ,9 ! foll[+ lecture1 ,i %all try to expla9 ! true solution1 :i* has be5 discov]$ by ! ma!maticians1 b nev]!less belongs ess5tially to philosophy4 ,! solution is def9itive1 9 ! s5se t x entirely satisfies & conv9ces all :o /udy x c>efully4 ,= ov] two ?\s& ye>s ! human intellect 0 baffl$ by ! problem2 its _m failures & its ultimate success make ?is problem peculi>ly apt = ! illu/ration ( me?od4 ,! problem appe>s to h fir/ aris5 9 "s su* way z ! foll[+4#bb ,py?agoras & 8 foll[]s1 :o 7 int]e/$1 l ,desc>tes1 9 ! application ( numb] to geometry1 adopt$ 9 t sci5ce m ari?metical me?ods ?an ^? ) :i* ,euclid has made u famili>4 ,!y1 or _! contempor>ies ! atomi/s1 believ$1 app>5tly1 t space is compos$ ( indivisible po9ts1 :ile "t is compos$ ( indivisible in/ants4#bc ,?is belief w\ld n1 by itself1 h rais$ ! difficulties :i* !y enc\nt]$1 b x 0 presumably accompani$ by ano!r belief1 t ! numb] ( po9ts 9 any f9ite area or ( in/ants 9 any f9ite p]iod mu/ be f9ite4 ,i d n suppose t ?is latt] belief 0 a consci\s "o1 because probably no o!r possibility _h occurr$ to !m4 ,b ! belief nev]!less op]at$1 & v soon br\ght !m into conflict ) facts :i* !y !mselves discov]$4 ,be=e expla9+ h[ ?is occurr$1 h[ev]1 x is necess>y to say "o ^w 9 explanation ( ! phrase f9ite numb]4 ,! exact explanation is a matt] = our next lecture2 = ! pres5t1 x mu/ suffice to say t ,i mean #j & #a & #b & #c & s on1 = ev]--9 o!r words1 any numb] t c be obta9$ by successively add+ ones4 ,?is includes all ! numb]s t c be express$ by means ( our ord9>y num]als1 & s9ce su* numb]s c be made great] & great]1 )\t ev] rea*+ an unsurpassable maximum1 x is easy to suppose t !re are no o!r numb]s4 ,b ?is supposition1 natural z x is1 is mi/ak54 #bb ,9 :at conc]ns ! e>ly ,greek philosoph]s1 my k is l>gely d]iv$ f ,burnet's valuable "w1 ,e>ly ,greek ,philosophy 7#bnd ed41 ,london1 #aijh74 ,i h also be5 greatly assi/$ by ,mr ,d4 ,s4 ,rob]tson ( ,tr9ity ,college1 :o has suppli$ ! defici5cies ( my k ( ,greek1 & br\ght important ref]5ces to my notice4 #bc ,cf4 ,ari/otle1 ,metaphysics1 ,m4 #f1 #ajhj;b1 #ah sqq41 & #ajhc;b1 #h sqq4 ,:e!r ! ,py?agoreans !mselves believ$ space & "t to be compos$ ( indivisible po9ts & in/ants is a debatable "q4#bd ,x w\ld seem t ! di/9ction betwe5 space & matt] _h n yet be5 cle>ly made1 & t !re=e1 :5 an atomi/ic view is express$1 x is difficult to decide :e!r p>ticles ( matt] or po9ts ( space are int5d$4 ,!re is an int]e/+ passage#be 9 ,ari/otle's ,physics1#bf :]e he says3 ,! ,py?agoreans all ma9ta9$ ! exi/5ce ( ! void1 & said t x ent]s into ! heav5 itself f ! b\ndless brea?1 inasmu* z ! heav5 brea!s 9 ! void also2 & ! void diff]5tiates natures1 z if x 7 a sort ( sep>ation ( consecutives1 & z if x 7 _! diff]5tiation2 & t ?is also is :at is fir/ 9 numb]s1 = x is ! void :i* diff]5tiates !m4 #bd ,!re is "s reason to ?9k t ! ,py?agoreans di/+ui%$ betwe5 discrete & cont9u\s quantity4 ,g4 ,j4 ,allman1 9 8 ,greek ,geometry f ,?ales to ,euclid1 says 7p4 #bc73 ,! ,py?agoreans made a f\rfold division ( ma!matical sci5ce1 attribut+ "o ( its p>ts to ! h[ _m1 to poson1 & ! o!r to ! h[ mu*1 to pelikon2 & !y assign$ to ea* ( ^! p>ts a tw(old division4 ,= !y said t discrete quantity1 or ! h[ _m1 ei!r subsi/s by itself or mu/ be consid]$ ) relation to "s o!r2 b t cont9u$ quantity1 or ! h[ mu*1 is ei!r /able or 9 motion4 ,h5ce !y affirm$ t ari?metic contemplates t discrete quantity :i* subsi/s by itself1 b music t :i* is relat$ to ano!r2 & t geometry consid]s cont9u$ quantity s f> z x is immovable2 b a/ronomy 7t5 sphairik57 contemplates cont9u$ quantity s f> z x is ( a self-motive nature4 7,proclus1 ed4 ,fri$le91 p4 #ce4 ,z to ! di/9ction betwe5 to pelikon1 cont9u\s1 & to poson1 discrete quantity1 see ,iambl41 9 ,nicoma*i ,g]as5i ,ari?meticam introductionem1 ed4 ,t5nulius1 p4 #adh47 ,cf4 p4 #dh4 #be ,ref]r$ to by ,burnet1 op4 cit41 p4 #abj4 #bf iv41 #f4 #bac;b1 #bb2 ,h4 ,ritt] & ,l4 ,prell]1 ,hi/oria ,philosophiae ,graecae1 #h? ed41 ,go?a1 #ahih1 p4 #ge 7?is "w w be ref]r$ to 9 future z ,r4 ,p474 ,?is seems to imply t !y reg>d$ matt] z consi/+ ( atoms ) empty space 9 betwe54 ,b if s1 !y mu/ h ?\ght space c\ld be /udi$ by only pay+ att5tion to ! atoms1 = o!rwise x w\ld be h>d to acc\nt = _! ari?metical me?ods 9 geometry1 or = _! /atem5t t ?+s are numb]s4 ,! difficulty :i* beset ! ,py?agoreans 9 _! attempts to apply numb]s arose ?r\gh _! discov]y ( incomm5surables1 & ?is1 9 turn1 arose z foll[s4 ,py?agoras1 z we all le>nt 9 y\?1 discov]$ ! proposition t ! sum ( ! squ>es on ! sides ( a "r-angl$ triangle is equal to ! squ>e on ! hypot5use4 ,x is said t he sacrific$ an ox :5 he discov]$ ?is !orem2 if s1 ! ox 0 ! fir/ m>tyr to sci5ce4 ,b ! !orem1 ?\gh x has rema9$ 8 *ief claim to immortality1 0 soon f\nd to h a consequ5ce fatal to 8 :ole philosophy4 ,consid] ! case ( a "r-angl$ triangle ^: two sides are equal1 su* a triangle z is =m$ by two sides ( a squ>e & a diagonal4 ,"h1 9 virtue ( ! !orem1 ! squ>e on ! diagonal is d\ble ( ! squ>e on ei!r ( ! sides4 ,b ,py?agoras or 8 e>ly foll[]s easily prov$ t ! squ>e ( "o :ole numb] _c be d\ble ( ! squ>e ( ano!r4#bg ,?us ! l5g? ( ! side & ! l5g? ( ! diagonal are incomm5surable2 t is to say1 h[ev] small a unit ( l5g? y take1 if x is conta9$ an exact numb] ( times 9 ! side1 x is n conta9$ any exact numb] ( times 9 ! diagonal1 & vice v]sa4 #bg ,! ,py?agorean pro( is r\ghly z foll[s4 ,if possible1 let ! ratio ( ! diagonal to ! side ( a squ>e be m_/n1 :]e m & n are :ole numb]s hav+ no common factor4 ,!n we mu/ h m#b #bn#b4 ,n[ ! squ>e ( an odd numb] is odd1 b m#b1 be+ equal to #bn#b1 is ev54 ,h5ce m mu/ be ev54 ,b ! squ>e ( an ev5 numb] divides by #d1 !re=e n#b1 :i* is half ( m#b1 mu/ be ev54 ,!re=e n mu/ be ev54 ,b1 s9ce m is ev51 & m & n h no common factor1 n mu/ be odd4 ,?us n mu/ be bo? odd & ev51 :i* is impossible2 & !re=e ! diagonal & ! side _c h a rational ratio4 ,n[ ?is fact might h be5 assimilat$ by "s philosophies )\t any great difficulty1 b to ! philosophy ( ,py?agoras x 0 absolutely fatal4 ,py?agoras held t numb] is ! con/itutive ess5ce ( all ?+s1 yet no two numb]s c\ld express ! ratio ( ! side ( a squ>e to ! diagonal4 ,x w\ld seem probable t we may exp& 8 difficulty1 )\t dep>t+ f 8 ?\ght1 by assum+ t he reg>d$ ! l5g? ( a l9e z det]m9$ by ! numb] ( atoms conta9$ 9 x--a l9e two in*es long w\ld conta9 twice z _m atoms z a l9e "o in* long1 & s on4 ,b if ?is 7 ! tru?1 !n !re mu/ be a def9ite num]ical ratio betwe5 any two f9ite l5g?s1 because x 0 suppos$ t ! numb] ( atoms 9 ea*1 h[ev] l>ge1 mu/ be f9ite4 ,"h !re 0 an insoluble contradiction4 ,! ,py?agoreans1 x is said1 resolv$ to keep ! exi/5ce ( incomm5surables a pr(\nd secret1 reveal$ only to a few ( ! supreme heads ( ! sect2 & "o ( _! numb]1 ,hippasos ( ,metapontion1 is ev5 said to h be5 %ipwreck$ at sea = impi\sly disclos+ ! t]rible discov]y to _! enemies4 ,x mu/ be rememb]$ t ,py?agoras 0 ! f\nd] ( a new religion z well z ! tea*] ( a new sci5ce3 if ! sci5ce came to be d\bt$1 ! disciples might fall into s91 & p]haps ev5 eat beans1 :i* accord+ to ,py?agoras is z bad z eat+ p>5ts' bones4 ,! problem fir/ rais$ by ! discov]y ( incomm5surables prov$1 z "t w5t on1 to be "o ( ! mo/ sev]e & at ! same "t mo/ f>-rea*+ problems t h confront$ ! human intellect 9 its endeav\r to und]/& ! _w4 ,x %[$ at once t num]ical measurem5t ( l5g?s1 if x 0 to be made accurate1 mu/ require an ari?metic m advanc$ & m difficult ?an any t ! anci5ts possess$4 ,!y !re=e set to "w to recon/ruct geometry on a basis :i* did n assume ! univ]sal possibility ( num]ical measurem5t--a recon/ruction :i*1 z may be se5 9 ,euclid1 !y effect$ ) extraord9>y skill & ) great logical acum54 ,! mod]ns1 "u ! influ5ce ( ,c>tesian geometry1 h reass]t$ ! univ]sal possibility ( num]ical measurem5t1 ext5d+ ari?metic1 p>tly = t purpose1 s z to include :at are call$ irrational numb]s1 :i* give ! ratios ( incomm5surable l5g?s4 ,b al?\gh irrational numb]s h long be5 us$ )\t a qualm1 x is only 9 q rec5t ye>s t logically satisfactory def9itions ( !m h be5 giv54 ,) ^! def9itions1 ! fir/ & mo/ obvi\s =m ( ! difficulty :i* confront$ ! ,py?agoreans has be5 solv$2 b o!r =ms ( ! difficulty rema9 to be consid]$1 & x is ^! t introduce u to ! problem ( inf9ity 9 its pure =m4 ,we saw t1 accept+ ! view t a l5g? is compos$ ( po9ts1 ! exi/5ce ( incomm5surables proves t e f9ite l5g? mu/ conta9 an inf9ite numb] ( po9ts4 ,9 o!r words1 if we 7 to take away po9ts "o by "o1 we %\ld nev] h tak5 away all ! po9ts1 h[ev] long we cont9u$ ! process4 ,! numb] ( po9ts1 !re=e1 _c be c\nt$1 = c\nt+ is a process :i* enum]ates ?+s "o by "o4 ,! prop]ty ( be+ unable to be c\nt$ is *>act]i/ic ( inf9ite collections1 & is a s\rce ( _m ( _! p>adoxical qualities4 ,s p>adoxical are ^! qualities t until our own day !y 7 ?\ght to con/itute logical contradictions4 ,a long l9e ( philosoph]s1 f ,z5o#bh to ,m4 ,b]gson1 h bas$ mu* ( _! metaphysics ^u ! suppos$ impossibility ( inf9ite collections4 ,broadly speak+1 ! difficulties 7 /at$ by ,z5o1 & no?+ mat]ial 0 add$ until we rea* ,bolzano's ,p>adoxi5 des ,un5dli*51 a little "w writt5 9 #ahdg-h1 & publi%$ po/hum\sly 9 #ahea4 ,int]v5+ attempts to deal ) ! problem are futile & negligible4 ,! def9itive solution ( ! difficulties is due1 n to ,bolzano1 b to ,georg ,cantor1 ^: "w on ?is subject fir/ appe>$ 9 #ahhb4 #bh ,9 reg>d to ,z5o & ! ,py?agoreans1 ,i h d]iv$ mu* valuable in=mation & criticism f ,mr ,p4 ,e4 ,b4 ,j\rda94 ,9 ord] to und]/& ,z5o1 & to realise h[ little mod]n or?odox metaphysics has add$ to ! a*ievem5ts ( ! ,greeks1 we mu/ consid] = a mom5t 8 ma/] ,p>m5ides1 9 ^: int]e/ ! p>adoxes 7 inv5t$4#bi ,p>m5ides exp\nd$ 8 views 9 a poem divid$ into two p>ts1 call$ ! way ( tru? & ! way ( op9ion--l ,mr ,bradley's ,appe>ance & ,reality1 except t ,p>m5ides tells u fir/ ab\t reality & !n ab\t appe>ance4 ,! way ( op9ion1 9 8 philosophy1 is1 broadly speak+1 ,py?agoreanism2 x beg9s ) a w>n+3 ,"h ,i %all close my tru/wor?y spee* & ?\ght ab\t ! tru?4 ,h5ce=w>d le>n ! op9ions ( mortals1 giv+ e> to ! deceptive ord]+ ( my words4 ,:at has gone be=e has be5 reveal$ by a goddess1 :o tells him :at really is4 ,reality1 %e says1 is uncreat$1 inde/ructible1 un*ang+1 indivisible2 x is immovable 9 ! bonds ( mighty *a9s1 )\t beg9n+ & )\t end2 s9ce com+ into be+ & pass+ away h be5 driv5 af>1 & true belief has ca/ !m away4 ,! fundam5tal pr9ciple ( 8 inquiry is /at$ 9 a s5t5ce :i* w\ld n be out ( place 9 ,hegel3#cj ,?\ can/ n "k :at is n--t is impossible--nor utt] x2 = x is ! same ?+ t c be ?\ght & t c be4 ,& aga93 ,x ne$s mu/ be t :at c be ?\ght & spok5 ( is2 = x is possible = x to be1 & x is n possible = :at is no?+ to be4 ,! impossibility ( *ange foll[s f ?is pr9ciple2 = :at is pa/ c be spok5 (1 & !re=e1 by ! pr9ciple1 /ill is4 #bi ,s ,plato makes ,z5o say 9 ! ,p>m5ides1 apropos ( 8 philosophy z a :ole2 & all int]nal & ext]nal evid5ce supports ?is view4 #cj ,) ,p>m5ides1 ,hegel says1 philosophis+ prop] began4 ,w]ke 7edition ( #ahdj71 vol4 xiii4 p4 #bgd4 ,! great conception ( a reality beh9d ! pass+ illusions ( s5se1 a reality "o1 indivisible1 & un*ang+1 0 ?us introduc$ into ,we/]n philosophy by ,p>m5ides1 n1 x w\ld seem1 = my/ical or religi\s reasons1 b on ! basis ( a logical argum5t z to ! impossibility ( n-be+4 ,all ! great metaphysical sy/ems--notably ^? ( ,plato1 ,sp9oza1 & ,hegel--are ! outcome ( ?is fundam5tal idea4 ,x is difficult to dis5tangle ! tru? & ! error 9 ?is view4 ,! cont5tion t "t is unreal & t ! _w ( s5se is illusory mu/1 ,i ?9k1 be reg>d$ z bas$ ^u fallaci\s reason+4 ,nev]!less1 !re is "s s5se--easi] to feel ?an to /ate--9 :i* "t is an unimportant & sup]ficial *>act]i/ic ( reality4 ,pa/ & future mu/ be ackn[l$g$ to be z real z ! pres5t1 & a c]ta9 emancipation f slav]y to "t is ess5tial to philosophic ?\ght4 ,! importance ( "t is r practical ?an !oretical1 r 9 relation to our desires ?an 9 relation to tru?4 ,a tru] image ( ! _w1 ,i ?9k1 is obta9$ by pictur+ ?+s z ent]+ into ! /ream ( "t f an et]nal _w outside1 ?an f a view :i* reg>ds "t z ! dev\r+ tyrant ( all t is4 ,bo? 9 ?\ght & 9 feel+1 to realise ! unimportance ( "t is ! gate ( wisdom4 ,b unimportance is n unreality2 & !re=e :at we %all h to say ab\t ,z5o's argum5ts 9 support ( ,p>m5ides mu/ be ma9ly critical4 ,! relation ( ,z5o to ,p>m5ides is expla9$ by ,plato#ca 9 ! dialogue 9 :i* ,socrates1 z a "y man1 le>ns logical acum5 & philosophic dis9t]e/$ness f _! dialectic4 ,i quote f ,j[ett's translation3 ,i see1 ,p>m5ides1 said ,socrates1 t ,z5o is y\r second self 9 8 writ+s too2 he puts :at y say 9 ano!r way1 & w\ld fa9 deceive u into believ+ t he is tell+ u :at is new4 ,= y1 9 y\r poems1 say ,all is "o1 & ( ?is y adduce excell5t pro(s2 & he on ! o!r h& says ,!re is no ,_m2 & on behalf ( ?is he (f]s ov]:elm+ evid5ce4 ,to deceive ! _w1 z y h done1 by say+ ! same ?+ 9 diff]5t ways1 "o ( y affirm+ ! "o1 & ! o!r d5y+ ! _m1 is a /ra9 ( art beyond ! rea* ( mo/ ( u4 ,yes1 ,socrates1 said ,z5o4 ,b al?\gh y are z ke5 z a ,sp>tan h\nd 9 pursu+ ! track1 y d n q appreh5d ! true motive ( ! composition1 :i* is n really su* an ambiti\s "w z y imag9e2 = :at y speak ( 0 an accid5t2 ,i _h no s]i\s int5tion ( deceiv+ ! _w4 ,! tru? is1 t ^! writ+s ( m9e 7 meant to protect ! argum5ts ( ,p>m5ides aga9/ ^? :o sc(f at him & %[ ! _m ridicul\s & contradictory results :i* !y suppose to foll[ f ! affirmation ( ! "o4 ,my answ] is an address to ! p>tisans ( ! _m1 ^: attack ,i return ) int]e/ by retort+ ^u !m t _! hypo!sis ( ! be+ ( ! _m if c>ri$ out appe>s 9 a /ill m ridicul\s light ?an ! hypo!sis ( ! be+ ( ! "o4 #ca ,p>m5ides1 #abh ,a-,d4 ,z5o's f\r argum5ts aga9/ motion 7 int5d$ to exhibit ! contradictions t result f suppos+ t !re is su* a ?+ z *ange1 & ?us to support ! ,p>m5idean doctr9e t reality is un*ang+4#cb ,un=tunately1 we only "k 8 argum5ts ?r\gh ,ari/otle1#cc :o /at$ !m 9 ord] to refute !m4 ,^? philosoph]s 9 ! pres5t day :o h _h _! doctr9es /at$ by oppon5ts w realise t a j or adequate pres5tation ( ,z5o's position is h>dly to be expect$ f ,ari/otle2 b by "s c>e 9 int]pretation x seems possible to recon/ruct ! s-call$ sophisms :i* h be5 refut$ by e tyro f t day to ?is4 #cb ,?is int]pretation is combat$ by ,milhaud1 ,les philosophes-geometres de la ,grece1 p4 #adj n41 b 8 reasons d n seem to me conv9c+4 ,all ! int]pretations 9 :at foll[s are op5 to "q1 b all h ! support ( reputable au?orities4 #cc ,physics1 vi4 #i4 #bcif 7,r4,p4 #acf-aci74 ,z5o's argum5ts w\ld seem to be ad hom9em2 t is to say1 !y seem to assume premisses grant$ by 8 oppon5ts1 & to %[ t1 grant+ ^! premisses1 x is possible to d$uce consequ5ces :i* 8 oppon5ts mu/ d5y4 ,9 ord] to decide :e!r !y are valid argum5ts or sophisms1 x is necess>y to guess at ! tacit premisses1 & to decide :o 0 ! homo at :om !y 7 aim$4 ,"s ma9ta9 t !y 7 aim$ at ! ,py?agoreans1#cd :ile o!rs h held t !y 7 int5d$ to refute ! atomi/s4#ce ,m4 ,evell91 on ! contr>y1 holds t !y con/itute a refutation ( inf9ite divisibility1#cf :ile ,m4 ,g4 ,noel1 9 ! int]e/s ( ,hegel1 ma9ta9s t ! fir/ two argum5ts refute inf9ite divisibility1 :ile ! next two refute indivisibles4#cg ,amid su* a bewild]+ v>iety ( int]pretations1 we c at lea/ n compla9 ( any re/rictions on our lib]ty ( *oice4 #cd ,cf4 ,ga/on ,milhaud1 ,les philosophes-geometres de la ,grece1 p4 #adj n42 ,paul ,tann]y1 ,p\r l'hi/oire de la sci5ce hell5e1 p4 #bdi2 ,burnet1 op4 cit41 p4 #cfb4 #ce ,cf4 ,r4 ,k4 ,gaye1 ,on ,ari/otle1 ,physics1 ,z ix4 ,j\rnal ( ,philology1 vol4 xxxi41 esp4 p4 #aaa4 ,also ,moritz ,cantor1 ,vorlesung5 ueb] ,ges*i*te d] ,ma!matik1 #a/ ed41 vol4 i41 #ahhj1 p4 #afh1 :o1 h[ev]1 subsequ5tly adopt$ ,paul ,tann]y's op9ion1 ,vorlesung51 #crd ed4 7vol4 i4 p4 #bjj74 #cf ,le m\vem5t et les p>tisans des indivisibles1 ,revue de ,metaphysique et de ,morale1 vol4 i4 pp4 #chb-cie4 #cg ,le m\vem5t et les argum5ts de ,z5on d',elee1 ,revue de ,metaphysique et de ,morale1 vol4 i4 pp4 #ajg-abe4 ,! hi/orical que/ions rais$ by ! above-m5tion$ discussions are no d\bt l>gely insoluble1 ow+ to ! v scanty mat]ial f :i* our evid5ce is d]iv$4 ,! po9ts :i* seem fairly cle> are ! foll[+3 7#a7 ,t1 9 spite ( ,,mm4 ,milhaud & ,paul ,tann]y1 ,z5o is anxi\s to prove t motion is really impossible1 & t he desires to prove ?is because he foll[s ,p>m5ides 9 d5y+ plurality2#ch 7#b7 t ! ?ird & f\r? argum5ts proce$ on ! hypo!sis ( indivisibles1 a hypo!sis :i*1 :e!r adopt$ by ! ,py?agoreans or n1 0 c]ta9ly mu* advocat$1 z may be se5 f ! treatise ,on ,indivisible ,l9es attribut$ to ,ari/otle4 ,z reg>ds ! fir/ two argum5ts1 !y w\ld seem to be valid on ! hypo!sis ( indivisibles1 & also1 )\t ?is hypo!sis1 to be su* z w\ld be valid if ! traditional contradictions 9 inf9ite numb]s 7 insoluble1 :i* !y are n4 #ch ,cf4 ,m4 ,bro*>d1 ,les pret5dus sophismes de ,z5on d',elee1 ,revue de ,metaphysique et de ,morale1 vol4 i4 pp4 #bji-bae4 ,we may conclude1 !re=e1 t ,z5o's polemic is direct$ aga9/ ! view t space & "t consi/ ( po9ts & in/ants2 & t z aga9/ ! view t a f9ite /ret* ( space or "t consi/s ( a f9ite numb] ( po9ts & in/ants1 8 argum5ts are n sophisms1 b p]fectly valid4 ,! conclusion :i* ,z5o wi%es u to draw is t plurality is a delusion1 & spaces & times are really indivisible4 ,! o!r conclusion :i* is possible1 namely1 t ! numb] ( po9ts & in/ants is inf9ite1 0 n t5able s long z ! inf9ite 0 infect$ ) contradictions4 ,9 a fragm5t :i* is n "o ( ! f\r fam\s argum5ts aga9/ motion1 ,z5o says3 ,if ?