,,! ,,organisation ,,( ,,?\ght ,,! ,,organisation ,,( ,,?\ght ,,educational ,,& ,,sci5tific ,,by ,a4 ,n4 ,,:itehead1 ,sc4,d41 ,f4,r4,s4 ,,fell[ ,,( ,,tr9ity ,,college1 ,,cambridge1 ,,& ,,pr(essor ,,( ,,appli$ ,,ma!matics ,,at ,,! ,,imp]ial ,,college ,,( ,,sci5ce ,,& ,,te*nology ,,london ,,williams ,,& ,,norgate #ad ,,h5rietta ,,/reet1 ,,cov5t ,,g>d51 ,w4,c4#b #aiag ,! rights ( translation are res]v$ ,,preface ,,! disc\rses includ$ 9 ?is volume h be5 deliv]$ z addresses on v>i\s occasions :i* are duly not$2 ! only exception is ,! ,anatomy ( ,"s ,sci5tific ,ideas1 :i* is n[ publi%$ = ! fir/ "t4 ,^! disc\rses fall into two sections1 ! fir/ five *apt]s deal ) education1 & ! rema9+ ?ree embody discussions on c]ta9 po9ts aris+ 9 ! philosophy ( sci5ce4 ,b a common l9e ( reflection ext5ds ?r\gh ! :ole1 & ! two sections influ5ce ea* o!r4 ,i h left 9 ea* *apt] ! ref]5ce to ! p>ticul> occasion ( its fir/ production1 & ,i h n s\ght = a v]bal consi/5cy cov]+ p]plexity4 ,b ! v>i\s p>ts ( ! book 7 9 fact compos$ ) express ref]5ce to ea* o!r1 s z to =m "o :ole4 ,i h to ?ank ! ,syndics ( ! ,cambridge ,univ]sity ,press = p]mission to republi% ! cont5ts ( ,*apt] ,v4 ,imp]ial ,college ( ,sci5ce & ,te*nology1 ,april #aiag4 ,,table ,,( ,,cont5ts ,,*ap4 ,,page ,,preface v ,i4 ,,! ,,aims ,,( ,,education--,a ,,plea ,,= ,,re=m #a 7,presid5tial ,address to ! ,ma!matical ,association1 ,janu>y1 #aiaf47 ,,ii4 ,,te*nical ,,education ,,& ,,its ,,relation ,,to ,,sci5ce ,,& ,,lit]ature #bi 7,presid5tial ,address to ! ,ma!matical ,association1 ,janu>y1 #aiag47 ,,iii4 ,a ,,polyte*nic ,,9 ,,w>-,,"t #eh 7,address at ! ,prize ,di/ribution1 ,bor\gh ,polyte*nic ,in/itute1 ,s\?w>k1 ,febru>y1 #aiag47 ,,iv4 ,,! ,,ma!matical ,,curriculum #fi 7,presid5tial ,address to ! ,london ,bran* ( ! ,ma!matical ,association1 #aiab47 ,v4 ,,! ,,pr9ciples ,,( ,,ma!matics ,,9 ,,relation ,,to ,,elem5t>y ,,tea*+ #ib 7,pap] read 9 ! ,educational ,section ( ! ,int]national ,congress ( ,ma!maticians1 ,cambridge1 #aiab47 ,,vi4 ,,! ,,organisation ,,( ,,?\ght #aje 7,presid5tial ,address to ,section ,a1 ,briti% ,association1 ,newca/le1 #aiaf2 also read subsequ5tly be=e ! ,ari/otelian ,society47 ,,vii4 ,,! ,,anatomy ,,( ,,"s ,,sci5tific ,,ideas #acd ,,viii4 ,,space1 ,,"t1 ,,& ,,relativity #aia 7,pap] read to ,section ,a at ! ,man*e/] ,meet+ ( ,section ,a1 #aiae2 also1 ) ! app5d$ ,comm5t>y1 read subsequ5tly be=e ! ,ari/otelian ,society47 ,,organisation ,,( ,,?\ght ,,*apt] ,i ,,! ,,aims ,,( ,,education--,a ,,plea ,,= ,,re=m 7,presid5tial ,address to ! ,ma!matical ,association1 ,janu>y1 #aiaf7 ,,:5 ,i _h ! hon\r ( be+ made ,presid5t ( ! ,ma!matical ,association1 ,i did n =esee ! unusual responsibility :i* x entail$4 ,x 0 my int5tion to take z ! !me ( a presid5tial address ! consid]ation ( "s aspect ( ^? special subjects to :i* my own rese>*es h pr9cipally be5 direct$4 ,ev5ts h =c$ me to ab&on t int5tion4 ,x is useless to discuss ab/ract que/ions 9 ! mid/ ( dom9ant practical preoccupation4 ,we _c disreg>d ! pres5t crisis 9 ,european civilisation4 ,x affects e function ( life4 ,9 ! h>d] /ruggle = exi/5ce :i* lies be=e ! nation1 all dep>tm5ts ( national ef=t w be review$ = judgm5t4 ,! m]e necessity = economy 9 res\rces w provoke ?is re=mation4 ,we are conc]n$ ) education4 ,?is ,association1 s ri* 9 its memb]%ip ( educationali/s1 ) ! conception ( re=m z ! v reason ( its be+1 is among ^? bodies :i* mu/ take ! lead 9 guid+ t educational recon/ruction :i* by a sociological law foll[s e social revolution4 ,we d n want impracticable ideals1 only to be realis$ beyond ! cl\ds 9 ,"s wild1 weird clime1 ,out ( ,space1 & out ( ,"t4 ,we require to "k :at is possible n[ 9 ,engl&1 a nation consci\s ( its high a*ievem5ts1 & ( great failures1 %ak5 to its f\ndations1 di/ru/ful ( ! old ways1 & dread+ fanta/ic novelties4 ,i w take my c\rage 9 bo? h&s1 & put be=e y an outl9e ( educational pr9ciples4 ,:at ,i am go+ to say is ( c\rse entirely )\t y\r au?ority1 & does n pl$ge or prejudge any action ( ! ,association4 ,we are prim>ily conc]n$ only ) ! intellectual side ( education1 &1 z ma!maticians1 are naturally conc]n$ to illu/rate details m p>ticul>ly by ref]5ce to ma!matics4 ,?us mu* to expla9 delib]ate omissions 9 :at foll[s4 ,consid] n[ ! g5]al & special education ( two types ( boys1 namely ^? 9 second>y s*ools :o 9 aft] life mu/ =m ! pr(essional & direct+ classes 9 comm]ce1 indu/ry1 & public adm9i/ration1 & aga9 ^? 9 junior te*nical s*ools & lat] 9 advanc$ cont9uation classes1 :o are go+ to =m ! class ( skill$ artisans & =em5 ( work%ops4 ,^! two sets compose ! educat$ /r5g? ( ! nation4 ,we mu/ =m no ideals :i* include less ?an ^! entire classes )9 _! scope4 ,:at ,i %all say1 w 9 phraseology apply m directly to ! second>y s*ools1 b ) uness5tial *anges x w apply equally to ! o!r gr\p4 ,:at is ! fir/ comm&m5t to be obey$ 9 any educational s*eme8 ,x is ?is3 ,d n tea* too _m subjects4 ,! second comm& is ?is3 ,:at y tea*1 tea* ?or\ghly4 ,! devil 9 ! s*ola/ic _w has assum$ ! =m ( a g5]al education consi/+ ( scraps ( a l>ge numb] ( disconnect$ subjects2 &1 ) ! artfulness ( ! s]p5t1 he has entr5*$ himself beh9d ! matriculation exam9ation ( ! ,univ]sity ( ,london1 ) a wire entanglem5t =m$ by ! ,ox=d & ,cambridge s*ools' exam9ation4 ,culture is activity ( ?\ght1 & receptiv5ess to beauty1 & humane feel+4 ,scraps ( in=mation h no?