+s are a _m1 !y mu/ be j z _m z !y are1 & nei!r m nor less4 ,n[1 if !y are z _m z !y are1 !y w be f9ite 9 numb]4 ,if ?+s are a _m1 !y w be inf9ite 9 numb]2 = !re w always be o!r ?+s betwe5 !m1 & o!rs aga9 betwe5 ^!4 ,& s ?+s are inf9ite 9 numb]4#ci #ci ,simplicius1 ,phys41 #adj1 #bh ,d 7,r4,p4 #acc72 ,burnet1 op4 cit41 pp4 #cfd-cfe4 ,?is argum5t attempts to prove t1 if !re are _m ?+s1 ! numb] ( !m mu/ be bo? f9ite & inf9ite1 :i* is impossible2 h5ce we are to conclude t !re is only "o ?+4 ,b ! weak po9t 9 ! argum5t is ! phrase3 ,if !y are j z _m z !y are1 !y w be f9ite 9 numb]4 ,?is phrase is n v cle>1 b x is pla9 t x assumes ! impossibility ( def9ite inf9ite numb]s4 ,)\t ?is assumption1 :i* is n[ kn[n to be false1 ! argum5ts ( ,z5o1 ?\gh !y suffice 7on c]ta9 v reasonable assumptions7 to dispel ! hypo!sis ( f9ite indivisibles1 d n suffice to prove t motion & *ange & plurality are impossible4 ,!y are n1 h[ev]1 on any view1 m]e fooli% quibbles3 !y are s]i\s argum5ts1 rais+ difficulties :i* x has tak5 two ?\s& ye>s to answ]1 & :i* ev5 n[ are fatal to ! tea*+s ( mo/ philosoph]s4 ,! fir/ ( ,z5o's argum5ts is ! argum5t ( ! race-c\rse1 :i* is p>aphras$ by ,burnet z foll[s3#dj ,y _c get to ! end ( a race-c\rse4 ,y _c trav]se an inf9ite numb] ( po9ts 9 a f9ite "t4 ,y mu/ trav]se ! half ( any giv5 di/ance be=e y trav]se ! :ole1 & ! half ( t aga9 be=e y c trav]se x4 ,?is goes on ad inf9itum1 s t !re are an inf9ite numb] ( po9ts 9 any giv5 space1 & y _c t\* an inf9ite numb] "o by "o 9 a f9ite "t4#da #dj ,op4 cit41 p4 #cfg4 #da ,ari/otle's words are3 ,! fir/ is ! "o on ! non-exi/5ce ( motion on ! gr\nd t :at is mov$ mu/ always atta9 ! middle po9t soon] ?an ! end-po9t1 on :i* we gave our op9ion 9 ! e>li] "p ( our disc\rse4 ,phys41 vi4 #i4 #ici;,b 7,r4,p4 #acf74 ,ari/otle seems to ref] to ,phys41 vi4 #b4 #bbc;,,ab ,r4,p4 #acf;,a3 ,all space is cont9u\s1 = "t & space are divid$ into ! same & equal divisions4444 ,:]e=e also ,z5o's argum5t is fallaci\s1 t x is impossible to g ?r\gh an inf9ite collection or to t\* an inf9ite collection "o by "o 9 a f9ite "t4 ,= !re are two s5ses 9 :i* ! t]m 'inf9ite' is appli$ bo? to l5g? & to "t1 & 9 fact to all cont9u\s ?+s1 ei!r 9 reg>d to divisibility1 or 9 reg>d to ! ends4 ,n[ x is n possible to t\* ?+s inf9ite 9 reg>d to numb] 9 a f9ite "t1 b x is possible to t\* ?+s inf9ite 9 reg>d to divisibility3 = "t itself also is inf9ite 9 ?is s5se4 ,s t 9 fact we g ?r\gh an inf9ite1 space 9 an inf9ite "t & n 9 a f9ite "t1 & we t\* inf9ite ?+s ) inf9ite ?+s1 n ) f9ite ?+s4 ,philoponus1 a six?-c5tury comm5tator 7,r4,p4 #acf;,a1 ,exc4 ,p>is ,philop4 9 ,ari/4 ,phys41 #hjc1 #b4 ,vit471 gives ! foll[+ illu/ration3 ,= if a ?+ 7 mov$ ! space ( a cubit 9 "o h\r1 s9ce 9 e space !re are an inf9ite numb] ( po9ts1 ! ?+ mov$ mu/ ne$s t\* all ! po9ts ( ! space3 x w !n g ?r\gh an inf9ite collection 9 a f9ite "t1 :i* is impossible4 ,z5o appeals "h1 9 ! fir/ place1 to ! fact t any di/ance1 h[ev] small1 c be halv$4 ,f ?is x foll[s1 ( c\rse1 t !re mu/ be an inf9ite numb] ( po9ts 9 a l9e4 ,b1 ,ari/otle repres5ts him z argu+1 y _c t\* an inf9ite numb] ( po9ts "o by "o 9 a f9ite "t4 ,! words "o by "o are important4 7#a7 ,if all ! po9ts t\*$ are conc]n$1 !n1 ?\gh y pass ?r\gh !m cont9u\sly1 y d n t\* !m "o by "o4 ,t is to say1 aft] t\*+ "o1 !re is n ano!r :i* y t\* next3 no two po9ts are next ea* o!r1 b betwe5 any two !re are always an inf9ite numb] ( o!rs1 :i* _c be enum]at$ "o by "o4 7#b7 ,if1 on ! o!r h&1 only ! successive middle po9ts are conc]n$1 obta9$ by always halv+ :at rema9s ( ! c\rse1 !n ! po9ts are rea*$ "o by "o1 &1 ?\gh !y are inf9ite 9 numb]1 !y are 9 fact all rea*$ 9 a f9ite "t4 ,8 argum5t to ! contr>y may be suppos$ to appeal to ! view t a f9ite "t mu/ consi/ ( a f9ite numb] ( in/ants1 9 :i* case :at he says w\ld be p]fectly true on ! assumption t ! possibility ( cont9u$ di*otomy is und5iable4 ,if1 on ! o!r h&1 we suppose ! argum5t direct$ aga9/ ! p>tisans ( inf9ite divisibility1 we mu/ suppose x to proce$ z foll[s3#db ,! po9ts giv5 by successive halv+ ( ! di/ances /ill to be trav]s$ are inf9ite 9 numb]1 & are rea*$ 9 succession1 ea* be+ rea*$ a f9ite "t lat] ?an its pr$ecessor2 b ! sum ( an inf9ite numb] ( f9ite times mu/ be inf9ite1 & !re=e ! process w nev] be complet$4 ,x is v possible t ?is is hi/orically ! "r int]pretation1 b 9 ?is =m ! argum5t is invalid4 ,if half ! c\rse takes half a m9ute1 & ! next qu>t] takes a qu>t] ( a m9ute1 & s on1 ! :ole c\rse w take a m9ute4 ,! app>5t =ce ( ! argum5t1 on ?is int]pretation1 lies solely 9 ! mi/ak5 supposition t !re _c be any?+ beyond ! :ole ( an inf9ite s]ies1 :i* c be se5 to be false by obs]v+ t #a is beyond ! :ole ( ! inf9ite s]ies #a_/b1 #c_/d1 #g_/h1 #ae_/af1 444 #db ,cf4 ,mr ,c4 ,d4 ,broad1 ,note on ,a*illes & ! ,tortoise1 ,m9d1 ,n4,s41 vol4 xxii4 pp4 #cah-i4 ,! second ( ,z5o's argum5ts is ! "o conc]n+ ,a*illes & ! tortoise1 :i* has a*iev$ m notoriety ?an ! o!rs4 ,x is p>aphras$ by ,burnet z foll[s3#dc ,a*illes w nev] ov]take ! tortoise4 ,he mu/ fir/ rea* ! place f :i* ! tortoise />t$4 ,by t "t ! tortoise w h got "s way ahead4 ,a*illes mu/ !n make up t1 & aga9 ! tortoise w be ahead4 ,he is always com+ ne>]1 b he nev] makes up to x4#dd #dc ,op4 cit4 #dd ,ari/otle's words are3 ,! second is ! s-call$ ,a*illes4 ,x consi/s 9 ?is1 t ! sl[] w nev] be ov]tak5 9 its c\rse by ! quicke/1 = ! pursu] mu/ always come fir/ to ! po9t f :i* ! pursu$ has j dep>t$1 s t ! sl[] mu/ necess>ily be always /ill m or less 9 advance4 ,phys41 vi4 #i4 #bci;,b 7,r4,p4 #acg74 ,?is argum5t is ess5tially ! same z ! previ\s "o4 ,x %[s t1 if ,a*illes ev] ov]takes ! tortoise1 x mu/ be aft] an inf9ite numb] ( in/ants h elaps$ s9ce he />t$4 ,?is is 9 fact true2 b ! view t an inf9ite numb] ( in/ants make up an inf9itely long "t is n true1 & !re=e ! conclusion t ,a*illes w nev] ov]take ! tortoise does n foll[4 ,! ?ird argum5t1#de t ( ! arr[1 is v int]e/+4 ,! text has be5 que/ion$4 ,burnet accepts ! alt]ations ( ,zell]1 & p>aphrases ?us3 ,! arr[ 9 flight is at re/4 ,=1 if ev]y?+ is at re/ :5 x occupies a space equal to itself1 & :at is 9 flight at any giv5 mom5t always occupies a space equal to itself1 x _c move4 #de ,phys41 vi4 #i4 #bci;,b 7,r4,p4 #ach74 ,b accord+ to ,prantl1 ! lit]al translation ( ! unem5d$ text ( ,ari/otle's /atem5t ( ! argum5t is z foll[s3 ,if ev]y?+1 :5 x is behav+ 9 a uni=m mann]1 is cont9ually ei!r mov+ or at re/1 b :at is mov+ is always 9 ! n[1 !n ! mov+ arr[ is motionless4 ,?is =m ( ! argum5t br+s out its =ce m cle>ly ?an ,burnet's p>aphrase4 ,"h1 if n 9 ! fir/ two argum5ts1 ! view t a f9ite "p ( "t consi/s ( a f9ite s]ies ( successive in/ants seems to be assum$2 at any rate ! plausibility ( ! argum5t seems to dep5d ^u suppos+ t !re are consecutive in/ants4 ,?r\gh\t an in/ant1 x is said1 a mov+ body is :]e x is3 x _c move dur+ ! in/ant1 = t w\ld require t ! in/ant %\ld h p>ts4 ,?us1 suppose we consid] a p]iod consi/+ ( a ?\s& in/ants1 & suppose ! arr[ is 9 flight ?r\gh\t ?is p]iod4 ,at ea* ( ! ?\s& in/ants1 ! arr[ is :]e x is1 ?\gh at ! next in/ant x is some:]e else4 ,x is nev] mov+1 b 9 "s miracul\s way ! *ange ( position has to occur betwe5 ! in/ants1 t is to say1 n at any "t :atev]4 ,?is is :at ,m4 ,b]gson calls ! c9ematographic repres5tation ( reality4 ,! m ! difficulty is m$itat$1 ! m real x becomes4 ,! solution lies 9 ! !ory ( cont9u\s s]ies3 we f9d x h>d to avoid suppos+ t1 :5 ! arr[ is 9 flight1 !re is a next position occupi$ at ! next mom5t2 b 9 fact !re is no next position & no next mom5t1 & :5 once ?is is imag9atively realis$1 ! difficulty is se5 to disappe>4 ,! f\r? & la/ ( ,z5o's argum5ts is#df ! argum5t ( ! /adium4 #df ,phys41 vi4 #i4 #bci;,b 7,r4,p4 #aci74 ,! argum5t z /at$ by ,burnet is z foll[s3 ,fir/ ,position4 ,second ,position4 ,a 4444 ,a 4444 ,b 4444 ,b 4444 ,c 4444 ,c 4444 ,half ! "t may be equal to d\ble ! "t4 ,let u suppose ?ree r[s ( bodies1 "o ( :i* 7,a7 is at re/ :ile ! o!r two 7,b1 ,c7 are mov+ ) equal velocity 9 opposite directions4 ,by ! "t !y are all 9 ! same "p ( ! c\rse1 ,b w h pass$ twice z _m ( ! bodies 9 ,c z 9 ,a4 ,!re=e ! "t :i* x takes to pass ,c is twice z long z ! "t x takes to pass ,a4 ,b ! "t :i* ,b & ,c take to rea* ! position ( ,a is ! same4 ,!re=e d\ble ! "t is equal to ! half4 ,gaye#dg devot$ an int]e/+ article to ! int]pretation ( ?is argum5t4 ,8 translation ( ,ari/otle's /atem5t is z foll[s3 ,! f\r? argum5t is t conc]n+ ! two r[s ( bodies1 ea* r[ be+ compos$ ( an equal numb] ( bodies ( equal size1 pass+ ea* o!r on a race-c\rse z !y proce$ ) equal velocity 9 opposite directions1 ! "o r[ orig9ally occupy+ ! space betwe5 ! goal & ! middle po9t ( ! c\rse1 & ! o!r t betwe5 ! middle po9t & ! />t+-po/4 ,?is1 he ?9ks1 involves ! conclusion t half a giv5 "t is equal to d\ble ! "t4 ,! fallacy ( ! reason+ lies 9 ! assumption t a body occupies an equal "t 9 pass+ ) equal velocity a body t is 9 motion & a body ( equal size t is at re/1 an assumption :i* is false4 ,= in/ance 7s runs ! argum5t71 let ,a ,a 444 be ! /ation>y bodies ( equal size1 ,b ,b 444 ! bodies1 equal 9 numb] & 9 size to ,a ,a 4441 orig9ally occupy+ ! half ( ! c\rse f ! />t+-po/ to ! middle ( ! ,a's1 & ,c ,c 444 ^? orig9ally occupy+ ! o!r half f ! goal to ! middle ( ! ,a's1 equal 9 numb]1 size1 & velocity1 to ,b ,b 444 ,!n ?ree consequ5ces foll[4 ,fir/1 z ! ,b's & ,c's pass "o ano!r1 ! fir/ ,b rea*es ! la/ ,c at ! same mom5t at :i* ! fir/ ,c rea*es ! la/ ,b4 ,secondly1 at ?is mom5t ! fir/ ,c has pass$ all ! ,a's1 :]eas ! fir/ ,b has pass$ only half ! ,a's & has consequ5tly occupi$ only half ! "t occupi$ by ! fir/ ,c1 s9ce ea* ( ! two occupies an equal "t 9 pass+ ea* ,a4 ,?irdly1 at ! same mom5t all ! ,b's h pass$ all ! ,c's3 = ! fir/ ,c & ! fir/ ,b w simultane\sly rea* ! opposite ends ( ! c\rse1 s9ce 7s says ,z5o7 ! "t occupi$ by ! fir/ ,c 9 pass+ ea* ( ! ,b's is equal to t occupi$ by x 9 pass+ ea* ( ! ,a's1 because an equal "t is occupi$ by bo? ! fir/ ,b & ! fir/ ,c 9 pass+ all ! ,a's4 ,?is is ! argum5t3 b x presupposes ! a=esaid fallaci\s assumption4 #dg ,loc4 cit4 ,fir/ ,position4 ,second ,position4 ,b ,b' ,b ,b ,b' ,b 4 4 4 4 4 4 ,a ,a' ,a ,a ,a' ,a 4 4 4 4 4 4 ,c ,c' ,c ,c ,c' ,c 4 4 4 4 4 4 ,?is argum5t is n q easy to foll[1 & x is only valid z aga9/ ! assumption t a f9ite "t consi/s ( a f9ite numb] ( in/ants4 ,we may re-/ate x 9 diff]5t language4 ,let u suppose ?ree drill-s]geants1 ,a1 ,a'1 & ,a1 /&+ 9 a r[1 :ile ! two files ( soldi]s m>* pa/ !m 9 opposite directions4 ,at ! fir/ mom5t :i* we consid]1 ! ?ree m5 ,b1 ,b'1 ,b 9 "o r[1 & ! ?ree m5 ,c1 ,c'1 ,c 9 ! o!r r[1 are respectively opposite to ,a1 ,a'1 & ,a4 ,at ! v next mom5t1 ea* r[ has mov$ on1 & n[ ,b & ,c are opposite ,a'4 ,?us ,b & ,c are opposite ea* o!r4 ,:51 !n1 did ,b pass ,c'8 ,x mu/ h be5 some:]e betwe5 ! two mom5ts :i* we suppos$ consecutive1 & !re=e ! two mom5ts _c really h be5 consecutive4 ,x foll[s t !re mu/ be o!r mom5ts betwe5 any two giv5 mom5ts1 & !re=e t !re mu/ be an inf9ite numb] ( mom5ts 9 any giv5 int]val ( "t4 ,! above difficulty1 t ,b mu/ h pass$ ,c' at "s "t betwe5 two consecutive mom5ts1 is a g5u9e "o1 b is n precisely ! difficulty rais$ by ,z5o4 ,:at ,z5o pr(esses to prove is t half ( a giv5 "t is equal to d\ble t "t4 ,! mo/ intelligible explanation ( ! argum5t kn[n to me is t ( ,gaye4#dh ,s9ce1 h[ev]1 8 explanation is n easy to set =? %ortly1 ,i w re-/ate :at seems to me to be ! logical ess5ce ( ,z5o's cont5tion4 ,if we suppose t "t consi/s ( a s]ies ( consecutive in/ants1 & t motion consi/s 9 pass+ ?r\gh a s]ies ( consecutive po9ts1 !n ! fa/e/ possible motion is "o :i*1 at ea* in/ant1 is at a po9t consecutive to t at :i* x 0 at ! previ\s in/ant4 ,any sl[] motion mu/ be "o :i* has int]vals ( re/ int]sp]s$1 & any fa/] motion mu/ :olly omit "s po9ts4 ,all ?is is evid5t f ! fact t we _c h m ?an "o ev5t = ea* in/ant4 ,b n[1 9 ! case ( our ,a's & ,b's & ,c's1 ,b is opposite a fre% ,a e in/ant1 & !re=e ! numb] ( ,a's pass$ gives ! numb] ( in/ants s9ce ! beg9n+ ( ! motion4 ,b dur+ ! motion ,b has pass$ twice z _m ,c's1 & yet _c h pass$ m ?an "o ea* in/ant4 ,h5ce ! numb] ( in/ants s9ce ! motion began is twice ! numb] ( ,a's pass$1 ?\gh we previ\sly f\nd x 0 equal to ?is numb]4 ,f ?is result1 ,z5o's conclusion foll[s4 #dh ,loc4 cit41 p4 #aje4 ,z5o's argum5ts1 9 "s =m1 h af=d$ gr\nds = almo/ all ! !ories ( space & "t & inf9ity :i* h be5 con/ruct$ f 8 day to our own4 ,we h se5 t all 8 argum5ts are valid 7) c]ta9 reasonable hypo!ses7 on ! assumption t f9ite spaces & times consi/ ( a f9ite numb] ( po9ts & in/ants1 & t ! ?ird & f\r? almo/ c]ta9ly 9 fact proce$$ on ?is assumption1 :ile ! fir/ & second1 :i* 7 p]haps int5d$ to refute ! opposite assumption1 7 9 t case fallaci\s4 ,we may !re=e escape f 8 p>adoxes ei!r by ma9ta9+ t1 ?\gh space & "t d consi/ ( po9ts & in/ants1 ! numb] ( !m 9 any f9ite int]val is inf9ite2 or by d5y+ t space & "t consi/ ( po9ts & in/ants at all2 or la/ly1 by d5y+ ! reality ( space & "t altoge!r4 ,x w\ld seem t ,z5o himself1 z a support] ( ,p>m5ides1 drew ! la/ ( ^! ?ree possible d$uctions1 at any rate 9 reg>d to "t4 ,9 ?is a v l>ge numb] ( philosoph]s h foll[$ him4 ,_m o!rs1 l ,m4 ,b]gson1 h pref]r$ to d5y t space & "t consi/ ( po9ts & in/ants4 ,ei!r ( ^! solutions w meet ! difficulties 9 ! =m 9 :i* ,z5o rais$ !m4 ,b1 z we saw1 ! difficulties c also be met if inf9ite numb]s are admissible4 ,& on gr\nds :i* are indep5d5t ( space & "t1 inf9ite numb]s1 & s]ies 9 :i* no two t]ms are consecutive1 mu/ 9 any case be admitt$4 ,consid]1 = example1 all ! fractions less ?an #a1 arrang$ 9 ord] ( magnitude4 ,betwe5 any two ( !m1 !re are o!rs1 = example1 ! ari?metical mean ( ! two4 ,?us no two fractions are consecutive1 & ! total numb] ( !m is inf9ite4 ,x w be f\nd t mu* ( :at ,z5o says z reg>ds ! s]ies ( po9ts on a l9e c be equally well appli$ to ! s]ies ( fractions4 ,& we _c d5y t !re are fractions1 s t two ( ! above ways ( escape are clos$ to u4 ,x foll[s t1 if we are to solve ! :ole class ( difficulties d]ivable f ,z5o's by analogy1 we mu/ discov] "s t5able !ory ( inf9ite numb]s4 ,:at1 !n1 are ! difficulties :i*1 until ! la/ ?irty ye>s1 l$ philosoph]s to ! belief t inf9ite numb]s are impossible8 ,! difficulties ( inf9ity are ( two k9ds1 ( :i* ! fir/ may be call$ %am1 :ile ! o!rs involve1 = _! solution1 a c]ta9 am\nt ( new & n altoge!r easy ?9k+4 ,! %am difficulties are ^? sugge/$ by ! etymology1 & ^? sugge/$ by confusion ( ! ma!matical inf9ite ) :at philosoph]s imp]t95tly call ! true inf9ite4 ,etymologically1 inf9ite %\ld mean hav+ no end4 ,b 9 fact "s inf9ite s]ies h ends1 "s h n2 :ile "s collections are inf9ite )\t be+ s]ial1 & c !re=e n prop]ly be reg>d$ z ei!r endless or hav+ ends4 ,! s]ies ( in/ants f any e>li] "o to any lat] "o 7bo? includ$7 is inf9ite1 b has two ends2 ! s]ies ( in/ants f ! beg9n+ ( "t to ! pres5t mom5t has "o end1 b is inf9ite4 ,kant1 9 8 fir/ ant9omy1 seems to hold t x is h>d] = ! pa/ to be inf9ite ?an = ! future to be s1 on ! gr\nd t ! pa/ is n[ complet$1 & t no?