+ to d ) x4 ,a m]ely well-in=m$ man is ! mo/ useless bore on ,god's e>?4 ,:at we %\ld aim at produc+ is m5 :o possess bo? culture & exp]t k 9 "s special direction4 ,_! exp]t k w give !m ! gr\nd to />t f1 & _! culture w lead !m z deep z philosophy & z high z art4 ,we h to rememb] t ! valuable intellectual developm5t is self-developm5t1 & t x mo/ly takes place betwe5 ! ages ( sixte5 & ?irty4 ,z to tra9+1 ! mo/ important "p is giv5 by mo!rs be=e ! age ( twelve4 ,a say+ due to ,ar*bi%op ,temple illu/rates my mean+4 ,surprise 0 express$ at ! success 9 aft]-life ( a man1 :o z a boy at ,rugby _h be5 some:at undi/+ui%$4 ,he answ]$1 ,x is n :at !y are at eighte51 x is :at !y become aft]w>ds t matt]s4 ,9 tra9+ a *ild to activity ( ?\ght1 above all ?+s we mu/ bew>e ( :at ,i w call in]t ideas--t is to say1 ideas t are m]ely receiv$ into ! m9d )\t be+ utilis$1 or te/$1 or ?r[n into fre% comb9ations4 ,9 ! hi/ory ( education1 ! mo/ /rik+ ph5om5on is t s*ools ( le>n+1 :i* at "o epo* are alive ) a f]m5t ( g5ius1 9 a succe$+ g5]ation exhibit m]ely p$antry & r\t9e4 ,! reason is1 t !y are ov]lad5 ) in]t ideas4 ,education ) in]t ideas is n only useless3 x is1 above all ?+s1 h>mful--,corruptio optimi1 pessima4 ,except at r>e int]vals ( intellectual f]m5t1 education 9 ! pa/ has be5 radically infect$ ) in]t ideas4 ,t is ! reason :y un$ucat$ clev] wom51 :o h se5 mu* ( ! _w1 are 9 middle life s mu* ! mo/ cultur$ "p ( ! community4 ,!y h be5 sav$ f ?is horrible burd5 ( in]t ideas4 ,e intellectual revolution :i* has ev] /irr$ humanity into greatness has be5 a passionate prote/ aga9/ in]t ideas4 ,!n1 alas1 ) pa!tic ignorance ( human psy*ology1 x has proce$$ by "s educational s*eme to b9d humanity afre% ) in]t ideas ( its own fa%ion+4 ,let u n[ ask h[ 9 our sy/em ( education we are to gu>d aga9/ ?is m5tal dry rot4 ,we recur to our two educational comm&m5ts1 ,d n tea* too _m subjects1 & aga91 ,:at y tea*1 tea* ?or\ghly4 ,! result ( tea*+ small p>ts ( a l>ge numb] ( subjects is ! passive reception ( disconnect$ ideas1 n illum9$ ) any sp>k ( vitality4 ,let ! ma9 ideas :i* are introduc$ into a *ild's education be few & important1 & let !m be ?r[n into e comb9ation possible4 ,! *ild %\ld make !m 8 own1 & %\ld und]/& _! application "h & n[ 9 ! circum/ances ( 8 actual life4 ,f ! v beg9n+ ( 8 education1 ! *ild %\ld exp]i5ce ! joy ( discov]y4 ,! discov]y :i* he has to make1 is t g5]al ideas give an und]/&+ ( t /ream ( ev5ts :i* p\rs ?r\gh 8 life1 :i* is 8 life4 ,by und]/&+ ,i mean m ?an a m]e logical analysis1 ?\gh t is includ$4 ,i mean und]/&+ 9 ! s5se 9 :i* x is us$ 9 ! ,fr5* prov]b1 ,to und]/& all1 is to =give all4 ,p$ants sne] at an education :i* is useful4 ,b if education is n useful1 :at is x8 ,is x a tal5t1 to be hidd5 away 9 a napk98 ,( c\rse1 education %\ld be useful1 :atev] y\r aim 9 life4 ,x 0 useful to ,sa9t ,augu/9e & x 0 useful to ,napoleon4 ,x is useful1 because und]/&+ is useful4 ,i pass lightly ov] t und]/&+ :i* %\ld be giv5 by ! lit]>y side ( education4 ,x is n peculi>ly ! function ( ?is ,association to consid] x4 ,nor d ,i wi% to be suppos$ to pron\nce on ! relative m]its ( a classical or a mod]n curriculum4 ,i w\ld only rem>k t ! und]/&+ :i* we want is an und]/&+ ( an insi/5t pres5t4 ,! only use ( a k ( ! pa/ is to equip u = ! pres5t4 ,no m deadly h>m c be done to "y m9ds ?an by depreciation ( ! pres5t4 ,! pres5t conta9s all t !re is4 ,x is holy gr\nd2 = x is ! pa/1 & x is ! future4 ,at ! same "t x mu/ be obs]v$ t an age is no less pa/ if x exi/$ two hundr$ ye>s ago ?an if x exi/$ two ?\s& ye>s ago4 ,d n be deceiv$ by ! p$antry ( dates4 ,! ages ( ,%akespe>e & ( ,molire are no less pa/ ?an are ! ages ( ,sophocles & ( ,virgil4 ,! communion ( sa9ts is a great & inspir+ assemblage1 b x has only "o possible hall ( meet+1 & t is1 ! pres5t2 & ! m]e lapse ( "t ?r\gh :i* any p>ticul> gr\p ( sa9ts mu/ travel to rea* t meet+-place1 makes v little diff]5ce4 ,pass+ n[ to ! sci5tific & logical side ( education1 we rememb] t "h also ideas :i* are n utilis$ are positively h>mful4 ,by utilis+ an idea1 ,i mean relat+ x to t /ream1 comp\nd$ ( s5se p]ceptions1 feel+s1 hopes1 desires1 & ( m5tal activities relat+ ?\ght to ?\ght1 :i* =ms our life4 ,i c imag9e a set ( be+s :i* might =tify _! s\ls by passively review+ disconnect$ ideas4 ,humanity is n built t way--except p]haps "s editors ( newspap]s4 ,9 sci5tific tra9+1 ! fir/ ?+ to d ) an idea is to prove x4 ,b all[ me = "o mom5t to ext5d ! mean+ ( prove2 ,i mean--to prove its wor?4 ,n[ an idea is n wor? mu* unless ! propositions 9 :i* x is embodi$ are true4 ,accord+ly an ess5tial "p ( ! pro( ( an idea is ! pro(1 ei!r by exp]im5t or by logic1 ( ! tru? ( ! propositions4 ,b x is n ess5tial t ?is pro( ( ! tru? %\ld con/itute ! fir/ introduction to ! idea4 ,aft] all1 its ass]tion by ! au?ority ( respectable tea*]s is suffici5t evid5ce to beg9 )4 ,9 our fir/ contact ) a set ( propositions1 we comm5ce by appreciat+ _! importance4 ,t is :at we all d 9 aft]-life4 ,we d n attempt1 9 ! /rict s5se1 to prove or to disprove any?+1 unless its importance makes x wor?y ( t hon\r4 ,^! two processes ( pro(1 9 ! n>r[ s5se1 & ( appreciation d n require a rigid sep>ation 9 "t4 ,bo? c be proce$$ ) ne>ly concurr5tly4 ,b 9 s f> z ei!r process mu/ h ! priority1 x %\ld be t ( appreciation by use4 ,fur!rmore1 we %\ld n endeav\r to use propositions 9 isolation4 ,emphatically ,i d n mean1 a neat little set ( exp]im5ts to illu/rate ,proposition ,i & !n ! pro( ( ,proposition ,i1 a neat little set ( exp]im5ts to illu/rate ,proposition ,,ii & !n ! pro( ( ,proposition ,,ii1 & s on to ! end ( ! book4 ,no?+ c\ld be m bor+4 ,int]-relat$ tru?s are utilis$ en bloc1 & ! v>i\s propositions are employ$ 9 any ord]1 & ) any reit]ation4 ,*oose "s important applications ( y\r !oretical subject2 & /udy !m concurr5tly ) ! sy/ematic !oretical exposition4 ,keep ! !oretical exposition %ort & simple1 b let x be /rict & rigid s f> z x goes4 ,x %\ld n be too long = x easily to be kn[n ) ?or\ghness & accuracy4 ,! consequ5ces ( a ple?ora ( half-dige/$ !oretical k are deplorable4 ,also ! !ory %\ld n be muddl$ up ) ! practice4 ,! *ild %\ld h no d\bt :5 x is prov+ & :5 x is utilis+4 ,my po9t is t :at is prov$ %\ld be utilis$1 & t :at is utilis$ %\ld--s f> z is practicable--be prov$4 ,i am f> f ass]t+ t pro( & utilisation are ! same ?+4 ,at ?is po9t ( my disc\rse1 ,i c mo/ directly c>ry =w>d my argum5t 9 ! outw>d =m ( a digression4 ,we are only j realis+ t ! art & sci5ce ( education require a g5ius & a /udy ( _! own2 & t ?is g5ius & ?is sci5ce are m ?an a b>e k ( "s bran* ( sci5ce or ( lit]ature4 ,?is tru? 0 p>tially p]ceiv$ 9 ! pa/ g5]ation2 & headma/]s1 some:at crudely1 7 apt to sup]s$e le>n+ 9 _! colleagues by requir+ left-h& b[l+ & a ta/e = football4 ,b culture is m ?an cricket1 & m ?an football1 & m ?an ext5t ( k4 ,education is ! acquisition ( ! art ( ! utilisation ( k4 ,?is is an art v difficult to imp>t4 ,:5ev] a text-book is writt5 ( real educational wor?1 y may be q c]ta9 t "s review] w say t x w be difficult to tea* f x4 ,( c\rse x w be difficult to tea* f x4 ,if x 7 easy1 ! book ought to be burn$2 = x _c be educational4 ,9 education1 z else:]e1 ! broad primrose pa? leads to a na/y place4 ,?is evil pa? is repres5t$ by a book or a set ( lectures :i* w practically enable ! /ud5t to le>n by he>t all ! que/ions likely to be ask$ at ! next ext]nal exam9ation4 ,& ,i may say 9 pass+ t no educational sy/em is possible unless e "q directly ask$ ( a pupil at any exam9ation is ei!r fram$ or modifi$ by ! actual tea*] ( t pupil 9 t subject4 ,! ext]nal assessor may report on ! curriculum or on ! p]=mance ( ! pupils1 b nev] %\ld be all[$ to ask ! pupil a "q :i* has n be5 /rictly sup]vis$ by ! actual tea*]1 or at lea/ inspir$ by a long conf]5ce ) him4 ,!re are a few exceptions to ?is rule1 b !y are exceptions1 & c\ld easily be all[$ = "u ! g5]al rule4 ,we n[ return to my previ\s po9t1 t !oretical ideas %\ld always f9d important applications )9 ! pupil's curriculum4 ,?is is n an easy doctr9e to apply1 b a v h>d "o4 ,x conta9s )9 itself ! problem ( keep+ k alive1 ( prev5t+ x f becom+ in]t1 :i* is ! c5tral problem ( all education4 ,! be/ proc$ure w dep5d on sev]al factors1 none ( :i* c be neglect$1 namely1 ! g5ius ( ! tea*]1 ! intellectual type ( ! pupils1 _! prospects 9 life1 ! opportunities (f]$ by ! imm$iate surr\nd+s ( ! s*ool1 & alli$ factors ( ?is sort4 ,x is = ?is reason t ! uni=m ext]nal exam9ation is s deadly4 ,we d n d5\nce x because we are cranks1 & l d5\nc+ e/abli%$ ?+s4 ,we are n s *ildi%4 ,also1 ( c\rse1 su* exam9ations h _! use 9 te/+ slackness4 ,our reason ( dislike is v def9ite & v practical4 ,x kills ! be/ "p ( culture4 ,:5 y analyse 9 ! light ( exp]i5ce ! c5tral task ( education1 y f9d t its successful accompli%m5t dep5ds on a delicate adju/m5t ( _m v>iable factors4 ,! reason is t we are deal+ ) human m9ds1 & n ) dead matt]4 ,! evocation ( curiosity1 ( judgm5t1 ( ! p[] ( ma/]+ a complicat$ tangle ( circum/ances1 ! use ( !ory 9 giv+ =esight 9 special cases--all ^! p[]s are n to be imp>t$ by a set rule embodi$ 9 "o s*$ule ( exam9ation subjects4 ,i appeal to y1 z practical tea*]s4 ,) good discipl9e1 x is always possible to pump into ! m9ds ( a class a c]ta9 quantity ( in]t k4 ,y take a text-book & make !m le>n x4 ,s f>1 s good4 ,! *ild !n kn[s h[ to solve a quadratic equation4 ,b :at is ! po9t ( tea*+ a *ild to solve a quadratic equation8 ,!re is a traditional answ] to ?is "q4 ,x runs ?us3 ,! m9d is an in/rum5t1 y fir/ %>p5 x1 & !n use x2 ! acquisition ( ! p[] ( solv+ a quadratic equation is "p ( ! process ( %>p5+ ! m9d4 ,n[ !re is j en\gh tru? 9 ?is answ] to h made x live ?r\gh ! ages4 ,b = all its half-tru?1 x embodies a radical error :i* bids fair to /ifle ! g5ius ( ! mod]n _w4 ,i d n "k :o 0 fir/ responsible = ?is analogy ( ! m9d to a dead in/rum5t4 ,= aught ,i "k1 x may h be5 "o ( ! sev5 wise m5 ( ,greece1 or a committee ( ! :ole lot ( !m4 ,:oev] 0 ! orig9ator1 !re c be no d\bt ( ! au?ority :i* x has acquir$ by ! cont9u\s approval :i* x has receiv$ f em95t p]sons4 ,b :atev] its weight ( au?ority1 :atev] ! high approval :i* x c quote1 ,i h no hesitation 9 d5\nc+ x z "o ( ! mo/ fatal1 errone\s1 & dang]\s conceptions ev] introduc$ into ! !ory ( education4 ,! m9d is nev] passive2 x is a p]petual activity1 delicate1 receptive1 responsive to /imulus4 ,y _c po/pone its life until y h %>p5$ x4 ,:atev] int]e/ atta*es to y\r subject-matt]1 mu/ be evok$ "h & n[2 :atev] p[]s y are /r5g!n+ 9 ! pupil1 mu/ be ex]cis$ "h & n[2 :atev] possibilities ( m5tal life y\r tea*+ %\ld imp>t1 mu/ be exhibit$ "h & n[4 ,t is ! gold5 rule ( education1 & a v difficult rule to foll[4 ,! difficulty is j ?is3 ! appreh5sion ( g5]al ideas1 intellectual habits ( m9d1 & pleasurable int]e/ 9 m5tal a*ievem5t c be evok$ by no =m ( words1 h[ev] accurately adju/$4 ,all practical tea*]s "k t education is a pati5t process ( ! ma/]y ( details1 m9ute by m9ute1 h\r by h\r1 day by day4 ,!re is no royal road to le>n+ ?r\gh an airy pa? ( brilliant g5]alisations4 ,!re is a prov]b ab\t ! difficulty ( see+ ! wood because ( ! trees4 ,t difficulty is exactly ! po9t :i* ,i am en=c+4 ,! problem ( education is to make ! pupil see ! wood by means ( ! trees4 ,! solution :i* ,i am urg+1 is to eradicate ! fatal disconnection ( subjects :i* kills ! vitality ( our mod]n curriculum4 ,!re is only "o subject-matt] = education1 & t is ,life 9 all its manife/ations4 ,in/ead ( ?is s+le unity1 we (f] *ildr5--,algebra1 f :i* no?+ foll[s2 ,geometry1 f :i* no?