+ inf9ite c be complet$4 ,x is v difficult to see h[ he c h imag9$ t !re 0 any s5se 9 ?is rem>k2 b x seems mo/ probable t he 0 ?9k+ ( ! inf9ite z ! un5d$4 ,x is odd t he did n see t ! future too has "o end at ! pres5t1 & is precisely on a level ) ! pa/4 ,8 reg>d+ ! two z diff]5t 9 ?is respect illu/rates j t k9d ( slav]y to "t :i*1 z we agre$ 9 speak+ ( ,p>m5ides1 ! true philosoph] mu/ le>n to leave beh9d him4 ,! confusions introduc$ into ! notions ( philosoph]s by ! s-call$ true inf9ite are curi\s4 ,!y see t ?is notion is n ! same z ! ma!matical inf9ite1 b !y *oose to believe t x is ! notion :i* ! ma!maticians are va9ly try+ to rea*4 ,!y !re=e in=m ! ma!maticians1 k9dly b firmly1 t !y are mi/ak5 9 adh]+ to ! false inf9ite1 s9ce pla9ly ! true inf9ite is some?+ q diff]5t4 ,! reply to ?is is t :at !y call ! true inf9ite is a notion totally irrelevant to ! problem ( ! ma!matical inf9ite1 to :i* x has only a fanciful & v]bal analogy4 ,s remote is x t ,i d n propose to confuse ! issue by ev5 m5tion+ :at ! true inf9ite is4 ,x is ! false inf9ite t conc]ns u1 & we h to %[ t ! epi!t false is undes]v$4 ,!re are1 h[ev]1 c]ta9 g5u9e difficulties 9 und]/&+ ! inf9ite1 c]ta9 habits ( m9d d]iv$ f ! consid]ation ( f9ite numb]s1 & easily ext5d$ to inf9ite numb]s "u ! mi/ak5 notion t !y repres5t logical necessities4 ,= example1 e numb] t we are accu/om$ to1 except #j1 has ano!r numb] imm$iately be=e x1 f :i* x results by add+ #a2 b ! fir/ inf9ite numb] does n h ?is prop]ty4 ,! numb]s be=e x =m an inf9ite s]ies1 conta9+ all ! ord9>y f9ite numb]s1 hav+ no maximum1 no la/ f9ite numb]1 aft] :i* "o little /ep w\ld plunge u into ! inf9ite4 ,if x is assum$ t ! fir/ inf9ite numb] is rea*$ by a succession ( small /eps1 x is easy to %[ t x is self-contradictory4 ,! fir/ inf9ite numb] is1 9 fact1 beyond ! :ole un5d+ s]ies ( f9ite numb]s4 ,b1 x w be said1 !re _c be any?+ beyond ! :ole ( an un5d+ s]ies4 ,?is1 we may po9t out1 is ! v pr9ciple ^u :i* ,z5o relies 9 ! argum5ts ( ! race-c\rse & ! ,a*illes4 ,take ! race-c\rse3 !re is ! mom5t :5 ! runn] /ill has half 8 di/ance to run1 !n ! mom5t :5 he /ill has a qu>t]1 !n :5 he /ill has an eigh?1 & s on 9 a /rictly un5d+ s]ies4 ,beyond ! :ole ( ?is s]ies is ! mom5t :5 he rea*es ! goal4 ,?us !re c]ta9ly c be some?+ beyond ! :ole ( an un5d+ s]ies4 ,b x rema9s to %[ t ?is fact is only :at might h be5 expect$4 ,! difficulty1 l mo/ ( ! vagu] difficulties besett+ ! ma!matical inf9ite1 is d]iv$1 ,i ?9k1 f ! m or less unconsci\s op]ation ( ! idea ( c\nt+4 ,if y set to "w to c\nt ! t]ms 9 an inf9ite collection1 y w nev] h complet$ y\r task4 ,?us1 9 ! case ( ! runn]1 if half1 ?ree-qu>t]s1 sev5-eigh?s1 & s on ( ! c\rse 7 m>k$1 & ! runn] 0 n all[$ to pass any ( ! m>ks until ! umpire said ,n[1 !n ,z5o's conclusion w\ld be true 9 practice1 & he w\ld nev] rea* ! goal4 ,b x is n ess5tial to ! exi/5ce ( a collection1 or ev5 to k & reason+ conc]n+ x1 t we %\ld be able to pass its t]ms 9 review "o by "o4 ,?is may be se5 9 ! case ( f9ite collections2 we c speak ( mank9d or ! human race1 ?\gh _m ( ! individuals 9 ?is collection are n p]sonally kn[n to u4 ,we c d ?is because we "k ( v>i\s *>act]i/ics :i* e individual has if he belongs to ! collection1 & n if he does n4 ,& exactly ! same happ5s 9 ! case ( inf9ite collections3 !y may be kn[n by _! *>act]i/ics al?\gh _! t]ms _c be enum]at$4 ,9 ?is s5se1 an un5d+ s]ies may nev]!less =m a :ole1 & !re may be new t]ms beyond ! :ole ( x4 ,"s purely ari?metical peculi>ities ( inf9ite numb]s h also caus$ p]plexity4 ,= in/ance1 an inf9ite numb] is n increas$ by add+ "o to x1 or by d\bl+ x4 ,su* peculi>ities h seem$ to _m to contradict logic1 b 9 fact !y only contradict confirm$ m5tal habits4 ,! :ole difficulty ( ! subject lies 9 ! necessity ( ?9k+ 9 an unfamili> way1 & 9 realis+ t _m prop]ties :i* we h ?\ght inh]5t 9 numb] are 9 fact peculi> to f9ite numb]s4 ,if ?is is rememb]$1 ! positive !ory ( inf9ity1 :i* w occupy ! next lecture1 w n be f\nd s difficult z x is to ^? :o cl+ ob/9ately to ! prejudices in/ill$ by ! ari?metic :i* is le>nt 9 *ildhood4 ,,lecture ,,vii ,,! ,,positive ,,!ory ,,( ,,inf9ity ,! positive !ory ( inf9ity1 & ! g5]al !ory ( numb] to :i* x has giv5 rise1 are among ! triumphs ( sci5tific me?od 9 philosophy1 & are !re=e specially suitable = illu/rat+ ! logical-analytic "* ( t me?od4 ,! "w 9 ?is subject has be5 done by ma!maticians1 & its results c be express$ 9 ma!matical symbolism4 ,:y1 !n1 x may be said1 %\ld ! subject be reg>d$ z philosophy r ?an z ma!matics8 ,?is raises a difficult "q1 p>tly conc]n$ ) ! use ( words1 b p>tly also ( real importance 9 und]/&+ ! function ( philosophy4 ,e subject-matt]1 x w\ld seem1 c give rise to philosophical inve/igations z well z to ! appropriate sci5ce1 ! diff]5ce betwe5 ! two treatm5ts be+ 9 ! direction ( movem5t & 9 ! k9d ( tru?s :i* x is s\ght to e/abli%4 ,9 ! special sci5ces1 :5 !y h become fully develop$1 ! movem5t is =w>d & syn!tic1 f ! simpl] to ! m complex4 ,b 9 philosophy we foll[ ! inv]se direction3 f ! complex & relatively concrete we proce$ t[>ds ! simple & ab/ract by means ( analysis1 seek+1 9 ! process1 to elim9ate ! p>ticul>ity ( ! orig9al subject-matt]1 & to conf9e our att5tion entirely to ! logical =m ( ! facts conc]n$4 ,betwe5 philosophy & pure ma!matics !re is a c]ta9 aff9ity1 9 ! fact t bo? are g5]al & a priori4 ,nei!r ( !m ass]ts propositions :i*1 l ^? ( hi/ory & geography1 dep5d ^u ! actual concrete facts be+ j :at !y are4 ,we may illu/rate ?is *>act]i/ic by means ( ,leibniz's conception ( _m possible worlds1 ( :i* "o only is actual4 ,9 all ! _m possible worlds1 philosophy & ma!matics w be ! same2 ! diff]5ces w only be 9 respect ( ^? p>ticul> facts :i* are *ronicl$ by ! descriptive sci5ces4 ,any quality1 !re=e1 by :i* our actual _w is di/+ui%$ f o!r ab/ractly possible worlds1 mu/ be ignor$ by ma!matics & philosophy alike4 ,ma!matics & philosophy diff]1 h[ev]1 9 _! mann] ( treat+ ! g5]al prop]ties 9 :i* all possible worlds agree2 = :ile ma!matics1 />t+ f comp>atively simple propositions1 seeks to build up m & m complex results by d$uctive syn!sis1 philosophy1 />t+ f data :i* are common k1 seeks to purify & g5]alise !m into ! simple/ /atem5ts ( ab/ract =m t c be obta9$ f !m by logical analysis4 ,! diff]5ce betwe5 philosophy & ma!matics may be illu/rat$ by our pres5t problem1 namely1 ! nature ( numb]4 ,bo? />t f c]ta9 facts ab\t numb]s :i* are evid5t to inspection4 ,b ma!matics uses ^! facts to d$uce m & m complicat$ !orems1 :ile philosophy seeks1 by analysis1 to g beh9d ^! facts to o!rs1 simpl]1 m fundam5tal1 & inh]5tly m fitt$ to =m ! premisses ( ! sci5ce ( ari?metic4 ,! "q1 ,:at is a numb]8 is ! pre-em95t philosophic "q 9 ?is subject1 b x is "o :i* ! ma!matician z su* ne$ n ask1 provid$ he kn[s en\gh ( ! prop]ties ( numb]s to enable him to d$uce 8 !orems4 ,we1 s9ce our object is philosophical1 mu/ grapple ) ! philosoph]'s "q4 ,! answ] to ! "q1 ,:at is a numb]8 :i* we %all rea* 9 ?is lecture1 w be f\nd to give also1 by implication1 ! answ] to ! difficulties ( inf9ity :i* we consid]$ 9 ! previ\s lecture4 ,! "q ,:at is a numb]8 is "o :i*1 until q rec5t times1 0 nev] consid]$ 9 ! k9d ( way t is capable ( yield+ a precise answ]4 ,philosoph]s 7 cont5t ) "s vague dictum su* z1 ,numb] is unity 9 plurality4 ,a typical def9ition ( ! k9d t cont5t$ philosoph]s is ! foll[+ f ,sigw>t's ,logic 7,sec4 #ff1 section #c73 ,e numb] is n m]ely a plurality1 b a plurality ?\ght z held toge!r & clos$1 & to t ext5t z a unity4 ,n[ !re is 9 su* def9itions a v elem5t>y blund]1 ( ! same k9d t w\ld be committ$ if we said yell[ is a fl[] because "s fl[]s are yell[4 ,take1 = example1 ! numb] #c4 ,a s+le collection ( ?ree ?+s might conceivably be describ$ z a plurality ?\ght z held toge!r & clos$1 & to t ext5t z a unity2 b a collection ( ?ree ?+s is n ! numb] #c4 ,! numb] #c is some?+ :i* all collections ( ?ree ?+s h 9 common1 b is n itself a collection ( ?ree ?+s4 ,! def9ition1 !re=e1 ap>t f any o!r defects1 has fail$ to rea* ! necess>y degree ( ab/raction3 ! numb] #c is some?+ m ab/ract ?an any collection ( ?ree ?+s4 ,su* vague philosophic def9itions1 h[ev]1 rema9$ inop]ative because ( _! v vagu5ess4 ,:at mo/ m5 :o ?\ght ab\t numb]s really _h 9 m9d 0 t numb]s are ! result ( c\nt+4 ,on ! consci\sness ( ! law ( c\nt+1 says ,sigw>t at ! beg9n+ ( 8 discussion ( numb]1 re/s ! possibility ( spontane\sly prolong+ ! s]ies ( numb]s ad inf9itum4 ,x is ?is view ( numb] z g5]at$ by c\nt+ :i* has be5 ! *ief psy*ological ob/acle to ! und]/&+ ( inf9ite numb]s4 ,c\nt+1 because x is famili>1 is errone\sly suppos$ to be simple1 :]eas x is 9 fact a highly complex process1 :i* has no mean+ unless ! numb]s rea*$ 9 c\nt+ h "s significance indep5d5t ( ! process by :i* !y are rea*$4 ,& inf9ite numb]s _c be rea*$ at all 9 ?is way4 ,! mi/ake is ( ! same k9d z if c[s 7 def9$ z :at c be b\ght f a cattle-m]*ant4 ,to a p]son :o knew sev]al cattle-m]*ants1 b _h nev] se5 a c[1 ?is might seem an admirable def9ition4 ,b if 9 8 travels he came across a h]d ( wild c[s1 he w\ld h to decl>e t !y 7 n c[s at all1 because no cattle-m]*ant c\ld sell !m4 ,s inf9ite numb]s 7 decl>$ n to be numb]s at all1 because !y c\ld n be rea*$ by c\nt+4 ,x w be wor? :ile to consid] = a mom5t :at c\nt+ actually is4 ,we c\nt a set ( objects :5 we let our att5tion pass f "o to ano!r1 until we h att5d$ once to ea*1 say+ ! names ( ! numb]s 9 ord] ) ea* successive act ( att5tion4 ,! la/ numb] nam$ 9 ?is process is ! numb] ( ! objects1 & !re=e c\nt+ is a me?od ( f9d+ out :at ! numb] ( ! objects is4 ,b ?is op]ation is really a v complicat$ "o1 & ^? :o imag9e t x is ! logical s\rce ( numb] %[ !mselves rem>kably incapable ( analysis4 ,9 ! fir/ place1 :5 we say "o1 two1 ?ree 444 z we c\nt1 we _c be said to be discov]+ ! numb] ( ! objects c\nt$ unless we atta* "s mean+ to ! words "o1 two1 ?ree1 444 ,a *ild may le>n to "k ^! words 9 ord]1 & to repeat !m correctly l ! lett]s ( ! alphabet1 )\t atta*+ any mean+ to !m4 ,su* a *ild may c\nt correctly f ! po9t ( view ( a gr[n-up li/5]1 )\t hav+ any idea ( numb]s at all4 ,! op]ation ( c\nt+1 9 fact1 c only be intellig5tly p]=m$ by a p]son :o already has "s idea :at ! numb]s are2 & f ?is x foll[s t c\nt+ does n give ! logical basis ( numb]4 ,aga91 h[ d we "k t ! la/ numb] rea*$ 9 ! process ( c\nt+ is ! numb] ( ! objects c\nt$8 ,?is is j "o ( ^? facts t are too famili> = _! significance to be realis$2 b ^? :o wi% to be logicians mu/ acquire ! habit ( dwell+ ^u su* facts4 ,!re are two propositions involv$ 9 ?is fact3 fir/1 t ! numb] ( numb]s f #a up to any giv5 numb] is t giv5 numb]--= in/ance1 ! numb] ( numb]s f #a to #ajj is a hundr$2 secondly1 t if a set ( numb]s c be us$ z names ( a set ( objects1 ea* numb] occurr+ only once1 !n ! numb] ( numb]s us$ z names is ! same z ! numb] ( objects4 ,! fir/ ( ^! propositions is capable ( an easy ari?metical pro( s long z f9ite numb]s are conc]n$2 b ) inf9ite numb]s1 aft] ! fir/1 x ceases to be true4 ,! second proposition rema9s true1 & is 9 fact1 z we %all see1 an imm$iate consequ5ce ( ! def9ition ( numb]4 ,b ow+ to ! falsehood ( ! fir/ proposition :]e inf9ite numb]s are conc]n$1 c\nt+1 ev5 if x 7 practically possible1 w\ld n be a valid me?od ( discov]+ ! numb] ( t]ms 9 an inf9ite collection1 & w\ld 9 fact give diff]5t results accord+ to ! mann] 9 :i* x 0 c>ri$ out4 ,!re are two respects 9 :i* ! inf9ite numb]s t are kn[n diff] f f9ite numb]s3 fir/1 inf9ite numb]s h1 :ile f9ite numb]s h n1 a prop]ty :i* ,i %all call reflexiv5ess2 secondly1 f9ite numb]s h1 :ile inf9ite numb]s h n1 a prop]ty :i* ,i %all call inductiv5ess4 ,let u consid] ^! two prop]ties successively4 7#a7 ,reflexiv5ess4--,a numb] is said to be reflexive :5 x is n increas$ by add+ #a to x4 ,x foll[s at once t any f9ite numb] c be add$ to a reflexive numb] )\t increas+ x4 ,?is prop]ty ( inf9ite numb]s 0 always ?\ght1 until rec5tly1 to be self-contradictory2 b ?r\gh ! "w ( ,georg ,cantor x has come to be recognis$ t1 ?\gh at fir/ a/oni%+1 x is no m self-contradictory ?an ! fact t p at ! antipodes d n tumble (f4 ,9 virtue ( ?is prop]ty1 giv5 any inf9ite collection ( objects1 any f9ite numb] ( objects c be add$ or tak5 away )\t increas+ or dim9i%+ ! numb] ( ! collection4 ,ev5 an inf9ite numb] ( objects may1 "u c]ta9 conditions1 be add$ or tak5 away )\t alt]+ ! numb]4 ,?is may be made cle>] by ! help ( "s examples4 ,imag9e all ! natural numb]s #j1 #a1 #b1 #c1 444 to be writt5 d[n 9 a r[1 & imm$iately b5ea? !m write d[n ! numb]s #a1 #b1 #c1 #d1 4441 s t #a is "u #j1 #b is "u #a1 & s on4 ,!n e numb] 9 ! top r[ has a numb] directly "u x 9 ! bottom r[1 & no numb] occurs twice 9 ei!r r[4 ,x foll[s t ! numb] ( numb]s 9 ! two r[s mu/ be ! same4 ,b all ! numb]s t occur 9 ! bottom r[ also occur 9 ! top r[1 & "o m1 namely #j2 ?us ! numb] ( t]ms 9 ! top r[ is obta9$ by add+ "o to ! numb] ( ! bottom r[4 ,s long1 !re=e1 z x 0 suppos$ t a numb] mu/ be increas$ by add+ #a to x1 ?is /ate ( ?+s con/itut$ a contradiction1 & l$ to ! d5ial t !re are inf9ite numb]s4 #j1 #a1 #b1 #c1 444 n 444 #a1 #b1 #c1 #d1 444 n #a 444 ,! foll[+ example is ev5 m surpris+4 ,write ! natural numb]s #a1 #b1 #c1 #d1 444 9 ! top r[1 & ! ev5 numb]s #b1 #d1 #f1 #h1 444 9 ! bottom r[1 s t "u ea* numb] 9 ! top r[ /&s its d\ble 9 ! bottom r[4 ,!n1 z be=e1 ! numb] ( numb]s 9 ! two r[s is ! same1 yet ! second r[ results f tak+ away all ! odd numb]s--an inf9ite collection--f ! top r[4 ,?is example is giv5 by ,leibniz to prove t !re c be no inf9ite numb]s4 ,he believ$ 9 inf9ite collections1 b1 s9ce he ?\ght t a numb] mu/ always be increas$ :5 x is add$ to & dim9i%$ :5 x is subtract$ f1 he ma9ta9$ t inf9ite collections d n h numb]s4 ,! numb] ( all numb]s1 he says1 implies a contradiction1 :i* ,i %[ ?us3 ,to any numb] !re is a correspond+ numb] equal to its d\ble4 ,!re=e ! numb] ( all numb]s is n great] ?an ! numb] ( ev5 numb]s1 i4e4 ! :ole is n great] ?an its "p4#di ,9 deal+ ) ?is argum5t1 we ought to sub/itute ! numb] ( all f9ite numb]s = ! numb] ( all numb]s2 we !n obta9 exactly ! illu/ration giv5 by our two r[s1 "o conta9+ all ! f9ite numb]s1 ! o!r only ! ev5 f9ite numb]s4 ,x w be se5 t ,leibniz reg>ds x z self-contradictory to ma9ta9 t ! :ole is n great] ?an its "p4 ,b ! ^w great] is "o :i* is capable ( _m mean+s2 = our purpose1 we mu/ sub/itute ! less ambigu\s phrase conta9+ a great] numb] ( t]ms4 ,9 ?is s5se1 x is n self-contradictory = :ole & "p to be equal2 x is ! realisation ( ?is fact :i* has made ! mod]n !ory ( inf9ity possible4 #di ,phil4 ,w]ke1 ,g]h>dt's edition1 vol4 i4 p4 #cch4 ,!re is an int]e/+ discussion ( ! reflexiv5ess ( inf9ite :oles 9 ! fir/ ( ,galileo's ,dialogues on ,motion4 ,i quote f a translation publi%$ 9 #agcj4ej ,! p]sonages 9 ! dialogue are ,salviati1 ,sagr$o1 & ,simplicius1 & !y reason z foll[s3 ,simp4 ,"h already arises a ,d\bt :i* ,i ?9k is n to be resolv'd2 & t is ?is3 ,s9ce 'tis pla9 t "o ,l9e is giv5 great] ?an ano!r1 & s9ce bo? conta9 inf9ite ,po9ts1 we mu/ surely necess>ily inf]1 t we h f\nd 9 ! same ,species some?+ great] ?an ,inf9ite1 s9ce ! ,inf9ity ( ,po9ts ( ! great] ,l9e exce$s ! ,inf9ity ( ,po9ts ( ! less]4 ,b n[1 to assign an ,inf9ite great] ?an an ,inf9ite1 is :at ,i c't possibly conceive4 ,salv4 ,^! are "s ( ^? ,difficulties :i* arise f ,disc\rses :i* our f9ite ,und]/&+ makes ab\t ,inf9ites1 by ascrib+ to !m ,attributes :i* we give to ,?