+ foll[s2 ,sci5ce1 f :i* no?+ foll[s2 ,hi/ory1 f :i* no?+ foll[s2 a ,c\ple ( ,languages1 nev] ma/]$2 & la/ly1 mo/ dre>y ( all1 ,lit]ature1 repres5t$ by plays ( ,%akespe>e1 ) philological notes & %ort analyses ( plot & "* to be 9 sub/ance committ$ to memory4 ,c su* a li/ be said to repres5t ,life1 z x is kn[n 9 ! mid/ ( ! liv+ ( x8 ,! be/ t c be said ( x is1 t x is a rapid table ( cont5ts :i* a deity might run ov] 9 8 m9d :ile he 0 ?9k+ ( creat+ a _w1 & _h n yet det]m9$ h[ to put x toge!r4 ,let u n[ return to quadratic equations4 ,we /ill h on h& ! unansw]$ "q4 ,:y %\ld *ildr5 be taught _! solution8 ,unless quadratic equations fit into a connect$ curriculum1 ( c\rse !re is no reason to tea* any?+ ab\t !m4 ,fur!rmore1 ext5sive z %\ld be ! place ( ma!matics 9 a complete culture1 ,i am a little d\btful :e!r = _m types ( boys algebraic solutions ( quadratic equations d n lie on ! speciali/ side ( ma!matics4 ,i may "h rem9d y t z yet ,i h n said any?+ ( ! psy*ology or ! cont5t ( ! specialism1 :i* is s necess>y a "p ( an ideal education4 ,b all t is an evasion ( our real "q1 & ,i m]ely /ate x 9 ord] to avoid be+ misund]/ood 9 my answ]4 ,quadratic equations are "p ( algebra1 & algebra is ! intellectual in/rum5t :i* has be5 creat$ = r5d]+ cle> ! quantitative aspects ( ! _w4 ,!re is no gett+ out ( x4 ,?r\gh & ?r\gh ! _w is infect$ ) quantity4 ,to talk s5se1 is to talk 9 quantities4 ,x is no use say+ t ! nation is l>ge1--,h[ l>ge8 ,x is no use say+ t radium is sc>ce1--,h[ sc>ce8 ,y _c evade quantity4 ,y may fly to poetry & to music1 & quantity & numb] w face y 9 y\r rhy?ms & y\r octaves4 ,elegant intellects :i* despise ! !ory ( quantity1 are b half develop$4 ,!y are m to be piti$ ?an blam$4 ,! scraps ( gibb]i%1 :i* 9 _! s*ool-days 7 taught to !m 9 ! "n ( algebra1 des]ve "s contempt4 ,?is "q ( ! deg5]ation ( algebra into gibb]i%1 bo? 9 ^w & 9 fact1 af=ds a pa!tic in/ance ( ! uselessness ( re=m+ educational s*$ules )\t a cle> conception ( ! attributes :i* y wi% to evoke 9 ! liv+ m9ds ( ! *ildr54 ,a few ye>s ago !re 0 an outcry t s*ool algebra 0 9 ne$ ( re=m1 b !re 0 a g5]al agreem5t t graphs w\ld put ev]y?+ "r4 ,s all sorts ( ?+s 7 extrud$1 & graphs 7 introduc$4 ,s f> z ,i c see1 ) no sort ( idea beh9d !m1 b j graphs4 ,n[ e exam9ation pap] has "o or two que/ions on graphs4 ,p]sonally1 ,i am an en?usia/ic adh]5t ( graphs4 ,b ,i wond] :e!r z yet we h ga9$ v mu*4 ,y _c put life into any s*$ule ( g5]al education unless y succe$ 9 exhibit+ its relation to "s ess5tial *>act]i/ic ( all intellig5t or emotional p]ception4 ,x is a h>d say+1 b x is true2 & ,i d n see h[ to make x any easi]4 ,9 mak+ ^! little =mal alt]ations y are beat5 by ! v nature ( ?+s4 ,y are pitt$ aga9/ too skilful an adv]s>y1 :o w see to x t ! pea is always "u ! o!r ?imble4 ,re=mation mu/ beg9 at ! o!r end4 ,fir/1 y mu/ make up y\r m9d z to ^? quantitative aspects ( ! _w :i* are simple en\gh to be introduc$ into g5]al education2 !n a s*$ule ( algebra %\ld be fram$ :i* w ab\t f9d its exemplification 9 ^! applications4 ,we ne$ n fe> = our pet graphs1 !y w be !re 9 pl5ty :5 we once beg9 to treat algebra z a s]i\s means ( /udy+ ! _w4 ,"s ( ! simple/ applications w be f\nd 9 ! quantities :i* occur 9 ! simple/ /udy ( society4 ,! curves ( hi/ory are m vivid & m in=m+ ?an ! dry catalogues ( names & dates :i* comprise ! great] "p ( t arid s*ool /udy4 ,:at purpose is effect$ by a catalogue ( undi/+ui%$ k+s & que5s8 ,tom1 ,dick1 or ,h>ry1 !y are all dead4 ,g5]al resurrections are failures1 & are bett] po/pon$4 ,! quantitative flux ( ! =ces ( mod]n society are capable ( v simple exhibition4 ,mean:ile1 ! idea ( ! v>iable1 ( ! function1 ( rate ( *ange1 ( equations & _! solution1 ( elim9ation1 are be+ /udi$ z an ab/ract sci5ce = _! own sake4 ,n1 ( c\rse1 9 ! pomp\s phrases ) :i* ,i am allud+ to !m "h1 b ) t it]ation ( simple special cases prop] to tea*+4 ,if ?is c\rse be foll[$1 ! r\te f ,*auc] to ! ,black ,dea?1 f ! ,black ,dea? to mod]n ,lab\r tr\bles1 w connect ! tales ( ! m$ival pilgrims ) ! ab/ract sci5ce ( algebra1 bo? yield+ div]se aspects ( t s+le !me1 ,life4 ,i "k :at mo/ ( y are ?9k+ at ?is po9t4 ,x is t ! exact c\rse :i* ,i h sket*$ out is n ! p>ticul> "o :i* y w\ld h *os51 or ev5 see h[ to "w4 ,i q agree4 ,i am n claim+ t ,i c\ld d x myself4 ,b y\r objection is ! precise reason :y a common ext]nal exam9ation sy/em is fatal to education4 ,! process ( exhibit+ ! applications ( k mu/1 = its success1 ess5tially dep5d on ! "* ( ! pupils & ! g5ius ( ! tea*]4 ,( c\rse ,i h left out ! easie/ applications ) :i* mo/ ( u are m at home4 ,i mean ! quantitative sides ( sci5ces1 su* z me*anics & physics4 ,my mean+ c be illu/rat$ by look+ m closely into a special case ( ?is type ( application4 ,9 my r\gh catalogue ( ! sort ( subjects :i* %\ld =m ! s*$ule = algebra1 ,i m5tion$ ,elim9ation4 ,x 0 n put !re by accid5t1 = x cov]s a v important body ( ?\ght4 ,9 ! fir/ place1 !re is ! ab/ract process ( algebraic elim9ation = suitable simple cases4 ,! pupil acquires a firm grasp ( ?is by ! process1 inevitable 9 education1 ( work+ an adequate numb] ( examples4 ,aga91 !re are ! graphical solutions ( ! same problem4 ,!n we consid] ! significance 9 ! ext]nal _w4 ,we consid] ! velocity1 "t1 space1 accel]ation diagrams4 ,we take uni=m accel]ation2 we elim9ate t betwe5 v u t1 & s ut t#b1 & elim9ate s betwe5 v#b u#b #bs1 & s ut t#b4 ,!n we rememb] t con/ant accel]ation is a v special case1 & we consid] graphical solutions or empirically giv5 v>iations ( v or ( 4 ,9 pref]5ce1 we use ^? empirical =mul :i* occur 9 ! pupil's exp]im5tal "w4 ,we comp>e ! /rong & weak po9ts ( ! algebraic & graphical solutions4 ,aga91 9 ! same connection we plot ! /ati/ics ( social ph5om5a aga9/ ! "t4 ,we !n elim9ate ! "t betwe5 suitable pairs4 ,we c speculate h[ f> we h exhibit$ a real casual connection1 or h[ f> a m]e temporal co9cid5ce4 ,we notice t we might h plott$ aga9/ ! "t "o set ( /ati/ics = "o c\ntry & ano!r set = ano!r c\ntry1 & ?us1 ) suitable *oice ( subjects1 h obta9$ graphs :i* c]ta9ly exhibit$ m]e co9cid5ce4 ,also o!r graphs exhibit obvi\s casual connections4 ,we wond] h[ to discrim9ate4 ,& s are drawn on z f> z we w4 ,b 9 consid]+ ?is description1 ,i mu/ beg y to rememb] :at ,i h be5 insi/+ on above4 ,9 ! fir/ place1 "o tra9 ( ?\ght w n suit all gr\ps ( *ildr54 ,= example1 ,i %\ld expect t artisan *ildr5 w want some?+ m concrete &1 9 a s5se1 swift] ?an ,i h set d[n "h4 ,p]haps ,i am wrong1 b t is :at ,i %\ld guess4 ,9 ! second place1 ,i am n contemplat+ "o beautiful lecture /imulat+1 once & = all1 an admir+ class4 ,t is n ! way 9 :i* education proce$s4 ,no2 all ! "t ! pupils are h>d at "w solv+ examples1 draw+ graphs1 & mak+ exp]im5ts1 until !y h a ?or\gh hold on ! :ole subject4 ,i am describ+ ! int]sp]s$ explanations1 ! directions :i* %\ld be giv5 to _! ?\ghts4 ,! pupils h got to be made to feel t !y are /udy+ some?+1 & are n m]ely execut+ intellectual m9uets4 ,9 ?is connection ! excell5ce ( "s ( ! mo/ rec5t text-books on elem5t>y algebra emanat+ f memb]s ( ?is ,association1 %\ld create an epo* 9 ! tea*+ ( ! subject4 ,f9ally1 if y are tea*+ pupils = "s g5]al exam9ation1 ! problem ( s\nd tea*+ is greatly complicat$4 ,h y ev] notic$ ! zig-zag m\ld+ r\nd a ,norman ar*8 ,! anci5t "w is beautiful1 ! mod]n "w is hide\s4 ,! reason is1 t ! mod]n "w is done to exact measure1 ! anci5t "w is v>i$ accord+ to ! idiosyncrasy ( ! workman4 ,"h x is cr[d$1 & !re x is exp&$4 ,n[ ! ess5ce ( gett+ pupils ?r\gh exam9ations is to give equal weight to all p>ts ( ! s*$ule4 ,b mank9d is naturally speciali/4 ,"o man sees a :ole subject1 :]e ano!r c f9d only a few deta*$ examples4 ,i "k t x seems contradictory to all[ = specialism 9 a curriculum especially design$ = a broad culture4 ,)\t contradictions ! _w w\ld be simpl]1 & p]haps dull]4 ,b ,i am c]ta9 t 9 education :]ev] y exclude specialism y de/roy life4 ,we n[ come to ! o!r great bran* ( a g5]al ma!matical education1 namely ,geometry4 ,! same pr9ciples apply4 ,! !oretical "p %\ld be cle>-cut1 rigid1 %ort1 & important4 ,e proposition n absolutely necess>y to exhibit ! ma9 connection ( ideas %\ld be cut out1 b ! great fundam5tal ideas %\ld be all !re4 ,no omission ( concepts1 su* z ^? ( ,simil>ity & ,proportion4 ,we mu/ rememb] t1 ow+ to ! aid r5d]$ by ! visual pres5ce ( a figure1 ,geometry is a field ( unequall$ excell5ce = ! ex]cise ( ! d$uctive faculties ( reason+4 ,!n1 ( c\rse1 !re foll[s ,geometrical ,draw+1 ) its tra9+ = ! h& & eye4 ,b1 l ,algebra1 ,geometry & ,geometrical ,draw+ mu/ be ext5d$ beyond ! m]e circle ( geometrical ideas4 ,9 an indu/rial neighb\rhood1 ma*9]y & work%op practice =m ! appropriate ext5sion4 ,= example1 9 ! ,london ,polyte*nics ?is has be5 a*iev$ ) conspicu\s success4 ,= _m second>y s*ools ,i sugge/ t survey+ & maps are ! natural applications4 ,9 p>ticul>1 plane-table survey+ %\ld lead pupils to a vivid appreh5sion ( ! imm$iate application ( geometric tru?s4 ,simple draw+ app>atus1 a surveyor's *a91 & a surveyor's compass1 %\ld enable ! pupils to rise f ! survey & m5suration ( a field to ! con/ruction ( ! map ( a small di/rict4 ,! be/ education is to be f\nd 9 ga9+ ! utmo/ in=mation f ! simple/ app>atus4 ,! provision ( elaborate in/rum5ts is greatly to be deprecat$4 ,to h con/ruct$ ! map ( a small di/rict1 to h consid]$ its roads1 its cont\rs1 its geology1 its climate1 its relation to o!r di/ricts1 ! effects on ! /atus ( its inhabitants1 w tea* m hi/ory & geography ?an any k ( ,p]k9 ,w>beck or ( ,behr5's ,/raits4 ,i mean n a nebul\s lecture on ! subject1 b a s]i\s inve/igation 9 :i* ! real facts are def9itely asc]ta9$ by ! aid ( accurate !oretical k4 ,a typical ma!matical problem %\ld be3 ,survey su* & su* a field1 draw a plan ( x to su* & su* a scale1 & f9d ! area4 ,x w\ld be q a good proc$ure to imp>t ! necess>y geometrical propositions )\t _! pro(s4 ,!n1 concurr5tly 9 ! same t]m1 ! pro(s ( ! propositions w\ld be le>nt :ile ! survey 0 be+ made4 ,=tunately1 ! speciali/ side ( education pres5ts an easi] problem ?an does ! provision ( a g5]al culture4 ,= ?is !re are _m reasons4 ,"o is t _m ( ! pr9ciples ( proc$ure to be obs]v$ are ! same 9 bo? cases1 & x is unnecess>y to recapitulate4 ,ano!r reason is t speciali/ tra9+ takes place--or %\ld take place--at a m advanc$ /age ( ! pupil's c\rse1 & ?us !re is easi] mat]ial to "w ^u4 ,b und\bt$ly ! *ief reason is t ! speciali/ /udy is normally a /udy ( peculi> int]e/ to ! /ud5t4 ,he is /udy+ x because1 = "s reason1 he wants to "k x4 ,?is makes all ! diff]5ce4 ,! g5]al culture is design$ to fo/] an activity ( m9d2 ! speciali/ c\rse utilises ?is activity4 ,b x does n d to lay too mu* /ress on ^! neat anti!ses4 ,z we h already se51 9 ! g5]al c\rse foci ( special int]e/ w arise2 & simil>ly 9 ! special /udy1 ! ext]nal connections ( ! subject drag ?\ght outw>ds4 ,aga91 !re is n "o c\rse ( /udy :i* m]ely gives g5]al culture1 & ano!r :i* gives special k4 ,! subjects pursu$ = ! sake ( a g5]al education are special subjects specially /udi$2 &1 on ! o!r h&1 "o ( ! ways ( enc\rag+ g5]al m5tal activity is to fo/] a special devotion4 ,y may n divide ! seamless coat ( le>n+4 ,:at education has to imp>t is an intimate s5se = ! p[] ( ideas1 = ! beauty ( ideas1 & = ! /ructure ( ideas1 toge!r ) a p>ticul> body ( k :i* has peculi> ref]5ce to ! life ( ! be+ possess+ x4 ,! appreciation ( ! /ructure ( ideas is t side ( a cultur$ m9d :i* c only gr[ "u ! influ5ce ( a special /udy4 ,i mean t eye = ! :ole *ess-bo>d1 = ! be>+ ( "o set ( ideas on ano!r4 ,no?