+s f9ite & t]m9ate1 :i* ,i ?9k mo/ improp]1 because ^? ,attributes ( ,majority1 ,m9ority1 & ,equality1 agree n ) ,inf9ities1 ( :i* we c't say t "o is great] ?an1 less ?an1 or equal to ano!r4 ,= ,pro( :]e( ,i h some?+ come into my ,head1 :i* 7t ,i may be ! bett] und]/ood7 ,i w propose by way ( ,int]rogatories to ,simplicius1 :o />t$ ?is ,difficulty4 ,to beg9 !n3 ,i suppose y "k :i* are squ>e ,numb]s1 & :i* n8 ,simp4 ,i "k v well t a squ>e ,numb] is t :i* arises f ! ,multiplication ( any ,numb] into itself2 ?us #d & #i are squ>e ,numb]s1 t aris+ f #b1 & ?is f #c1 multipli$ by !mselves4 ,salv4 ,v well2 ,& y also "k1 t z ! ,products are call'd ,squ>es1 ! ,factors are call'd ,roots3 ,& t ! o!r ,numb]s1 :i* proce$ n f ,numb]s multipli$ into !mselves1 are n ,squ>es4 ,:5ce tak+ 9 all ,numb]s1 bo? ,squ>es & ,n ,squ>es1 if ,i %\ld say1 t ! ,n ,squ>es are m ?an ! ,squ>es1 %\ld ,i n be 9 ! "r8 ,simp4 ,mo/ c]ta9ly4 ,salv4 ,if ,i g on ) y !n1 & ask y1 ,h[ _m squ>'d ,numb]s !re are8 y may truly answ]1 ,t !re are z _m z are _! prop] ,roots1 s9ce e ,squ>e has its own ,root1 & e ,root its own ,squ>e1 & s9ce no ,squ>e has m ?an "o ,root1 nor any ,root m ?an "o ,squ>e4 ,simp4 ,v true4 ,salv4 ,b n[1 if ,i %\ld ask h[ _m ,roots !re are1 y c't d5y b !re are z _m z !re are ,numb]s1 s9ce !re's no ,numb] b :at's ! ,root to "s ,squ>e4 ,& ?is be+ grant$1 we may likewise affirm1 t !re are z _m squ>e ,numb]s1 z !re are ,numb]s2 = !re are z _m ,squ>es z !re are ,roots1 & z _m ,roots z ,numb]s4 ,& yet 9 ! ,beg9n+ ( ?is1 we said1 !re 7 _m m ,numb]s ?an ,squ>es1 ! great] ,"p ( ,numb]s be+ n ,squ>es3 ,& ?o' ! ,numb] ( ,squ>es decreases 9 a great] proportion1 z we g on to bigg] ,numb]s1 = c\nt to an ,hundr$ y'll f9d #aj ,squ>es1 viz4 #a1 #d1 #i1 #af1 #be1 #cf1 #di1 #fd1 #ha1 #ajj1 :i* is ! same z to say ! #aj? ,"p are ,squ>es2 9 ,t5 ?\s& only ! #ajj? ,"p are ,squ>es2 9 a ,million only ! #ajjj?3 ,& yet 9 an inf9ite ,numb]1 if we c b compreh5d x1 we may say ! ,squ>es are z _m z all ! ,numb]s tak5 toge!r4 ,sagr4 ,:at mu/ be det]m9'd !n 9 ?is ,case8 ,salv4 ,i see no o!r way1 b by say+ t all ,numb]s are inf9ite2 ,squ>es are ,inf9ite1 _! ,roots ,inf9ite1 & t ! ,numb] ( ,squ>es is n less ?an ! ,numb] ( ,numb]s1 nor ?is less ?an t3 & !n by conclud+ t ! ,attributes or ,t]ms ( ,equality1 ,majority1 & ,m9ority1 h no ,place 9 ,inf9ites1 b are conf9'd to t]m9ate ,quantities4 #ej ,ma!matical ,disc\rses conc]n+ two new sci5ces relat+ to me*anics & local motion1 9 f\r dialogues4 ,by ,galileo ,galilei1 ,*ief ,philosoph] & ,ma!matician to ! ,gr& ,duke ( ,tuscany4 ,done into ,engli% f ! ,italian1 by ,?o4 ,we/on1 late ,ma/]1 & n[ publi%$ by ,john ,we/on1 pres5t ,ma/]1 ( ! ,academy at ,gre5wi*4 ,see pp4 #df ff4 ,! way 9 :i* ! problem is exp\nd$ 9 ! above discussion is wor?y ( ,galileo1 b ! solution sugge/$ is n ! "r "o4 ,x is actually ! case t ! numb] ( squ>e 7f9ite7 numb]s is ! same z ! numb] ( 7f9ite7 numb]s4 ,! fact t1 s long z we conf9e ourselves to numb]s less ?an "s giv5 f9ite numb]1 ! proportion ( squ>es t5ds t[>ds z]o z ! giv5 f9ite numb] increases1 does n contradict ! fact t ! numb] ( all f9ite squ>es is ! same z ! numb] ( all f9ite numb]s4 ,?is is only an in/ance ( ! fact1 n[ famili> to ma!maticians1 t ! limit ( a function z ! v>iable approa*es a giv5 po9t may n be ! same z its value :5 ! v>iable actually rea*es ! giv5 po9t4 ,b al?\gh ! inf9ite numb]s :i* ,galileo discusses are equal1 ,cantor has %[n t :at ,simplicius c\ld n conceive is true1 namely1 t !re are an inf9ite numb] ( diff]5t inf9ite numb]s1 & t ! conception ( great] & less c be p]fectly well appli$ to !m4 ,! :ole ( ,simplicius's difficulty comes1 z is evid5t1 f 8 belief t1 if great] & less c be appli$1 a "p ( an inf9ite collection mu/ h few] t]ms ?an ! :ole2 & :5 ?is is d5i$1 all contradictions disappe>4 ,z reg>ds great] & less l5g?s ( l9es1 :i* is ! problem f :i* ! above discussion />ts1 t involves a mean+ ( great] & less :i* is n ari?metical4 ,! numb] ( po9ts is ! same 9 a long l9e & 9 a %ort "o1 be+ 9 fact ! same z ! numb] ( po9ts 9 all space4 ,! great] & less ( metrical geometry involves ! new metrical conception ( congru5ce1 :i* _c be develop$ out ( ari?metical consid]ations alone4 ,b ?is "q has n ! fundam5tal importance :i* belongs to ! ari?metical !ory ( inf9ity4 7#b7 ,non-inductiv5ess4--,! second prop]ty by :i* inf9ite numb]s are di/+ui%$ f f9ite numb]s is ! prop]ty ( non-inductiv5ess4 ,?is w be be/ expla9$ by def9+ ! positive prop]ty ( inductiv5ess :i* *>act]ises ! f9ite numb]s1 & :i* is nam$ aft] ! me?od ( pro( kn[n z ma!matical induction4 ,let u fir/ consid] :at is meant by call+ a prop]ty h]$it>y 9 a giv5 s]ies4 ,take su* a prop]ty z be+ nam$ ,jones4 ,if a man is nam$ ,jones1 s is 8 son2 we w !re=e call ! prop]ty ( be+ call$ ,jones h]$it>y ) respect to ! relation ( fa!r & son4 ,if a man is call$ ,jones1 all 8 desc5dants 9 ! direct male l9e are call$ ,jones2 ?is foll[s f ! fact t ! prop]ty is h]$it>y4 ,n[1 in/ead ( ! relation ( fa!r & son1 consid] ! relation ( a f9ite numb] to its imm$iate successor1 t is1 ! relation :i* holds betwe5 #j & #a1 betwe5 #a & #b1 betwe5 #b & #c1 & s on4 ,if a prop]ty ( numb]s is h]$it>y ) respect to ?is relation1 !n if x belongs to 7say7 #ajj1 x mu/ belong also to all f9ite numb]s great] ?an #ajj2 =1 be+ h]$it>y1 x belongs to #aja because x belongs to #ajj1 & x belongs to #ajb because x belongs to #aja1 & s on--:]e ! & s on w take u1 soon] or lat]1 to any f9ite numb] great] ?an #ajj4 ,?us1 = example1 ! prop]ty ( be+ great] ?an #ii is h]$it>y 9 ! s]ies ( f9ite numb]s2 & g5]ally1 a prop]ty is h]$it>y 9 ?is s]ies :51 giv5 any numb] t possesses ! prop]ty1 ! next numb] mu/ always also possess x4 ,x w be se5 t a h]$it>y prop]ty1 ?\gh x mu/ belong to all ! f9ite numb]s great] ?an a giv5 numb] possess+ ! prop]ty1 ne$ n belong to all ! numb]s less ?an ?is numb]4 ,= example1 ! h]$it>y prop]ty ( be+ great] ?an #ii belongs to #ajj & all great] numb]s1 b n to any small] numb]4 ,simil>ly1 ! h]$it>y prop]ty ( be+ call$ ,jones belongs to all ! desc5dants 79 ! direct male l9e7 ( ^? :o h ?is prop]ty1 b n to all _! ance/ors1 because we rea* at la/ a fir/ ,jones1 be=e :om ! ance/ors h no surname4 ,x is obvi\s1 h[ev]1 t any h]$it>y prop]ty possess$ by ,adam mu/ belong to all m52 & simil>ly any h]$it>y prop]ty possess$ by #j mu/ belong to all f9ite numb]s4 ,?is is ! pr9ciple ( :at is call$ ma!matical induction4 ,x frequ5tly happ5s1 :5 we wi% to prove t all f9ite numb]s h "s prop]ty1 t we h fir/ to prove t #j has ! prop]ty1 & !n t ! prop]ty is h]$it>y1 i4e4 t1 if x belongs to a giv5 numb]1 !n x belongs to ! next numb]4 ,ow+ to ! fact t su* pro(s are call$ inductive1 ,i %all call ! prop]ties to :i* !y are applicable inductive prop]ties4 ,?us an inductive prop]ty ( numb]s is "o :i* is h]$it>y & belongs to #j4 ,tak+ any "o ( ! natural numb]s1 say #bi1 x is easy to see t x mu/ h all inductive prop]ties4 ,= s9ce su* prop]ties belong to #j & are h]$it>y1 !y belong to #a2 !re=e1 s9ce !y are h]$it>y1 !y belong to #b1 & s on2 by tw5ty-n9e repetitions ( su* argum5ts we %[ t !y belong to #bi4 ,we may def9e ! inductive numb]s z all ^? t possess all inductive prop]ties2 !y w be ! same z :at are call$ ! natural numb]s1 i4e4 ! ord9>y f9ite :ole numb]s4 ,to all su* numb]s1 pro(s by ma!matical induction c be validly appli$4 ,!y are ^? numb]s1 we may loosely say1 :i* c be rea*$ f #j by successive additions ( #a2 9 o!r words1 !y are all ! numb]s t c be rea*$ by c\nt+4 ,b beyond all ^! numb]s1 !re are ! inf9ite numb]s1 & inf9ite numb]s d n h all inductive prop]ties4 ,su* numb]s1 !re=e1 may be call$ non-inductive4 ,all ^? prop]ties ( numb]s :i* are prov$ by an imag9>y /ep-by-/ep process f "o numb] to ! next are liable to fail :5 we come to inf9ite numb]s4 ,! fir/ ( ! inf9ite numb]s has no imm$iate pr$ecessor1 because !re is no greate/ f9ite numb]2 ?us no succession ( /eps f "o numb] to ! next w ev] rea* f a f9ite numb] to an inf9ite "o1 & ! /ep-by-/ep me?od ( pro( fails4 ,?is is ano!r reason = ! suppos$ self-contradictions ( inf9ite numb]s4 ,_m ( ! mo/ famili> prop]ties ( numb]s1 :i* cu/om _h l$ p to reg>d z logically necess>y1 are 9 fact only demon/rable by ! /ep-by-/ep me?od1 & fail to be true ( inf9ite numb]s4 ,b s soon z we realise ! necessity ( prov+ su* prop]ties by ma!matical induction1 & ! /rictly limit$ scope ( ?is me?od ( pro(1 ! suppos$ contradictions are se5 to contradict1 n logic1 b only our prejudices & m5tal habits4 ,! prop]ty ( be+ increas$ by ! addition ( #a--;i4e4 ! prop]ty ( non-reflexiv5ess--may s]ve to illu/rate ! limitations ( ma!matical induction4 ,x is easy to prove t #j is increas$ by ! addition ( #a1 & t1 if a giv5 numb] is increas$ by ! addition ( #a1 s is ! next numb]1 i4e4 ! numb] obta9$ by ! addition ( #a4 ,x foll[s t ea* ( ! natural numb]s is increas$ by ! addition ( #a4 ,?is foll[s g5]ally f ! g5]al argum5t1 & foll[s = ea* p>ticul> case by a suffici5t numb] ( applications ( ! argum5t4 ,we fir/ prove t #j is n equal to #a2 !n1 s9ce ! prop]ty ( be+ increas$ by #a is h]$it>y1 x foll[s t #a is n equal to #b2 h5ce x foll[s t #b is n equal to #c2 if we wi% to prove t #cj1jjj is n equal to #cj1jja1 we c d s by repeat+ ?is reason+ #cj1jjj times4 ,b we _c prove 9 ?is way t all numb]s are increas$ by ! addition ( #a2 we c only prove t ?is holds ( ! numb]s atta9able by successive additions ( #a />t+ f #j4 ,! reflexive numb]s1 :i* lie beyond all ^? atta9able 9 ?is way1 are z a matt] ( fact n increas$ by ! addition ( #a4 ,! two prop]ties ( reflexiv5ess & non-inductiv5ess1 :i* we h consid]$ z *>act]i/ics ( inf9ite numb]s1 h n s f> be5 prov$ to be always f\nd toge!r4 ,x is kn[n t all reflexive numb]s are non-inductive1 b x is n kn[n t all non-inductive numb]s are reflexive4 ,fallaci\s pro(s ( ?is proposition h be5 publi%$ by _m writ]s1 includ+ myself1 b up to ! pres5t no valid pro( has be5 discov]$4 ,! inf9ite numb]s actually kn[n1 h[ev]1 are all reflexive z well z non-inductive2 ?us1 9 ma!matical practice1 if n 9 !ory1 ! two prop]ties are always associat$4 ,= our purposes1 !re=e1 x w be conv5i5t to ignore ! b>e possibility t !re may be non-inductive non-reflexive numb]s1 s9ce all kn[n numb]s are ei!r inductive or reflexive4 ,:5 inf9ite numb]s are fir/ introduc$ to p1 !y are apt to refuse ! "n ( numb]s to !m1 because _! behavi\r is s diff]5t f t ( f9ite numb]s t x seems a wilful misuse ( t]ms to call !m numb]s at all4 ,9 ord] to meet ?is feel+1 we mu/ n[ turn to ! logical basis ( ari?metic1 & consid] ! logical def9ition ( numb]s4 ,! logical def9ition ( numb]s1 ?\gh x seems an ess5tial support to ! !ory ( inf9ite numb]s1 0 9 fact discov]$ indep5d5tly & by a diff]5t man4 ,! !ory ( inf9ite numb]s--t is to say1 ! ari?metical z oppos$ to ! logical "p ( ! !ory--0 discov]$ by ,georg ,cantor1 & publi%$ by him 9 #ahhb-c4ea ,! def9ition ( numb] 0 discov]$ ab\t ! same "t by a man ^: great g5ius has n receiv$ ! recognition x des]ves--,i mean ,gottlob ,frege ( ,j5a4 ,8 fir/ "w1 ,begriffss*rift1 publi%$ 9 #ahgi1 conta9$ ! v important !ory ( h]$it>y prop]ties 9 a s]ies to :i* ,i allud$ 9 connection ) inductiv5ess4 ,8 def9ition ( numb] is conta9$ 9 8 second "w1 publi%$ 9 #ahhd1 & entitl$ ,die ,grundlag5 d] ,ari?metik1 e9e logis*-ma!matis*e ,unt]su*ung ueb] d5 ,begriff d] ,zahl4#eb ,x is ) ?is book t ! logical !ory ( ari?metic beg9s1 & x w repay u to consid] ,frege's analysis 9 "s detail4 #ea ,9 8 ,grundlag5 e9] allgeme95 ,manni*faltigkeitslehre & 9 articles 9 ,acta ,ma!matica1 vol4 ii4 #eb ,! def9ition ( numb] conta9$ 9 ?is book1 & elaborat$ 9 ! ,grundgesetze d] ,ari?metik 7vol4 i41 #ahic2 vol4 ii41 #aijc71 0 r$iscov]$ by me 9 ignorance ( ,frege's "w4 ,i wi% to /ate z emphatically z possible--:at seems /ill (t5 ignor$--t 8 discov]y ant$at$ m9e by eighte5 ye>s4 ,frege beg9s by not+ ! increas$ desire = logical /rictness 9 ma!matical demon/rations :i* di/+ui%es mod]n ma!maticians f _! pr$ecessors1 & po9ts out t ?is mu/ lead to a critical inve/igation ( ! def9ition ( numb]4 ,he proce$s to %[ ! inadequacy ( previ\s philosophical !ories1 especially ( ! syn!tic a priori !ory ( ,kant & ! empirical !ory ( ,mill4 ,?is br+s him to ! "q3 ,:at k9d ( object is x t numb] c prop]ly be ascrib$ to8 ,he po9ts out t physical ?+s may be reg>d$ z "o or _m3 = example1 if a tree has a ?\s& leaves1 !y may be tak5 altoge!r z con/itut+ its foliage1 :i* w\ld c\nt z "o1 n z a ?\s&2 & "o pair ( boots is ! same object z two boots4 ,x foll[s t physical ?+s are n ! subjects ( :i* numb] is prop]ly pr$icat$2 = :5 we h discov]$ ! prop] subjects1 ! numb] to be ascrib$ mu/ be unambigu\s4 ,?is leads to a discussion ( ! v preval5t view t numb] is really some?+ psy*ological & subjective1 a view :i* ,frege emphatically rejects4 ,numb]1 he says1 is z little an object ( psy*ology or an outcome ( psy*ical processes z ! ,nor? ,sea4444 ,! botani/ wi%es to /ate some?+ :i* is j z mu* a fact :5 he gives ! numb] ( petals 9 a fl[] z :5 he gives its col\r4 ,! "o dep5ds z little z ! o!r ^u our caprice4 ,!re is !re=e a c]ta9 simil>ity betwe5 numb] & col\r2 b ?is does n consi/ 9 ! fact t bo? are s5sibly p]ceptible 9 ext]nal ?+s1 b 9 ! fact t bo? are objective 7p4 #cd74 ,i di/+ui% ! objective1 he cont9ues1 f ! palpable1 ! spatial1 ! actual4 ,! e>?'s axis1 ! c5tre ( mass ( ! sol> sy/em1 are objective1 b ,i %\ld n call !m actual1 l ! e>? itself 7p4 #ce74 ,he concludes t numb] is nei!r spatial & physical1 nor subjective1 b non-s5sible & objective4 ,?is conclusion is important1 s9ce x applies to all ! subject-matt] ( ma!matics & logic4 ,mo/ philosoph]s h ?\ght t ! physical & ! m5tal betwe5 !m exhau/$ ! _w ( be+4 ,"s h argu$ t ! objects ( ma!matics 7 obvi\sly n subjective1 & !re=e mu/ be physical & empirical2 o!rs h argu$ t !y 7 obvi\sly n physical1 & !re=e mu/ be subjective & m5tal4 ,bo? sides 7 "r 9 :at !y d5i$1 & wrong 9 :at !y ass]t$2 ,frege has ! m]it ( accept+ bo? d5ials1 & f9d+ a ?ird ass]tion by recognis+ ! _w ( logic1 :i* is nei!r m5tal nor physical4 ,! fact is1 z ,frege po9ts out1 t no numb]1 n ev5 #a1 is applicable to physical ?+s1 b only to g5]al t]ms or descriptions1 su* z man1 satellite ( ! e>?1 satellite ( ,v5us4 ,! g5]al t]m man is applicable to a c]ta9 numb] ( objects3 !re are 9 ! _w s & s _m m54 ,! unity :i* philosoph]s rightly feel to be necess>y = ! ass]tion ( a numb] is ! unity ( ! g5]al t]m1 & x is ! g5]al t]m :i* is ! prop] subject ( numb]4 ,& ?is applies equally :5 !re is "o object or none :i* falls "u ! g5]al t]m4 ,satellite ( ! e>? is a t]m only applicable to "o object1 namely1 ! moon4 ,b "o is n a prop]ty ( ! moon itself1 :i* may equally well be reg>d$ z _m molecules3 x is a prop]ty ( ! g5]al t]m e>?'s satellite4 ,simil>ly1 #j is a prop]ty ( ! g5]al t]m satellite ( ,v5us1 because ,v5us has no satellite4 ,"h at la/ we h an intelligible !ory ( ! numb] #j4 ,?is 0 impossible if numb]s appli$ to physical objects1 because obvi\sly no physical object c\ld h ! numb] #j4 ,?us1 9 seek+ our def9ition ( numb] we h arriv$ s f> at ! result t numb]s are prop]ties ( g5]al t]ms or g5]al descriptions1 n ( physical ?+s or ( m5tal occurr5ces4 ,in/ead ( speak+ ( a g5]al t]m1 su* z man1 z ! subject ( :i* a numb] c be ass]t$1 we may1 )\t mak+ any s]i\s *ange1 take ! subject z ! class or collection ( objects--i4e4 mank9d 9 ! above in/ance--to :i* ! g5]al t]m 9 "q is applicable4 ,two g5]al t]ms1 su* z man & fea!rless bip$1 :i* are applicable to ! same collection ( objects1 w obvi\sly h ! same numb] ( in/ances2 ?us ! numb] dep5ds ^u ! class1 n ^u ! selection ( ?is or t g5]al t]m to describe x1 provid$ sev]al g5]al t]ms c be f\nd to describe ! same class4 ,b "s g5]al t]m is always necess>y 9 ord] to describe a class4 ,ev5 :5 ! t]ms are enum]at$1 z ?is & t & ! o!r1 ! collection is con/itut$ by ! g5]al prop]ty ( be+ ei!r ?is1 or t1 or ! o!r1 & only s acquires ! unity :i* enables u to speak ( x z "o collection4 ,& 9 ! case ( an inf9ite class1 enum]ation is impossible1 s t description by a g5]al *>act]i/ic common & peculi> to ! memb]s ( ! class is ! only possible description4 ,"h1 z we see1 ! !ory ( numb] to :i* ,frege 0 l$ by purely logical consid]ations becomes ( use 9 %[+ h[ inf9ite classes c be am5able to numb] 9 spite ( be+ incapable ( enum]ation4 ,frege next asks ! "q3 ,:5 d two collections h ! same numb] ( t]ms8 ,9 ord9>y life1 we decide ?is "q by c\nt+2 b c\nt+1 z we saw1 is impossible 9 ! case ( inf9ite collections1 & is n logically fundam5tal ) f9ite collections4 ,we want1 !re=e1 a diff]5t me?od ( answ]+ our "q4 ,an illu/ration may help to make ! me?od cle>4 ,i d n "k h[ _m m>ri$ m5 !re are 9 ,engl&1 b ,i d "k t ! numb] is ! same z ! numb] ( m>ri$ wom54 ,! reason ,i "k ?is is t ! relation ( husb& & wife relates "o man to "o woman & "o woman to "o man4 ,a relation ( ?is sort is call$ a "o-"o relation4 ,! relation ( fa!r to son is call$ a "o-_m relation1 because a man c h only "o fa!r b may h _m sons2 conv]sely1 ! relation ( son to fa!r is call$ a _m-"o relation4 ,b ! relation ( husb& to wife 79 ,*ri/ian c\ntries7 is call$ "o-"o1 because a man _c h m ?an "o wife1 or a woman m ?an "o husb&4 ,n[1 :5ev] !re is a "o-"o relation betwe5 all ! t]ms ( "o collection & all ! t]ms ( ano!r sev]ally1 z 9 ! case ( ,engli% husb&s & ,engli% wives1 ! numb] ( t]ms 9 ! "o collection is ! same z ! numb] 9 ! o!r2 b :5 !re is n su* a relation1 ! numb] is diff]5t4 ,?is is ! answ] to ! "q3 ,:5 d two collections h ! same numb] ( t]ms8 ,we c n[ at la/ answ] ! "q3 ,:at is meant by ! numb] ( t]ms 9 a giv5 collection8 ,:5 !re is a "o-"o relation betwe5 all ! t]ms ( "o collection & all ! t]ms ( ano!r sev]ally1 we %all say t ! two collections are simil>4 ,we h j se5 t two simil> collections h ! same numb] ( t]ms4 ,?is leads u to def9e ! numb] ( a giv5 collection z ! class ( all collections t are simil> to x2 t is to say1 we set up ! foll[+ =mal def9ition3 ,! numb] ( t]ms 9 a giv5 class is def9$ z mean+ ! class ( all classes t are simil> to ! giv5 class4 ,?is def9ition1 z ,frege 7express+ x 9 slightly diff]5t t]ms7 %[$1 yields ! usual ari?metical prop]ties ( numb]s4 ,x is applicable equally to f9ite & inf9ite numb]s1 & x does n require ! admission ( "s new & my/]i\s set ( metaphysical entities4 ,x %[s t x is n physical objects1 b classes or ! g5]al t]ms by :i* !y are def9$1 ( :i* numb]s c be ass]t$2 & x applies to #j & #a )\t any ( ! difficulties :i* o!r !ories f9d 9 deal+ ) ^! two special cases4 ,! above def9ition is sure to produce1 at fir/ sight1 a feel+ ( oddity1 :i* is liable to cause a c]ta9 dissatisfaction4 ,x def9es ! numb] #b1 = in/ance1 z ! class ( all c\ples1 & ! numb] #c z ! class ( all triads4 ,?is does n seem to be :at we h hi!rto be5 mean+ :5 we spoke ( #b & #c1 ?\gh x w\ld be difficult to say :at we _h be5 mean+4 ,! answ] to a feel+ _c be a logical argum5t1 b nev]!less ! answ] 9 ?is case is n )\t importance4 ,9 ! fir/ place1 x w be f\nd t :5 an idea :i* has gr[n famili> z an unanalys$ :ole is fir/ resolv$ accurately into its compon5t p>ts--:i* is :at we d :5 we def9e x--!re is almo/ always a feel+ ( unfamili>ity produc$ by ! analysis1 :i* t5ds to cause a prote/ aga9/ ! def9ition4 ,9 ! second place1 x may be admitt$ t ! def9ition1 l all def9itions1 is to a c]ta9 ext5t arbitr>y4 ,9 ! case ( ! small f9ite numb]s1 su* z #b & #c1 x w\ld be possible to frame def9itions m ne>ly 9 accordance ) our unanalys$ feel+ ( :at we mean2 b ! me?od ( su* def9itions w\ld lack uni=mity1 & w\ld be f\nd to fail soon] or lat]--at late/ :5 we rea*$ inf9ite numb]s4 ,9 ! ?ird place1 ! real desid]atum ab\t su* a def9ition z t ( numb] is n t x %\ld repres5t z ne>ly z possible ! ideas ( ^? :o h n gone ?r\gh ! analysis requir$ 9 ord] to rea* a def9ition1 b t x %\ld give u objects hav+ ! requisite prop]ties4 ,numb]s1 9 fact1 mu/ satisfy ! =mulae ( ari?metic2 any indubitable set ( objects fulfill+ ?is requirem5t may be call$ numb]s4 ,s f>1 ! simple/ set kn[n to fulfil ?is requirem5t is ! set introduc$ by ! above def9ition4 ,9 comp>ison ) ?is m]it1 ! "q :e!r ! objects to :i* ! def9ition applies are l or unlike ! vague ideas ( numb]s ent]ta9$ by ^? :o _c give a def9ition1 is "o ( v little importance4 ,all ! important requirem5ts are fulfill$ by ! above def9ition1 & ! s5se ( oddity :i* is at fir/ unavoidable w be f\nd to we> (f v quickly ) ! gr[? ( famili>ity4 ,!re is1 h[ev]1 a c]ta9 logical doctr9e :i* may be ?\ght to =m an objection to ! above def9ition ( numb]s z classes ( classes--,i mean ! doctr9e t !re are no su* objects z classes at all4 ,x might be ?\ght t ?is doctr9e w\ld make havoc ( a !ory :i* r$uces numb]s to classes1 & ( ! _m o!r !ories 9 :i* we h made use ( classes4 ,?is1 h[ev]1 w\ld be a mi/ake3 none ( ^! !ories are any ! worse = ! doctr9e t classes are fictions4 ,:at ! doctr9e is1 & :y x is n de/ructive1 ,i w try briefly to expla94 ,on acc\nt ( c]ta9 r complicat$ difficulties1 culm9at+ 9 def9ite contradictions1 ,i 0 l$ to ! view t no?+ t c be said significantly ab\t ?+s1 i4e4 p>ticul>s1 c be said significantly 7i4e4 ei!r truly or falsely7 ab\t classes ( ?+s4 ,t is to say1 if1 9 any s5t5ce 9 :i* a ?+ is m5tion$1 y sub/itute a class = ! ?+1 y no long] h a s5t5ce t has any mean+3 ! s5t5ce is no long] ei!r true or false1 b a mean+less collection ( words4 ,appe>ances to ! contr>y c be dispell$ by a mom5t's reflection4 ,= example1 9 ! s5t5ce1 ,adam is fond ( apples1 y may sub/itute mank9d1 & say1 ,mank9d is fond ( apples4 ,b obvi\sly y d n mean t !re is "o individual1 call$ mank9d1 :i* mun*es apples3 y mean t ! sep>ate individuals :o compose mank9d are ea* sev]ally fond ( apples4 ,n[1 if no?+ t c be said significantly ab\t a ?+ c be said significantly ab\t a class ( ?+s1 x foll[s t classes ( ?+s _c h ! same k9d ( reality z ?+s h2 = if !y _h1 a class c\ld be sub/itut$ = a ?+ 9 a proposition pr$icat+ ! k9d ( reality :i* w\ld be common to bo?4 ,?is view is really consonant to common s5se4 ,9 ! ?ird or f\r? c5tury ,b4,c4 !re liv$ a ,*9ese philosoph] nam$ ,hui ,tzu1 :o ma9ta9$ t a bay horse & a dun c[ are ?ree2 because tak5 sep>ately !y are two1 & tak5 toge!r !y are "o3 two & "o make ?ree4#ec ,! au?or f :om ,i quote says t ,hui ,tzu 0 p>ticul>ly fond ( ! quibbles :i* s delight$ ! sophi/s or uns\nd reason]s ( anci5t ,greece1 & ?is no d\bt repres5ts ! judgm5t ( common s5se ^u su* argum5ts4 ,yet if collections ( ?+s 7 ?+s1 8 cont5tion w\ld be irrefragable4 ,x is only because ! bay horse & ! dun c[ tak5 toge!r are n a new ?+ t we c escape ! conclusion t !re are ?ree ?+s :]ev] !re are two4 #ec ,giles1 ,! ,civilisation ( ,*9a 7,home ,univ]sity ,libr>y71 p4 #adg4 ,:5 x is admitt$ t classes are n ?+s1 ! "q arises3 ,:at d we mean by /atem5ts :i* are nom9ally ab\t classes8 ,take su* a /atem5t z1 ,! class ( p int]e/$ 9 ma!matical logic is n v num]\s4 ,obvi\sly ?is r$uces itself to1 ,n v _m p are int]e/$ 9 ma!matical logic4 ,= ! sake ( def9it5ess1 let u sub/itute "s p>ticul> numb]1 say #c1 = v _m4 ,!n our /atem5t is1 ,n ?ree p are int]e/$ 9 ma!matical logic4 ,?is may be express$ 9 ! =m3 ,if x is int]e/$ 9 ma!matical logic1 & also y is int]e/$1 & also z is int]e/$1 !n x is id5tical ) y1 or x is id5tical ) z1 or y is id5tical ) z4 ,"h !re is no long] any ref]5ce at all to a class4 ,9 "s su* way1 all /atem5ts nom9ally ab\t a class c be r$uc$ to /atem5ts ab\t :at foll[s f ! hypo!sis ( any?+'s hav+ ! def9+ prop]ty ( ! class4 ,all t is want$1 !re=e1 9 ord] to r5d] ! v]bal use ( classes legitimate1 is a uni=m me?od ( int]pret+ propositions 9 :i* su* a use occurs1 s z to obta9 propositions 9 :i* !re is no long] any su* use4 ,! def9ition ( su* a me?od is a te*nical matt]1 :i* ,dr ,:itehead & ,i h dealt ) else:]e1 & :i* we ne$ n ent] into on ?is occasion4#ed #ed ,cf4 ,pr9cipia ,ma!matica1 ,sec4 #bj1 & ,introduction1 *apt] iii4 ,if ! !ory t classes are m]ely symbolic is accept$1 x foll[s t numb]s are n actual entities1 b t propositions 9 :i* numb]s v]bally occur h n really any con/itu5ts correspond+ to numb]s1 b only a c]ta9 logical =m :i* is n a "p ( propositions hav+ ?is =m4 ,?is is 9 fact ! case ) all ! app>5t objects ( logic & ma!matics4 ,su* words z or1 n1 if1 !re is1 id5tity1 great]1 plus1 no?+1 ev]y?+1 function1 & s on1 are n names ( def9ite objects1 l ,john or ,jones1 b are words :i* require a context 9 ord] to h mean+4 ,all ( !m are =mal1 t is to say1 _! occurr5ce indicates a c]ta9 =m ( proposition1 n a c]ta9 con/itu5t4 ,logical con/ants1 9 %ort1 are n entities2 ! words express+ !m are n names1 & _c significantly be made into logical subjects except :5 x is ! words !mselves1 z oppos$ to _! mean+s1 t are be+ discuss$4#ee ,?is fact has a v important be>+ on all logic & philosophy1 s9ce x %[s h[ !y diff] f ! special sci5ces4 ,b ! que/ions rais$ are s l>ge & s difficult t x is impossible to pursue !m fur!r on ?is occasion4 #ee ,9 ! above rem>ks ,i am mak+ use ( unpubli%$ "w by my fri5d ,ludwig ,wittg5/e94 ,,lecture ,,viii ,,on ,,! ,,notion ,,( ,,cause1 ,,) ,,applications ,,to ,,! ,,free-,,w ,,problem ,! nature ( philosophic analysis1 z illu/rat$ 9 our previ\s lectures1 c n[ be /at$ 9 g5]al t]ms4 ,we />t f a body ( common k1 :i* con/itutes our data4 ,on exam9ation1 ! data are f\nd to be complex1 r vague1 & l>gely int]dep5d5t logically4 ,by analysis we r$uce !m to propositions :i* are z ne>ly z possible simple & precise1 & we arrange !m 9 d$uctive *a9s1 9 :i* a c]ta9 numb] ( initial propositions =m a logical gu>antee = all ! re/4 ,^! initial propositions are premisses = ! body ( k 9 "q4 ,premisses are ?us q diff]5t f data--!y are simpl]1 m precise1 & less infect$ ) logical r$undancy4 ,if ! "w ( analysis has be5 p]=m$ completely1 !y w be :olly free f logical r$undancy1 :olly precise1 & z simple z is logically compatible ) _! lead+ to ! giv5 body ( k4 ,! discov]y ( ^! premisses belongs to philosophy2 b ! "w ( d$uc+ ! body ( common k f !m belongs to ma!matics1 if ma!matics is int]pret$ 9 a some:at lib]al s5se4 ,b besides ! logical analysis ( ! common k :i* =ms our data1 !re is ! consid]ation ( its degree ( c]ta9ty4 ,:5 we h arriv$ at its premisses1 we may f9d t "s ( !m seem op5 to d\bt1 & we may f9d fur!r t ?is d\bt ext5ds to ^? ( our orig9al data :i* dep5d ^u ^! d\btful premisses4 ,9 our ?ird lecture1 = example1 we saw t ! "p ( physics :i* dep5ds ^u te/imony1 & ?us ^u ! exi/5ce ( o!r m9ds ?an our own1 does n seem s c]ta9 z ! "p :i* dep5ds exclusively ^u our own s5se-data & ! laws ( logic4 ,simil>ly1 x us$ to be felt t ! p>ts ( geometry :i* dep5d ^u ! axiom ( p>allels h less c]ta9ty ?an ! p>ts :i* are indep5d5t ( ?is premiss4 ,we may say1 g5]ally1 t :at commonly passes z k is n all equally c]ta91 & t1 :5 analysis into premisses has be5 effect$1 ! degree ( c]ta9ty ( any consequ5ce ( ! premisses w dep5d ^u t ( ! mo/ d\btful premiss employ$ 9 prov+ ?is consequ5ce4 ,?us analysis into premisses s]ves n only a logical purpose1 b also ! purpose ( facilitat+ an e/imate z to ! degree ( c]ta9ty to be atta*$ to ?is or t d]ivative belief4 ,9 view ( ! fallibility ( all human beliefs1 ?is s]vice seems at lea/ z important z ! purely logical s]vices r5d]$ by philosophical analysis4 ,9 ! pres5t lecture1 ,i wi% to apply ! analytic me?od to ! notion ( cause1 & to illu/rate ! discussion by apply+ x to ! problem ( free w4 ,= ?is purpose ,i %all inquire3 ,i41 :at is meant by a causal law2 ,,ii41 :at is ! evid5ce t causal laws h held hi!rto2 ,,iii41 :at is ! evid5ce t !y w cont9ue to hold 9 ! future2 ,,iv41 h[ ! causality :i* is us$ 9 sci5ce diff]s f t ( common s5se & traditional philosophy2 ,v41 :at new light is ?r[n on ! "q ( free w by our analysis ( ! notion ( cause4 ,i4 ,by a causal law ,i mean any g5]al proposition 9 virtue ( :i* x is possible to inf] ! exi/5ce ( "o ?+ or ev5t f ! exi/5ce ( ano!r or ( a numb] ( o!rs4 ,if y he> ?und] )\t hav+ se5 lightn+1 y inf] t !re nev]!less 0 a fla%1 because ( ! g5]al proposition1 ,all ?und] is prec$$ by lightn+4 ,:5 ,rob9son ,crusoe sees a footpr9t1 he inf]s a human be+1 & he might ju/ify 8 inf]5ce by ! g5]al proposition1 ,all m>ks 9 ! gr\nd %ap$ l a human foot are subsequ5t to a human be+'s /&+ :]e ! m>ks are4 ,:5 we see ! sun set1 we expect t x w rise aga9 ! next day4 ,:5 we he> a man speak+1 we inf] t he has c]ta9 ?\ghts4 ,all ^! inf]5ces are due to causal laws4 ,a causal law1 we said1 all[s u to inf] ! exi/5ce ( "o ?+ 7or ev5t7 f ! exi/5ce ( "o or m o!rs4 ,! ^w ?+ "h is to be und]/ood z only apply+ to p>ticul>s1 i4e4 z exclud+ su* logical objects z numb]s or classes or ab/ract prop]ties & relations1 & includ+ s5se-data1 ) :atev] is logically ( ! same type z s5se-data4#ef ,9 s f> z a causal law is directly v]ifiable1 ! ?+ inf]r$ & ! ?+ f :i* x is inf]r$ mu/ bo? be data1 ?\gh !y ne$ n bo? be data at ! same "t4 ,9 fact1 a causal law :i* is be+ us$ to ext5d our k ( exi/5ce mu/ be appli$ to :at1 at ! mom5t1 is n a datum2 x is 9 ! possibility ( su* application t ! practical utility ( a causal law consi/s4 ,! important po9t1 = our pres5t purpose1 h[ev]1 is t :at is inf]r$ is a ?+1 a p>ticul>1 an object hav+ ! k9d ( reality t belongs to objects ( s5se1 n an ab/ract object su* z virtue or ! squ>e root ( two4 #ef ,?us we are n us+ ?+ "h 9 ! s5se ( a class ( correlat$ aspects1 z we did 9 ,lecture ,,iii4 ,ea* aspect w c\nt sep>ately 9 /at+ causal laws4 ,b we _c become acqua9t$ ) a p>ticul> except by its be+ actually giv54 ,h5ce ! p>ticul> inf]r$ by a causal law mu/ be only describ$ ) m or less exactness2 x _c be nam$ until ! inf]5ce is v]ifi$4 ,moreov]1 s9ce ! causal law is g5]al1 & capable ( apply+ to _m cases1 ! giv5 p>ticul> f :i* we inf] mu/ all[ ! inf]5ce 9 virtue ( "s g5]al *>act]i/ic1 n 9 virtue ( its be+ j ! p>ticul> t x is4 ,?is is obvi\s 9 all our previ\s in/ances3 we inf] ! unp]ceiv$ lightn+ f ! ?und]1 n 9 virtue ( any peculi>ity ( ! ?und]1 b 9 virtue ( its resemblance to o!r claps ( ?und]4 ,?us a causal law mu/ /ate t ! exi/5ce ( a ?+ ( a c]ta9 sort 7or ( a numb] ( ?+s ( a numb] ( assign$ sorts7 implies ! exi/5ce ( ano!r ?+ hav+ a relation to ! fir/ :i* rema9s inv>iable s long z ! fir/ is ( ! k9d 9 "q4 ,x is to be obs]v$ t :at is con/ant 9 a causal law is n ! object or objects giv51 nor yet ! object inf]r$1 bo? ( :i* may v>y )9 wide limits1 b ! relation betwe5 :at is giv5 & :at is inf]r$4 ,! pr9ciple1 same cause1 same effect1 :i* is sometimes said to be ! pr9ciple ( causality1 is mu* n>r[] 9 its scope ?an ! pr9ciple :i* really occurs 9 sci5ce2 inde$1 if /rictly int]pret$1 x has no scope at all1 s9ce ! same cause nev] recurs exactly4 ,we %all return to ?is po9t at a lat] /age ( ! discussion4 ,! p>ticul> :i* is inf]r$ may be uniquely det]m9$ by ! causal law1 or may be only describ$ 9 su* g5]al t]ms t _m diff]5t p>ticul>s might satisfy ! description4 ,?is dep5ds ^u :e!r ! con/ant relation affirm$ by ! causal law is "o :i* only "o t]m c h to ! data1 or "o :i* _m t]ms may h4 ,if _m t]ms may h ! relation 9 "q1 sci5ce w n be satisfi$ until x has f\nd "s m /r+5t law1 :i* w enable u to det]m9e ! inf]r$ ?+s uniquely4 ,s9ce all kn[n ?+s are 9 "t1 a causal law mu/ take acc\nt ( temporal relations4 ,x w be "p ( ! causal law to /ate a relation ( succession or coexi/5ce betwe5 ! ?+ giv5 & ! ?+ inf]r$4 ,:5 we he> ?und] & inf] t !re 0 lightn+1 ! law /ates t ! ?+ inf]r$ is e>li] ?an ! ?+ giv54 ,conv]sely1 :5 we see lightn+ & wait expectantly = ! ?und]1 ! law /ates t ! ?+ giv5 is e>li] ?an ! ?+ inf]r$4 ,:5 we inf] a man's ?\ghts f 8 words1 ! law /ates t ! two are 7at lea/ approximately7 simultane\s4 ,if a causal law is to a*ieve ! precision at :i* sci5ce aims1 x mu/ n be cont5t ) a vague e>li] or lat]1 b mu/ /ate h[ mu* e>li] or h[ mu* lat]4 ,t is to say1 ! "t-relation betwe5 ! ?+ giv5 & ! ?+ inf]r$ ought to be capable ( exact /atem5t2 & usually ! inf]5ce to be drawn is diff]5t accord+ to ! l5g? & direction ( ! int]val4 ,a qu>t] ( an h\r ago ?is man 0 alive2 an h\r h5ce he w be cold4 ,su* a /atem5t involves two causal laws1 "o inf]r+ f a datum some?