+ b a special /udy c give any appreciation = ! exact =mulation ( g5]al ideas1 = _! relations :5 =mulat$1 = _! s]vice 9 ! compreh5sion ( life4 ,a m9d s discipl9$ %\ld be bo? m ab/ract & m concrete4 ,x has be5 tra9$ 9 ! compreh5sion ( ab/ract ?\ght & 9 ! analysis ( facts4 ,f9ally1 !re %\ld gr[ ! mo/ au/]e ( all m5tal qualities2 ,i mean ! s5se = /yle4 ,x is an /hetic s5se1 bas$ on admiration = ! direct atta9m5t ( a =ese5 end1 simply & )\t wa/e4 ,/yle 9 art1 /yle 9 lit]ature1 /yle 9 sci5ce1 /yle 9 logic1 /yle 9 practical execution h fundam5tally ! same /hetic qualities1 namely1 atta9m5t & re/ra9t4 ,! love ( a subject 9 itself & = itself1 :]e x is n ! sleepy pleasure ( pac+ a m5tal qu>t]-deck1 is ! love ( /yle z manife/$ 9 t /udy4 ,"h we are br\ght back to ! position f :i* we />t$1 ! utility ( education4 ,/yle1 9 its f9e/ s5se1 is ! la/ acquirem5t ( ! educat$ m9d2 x is also ! mo/ useful4 ,x p]vades ! :ole be+4 ,! adm9i/rator ) a s5se = /yle1 hates wa/e2 ! eng9e] ) a s5se = /yle1 economises 8 mat]ial2 ! artisan ) a s5se = /yle1 pref]s good "w4 ,/yle is ! ultimate morality ( m9d4 ,b above /yle1 & above k1 !re is some?+1 a vague %ape l fate above ! ,greek gods4 ,t some?+ is ,p[]4 ,/yle is ! fa%ion+ ( p[]1 ! re/ra9+ ( p[]4 ,b1 aft] all1 ! p[] ( atta9m5t ( ! desir$ end is fundam5tal4 ,! fir/ ?+ is to get !re4 ,d n bo!r ab\t y\r /yle1 b solve y\r problem1 ju/ify ! ways ( ,god to man1 adm9i/] y\r prov9ce1 or d :atev] else is set be=e y4 ,:]e1 !n1 does /yle help8 ,9 ?is1 ) /yle ! end is atta9$ )\t side issues1 )\t rais+ undesirable inflammations4 ,) /yle y atta9 y\r end & no?+ b y\r end4 ,) /yle ! effect ( y\r activity is calculable1 & =esight is ! la/ gift ( gods to m54 ,) /yle y\r p[] is increas$1 = y\r m9d is n di/ract$ ) irrelevancies1 & y are m likely to atta9 y\r object4 ,n[ /yle is ! exclusive privilege ( ! exp]t4 ,:oev] he>d ( ! /yle ( an amateur pa9t]1 ( ! /yle ( an amateur poet8 ,/yle is always ! product ( speciali/ /udy1 ! peculi> contribution ( specialism to culture4 ,engli% education 9 its pres5t phase suff]s f a lack ( def9ite aim1 & f an ext]nal ma*9]y :i* kills its vitality4 ,hi!rto 9 ?is address ,i h be5 consid]+ ! aims :i* %\ld gov]n education4 ,9 ?is respect ,engl& halts betwe5 two op9ions4 ,x has n decid$ :e!r to produce amateurs or exp]ts4 ,! pr(\nd *ange 9 ! _w :i* ! n9ete5? c5tury has produc$ is t ! gr[? ( k has giv5 =esight4 ,! amateur is ess5tially a man ) appreciation & ) imm5se v]satility 9 ma/]+ a giv5 r\t9e4 ,b he lacks ! =esight :i* comes f special k4 ,! object ( ?is address is to sugge/ h[ to produce ! exp]t )\t loss ( ! ess5tial virtues ( ! amateur4 ,! ma*9]y ( our second>y education is rigid :]e x %\ld be yield+1 & lax :]e x %\ld be rigid4 ,e s*ool is b\nd on pa9 ( ext9ction to tra9 its boys = a small set ( def9ite exam9ations4 ,no headma/] has a free h& to develop 8 g5]al education or 8 speciali/ /udies 9 accordance ) ! opportunities ( 8 s*ool1 :i* are creat$ by its /aff1 its environm5t1 its class ( boys1 & its end[m5ts4 ,i sugge/ t no sy/em ( ext]nal te/s :i* aims prim>ily at exam9+ individual s*ol>s c result 9 any?+ b educational wa/e4 ,prim>ily x is ! s*ools & n ! s*ol>s :i* %\ld be inspect$4 ,ea* s*ool %\ld grant its own leav+ c]tificates1 bas$ on its own curriculum4 ,! /&>ds ( ^! s*ools %\ld be sampl$ & correct$4 ,b ! fir/ requisite = educational re=m is ! s*ool z a unit1 ) its approv$ curriculum bas$ on its own ne$s1 & evolv$ by its own /aff4 ,if we fail to secure t1 we simply fall f "o =malism into ano!r1 f "o dung-hill ( in]t ideas into ano!r4 ,9 /at+ t ! s*ool is ! true educational unit 9 any national sy/em = ! safe-gu>d+ ( effici5cy1 ,i h conceiv$ ! alt]native sy/em z be+ ! ext]nal exam9ation ( ! individual s*ol>4 ,b e ,scylla is fac$ by its ,*>ybdis--or1 9 m homely language1 !re is a dit* on bo? sides ( ! road4 ,x w be equally fatal to education if we fall into ! h&s ( a sup]vis+ dep>tm5t :i* is "u ! impression t x c divide all s*ools into two or ?ree rigid categories1 ea* type be+ =c$ to adopt a rigid curriculum4 ,:5 ,i say t ! s*ool is ! educational unit1 ,i mean exactly :at ,i say1 no l>g] unit1 no small] unit4 ,ea* s*ool mu/ h ! claim to be consid]$ 9 relation to its special circum/ances4 ,! classify+ ( s*ools = "s purposes is necess>y4 ,b no absolutely rigid curriculum1 n modifi$ by its own /aff1 %\ld be p]missible4 ,exactly ! same pr9ciples apply1 ) ! prop] modifications1 to univ]sities & to te*nical colleges4 ,:5 "o consid]s 9 its l5g? & 9 its bread? ! importance ( ?is "q ( ! education ( a nation's "y1 ! brok5 lives1 ! defeat$ hopes1 ! national failures1 :i* result f ! frivol\s in]tia ) :i* x is treat$1 x is difficult to re/ra9 )9 oneself a savage rage4 ,9 ! conditions ( mod]n life ! ride is absolute1 ! race :i* does n value tra9$ intellig5ce is doom$4 ,n all y\r h]oism1 n all y\r social *>m1 n all y\r wit1 n all y\r victories on l& or at sea1 c move back ! f+] ( fate4 ,to-day we ma9ta9 ourselves4 ,to-morr[ sci5ce w h mov$ =w>d yet "o m /ep1 & !re w be no appeal f ! judgm5t :i* w !n be pron\nc$ on ! un$ucat$4 ,we c be cont5t ) no less ?an ! old summ>y ( educational ideal :i* has be5 curr5t at any "t f ! dawn ( our civilisation4 ,! ess5ce ( education is t x be religi\s4 ,pray1 :at is religi\s education8 ,a religi\s education is an education :i* inculcates duty & rev]5ce4 ,duty arises f our pot5tial control