+ :i* exi/$ a qu>t] ( an h\r ago1 ! o!r inf]r+ f ! same datum some?+ :i* w exi/ an h\r h5ce4 ,(t5 a causal law involves n "o datum1 b _m1 :i* ne$ n be all simultane\s ) ea* o!r1 ?\gh _! "t-relations mu/ be giv54 ,! g5]al s*eme ( a causal law w be z foll[s3 ,:5ev] ?+s occur 9 c]ta9 relations to ea* o!r 7among :i* _! "t-relations mu/ be includ$71 !n a ?+ hav+ a fix$ relation to ^! ?+s w occur at a date fix$ relatively to _! dates4 ,! ?+s giv5 w n1 9 practice1 be ?+s t only exi/ = an in/ant1 = su* ?+s1 if !re are any1 c nev] be data4 ,! ?+s giv5 w ea* occupy "s f9ite "t4 ,!y may be n /atic ?+s1 b processes1 especially motions4 ,we h consid]$ 9 an e>li] lecture ! s5se 9 :i* a motion may be a datum1 & ne$ n n[ recur to ?is topic4 ,x is n ess5tial to a causal law t ! object inf]r$ %\ld be lat] ?an "s or all ( ! data4 ,x may equally well be e>li] or at ! same "t4 ,! only ?+ ess5tial is t ! law %\ld be su* z to enable u to inf] ! exi/5ce ( an object :i* we c m or less accurately describe 9 t]ms ( ! data4 ,,ii4 ,i come n[ to our second "q1 namely3 ,:at is ! nature ( ! evid5ce t causal laws h held hi!rto1 at lea/ 9 ! obs]v$ portions ( ! pa/8 ,?is "q mu/ n be confus$ ) ! fur!r "q3 ,does ?is evid5ce w>rant u 9 assum+ ! tru? ( causal laws 9 ! future & 9 unobs]v$ portions ( ! pa/8 ,= ! pres5t1 ,i am only ask+ :at are ! gr\nds :i* lead to a belief 9 causal laws1 n :e!r ^! gr\nds are adequate to support ! belief 9 univ]sal causation4 ,! fir/ /ep is ! discov]y ( approximate unanalys$ uni=mities ( sequ5ce or coexi/5ce4 ,aft] lightn+ comes ?und]1 aft] a bl[ receiv$ comes pa91 aft] approa*+ a fire comes w>m?2 aga91 !re are uni=mities ( coexi/5ce1 = example betwe5 t\* & sight1 betwe5 c]ta9 s5sations 9 ! ?roat & ! s\nd ( "o's own voice1 & s on4 ,e su* uni=mity ( sequ5ce or coexi/5ce1 aft] x has be5 exp]i5c$ a c]ta9 numb] ( times1 is foll[$ by an expectation t x w be repeat$ on future occasions1 i4e4 t :]e "o ( ! correlat$ ev5ts is f\nd1 ! o!r w be f\nd also4 ,! connection ( exp]i5c$ pa/ uni=mity ) expectation z to ! future is j "o ( ^? uni=mities ( sequ5ce :i* we h obs]v$ to be true hi!rto4 ,?is af=ds a psy*ological acc\nt ( :at may be call$ ! animal belief 9 causation1 because x is some?+ :i* c be obs]v$ 9 horses & dogs1 & is r a habit ( act+ ?an a real belief4 ,s f>1 we h m]ely repeat$ ,hume1 :o c>ri$ ! discussion ( cause up to ?is po9t1 b did n1 app>5tly1 p]ceive h[ mu* rema9$ to be said4 ,is !re1 9 fact1 any *>act]i/ic1 su* z might be call$ causality or uni=mity1 :i* is f\nd to hold ?r\gh\t ! obs]v$ pa/8 ,& if s1 h[ is x to be /at$8 ,! p>ticul> uni=mities :i* we m5tion$ be=e1 su* z lightn+ be+ foll[$ by ?und]1 are n f\nd to be free f exceptions4 ,we sometimes see lightn+ )\t he>+ ?und]2 & al?\gh1 9 su* a case1 we suppose t ?und] might h be5 he>d if we _h be5 ne>] to ! lightn+1 t is a supposition bas$ on !ory1 & !re=e incapable ( be+ invok$ to support ! !ory4 ,:at does seem1 h[ev]1 to be %[n by sci5tific exp]i5ce is ?is3 t :]e an obs]v$ uni=mity fails1 "s wid] uni=mity c be f\nd1 embrac+ m circum/ances1 & subsum+ bo? ! successes & ! failures ( ! previ\s uni=mity4 ,unsupport$ bodies 9 air fall1 unless !y are balloons or a]oplanes2 b ! pr9ciples ( me*anics give uni=mities :i* apply to balloons & a]oplanes j z accurately z to bodies t fall4 ,!re is mu* t is hypo!tical & m or less artificial 9 ! uni=mities affirm$ by me*anics1 because1 :5 !y _c o!rwise be made applicable1 unobs]v$ bodies are inf]r$ 9 ord] to acc\nt = obs]v$ peculi>ities4 ,/ill1 x is an empirical fact t x is possible to pres]ve ! laws by assum+ su* bodies1 & t !y nev] h to be assum$ 9 circum/ances 9 :i* !y ought to be obs]vable4 ,?us ! empirical v]ification ( me*anical laws may be admitt$1 al?\gh we mu/ also admit t x is less complete & triumphant ?an is sometimes suppos$4 ,assum+ n[1 :at mu/ be admitt$ to be d\btful1 t ! :ole ( ! pa/ has proce$$ accord+ to inv>iable laws1 :at c we say z to ! nature ( ^! laws8 ,!y w n be ( ! simple type :i* ass]ts t ! same cause always produces ! same effect4 ,we may take ! law ( gravitation z a sample ( ! k9d ( law t appe>s to be v]ifi$ )\t exception4 ,9 ord] to /ate ?is law 9 a =m :i* obs]vation c confirm1 we w conf9e x to ! sol> sy/em4 ,x !n /ates t ! motions ( planets & _! satellites h at e in/ant an accel]ation comp\nd$ ( accel]ations t[>ds all ! o!r bodies 9 ! sol> sy/em1 proportional to ! masses ( ^? bodies & inv]sely proportional to ! squ>es ( _! di/ances4 ,9 virtue ( ?is law1 giv5 ! /ate ( ! sol> sy/em ?r\gh\t any f9ite "t1 h[ev] %ort1 its /ate at all e>li] & lat] times is det]m9ate except 9 s f> z o!r =ces ?an gravitation or o!r bodies ?an ^? 9 ! sol> sy/em h to be tak5 into consid]ation4 ,b o!r =ces1 s f> z sci5ce c discov]1 appe> to be equally regul>1 & equally capable ( be+ summ$ up 9 s+le causal laws4 ,if ! me*anical acc\nt ( matt] 7 complete1 ! :ole physical hi/ory ( ! univ]se1 pa/ & future1 c\ld be inf]r$ f a suffici5t numb] ( data conc]n+ an assign$ f9ite "t1 h[ev] %ort4 ,9 ! m5tal _w1 ! evid5ce = ! univ]sality ( causal laws is less complete ?an 9 ! physical _w4 ,psy*ology _c boa/ ( any triumph comp>able to gravitational a/ronomy4 ,nev]!less1 ! evid5ce is n v greatly less ?an 9 ! physical _w4 ,! crude & approximate causal laws f :i* sci5ce />ts are j z easy to discov] 9 ! m5tal sph]e z 9 ! physical4 ,9 ! _w ( s5se1 !re are to beg9 ) ! correlations ( sight & t\* & s on1 & ! facts :i* lead u to connect v>i\s k9ds ( s5sations ) eyes1 e>s1 nose1 tongue1 etc4 ,!n !re are su* facts z t our body moves 9 answ] to our volitions4 ,exceptions exi/1 b are capable ( be+ expla9$ z easily z ! exceptions to ! rule t unsupport$ bodies 9 air fall4 ,!re is1 9 fact1 j su* a degree ( evid5ce = causal laws 9 psy*ology z w w>rant ! psy*ologi/ 9 assum+ !m z a matt] ( c\rse1 ?\gh n su* a degree z w suffice to remove all d\bt f ! m9d ( a sceptical inquir]4 ,x %\ld be obs]v$ t causal laws 9 :i* ! giv5 t]m is m5tal & ! inf]r$ t]m physical1 or vice v]sa1 are at lea/ z easy to discov] z causal laws 9 :i* bo? t]ms are m5tal4 ,x w be notic$ t1 al?\gh we h spok5 ( causal laws1 we h n hi!rto introduc$ ! ^w cause4 ,at ?is /age1 x w be well to say a few words on legitimate & illegitimate uses ( ?is ^w4 ,! ^w cause1 9 ! sci5tific acc\nt ( ! _w1 belongs only to ! e>ly /ages1 9 :i* small prelim9>y1 approximate g5]alisations are be+ asc]ta9$ ) a view to subsequ5t l>g] & m inv>iable laws4 ,we may say1 ,ars5ic causes dea?1 s long z we are ignorant ( ! precise process by :i* ! result is br\ght ab\t4 ,b 9 a suffici5tly advanc$ sci5ce1 ! ^w cause w n occur 9 any /atem5t ( inv>iable laws4 ,!re is1 h[ev]1 a some:at r\gh & loose use ( ! ^w cause :i* may be pres]v$4 ,! approximate uni=mities :i* lead to its pre-sci5tific employm5t may turn out to be true 9 all b v r>e & exceptional circum/ances1 p]haps 9 all circum/ances t actually occur4 ,9 su* cases1 x is conv5i5t to be able to speak ( ! antec$5t ev5t z ! cause & ! subsequ5t ev5t z ! effect4 ,9 ?is s5se1 provid$ x is realis$ t ! sequ5ce is n necess>y & may h exceptions1 x is /ill possible to employ ! words cause & effect4 ,x is 9 ?is s5se1 & 9 ?is s5se only1 t we %all int5d ! words :5 we speak ( "o p>ticul> ev5t caus+ ano!r p>ticul> ev5t1 z we mu/ sometimes d if we are to avoid intol]able circumlocution4 ,,iii4 ,we come n[ to our ?ird "q1 namely3 ,:at reason c be giv5 = believ+ t causal laws w hold 9 future1 or t !y h held 9 unobs]v$ portions ( ! pa/8 ,:at we h said s f> is t !re h be5 hi!rto c]ta9 obs]v$ causal laws1 & t all ! empirical evid5ce we possess is compatible ) ! view t ev]y?+1 bo? m5tal & physical1 s f> z our obs]vation has ext5d$1 has happ5$ 9 accordance ) causal laws4 ,! law ( univ]sal causation1 sugge/$ by ^! facts1 may be enunciat$ z foll[s3 ,!re are su* inv>iable relations betwe5 diff]5t ev5ts at ! same or diff]5t times t1 giv5 ! /ate ( ! :ole univ]se ?r\gh\t any f9ite "t1 h[ev] %ort1 e previ\s & subsequ5t ev5t c !oretically be det]m9$ z a function ( ! giv5 ev5ts dur+ t "t4 ,h we any reason to believe ?is univ]sal law8 ,or1 to ask a m mode/ "q1 h we any reason to believe t a p>ticul> causal law1 su* z ! law ( gravitation1 w cont9ue to hold 9 ! future8 ,among obs]v$ causal laws is ?is1 t obs]vation ( uni=mities is foll[$ by expectation ( _! recurr5ce4 ,a horse :o has be5 driv5 always along a c]ta9 road expects to be driv5 along t road aga92 a dog :o is always f$ at a c]ta9 h\r expects food at t h\r & n at any o!r4 ,su* expectations1 z ,hume po9t$ out1 expla9 only too well ! common-s5se belief 9 uni=mities ( sequ5ce1 b !y af=d absolutely no logical gr\nd = beliefs z to ! future1 n ev5 = ! belief t we %all cont9ue to expect ! cont9uation ( exp]i5c$ uni=mities1 = t is precisely "o ( ^? causal laws = :i* a gr\nd has to be s\ght4 ,if ,hume's acc\nt ( causation is ! la/ ^w1 we h n only no reason to suppose t ! sun w rise to-morr[1 b no reason to suppose t five m9utes h5ce we %all /ill expect x to rise to-morr[4 ,x may1 ( c\rse1 be said t all inf]5ces z to ! future are 9 fact invalid1 & ,i d n see h[ su* a view c\ld be disprov$4 ,b1 :ile admitt+ ! legitimacy ( su* a view1 we may nev]!less inquire3 ,if inf]5ces z to ! future are valid1 :at pr9ciple mu/ be involv$ 9 mak+ !m8 ,! pr9ciple involv$ is ! pr9ciple ( induction1 :i*1 if x is true1 mu/ be an a priori logical law1 n capable ( be+ prov$ or disprov$ by exp]i5ce4 ,x is a difficult "q h[ ?is pr9ciple ought to be =mulat$2 b if x is to w>rant ! inf]5ces :i* we wi% to make by its means1 x mu/ lead to ! foll[+ proposition3 ,if1 9 a great numb] ( in/ances1 a ?+ ( a c]ta9 k9d is associat$ 9 a c]ta9 way ) a ?+ ( a c]ta9 o!r k9d1 x is probable t a ?+ ( ! "o k9d is always simil>ly associat$ ) a ?+ ( ! o!r k9d2 & z ! numb] ( in/ances increases1 ! probability approa*es indef9itely ne> to c]ta9ty4 ,x may well be que/ion$ :e!r ?is proposition is true2 b if we admit x1 we c inf] t any *>act]i/ic ( ! :ole ( ! obs]v$ pa/ is likely to apply to ! future & to ! unobs]v$ pa/4 ,?is proposition1 !re=e1 if x is true1 w w>rant ! inf]5ce t causal laws probably hold at all times1 future z well z pa/2 b )\t ?is pr9ciple1 ! obs]v$ cases ( ! tru? ( causal laws af=d no presumption z to ! unobs]v$ cases1 & !re=e ! exi/5ce ( a ?+ n directly obs]v$ c nev] be validly inf]r$4 ,x is ?us ! pr9ciple ( induction1 r ?an ! law ( causality1 :i* is at ! bottom ( all inf]5ces z to ! exi/5ce ( ?+s n imm$iately giv54 ,) ! pr9ciple ( induction1 all t is want$ = su* inf]5ces c be prov$2 )\t x1 all su* inf]5ces are invalid4 ,?is pr9ciple has n receiv$ ! att5tion :i* its great importance des]ves4 ,^? :o 7 int]e/$ 9 d$uctive logic naturally en\gh ignor$ x1 :ile ^? :o emphasis$ ! scope ( induction wi%$ to ma9ta9 t all logic is empirical1 & !re=e c\ld n be expect$ to realise t induction itself1 _! own d>l+1 requir$ a logical pr9ciple :i* obvi\sly c\ld n be prov$ inductively1 & mu/ !re=e be a priori if x c\ld be kn[n at all4 ,! view t ! law ( causality itself is a priori _c1 ,i ?9k1 be ma9ta9$ by anyone :o realises :at a complicat$ pr9ciple x is4 ,9 ! =m :i* /ates t e ev5t has a cause x looks simple2 b on exam9ation1 cause is m]g$ 9 causal law1 & ! def9ition ( a causal law is f\nd to be f> f simple4 ,!re mu/ necess>ily be "s a priori pr9ciple involv$ 9 inf]5ce f ! exi/5ce ( "o ?+ to t ( ano!r1 if su* inf]5ce is ev] valid2 b x w\ld appe> f ! above analysis t ! pr9ciple 9 "q is induction1 n causality4 ,:e!r inf]5ces f pa/ to future are valid dep5ds :olly1 if our discussion has be5 s\nd1 ^u ! inductive pr9ciple3 if x is true1 su* inf]5ces are valid1 & if x is false1 !y are invalid4 ,,iv4 ,i come n[ to ! "q h[ ! conception ( causal laws :i* we h arriv$ at is relat$ to ! traditional conception ( cause z x occurs 9 philosophy & common s5se4 ,hi/orically1 ! notion ( cause has be5 b\nd up ) t ( human volition4 ,! typical cause w\ld be ! fiat ( a k+4 ,! cause is suppos$ to be active1 ! effect passive4 ,f ?is x is easy to pass on to ! sugge/ion t a true cause mu/ conta9 "s prevision ( ! effect2 h5ce ! effect becomes ! end at :i* ! cause aims1 & teleology replaces causation 9 ! explanation ( nature4 ,b all su* ideas1 z appli$ to physics1 are m]e an?ropomorphic sup]/itions4 ,x is z a reaction aga9/ ^! errors t ,ma* & o!rs h urg$ a purely descriptive view ( physics3 physics1 !y say1 does n aim at tell+ u :y ?+s happ51 b only h[ !y happ54 ,& if ! "q :y8 means any?+ m ?an ! se>* = a g5]al law accord+ to :i* a ph5om5on occurs1 !n x is c]ta9ly ! case t ?is "q _c be answ]$ 9 physics & ought n to be ask$4 ,9 ?is s5se1 ! descriptive view is indubitably 9 ! "r4 ,b 9 us+ causal laws to support inf]5ces f ! obs]v$ to ! unobs]v$1 physics ceases to be purely descriptive1 & x is ^! laws :i* give ! sci5tifically useful "p ( ! traditional notion ( cause4 ,!re is !re=e some?+ to pres]ve 9 ?is notion1 ?\gh x is a v t9y "p ( :at is commonly assum$ 9 or?odox metaphysics4 ,9 ord] to und]/& ! diff]5ce betwe5 ! k9d ( cause :i* sci5ce uses & ! k9d :i* we naturally imag9e1 x is necess>y to %ut out1 by an ef=t1 ev]y?+ t diff]5tiates betwe5 pa/ & future4 ,?is is an extraord9>ily difficult ?+ to d1 because our m5tal life is s intimately b\nd up ) diff]5ce4 ,n only d memory & hope make a diff]5ce 9 our feel+s z reg>ds pa/ & future1 b almo/ our :ole vocabul>y is fill$ ) ! idea ( activity1 ( ?+s done n[ = ! sake ( _! future effects4 ,all transitive v]bs involve ! notion ( cause z activity1 & w\ld h to be replac$ by "s cumbr\s p]iphrasis be=e ?is notion c\ld be elim9at$4 ,consid] su* a /atem5t z1 ,brutus kill$ ,caes>4 ,on ano!r occasion1 ,brutus & ,caes> might engage our att5tion1 b = ! pres5t x is ! kill+ t we h to /udy4 ,we may say t to kill a p]son is to cause 8 dea? int5tionally4 ,?is means t desire = a p]son's dea? causes a c]ta9 act1 because x is believ$ t t act w cause ! p]son's dea?2 or m accurately1 ! desire & ! belief jo9tly cause ! act4 ,brutus desires t ,caes> %\ld be dead1 & believes t he w be dead if he is /abb$2 ,brutus !re=e /abs him1 & ! /ab causes ,caes>'s dea?1 z ,brutus expect$ x w\ld4 ,e act :i* realises a purpose involves two causal /eps 9 ?is way3 ,c is desir$1 & x is believ$ 7truly if ! purpose is a*iev$7 t ,b w cause ,c2 ! desire & ! belief toge!r cause ,b1 :i* 9 turn causes ,c4 ,?us we h fir/ ,a1 :i* is a desire = ,c & a belief t ,b 7an act7 w cause ,c2 !n we h ,b1 ! act caus$ by ,a1 & believ$ to be a cause ( ,c2 !n1 if ! belief 0 correct1 we h ,c1 caus$ by ,b1 & if ! belief 0 incorrect we h disappo9tm5t4 ,reg>d$ purely sci5tifically1 ?is s]ies ,a1 ,b1 ,c may equally well be consid]$ 9 ! inv]se ord]1 z !y w\ld be at a coron]'s inque/4 ,b f ! po9t ( view ( ,brutus1 ! desire1 :i* comes at ! beg9n+1 is :at makes ! :ole s]ies int]e/+4 ,we feel t if 8 desires _h be5 diff]5t1 ! effects :i* he 9 fact produc$ w\ld n h occurr$4 ,?is is true1 & gives him a s5se ( p[] & fre$om4 ,x is equally true t if ! effects _h n occurr$1 8 desires w\ld h be5 diff]5t1 s9ce be+ :at !y 7 ! effects did occur4 ,?us ! desires are det]m9$ by _! consequ5ces j z mu* z ! consequ5ces by ! desires2 b z we _c 79 g5]al7 "k 9 advance ! consequ5ces ( our desires )\t kn[+ our desires1 ?is =m ( inf]5ce is un9t]e/+ z appli$ to our own acts1 ?\gh q vital z appli$ to ^? ( o!rs4 ,a cause1 consid]$ sci5tifically1 has none ( t analogy ) volition :i* makes u imag9e t ! effect is compell$ by x4 ,a cause is an ev5t or gr\p ( ev5ts1 ( "s kn[n g5]al "*1 & hav+ a kn[n relation to "s o!r ev5t1 call$ ! effect2 ! relation be+ ( su* a k9d t only "o ev5t1 or at any rate only "o well-def9$ sort ( ev5t1 c h ! relation to a giv5 cause4 ,x is cu/om>y only to give ! "n effect to an ev5t :i* is lat] ?an ! cause1 b !re is no k9d ( reason = ?is re/riction4 ,we %all d bett] to all[ ! effect to be be=e ! cause or simultane\s ) x1 because no?+ ( any sci5tific importance dep5ds ^u its be+ aft] ! cause4 ,if ! inf]5ce f cause to effect is to be indubitable1 x seems t ! cause c h>dly /op %ort ( ! :ole univ]se4 ,s long z any?+ is left out1 some?+ may be left out :i* alt]s ! expect$ result4 ,b = practical & sci5tific purposes1 ph5om5a c be collect$ into gr\ps :i* are causally self-conta9$1 or ne>ly s4 ,9 ! common notion ( causation1 ! cause is a s+le ev5t--we say ! lightn+ causes ! ?und]1 & s on4 ,b x is difficult to "k :at we mean by a s+le ev5t2 & x g5]ally appe>s t1 9 ord] to h any?+ approa*+ c]ta9ty conc]n+ ! effect1 x is necess>y to include _m m circum/ances 9 ! cause ?an unsci5tific common s5se w\ld suppose4 ,b (t5 a probable causal connection1 :]e ! cause is fairly simple1 is ( m practical importance ?an a m indubitable connection 9 :i* ! cause is s complex z to be h>d to asc]ta94 ,to sum up3 ! /rict1 c]ta91 univ]sal law ( causation :i* philosoph]s advocate is an ideal1 possibly true1 b n kn[n to be true 9 virtue ( any available evid5ce4 ,:at is actually kn[n1 z a matt] ( empirical sci5ce1 is t c]ta9 con/ant relations are obs]v$ to hold betwe5 ! memb]s ( a gr\p ( ev5ts at c]ta9 times1 & t :5 su* relations fail1 z !y sometimes d1 x is usually possible to discov] a new1 m con/ant relation by enl>g+ ! gr\p4 ,any su* con/ant relation betwe5 ev5ts ( specifi$ k9ds ) giv5 int]vals ( "t betwe5 !m is a causal law4 ,b all causal laws are liable to exceptions1 if ! cause is less ?an ! :ole /ate ( ! univ]se2 we believe1 on ! basis ( a good deal ( exp]i5ce1 t su* exceptions c be dealt ) by enl>g+ ! gr\p we call ! cause1 b ?is belief1 :]ev] x is /ill unv]ifi$1 ought n to be reg>d$ z c]ta91 b only z sugge/+ a direction = fur!r inquiry4 ,a v common causal gr\p consi/s ( volitions & ! consequ5t bodily acts1 ?\gh exceptions arise 7= example7 ?r\gh sudd5 p>alysis4 ,ano!r v frequ5t connection 7?\gh "h ! exceptions are mu* m num]\s7 is betwe5 a bodily act & ! realisation ( ! purpose :i* l$ to ! act4 ,^! connections are pat5t1 :]eas ! causes ( desires are m obscure4 ,?us x is natural to beg9 causal s]ies ) desires1 to suppose t all causes are analog\s to desires1 & t desires !mselves arise spontane\sly4 ,su* a view1 h[ev]1 is n "o :i* any s]i\s psy*ologi/ w\ld ma9ta94 ,b ?is br+s u to ! "q ( ! application ( our analysis ( cause to ! problem ( free w4 ,v4 ,! problem ( free w is s intimately b\nd up ) ! analysis ( causation t1 old z x is1 we ne$ n despair ( obta9+ new light on x by ! help ( new views on ! notion ( cause4 ,! free-w problem has1 at "o "t or ano!r1 /irr$ m5's passions pr(\ndly1 & ! fe> t ! w might n be free has be5 to "s m5 a s\rce ( great unhapp9ess4 ,i believe t1 "u ! influ5ce ( a cool analysis1 ! d\btful que/ions involv$ w be f\nd to h no su* emotional importance z is sometimes ?\ght1 s9ce ! disagreeable consequ5ces suppos$ to fl[ f a d5ial ( free w d n fl[ f ?is d5ial 9 any =m 9 :i* !re is reason to make x4 ,x is n1 h[ev]1 on ?is acc\nt *iefly t ,i wi% to discuss ?is problem1 b r because x af=ds a good example ( ! cl>ify+ effect ( analysis & ( ! int]m9able controv]sies :i* may result f its neglect4 ,let u fir/ try to discov] :at x is we really desire :5 we desire free w4 ,"s ( our reasons = desir+ free w are pr(\nd1 "s trivial4 ,to beg9 ) ! =m]3 we d n wi% to feel ourselves 9 ! h&s ( fate1 s t1 h[ev] mu* we may desire to w "o ?+1 we may nev]!less be compell$ by an outside =ce to w ano!r4 ,we d n wi% to ?9k t1 h[ev] mu* we may desire to act well1 h]$ity & surr\nd+s may =ce u into act+ ill4 ,we wi% to feel t1 9 cases ( d\bt1 our *oice is mom5t\s & lies )9 our p[]4 ,besides ^! desires1 :i* are wor?y ( all respect1 we h1 h[ev]1 o!rs n s respectable1 :i* equally make u desire free w4 ,we d n l to ?9k t o!r p1 if !y knew en\gh1 c\ld pr$ict our actions1 ?\gh we "k t we c (t5 pr$ict ^? ( o!r p1 especially if !y are eld]ly4 ,mu* z we e/eem ! old g5tleman :o is our neighb\r 9 ! c\ntry1 we "k t :5 gr\se are m5tion$ he w tell ! /ory ( ! gr\se 9 ! gun-room4 ,b we ourselves are n s me*anical3 we nev] tell an anecdote to ! same p]son twice1 or ev5 once unless he is sure to enjoy x2 al?\gh we once met 7say7 ,bism>ck1 we are q capable ( he>+ him m5tion$ )\t relat+ ! occasion :5 we met him4 ,9 ?is s5se1 ev]ybody ?9ks t he himself has free w1 ?\gh he kn[s t no "o else has4 ,! desire = ?is k9d ( free w seems to be no bett] ?an a =m ( vanity4 ,i d n believe t ?is desire c be gratifi$ ) any c]ta9ty2 b ! o!r1 m respectable desires are1 ,i believe1 n inconsi/5t ) any t5able =m ( det]m9ism4 ,we h ?us two que/ions to consid]3 7#a7 ,are human actions !oretically pr$ictable f a suffici5t numb] ( antec$5ts8 7#b7 ,are human actions subject to an ext]nal compulsion8 ,! two que/ions1 z ,i %all try to %[1 are entirely di/9ct1 & we may answ] ! fir/ 9 ! affirmative )\t !re=e be+ =c$ to give an affirmative answ] to ! second4 7#a7 ,are human actions !oretically pr$ictable f a suffici5t numb] ( antec$5ts8 ,let u fir/ endeav\r to give precision to ?is "q4 ,we may /ate ! "q ?us3 ,is !re "s con/ant relation betwe5 an act & a c]ta9 numb] ( e>li] ev5ts1 su* t1 :5 ! e>li] ev5ts are giv51 only "o act1 or at mo/ only acts ) "s well-m>k$ "*1 c h ?is relation to ! e>li] ev5ts8 ,if ?is is ! case1 !n1 z soon z ! e>li] ev5ts are kn[n1 x is !oretically possible to pr$ict ei!r ! precise act1 or at lea/ ! "* necess>y to its fulfill+ ! con/ant relation4 ,to ?is "q1 a negative answ] has be5 giv5 by ,b]gson1 9 a =m :i* calls 9 "q ! g5]al applicability ( ! law ( causation4 ,he ma9ta9s t e ev5t1 & m p>ticul>ly e m5tal ev5t1 embodies s mu* ( ! pa/ t x c\ld n possibly h occurr$ at any e>li] "t1 & is !re=e necess>ily q diff]5t f all previ\s & subsequ5t ev5ts4 ,if1 = example1 ,i read a c]ta9 poem _m times1 my exp]i5ce on ea* occasion is modifi$ by ! previ\s read+s1 & my emotions are nev] repeat$ exactly4 ,! pr9ciple ( causation1 accord+ to him1 ass]ts t ! same cause1 if repeat$1 w produce ! same effect4 ,b ow+ to memory1 he cont5ds1 ?is pr9ciple does n apply to m5tal ev5ts4 ,:at is app>5tly ! same cause1 if repeat$1 is modifi$ by ! m]e fact ( repetition1 & _c produce ! same effect4 ,he inf]s t e m5tal ev5t is a g5u9e novelty1 n pr$ictable f ! pa/1 because ! pa/ conta9s no?+ exactly l x by :i* we c\ld imag9e x4 ,& on ?is gr\nd he reg>ds ! fre$om ( ! w z unassailable4 ,b]gson's cont5tion has und\bt$ly a great deal ( tru?1 & ,i h no wi% to d5y its importance4 ,b ,i d n ?9k its consequ5ces are q :at he believes !m to be4 ,x is n necess>y = ! det]m9i/ to ma9ta9 t he c =esee ! :ole p>ticul>ity ( ! act :i* w be p]=m$4 ,if he c\ld =esee t ,a 0 go+ to murd] ,b1 8 =esight w\ld n be invalidat$ by ! fact t he c\ld n "k all ! inf9ite complexity ( ,a's /ate ( m9d 9 committ+ ! murd]1 nor :e!r ! murd] 0 to be p]=m$ ) a knife or ) a revolv]4 ,if ! k9d ( act :i* w be p]=m$ c be =ese5 )9 n>r[ limits1 x is ( little practical int]e/ t !re are f9e %ades :i* _c be =ese54 ,no d\bt e "t ! /ory ( ! gr\se 9 ! gun-room is told1 !re w be slight diff]5ces due to increas+ habitualness1 b !y d n invalidate ! pr$iction t ! /ory w be told4 ,& !re is no?+ 9 ,b]gson's argum5t to %[ t we c nev] pr$ict :at k9d ( act w be p]=m$4 ,aga91 8 /atem5t ( ! law ( causation is inadequate4 ,! law does n /ate m]ely t1 if ! same cause is repeat$1 ! same effect w result4 ,x /ates r t !re is a con/ant relation betwe5 causes ( c]ta9 k9ds & effects ( c]ta9 k9ds4 ,= example1 if a body falls freely1 !re is a con/ant relation betwe5 ! height ?r\gh :i* x falls & ! "t x takes 9 fall+4 ,x is n necess>y to h a body fall ?r\gh ! same height :i* has be5 previ\sly obs]v$1 9 ord] to be able to =etell ! l5g? ( "t occupi$ 9 fall+4 ,if ?is 7 necess>y1 no pr$iction w\ld be possible1 s9ce x w\ld be impossible to make ! height exactly ! same on two occasions4 ,simil>ly1 ! attraction :i* ! sun w ex]t on ! e>? is n only kn[n at di/ances = :i* x has be5 obs]v$1 b at all di/ances1 because x is kn[n to v>y z ! inv]se squ>e ( ! di/ance4 ,9 fact1 :at is f\nd to be repeat$ is always ! relation ( cause & effect1 n ! cause itself2 all t is necess>y z reg>ds ! cause is t x %\ld be ( ! same k9d 79 ! relevant respect7 z e>li] causes ^: effects h be5 obs]v$4 ,ano!r respect 9 :i* ,b]gson's /atem5t ( causation is inadequate is 9 its assumption t ! cause mu/ be "o ev5t1 :]eas x may be two or m ev5ts1 or ev5 "s cont9u\s process4 ,! sub/antive "q at issue is :e!r m5tal ev5ts are det]m9$ by ! pa/4 ,n[ 9 su* a case z ! repeat$ read+ ( a poem1 x is obvi\s t our feel+s 9 read+ ! poem are mo/ emphatically dep5d5t ^u ! pa/1 b n ^u "o s+le ev5t 9 ! pa/4 ,all our previ\s read+s ( ! poem mu/ be includ$ 9 ! cause4 ,b we easily p]ceive a c]ta9 law accord+ to :i* ! effect v>ies z ! previ\s read+s increase 9 numb]1 & 9 fact ,b]gson himself tacitly assumes su* a law4 ,we decide at la/ n to read ! poem aga91 because we "k t ?is "t ! effect w\ld be bor$om4 ,we may n "k all ! niceties & %ades ( ! bor$om we %\ld feel1 b we "k en\gh to guide our decision1 & ! prophecy ( bor$om is none ! less true = be+ m or less g5]al4 ,?us ! k9ds ( cases ^u :i* ,b]gson relies are insuffici5t to %[ ! impossibility ( pr$iction 9 ! only s5se 9 :i* pr$iction has practical or emotional int]e/4 ,we may !re=e leave ! consid]ation ( 8 argum5ts & address ourselves to ! problem directly4 ,! law ( causation1 accord+ to :i* lat] ev5ts c !oretically be pr$ict$ by means ( e>li] ev5ts1 has (t5 be5 held to be a priori1 a necessity ( ?\ght1 a category )\t :i* sci5ce w\ld be impossible4 ,^! claims seem to me excessive4 ,9 c]ta9 directions ! law has be5 v]ifi$ empirically1 & 9 o!r directions !re is no positive evid5ce aga9/ x4 ,b sci5ce c use x :]e x has be5 f\nd to be true1 )\t be+ =c$ into any assumption z to its tru? 9 o!r fields4 ,we _c1 !re=e1 feel any a priori c]ta9ty t causation mu/ apply to human volitions4 ,! "q h[ f> human volitions are subject to causal laws is a purely empirical "o4 ,empirically x seems pla9 t ! great majority ( our volitions h causes1 b x _c1 on ?is acc\nt1 be held necess>ily c]ta9 t all h causes4 ,!re are1 h[ev]1 precisely ! same k9ds ( reasons = reg>d+ x z probable t !y all h causes z !re are 9 ! case ( physical ev5ts4 ,we may suppose--?\gh ?is is d\btful--t !re are laws ( correlation ( ! m5tal & ! physical1 9 virtue ( :i*1 giv5 ! /ate ( all ! matt] 9 ! _w1 & !re=e ( all ! bra9s & liv+ organisms1 ! /ate ( all ! m9ds 9 ! _w c\ld be inf]r$1 :ile conv]sely ! /ate ( all ! matt] 9 ! _w c\ld be inf]r$ if ! /ate ( all ! m9ds 7 giv54 ,x is obvi\s t !re is "s degree ( correlation betwe5 bra9 & m9d1 & x is impossible to say h[ complete x may be4 ,?is1 h[ev]1 is n ! po9t :i* ,i wi% to elicit4 ,:at ,i wi% to urge is t1 ev5 if we admit ! mo/ extreme claims ( det]m9ism & ( correlation ( m9d & bra91 /ill ! consequ5ces inimical to :at is wor? pres]v+ 9 free w d n foll[4 ,! belief t !y foll[ results1 ,i ?9k1 entirely f ! assimilation ( causes to volitions1 & f ! notion t causes compel _! effects 9 "s s5se analog\s to t 9 :i* a human au?ority c compel a man to d :at he w\ld r n d4 ,?is assimilation1 z soon z ! true nature ( sci5tific causal laws is realis$1 is se5 to be a %e] mi/ake4 ,b ?is br+s u to ! second ( ! two que/ions :i* we rais$ 9 reg>d to free w1 namely1 :e!r1 assum+ det]m9ism1 our actions c be 9 any prop] s5se reg>d$ z compell$ by outside =ces4 7#b7 ,are human actions subject to an ext]nal compulsion8 ,we h1 9 delib]ation1 a subjective s5se ( fre$om1 :i* is sometimes alleg$ aga9/ ! view t volitions h causes4 ,?is s5se ( fre$om1 h[ev]1 is only a s5se t we c *oose :i* we please ( a numb] ( alt]natives3 x does n %[ u t !re is no causal connection betwe5 :at we please to *oose & our previ\s hi/ory4 ,! suppos$ inconsi/5cy ( ^! two spr+s f ! habit ( conceiv+ causes z analog\s to volitions--a habit :i* (t5 survives unconsci\sly 9 ^? :o int5d to conceive causes 9 a m sci5tific mann]4 ,if a cause is analog\s to a volition1 outside causes w be analog\s to an ali5 w1 & acts pr$ictable f outside causes w be subject to compulsion4 ,b ?is view ( cause is "o to :i* sci5ce l5ds no c\nt5ance4 ,causes1 we h se51 d n compel _! effects1 any m ?an effects compel _! causes4 ,!re is a mutual relation1 s t ei!r c be inf]r$ f ! o!r4 ,:5 ! geologi/ inf]s ! pa/ /ate ( ! e>? f its pres5t /ate1 we %\ld n say t ! pres5t /ate compels ! pa/ /ate to h be5 :at x 02 yet x r5d]s x necess>y z a consequ5ce ( ! data1 9 ! only s5se 9 :i* effects are r5d]$ necess>y by _! causes4 ,! diff]5ce :i* we feel1 9 ?is respect1 betwe5 causes & effects is a m]e confusion due to ! fact t we rememb] pa/ ev5ts b d n happ5 to h memory ( ! future4 ,! app>5t indet]m9at5ess ( ! future1 ^u :i* "s advocates ( free w rely1 is m]ely a result ( our ignorance4 ,x is pla9 t no desirable k9d ( free w c be dep5d5t simply ^u our ignorance2 = if t 7 ! case1 animals w\ld be m free ?an m51 & savages ?an civilis$ p4 ,free w 9 any valuable s5se mu/ be compatible ) ! fulle/ k4 ,n[1 q ap>t f any assumption z to causality1 x is obvi\s t complete k w\ld embrace ! future z well z ! pa/4 ,our k ( ! pa/ is n :olly bas$ ^u causal inf]5ces1 b is p>tly d]iv$ f memory4 ,x is a m]e accid5t t we h no memory ( ! future4 ,we might--z 9 ! pret5d$ visions ( se]s--see future ev5ts imm$iately1 9 ! way 9 :i* we see pa/ ev5ts4 ,!y c]ta9ly w be :at !y w be1 & are 9 ?is s5se j z det]m9$ z ! pa/4 ,if we saw future ev5ts 9 ! same imm$iate way 9 :i* we see pa/ ev5ts1 :at k9d ( free w w\ld /ill be possible8 ,su* a k9d w\ld be :olly indep5d5t ( det]m9ism3 x c\ld n be contr>y to ev5 ! mo/ entirely univ]sal reign ( causality4 ,& su* a k9d mu/ conta9 :atev] is wor? hav+ 9 free w1 s9ce x is impossible to believe t m]e ignorance c be ! ess5tial condition ( any good ?+4 ,let u !re=e imag9e a set ( be+s :o "k ! :ole future ) absolute c]ta9ty1 & let u ask ourselves :e!r !y c\ld h any?+ t we %\ld call free w4 ,su* be+s z we are imag9+ w\ld n h to wait = ! ev5t 9 ord] to "k :at decision !y 7 go+ to adopt on "s future occasion4 ,!y w\ld "k n[ :at _! volitions 7 go+ to be4 ,b w\ld !y h any reason to regret ?is k8 ,surely n1 unless ! =ese5 volitions 7 9 !mselves regrettable4 ,& x is less likely t ! =ese5 volitions w\ld be regrettable if ! /eps :i* w\ld lead to !m 7 also =ese54 ,x is difficult n to suppose t :at is =ese5 is fat$1 & mu/ happ5 h[ev] mu* x may be dread$4 ,b human actions are ! outcome ( desire1 & no =esee+ c be true unless x takes acc\nt ( desire4 ,a =ese5 volition w h to be "o :i* does n become odi\s ?r\gh be+ =ese54 ,! be+s we are imag9+ w\ld easily come to "k ! causal connections ( volitions1 & !re=e _! volitions w\ld be bett] calculat$ to satisfy _! desires ?an ours are4 ,s9ce volitions are ! outcome ( desires1 a prevision ( volitions contr>y to desires c\ld n be a true "o4 ,x mu/ be rememb]$ t ! suppos$ prevision w\ld n create ! future any m ?an memory creates ! pa/4 ,we d n ?9k we 7 necess>ily n free 9 ! pa/1 m]ely because we c n[ rememb] our pa/ volitions4 ,simil>ly1 we might be free 9 ! future1 ev5 if we c\ld n[ see :at our future volitions 7 go+ to be4 ,fre$om1 9 %ort1 9 any valuable s5se1 dem&s only t our volitions %all be1 z !y are1 ! result ( our own desires1 n ( an outside =ce compell+ u to w :at we w\ld r n w4 ,ev]y?+ else is confusion ( ?\ght1 due to ! feel+ t k compels ! happ5+ ( :at x kn[s :5 ?is is future1 ?\gh x is at once obvi\s t k has no su* p[] 9 reg>d to ! pa/4 ,free w1 !re=e1 is true 9 ! only =m :i* is important2 & ! desire = o!r =ms is a m]e effect ( insuffici5t analysis4 99 99 99 99 99 ,:at has be5 said on philosophical me?od 9 ! =ego+ lectures has be5 r by means ( illu/rations 9 p>ticul> cases ?an by means ( g5]al precepts4 ,no?