ov] ! c\rse ( ev5ts4 ,:]e atta9able k c\ld h *ang$ ! issue1 ignorance has ! guilt ( vice4 ,& ! f\ndation ( rev]5ce is ?is p]ception1 t ! pres5t holds )9 itself ! complete sum ( exi/5ce1 backw>ds & =w>ds1 t :ole amplitude ( "t1 :i* is et]nity4 ,,*apt] ,,ii ,,te*nical ,,education ,,& ,,its ,,relation ,,to ,,sci5ce ,,& ,,lit]ature 7,presid5tial ,address to ! ,ma!matical ,association1 ,janu>y1 #aiag7 ,,! subject ( ?is address is ,te*nical ,education4 ,i wi% to exam9e its ess5tial nature & also its relation to a lib]al education4 ,su* an inquiry may help u to realise ! conditions = ! successful work+ ( a national sy/em ( te*nical tra9+4 ,x is also a v burn+ "q among ma!matical tea*]s2 = ma!matics is includ$ 9 mo/ te*nological c\rses4 ,n[ x is unpractical to plunge into su* a discussion )\t fram+ 9 our own m9ds ! be/ ideal t[>ds :i* we desire to "w1 h[ev] mode/ly we may frame our hopes z to ! result :i* 9 ! ne> future is likely to be a*iev$4 ,p are %y ( ideals2 & accord+ly we f9d a =mulation ( ! ideal /ate ( mank9d plac$ by a mod]n dramati/#a 9 ! m\? ( a mad prie/3 ,9 my dreams x is a c\ntry :]e ! ,/ate is ! ,*ur* & ! ,*ur* ! p3 ?ree 9 "o & "o 9 ?ree4 ,x is a commonweal? 9 :i* "w is play & play is life3 ?ree 9 "o & "o 9 ?ree4 ,x is a temple 9 :i* ! prie/ is ! wor%ipp] & ! wor%ipp] ! wor%ipp$3 ?ree 9 "o & "o 9 ?ree4 ,x is a godhead 9 :i* all life is human & all humanity div9e3 ?ree 9 "o & "o 9 ?ree4 ,x is1 9 %ort1 ! dream ( a madman4 ,n[ ! "p ( ?is spee* to :i* ,i w\ld direct att5tion is embodi$ 9 ! phrase1 ,x is a commonweal? 9 :i* "w is play & play is life4 ,?is is ! ideal ( te*nical education4 ,x s\nds v my/ical :5 we confront x ) ! actual facts1 ! toil+ millions1 tir$1 discont5t$1 m5tally indiff]5t1 & !n ! employ]s---- ,i am n und]tak+ a social analysis1 b ,i %all c>ry y ) me :5 ,i admit t ! pres5t facts ( society are a long way (f ?is ideal4 ,fur!rmore1 we are agre$ t an employ] :o conduct$ 8 work%op on ! pr9ciple t "w %\ld be play w\ld be ru9$ 9 a week4 ,! curse t has be5 laid on humanity1 9 fable & 9 fact1 is1 t by ! sweat ( its br[ %all x live4 ,b reason & moral intuition h se5 9 ?is curse ! f\ndation = advance4 ,! e>ly ,b5$ict9e monks rejoic$ 9 _! lab\rs because !y conceiv$ !mselves z !reby made fell[-work]s ) ,*ri/4 ,/ripp$ ( its !ological trapp+s1 ! ess5tial idea rema9s1 t "w %\ld be transfus$ ) intellectual & moral vision & !reby turn$ into a joy1 triumph+ ov] its we>9ess & its pa94 ,ea* ( u w re-/ate ?is ab/ract =mulation 9 a m concrete %ape 9 accordance ) 8 private outlook4 ,/ate x h[ y l1 s long z y d n lose ! ma9 po9t 9 y\r details4 ,h[ev] y phrase x1 x rema9s ! sole real hope ( toil+ humanity2 & x is 9 ! h&s ( te*nical tea*]s1 & ( ^? :o control _! sph]es ( activity1 s to m\ld ! nation t daily x may pass to its lab\rs 9 ! _s ( ! monks ( old4 ,! imm$iate ne$ ( ! nation is a l>ge supply ( skill$ workm51 ( m5 ) inv5tive g5ius1 & ( employ]s al]t 9 ! developm5t ( new ideas4 ,!re is "o--& only "o--way to obta9 ^! admirable results4 ,x is by produc+ workm51 m5 ( sci5ce1 & employ]s :o enjoy _! "w4 ,view ! matt] practically 9 ! light ( our k ( av]age human nature4 ,is x likely t a tir$1 bor$ workman1 h[ev] skilful 8 h&s1 w produce a l>ge output ( fir/-class "w8 ,he w limit 8 production1 w scamp 8 "w1 & be an adept at evad+ inspection2 he w be sl[ 9 adapt+ himself to new me?ods2 he w be a focus ( discont5t1 full ( unpractical revolution>y ideas1 controll$ by no sympa!tic appreh5sion ( ! real work+ ( trade conditions4 ,if1 9 ! tr\bl$ times :i* may be be=e u1 y wi% appreciably to increase ! *ance ( "s savage upheaval1 introduce widespread te*nical education & ignore ! ,b5$ict9e ideal4 ,society w !n get :at x des]ves4 ,aga91 inv5tive g5ius requires pleasurable m5tal activity z a condition = its vigor\s ex]cise4 ,necessity is ! "m ( inv5tion is a silly prov]b4 ,necessity is ! "m ( futile dodges is mu* ne>] to ! tru?4 ,! basis ( ! gr[? ( mod]n inv5tion is sci5ce1 & sci5ce is almo/ :olly ! outgr[? ( pleasurable intellectual curiosity4 ,! ?ird class are ! employ]s1 :o are to be ent]pris+4 ,n[ x is to be obs]v$ t x is ! successful employ]s :o are ! important p to get at1 ! m5 ) bus9ess connections all ov] ! _w1 m5 :o are already ri*4 ,no d\bt !re w always be a cont9u\s process ( rise & fall ( bus9esses4 ,b x is futile to expect fl\ri%+ trade1 if 9 ! mass ! successful h\ses ( bus9ess are suff]+ f atrophy4 ,n[ if ^! m5 conceive _! bus9esses z m]ely indiff]5t means = acquir+ o!r disconnect$ opportunities ( life1 !y h no spur to al]tness4 ,!y are already do+ v well1 ! m]e mom5tum ( _! pres5t bus9ess engagem5ts w c>ry !m on = _! "t4 ,!y are n at all likely to bo!r !mselves ) ! d\btful *ances ( new me?ods4 ,_! real s\l is 9 ! o!r side ( _! life4 ,desire = money w produce h>d-fi/$ness & n ent]prise4 ,!re is mu* m hope = humanity f manufactur]s :o enjoy _! "w ?an f ^? :o cont9ue 9 irksome bus9ess ) ! object ( f\nd+ hospitals4 ,f9ally1 !re c be no prospect ( indu/rial peace s long z ma/]s & m5 9 ! mass conceive !mselves z engag$ 9 a s\lless op]ation ( extract+ money f ! public4 ,enl>g$ views ( ! "w p]=m$1 & ( ! communal s]vice !reby r5d]$1 c be ! only basis on :i* to f\nd sympa!tic co-op]ation4 ,! conclusion to be drawn f ?is discussion is1 t alike = ma/]s & = m5 a te*nical or te*nological education1 :i* is to h any *ance ( satisfy+ ! practical ne$s ( ! nation1 mu/ be conceiv$ 9 a lib]al _s z a real intellectual enlight5m5t 9 reg>d to pr9ciples appli$ & s]vices r5d]$4 ,9 su* an education geometry & poetry are z ess5tial z turn+ la!s4 ,! my?ical figure ( ,plato may /& = mod]n lib]al education z does t ( ,/4 ,b5$ict = te*nical education4 ,we ne$ n entangle ourselves 9 ! qualifications necess>y = a balanc$ repres5tation ( ! actual ?