+ ( any value c be said on me?od except ?r\gh examples2 b n[1 at ! end ( our c\rse1 we may collect c]ta9 g5]al maxims :i* may possibly be a help 9 acquir+ a philosophical habit ( m9d & a guide 9 look+ = solutions ( philosophic problems4 ,philosophy does n become sci5tific by mak+ use ( o!r sci5ces1 9 ! k9d ( way 9 :i* 7e4g47 ,h]b]t ,sp5c] does4 ,philosophy aims at :at is g5]al1 & ! special sci5ces1 h[ev] !y may sugge/ l>ge g5]alisations1 _c make !m c]ta94 ,& a ha/y g5]alisation1 su* z ,sp5c]'s g5]alisation ( evolution1 is none ! less ha/y because :at is g5]alis$ is ! late/ sci5tific !ory4 ,philosophy is a /udy ap>t f ! o!r sci5ces3 its results _c be e/abli%$ by ! o!r sci5ces1 & conv]sely mu/ n be su* z "s o!r sci5ce might conceivably contradict4 ,prophecies z to ! future ( ! univ]se1 = example1 are n ! bus9ess ( philosophy2 :e!r ! univ]se is progressive1 retrograde1 or /ation>y1 x is n = ! philosoph] to say4 ,9 ord] to become a sci5tific philosoph]1 a c]ta9 peculi> m5tal discipl9e is requir$4 ,!re mu/ be pres5t1 fir/ ( all1 ! desire to "k philosophical tru?1 & ?is desire mu/ be suffici5tly /rong to survive ?r\gh ye>s :5 !re seems no hope ( its f9d+ any satisfaction4 ,! desire to "k philosophical tru? is v r>e--9 its purity1 x is n (t5 f\nd ev5 among philosoph]s4 ,x is obscur$ sometimes--p>ticul>ly aft] long p]iods ( fruitless se>*--by ! desire to ?9k we "k4 ,"s plausible op9ion pres5ts itself1 & by turn+ our att5tion away f ! objections to x1 or m]ely by n mak+ great ef=ts to f9d objections to x1 we may obta9 ! com=t ( believ+ x1 al?\gh1 if we _h resi/$ ! wi% = com=t1 we %\ld h come to see t ! op9ion 0 false4 ,aga9 ! desire = unadult]at$ tru? is (t5 obscur$1 9 pr(essional philosoph]s1 by love ( sy/em3 ! "o little fact :i* w n come inside ! philosoph]'s edifice has to be pu%$ & tortur$ until x seems to cons5t4 ,yet ! "o little fact is m likely to be important = ! future ?an ! sy/em ) :i* x is inconsi/5t4 ,py?agoras inv5t$ a sy/em :i* fitt$ admirably ) all ! facts he knew1 except ! incomm5surability ( ! diagonal ( a squ>e & ! side2 ?is "o little fact /ood out1 & rema9$ a fact ev5 aft] ,hippasos ( ,metapontion 0 dr[n$ = reveal+ x4 ,to u1 ! discov]y ( ?is fact is ! *ief claim ( ,py?agoras to immortality1 :ile 8 sy/em has become a matt] ( m]ely hi/orical curiosity4#eg ,love ( sy/em1 !re=e1 & ! sy/em-mak]'s vanity :i* becomes associat$ ) x1 are among ! sn>es t ! /ud5t ( philosophy mu/ gu>d aga9/4 #eg ,! above rem>ks1 = purposes ( illu/ration1 adopt "o ( sev]al possible op9ions on ea* ( sev]al disput$ po9ts4 ,! desire to e/abli% ?is or t result1 or g5]ally to discov] evid5ce = agreeable results1 ( :atev] k9d1 has ( c\rse be5 ! *ief ob/acle to hone/ philosophis+4 ,s /rangely p]v]t$ d m5 become by unrecognis$ passions1 t a det]m9ation 9 advance to arrive at ?is or t conclusion is g5]ally reg>d$ z a m>k ( virtue1 & ^? ^: /udies lead to an opposite conclusion are ?\ght to be wick$4 ,no d\bt x is common] to wi% to arrive at an agreeable result ?an to wi% to arrive at a true result4 ,b only ^? 9 :om ! desire to arrive at a true result is p>am\nt c hope to s]ve any good purpose by ! /udy ( philosophy4 ,b ev5 :5 ! desire to "k exi/s 9 ! requisite /r5g?1 ! m5tal vision by :i* ab/ract tru? is recognis$ is h>d to di/+ui% f vivid imag9ability & consonance ) m5tal habits4 ,x is necess>y to practise me?odological d\bt1 l ,desc>tes1 9 ord] to loos5 ! hold ( m5tal habits2 & x is necess>y to cultivate logical imag9ation1 9 ord] to h a numb] ( hypo!ses at comm&1 & n to be ! slave ( ! "o :i* common s5se has r5d]$ easy to imag9e4 ,^! two processes1 ( d\bt+ ! famili> & imag9+ ! unfamili>1 are correlative1 & =m ! *ief "p ( ! m5tal tra9+ requir$ = a philosoph]4 ,! naive beliefs :i* we f9d 9 ourselves :5 we fir/ beg9 ! process ( philosophic reflection may turn out1 9 ! end1 to be almo/ all capable ( a true int]pretation2 b !y ought all1 be=e be+ admitt$ into philosophy1 to und]go ! ordeal ( sceptical criticism4 ,until !y h gone ?r\gh ?is ordeal1 !y are m]e bl9d habits1 ways ( behav+ r ?an intellectual convictions4 ,& al?\gh x may be t a majority w pass ! te/1 we may be pretty sure t "s w n1 & t a s]i\s readju/m5t ( our outlook ought to result4 ,9 ord] to break ! dom9ion ( habit1 we mu/ d our be/ to d\bt ! s5ses1 reason1 morals1 ev]y?+ 9 %ort4 ,9 "s directions1 d\bt w be f\nd possible2 9 o!rs1 x w be *eck$ by t direct vision ( ab/ract tru? ^u :i* ! possibility ( philosophical k dep5ds4 ,at ! same "t1 & z an ess5tial aid to ! direct p]ception ( ! tru?1 x is necess>y to acquire f]tility 9 imag9+ ab/ract hypo!ses4 ,?is is1 ,i ?9k1 :at has mo/ ( all be5 lack+ hi!rto 9 philosophy4 ,s meagre 0 ! logical app>atus t all ! hypo!ses philosoph]s c\ld imag9e 7 f\nd to be inconsi/5t ) ! facts4 ,too (t5 ?is /ate ( ?+s l$ to ! adoption ( h]oic measures1 su* z a :olesale d5ial ( ! facts1 :5 an imag9ation bett] /ock$ ) logical tools w\ld h f\nd a key to unlock ! my/]y4 ,x is 9 ?is way t ! /udy ( logic becomes ! c5tral /udy 9 philosophy3 x gives ! me?od ( rese>* 9 philosophy1 j z ma!matics gives ! me?od 9 physics4 ,& z physics1 :i*1 f ,plato to ! ,r5aissance1 0 z unprogressive1 dim1 & sup]/iti\s z philosophy1 became a sci5ce ?r\gh ,galileo's fre% obs]vation ( facts & subsequ5t ma!matical manipulation1 s philosophy1 9 our own day1 is becom+ sci5tific ?r\gh ! simultane\s acquisition ( new facts & logical me?ods4 ,9 spite1 h[ev]1 ( ! new possibility ( progress 9 philosophy1 ! fir/ effect1 z 9 ! case ( physics1 is to dim9i% v greatly ! ext5t ( :at is ?\ght to be kn[n4 ,be=e ,galileo1 p believ$ !mselves possess$ ( imm5se k on all ! mo/ int]e/+ que/ions 9 physics4 ,he e/abli%$ c]ta9 facts z to ! way 9 :i* bodies fall1 n v int]e/+ on _! own acc\nt1 b ( q immeasurable int]e/ z examples ( real k & ( a new me?od ^: future fruitfulness he himself div9$4 ,b 8 few facts suffic$ to de/roy ! :ole va/ sy/em ( suppos$ k h&$ d[n f ,ari/otle1 z ev5 ! pale/ morn+ sun suffices to ext+ui% ! />s4 ,s 9 philosophy3 ?\gh "s h believ$ "o sy/em1 & o!rs ano!r1 almo/ all h be5 ( op9ion t a great deal 0 kn[n2 b all ?is suppos$ k 9 ! traditional sy/ems mu/ be swept away1 & a new beg9n+ mu/ be made1 :i* we %all e/eem =tunate inde$ if x c atta9 results comp>able to ,galileo's law ( fall+ bodies4 ,by ! practice ( me?odological d\bt1 if x is g5u9e & prolong$1 a c]ta9 humility z to our k is induc$3 we become glad to "k any?+ 9 philosophy1 h[ev] seem+ly trivial4 ,philosophy has suff]$ f ! lack ( ?is k9d ( mode/y4 ,x has made ! mi/ake ( attack+ ! int]e/+ problems at once1 in/ead ( proce$+ pati5tly & sl[ly1 accumulat+ :atev] solid k 0 obta9able1 & tru/+ ! great problems to ! future4 ,m5 ( sci5ce are n a%am$ ( :at is intr9sically trivial1 if its consequ5ces are likely to be important2 ! imm$iate outcome ( an exp]im5t is h>dly ev] int]e/+ on its own acc\nt4 ,s 9 philosophy1 x is (t5 desirable to exp5d "t & c>e on matt]s :i*1 judg$ alone1 might seem frivol\s1 = x is (t5 only ?r\gh ! consid]ation ( su* matt]s t ! great] problems c be approa*$4 ,:5 our problem has be5 select$1 & ! necess>y m5tal discipl9e has be5 acquir$1 ! me?od to be pursu$ is fairly uni=m4 ,! big problems :i* provoke philosophical inquiry are f\nd1 on exam9ation1 to be complex1 & to dep5d ^u a numb] ( compon5t problems1 usually m ab/ract ?an ^? ( :i* !y are ! compon5ts4 ,x w g5]ally be f\nd t all our initial data1 all ! facts t we seem to "k to beg9 )1 suff] f vagu5ess1 confusion1 & complexity4 ,curr5t philosophical ideas %>e ^! defects2 x is !re=e necess>y to create an app>atus ( precise conceptions z g5]al & z free f complexity z possible1 be=e ! data c be analys$ into ! k9d ( premisses :i* philosophy aims at discov]+4 ,9 ?is process ( analysis1 ! s\rce ( difficulty is track$ fur!r & fur!r back1 gr[+ at ea* /age m ab/ract1 m ref9$1 m difficult to appreh5d4 ,usually x w be f\nd t a numb] ( ^! extraord9>ily ab/ract que/ions und]lie any "o ( ! big obvi\s problems4 ,:5 ev]y?+ has be5 done t c be done by me?od1 a /age is rea*$ :]e only direct philosophic vision c c>ry matt]s fur!r4 ,"h only g5ius w avail4 ,:at is want$1 z a rule1 is "s new ef=t ( logical imag9ation1 "s glimpse ( a possibility nev] conceiv$ be=e1 & !n ! direct p]ception t ?is possibility is realis$ 9 ! case 9 "q4 ,failure to ?9k ( ! "r possibility leaves insoluble difficulties1 balanc$ argum5ts pro & con1 utt] bewild]m5t & despair4 ,b ! "r possibility1 z a rule1 :5 once conceiv$1 ju/ifies itself swiftly by its a/oni%+ p[] ( absorb+ app>5tly conflict+ facts4 ,f ?is po9t onw>d1 ! "w ( ! philosoph] is syn!tic & comp>atively easy2 x is 9 ! v la/ /age ( ! analysis t ! real difficulty consi/s4 ,( ! prospect ( progress 9 philosophy1 x w\ld be ra% to speak ) confid5ce4 ,_m ( ! traditional problems ( philosophy1 p]haps mo/ ( ^? :i* h int]e/$ a wid] circle ?an t ( te*nical /ud5ts1 d n appe> to be soluble by sci5tific me?ods4 ,j z a/ronomy lo/ mu* ( its human int]e/ :5 x ceas$ to be a/rology1 s philosophy mu/ lose 9 attractiv5ess z x gr[s less prodigal ( promises4 ,b to ! l>ge & /ill gr[+ body ( m5 engag$ 9 ! pursuit ( sci5ce--m5 :o hi!rto1 n )\t ju/ification1 h turn$ aside f philosophy ) a c]ta9 contempt--! new me?od1 successful already 9 su* "t-hon\r$ problems z numb]1 inf9ity1 cont9uity1 space & "t1 %\ld make an appeal :i* ! old] me?ods h :olly fail$ to make4 ,physics1 ) its pr9ciple ( relativity & its revolution>y inve/igations into ! nature ( matt]1 is feel+ ! ne$ = t k9d ( novelty 9 fundam5tal hypo!ses :i* sci5tific philosophy aims at facilitat+4 ,! "o & only condition1 ,i believe1 :i* is necess>y 9 ord] to secure = philosophy 9 ! ne> future an a*ievem5t surpass+ all t has hi!rto be5 accompli%$ by philosoph]s1 is ! creation ( a s*ool ( m5 ) sci5tific tra9+ & philosophical int]e/s1 unhamp]$ by ! traditions ( ! pa/1 & n misl$ by ! lit]>y me?ods ( ^? :o copy ! anci5ts 9 all except _! m]its4 ,,index ,absolute1 #f1 #ci4 ,ab/raction1 pr9ciple (1 #db1 #abd ff4 ,a*illes1 ,z5o's argum5t (1 #agc4 ,acqua9tance1 #be1 #add4 ,activity1 #bbd ff4 ,allman1 #afa n4 ,analysis1 #ahe1 #bjd1 #baa1 #bda4 legitimacy (1 #aej4 ,anaxim&]1 #c4 ,ant9omies1 ,kant's1 #aee ff4 ,aqu9as1 #aj4 ,ari/otle1 #dj1 #afj n41 #afa ff41 #bdj4 ,arr[1 ,z5o's argum5t (1 #agc4 ,ass]tion1 #eb4 ,atomism1 logical1 #d4 ,atomi/s1 #afj4 ,belief1 #eh4 primitive & d]ivative1 #fi ff4 ,b]gson1 #d1 #aa1 #ac1 #bj ff41 #acg1 #ach1 #aej1 #aeh1 #afe1 #agd1 #agh1 #bbi ff4 ,b]keley1 #fc1 #fd1 #ajb4 ,bolzano1 #afe4 ,boole1 #dj4 ,bradley1 #f1 #ci1 #afe4 ,broad1 #agb n4 ,bro*>d1 #afi n4 ,burnet1 #ai n41 #afj n41 #afa n41 #agj n41 #aga ff4 ,cald]on1 #ie4 ,cantor1 vi1 vii1 #aee1 #afe1 #aij1 #aid1 #aii4 ,categories1 #ch4 ,causal laws1 #aji1 #bab ff4 evid5ce =1 #baf ff4 9 psy*ology1 #bai4 ,causation1 #cd ff41 #gi1 #bab ff4 law (1 #bba4 n a priori1 #bbc1 #bcb4 ,cause1 #bbj1 #bbc4 ,c]ta9ty1 degrees (1 #fg1 #fh1 #bab4 ,*ange1 dem&s analysis1 #aea4 ,c9ematograph1 #adh1 #agd4 ,classes1 #bjb4 non-exi/5ce (1 #bje ff4 ,classical tradition1 #c ff41 #eh4 ,complexity1 #ade1 #aeg ff4 ,compulsion1 #bbi1 #bcc ff4 ,congru5ce1 #aie4 ,consecutiv5ess1 #acd4 ,cons]vation1 #aje4 ,con/itu5ts ( facts1 #ea1 #ade4 ,con/ruction v4 inf]5ce1 iv4 ,contempor>ies1 initial1 #aai1 #abj n4 ,cont9uity1 #fd1 #abi ff41 #ada ff41 #aee ff4 ( *ange1 #ajf1 #ajh1 #acj ff4 ,correlation ( m5tal & physical1 #bcc4 ,c\nt+1 #afd1 #aha1 #ahg ff41 #bjc4 ,c\turat1 #dj n4 ,dante1 #aj4 ,d>w91 #d1 #aa1 #bc1 #cj4 ,data1 #fe ff41 #baa4 h>d & s(t1 #gj ff4 ,dates1 #aag4 ,def9ition1 #bjd4 ,desc>tes1 #e1 #gc1 #bch4 ,descriptions1 #bja1 #bad4 ,desire1 #bbg1 #bce4 ,det]m9ism1 #bcc4 ,d\bt1 #bcg4 ,dreams1 #he1 #ic4 ,duration1 #adf1 #adi4 ,e>li] & lat]1 #aaf4 ,effect1 #bbj4 ,eleatics1 #ai4 ,empiricism1 #cg1 #bbb4 ,enclosure1 #aad ff41 #abj4 ,enum]ation1 #bjb4 ,euclid1 #afj1 #afd4 ,evell91 #afi4 ,evolutionism1 #d1 #aa ff4 ,ext5sion1 #adf1 #adi4 ,ext]nal _w1 k (1 #fc ff4 ,fact1 #ea4 atomic1 #eb4 ,f9alism1 #ac4 ,=m1 logical1 #db ff41 #ahe1 #bjh4 ,fractions1 #acb1 #agi4 ,free w1 #bac1 #bbg ff4 ,frege1 #e1 #dj1 #aii ff4 ,galileo1 #d1 #ei1 #aib1 #aid1 #bci1 #bdj4 ,gaye1 #afi n41 #age1 #agg4 ,geometry1 #e4 ,giles1 #bjf n4 ,great] & less1 #aie4 ,h>v>d1 #d4 ,hegel1 #c1 #cg ff41 #df1 #aff4 ,"h1 #gc1 #ib4 ,h]$it>y prop]ties1 #aie4 ,hippasos1 #afc1 #bcg4 ,hui ,tzu1 #bjf4 ,hume1 #bag1 #bba4 ,hypo!ses 9 philosophy1 #bci4 ,illusions1 #he4 ,incomm5surables1 #afb ff41 #bcg4 ,indep5d5ce1 #gc1 #gd4 causal & logical1 #gd1 #ge4 ,indisc]nibility1 #ada1 #adh4 ,indivisibles1 #afj4 ,induction1 #cd1 #bbb4 ma!matical1 #aie ff4 ,inductiv5ess1 #aij1 #aie ff4 ,inf]5ce1 #dd1 #ed4 ,inf9ite1 vi1 #fd1 #acc1 #adi4 hi/orically consid]$1 #aee ff4 true1 #agi1 #ahj4 positive !ory (1 #ahe ff4 ,inf9itesimals1 #ace4 ,in/ants1 #aaf ff41 #abi1 #aea1 #baf4 def9$1 #aah4 ,in/9ct v4 ,reason1 #bj ff4 ,intellect1 #bb ff4 ,intellig5ce1 h[ display$ by fri5ds1 #ic4 inadequacy ( display1 #if4 ,int]pretation1 #add4 ,james1 #d1 #aj1 #ac4 ,j\rda91 #afe n4 ,j[ett1 #afg4 ,judgm5t1 #eh4 ,kant1 #c1 #aab1 #aaf1 #aee ff41 #bjj4 ,k ab\t1 #add4 ,language1 bad1 #hb1 #ace4 ,laplace1 #ab4 ,laws ( nature1 #bah ff4 ,leibniz1 #ac1 #dj1 #hg1 #ahf1 #aia4 ,logic1 #bja4 analytic n con/ructive1 #h4 ,ari/otelian1 #e4 & fact1 #ec4 inductive1 #cd1 #bbb4 ma!matical1 vi1 #dj ff4 my/ical1 #df4 & philosophy1 #h1 #cc ff41 #bci4 ,logical con/ants1 #bjh1 #bac4 ,ma*1 #abc1 #bbd4 ,macran1 #ci n4 ,ma!matics1 #dj1 #eg4 ,matt]1 #ge1 #aja ff4 p]man5ce (1 #ajb ff4 ,measurem5t1 #afd4 ,memory1 #bcj1 #bcd1 #bcf4 ,me?od1 d$uctive1 #e4 logical-analytic1 v1 #fe1 #baa1 #bcf ff4 ,milhaud1 #afh n41 #afi n4 ,mill1 #cd1 #bjj4 ,montaigne1 #bh4 ,motion1 #acj1 #baf4 cont9u\s1 #acc1 #acf4 ma!matical !ory (1 #acc4 p]ception (1 #acg ff4 ,z5o's argum5ts on1 #afh ff4 ,my/icism1 #ai1 #df1 #fc1 #ie4 ,newton1 #cj1 #adf4 ,nietzs*e1 #aj1 #aa4 ,noel1 #afi4 ,numb]1 c>d9al1 #aca1 #ahf ff4 def9$1 #aii ff4 f9ite1 #afj1 #aij ff4 inductive1 #aig4 inf9ite1 #agh1 #ahj1 #ahh ff41 #aig4 reflexive1 #aij ff4 ,occam1 #ajg1 #adf4 ,"o & _m1 #afg1 #agj4 ,ord]1 #aca4 ,p>m5ides1 #fc1 #afe ff41 #agh4 ,pa/ & future1 #bbd1 #bcd ff4 ,peano1 #dj4 ,p]spectives1 #hh ff41 #aaa4 ,philoponus1 #aga n4 ,philosophy & e?ics1 #bf ff4 & ma!matics1 #ahe ff4 prov9ce (1 #ag1 #bf1 #ahe1 #bcf4 sci5tific1 #aa1 #af1 #ah1 #bi1 #bcf ff4 ,physics1 #aja ff41 #adg1 #bci1 #bdb4 descriptive1 #bbd4 v]ifiability (1 #ha1 #aaj4 ,place1 #hf1 #ij4 at & f1 #ib4 ,plato1 #d1 #ai1 #bg1 #df1 #fc1 #afe n41 #aff1 #afg4 ,po9c>e1 #abc1 #ada4 ,po9ts1 #aac ff41 #abi1 #aeh4 def9ition (1 vi1 #aae4 ,pragmatism1 #aa4 ,prantl1 #agd4 ,pr$ictability1 #bbi ff4 ,premisses1 #baa4 ,probability1 #cf4 ,propositions1 #eb4 atomic1 #eb4 g5]al1 #ee4 molecul>1 #ed4 ,py?agoras1 #ai1 #afj ff41 #bcg4 ,race-c\rse1 ,z5o's argum5t (1 #aga ff4 ,realism1 new1 #f4 ,reflexiv5ess1 #aij ff4 ,relations1 #de4 asymmetrical1 #dg4 ,bradley's reasons aga9/1 #f4 ext]nal1 #aej4 intransitive1 #dh4 multiple1 #ej4 "o-"o1 #bjc4 reality (1 #di4 symmetrical1 #dg1 #abd4 transitive1 #dh1 #abd4 ,relativity1 #ajc1 #bdb4 ,repetitions1 #bcj ff4 ,re/1 #acf4 ,ritt] & ,prell]1 #afa n4 ,rob]tson1 ,d4 ,s41 #afj n4 ,r\sseau1 #bj4 ,royce1 #ej4 ,santayana1 #df4 ,scepticism1 #ff1 #fg4 ,see+ d\ble1 #hf4 ,self1 #gc4 ,s5sation1 #be1 #ge1 #abc4 & /imulus1 #aci4 ,s5se-data1 #ef1 #fc1 #fg1 #ge1 #aaj1 #ada1 #adc1 #bac4 & physics1 v1 #fd1 #ha1 #ig1 #aja ff41 #adj4 inf9itely num]\s8 #adi1 #aei4 ,s5se-p]ception1 #ec4 ,s]ies1 #di4 compact1 #acb1 #adb1 #agh4 cont9u\s1 #aca1 #acb4 ,sigw>t1 #ahg4 ,simplicius1 #agj n4 ,simultaneity1 #aaf4 ,space1 #gc1 #hh1 #ajc1 #aab ff41 #acj4 absolute & relative1 #adf1 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alt]natives :i* seem$ prima m (t5 ?an ! impossibility ( alt]natives :i* seem$ prima ) x4 ,we w call ^! ! initial contempor>ies ( ! giv5 ) x4 ,we w call ^! ! initial contempor>ies ( ! giv5 ! next are liable to fail :5 we come to inf9ite numb]4 ,! fir/ ! next are liable to fail :5 we come to inf9ite numb]s4 ,! fir/ ( psy*ology or an outcome ( pscyhical processes z ! ,nor? ,sea4444 ( psy*ology or an outcome ( psy*ical processes z ! ,nor? ,sea4444 accord+ to ! l5g? & direction ( ! int]val4 ,a qu>t] ( a accord+ to ! l5g? & direction ( ! int]val4 ,a qu>t] ( an ,intellig5ce1 h[ display$ by fri5ds1 #ic ,intellig5ce1 h[ display$ by fri5ds1 #ic4 ,numb]1 c>d9al1 #aca #ahf ff4 ,numb]1 c>d9al1 #aca1 #ahf ff4