\ghts ( ! actual m54 ,!y are us$ "h z symbolic figures typical ( anti!tical notions4 ,we consid] ,plato 9 ! light ( ! type ( culture he n[ inspires4 ,9 its ess5ce a lib]al education is an education = ?\ght & = /hetic appreciation4 ,x proce$s by imp>t+ a k ( ! ma/]pieces ( ?\ght1 ( imag9ative lit]ature1 & ( art4 ,! action :i* x contemplates is comm&4 ,x is an ari/ocratic education imply+ leisure4 ,?is ,platonic ideal has r5d]$ imp]i%able s]vices to ,european civilisation4 ,x has enc\rag$ art1 x has fo/]$ t _s ( dis9t]e/$ curiosity :i* is ! orig9 ( sci5ce1 x has ma9ta9$ ! dignity ( m9d 9 ! face ( mat]ial =ce1 a dignity :i* claims fre$om ( ?\ght4 ,plato did n1 l ,/4 ,b5$ict1 bo!r himself to be a fell[-work] ) 8 slaves2 b he mu/ rank among ! emancipators ( mank9d4 ,8 type ( culture is ! peculi> inspiration ( ! lib]al ari/ocrat1 ! class f :i* ,europe d]ives :at ord]$ lib]ty x n[ possesses4 ,= c5turies1 f ,pope ,ni*olas ,v to ! s*ools ( ! ,jesuits1 & f ! ,jesuits to ! mod]n headma/]s ( ,engli% public s*ools1 ?is educational ideal has _h ! /r5u\s support ( ! cl]gy4 ,= c]ta9 p x is a v good education4 ,x suits _! type ( m9d & ! circum/ances amid :i* _! life is pass$4 ,b m has be5 claim$ = x ?an ?is4 ,all education has be5 judg$ adequate or defective accord+ to its approximation to ?is sole type4 ,! ess5ce ( ! type is a l>ge discursive k ( ! be/ lit]ature4 ,! ideal product ( ! type is ! man :o is acqua9t$ ) ! be/ t has be5 writt54 ,he w h acquir$ ! *ief languages1 he w h consid]$ ! hi/ories ( ! rise & fall ( nations1 ! poetic expression ( human feel+1 & h read ! great dramas & novels4 ,he w also be well gr\nd$ 9 ! *ief philosophies1 & h att5tively read ^? philosophic au?ors :o are di/+ui%$ = lucidity ( /yle4 ,x is obvi\s t1 except at ! close ( a long life1 he w n h mu* "t = any?+ else if any approximation is to be made to ! fulfilm5t ( ?is programme4 ,"o is rem9d$ ( ! calculation 9 a dialogue ( ,lucian t1 be=e a man c\ld be ju/ifi$ 9 practis+ any "o ( ! curr5t e?ical sy/ems1 he %\ld h sp5t a hundr$ & fifty ye>s 9 exam9+ _! cr$5tials4 ,su* ideals are n = human be+s4 ,:at is meant by a lib]al culture is no?+ s ambiti\s z a full acqua9tance ) ! v>i$ lit]>y expression ( civilis$ mank9d f ,asia to ,europe1 & f ,europe to ,am]ica4 ,a small selection only is requir$2 b !n1 z we are told1 x is a selection ( ! v be/4 ,i h my d\bts ( a selection :i* includes ,x5ophon & omits ,confucius1 b !n ,i h read nei!r 9 ! orig9al4 ,! ambiti\s programme ( a lib]al education really %r9ks to a /udy ( "s fragm5ts ( lit]ature includ$ 9 a c\ple ( important languages4 ,b ! expression ( ! human _s is n conf9$ to lit]ature4 ,!re are ! o!r arts1 & !re are ! sci5ces4 ,also education mu/ pass beyond ! passive reception ( ! ideas ( o!rs4 ,p[]s ( initiative mu/ be /r5g!n$4 ,un=tunately initiative does n mean j "o acquirem5t--!re is initiative 9 ?\ght1 initiative 9 action1 & ! imag9ative initiative ( art2 & ^! ?ree categories require _m subdivisions4 ,! field ( acquirem5t is l>ge1 & ! individual s fleet+ & s fragm5t>y3 classical s*ol>s1 sci5ti/s1 headma/]s are alike ignoramuses4 ,!re is a curi\s illusion t a m complete culture 0 possible :5 !re 0 less to "k4 ,surely ! only ga9 01 t x 0 m possible to rema9 unconsci\s ( ignorance4 ,x _c h be5 a ga9 to ,plato to h read nei!r ,%akespe>e1 nor ,newton1 nor ,d>w94 ,! a*ievem5ts ( a lib]al education h 9 rec5t times n be5 wors5$4 ,! *ange is t its pret5sions h be5 f\nd out4 ,my po9t is1 t no c\rse ( /udy c claim any position ( ideal complet5ess4 ,nor are ! omitt$ factors ( subord9ate importance4 ,! insi/5ce 9 ! ,platonic culture on dis9t]e/$ intellectual appreciation is a psy*ological error4 ,action & our implication 9 ! transition ( ev5ts amid ! evitable bond ( cause to effect are fundam5tal4 ,an education :i* /rives to divorce intellectual or /hetic life f ^! fundam5tal facts c>ries ) x ! decad5ce ( civilisation4 ,ess5tially culture %\ld be = action1 & its effect %\ld be to dive/ lab\r f ! associations ( aimless toil4 ,art exi/s t we may "k ! deliv]ances ( our s5ses z good4 ,x height5s ! s5se-_w4 ,dis9t]e/$ sci5tific curiosity is a passion = an ord]$ intellectual vision ( ! connection ( ev5ts4 ,b ! goal ( su* curiosity is ! m>riage ( action to ?\ght4 ,?is ess5tial int]v5tion ( action ev5 9 ab/ract sci5ce is (t5 ov]look$4 ,no man ( sci5ce wants m]ely to "k4 ,he acquires k to appease 8 passion = discov]y4 ,he does n discov] 9 ord] to "k1 he kn[s 9 ord] to discov]4 ,! pleasure :i* art & sci5ce c give to toil is ! enjoym5t :i* arises f successfully direct$ int5tion4 ,also x is ! same pleasure :i* is yield$ to ! sci5ti/ & to ! arti/4 ,! anti!sis betwe5 a te*nical & a lib]al education is fallaci\s4 ,!re c be no adequate te*nical education :i* is n lib]al1 & no lib]al education :i* is n te*nical3 t is1 no education :i* does n imp>t bo? te*nique & intellectual vision4 ,9 simpl] language1 education %\ld turn out ! pupil ) some?+ he kn[s well & some?+ he c d well4 ,?is intimate union ( practice & !ory aids bo?4 ,! intellect does n "w be/ 9 a vacuum4 ,! /imulation ( creative impulse requires1 especially 9 ! case ( a *ild1 ! quick transition to practice4 ,geometry & me*anics1 foll[$ by work%op practice1 ga9 t reality )\t :i* ma!matics is v]biage4 ,!re are ?ree ma9 me?ods :i* are requir$ 9 a national sy/em ( education1 namely1 ! lit]>y curriculum1 ! sci5tific curriculum1 ! te*nical curriculum4 ,b ea* ( ^! curricula %\ld include ! o!r two4 ,:at ,i mean is1 t e =m ( education %\ld give ! pupil a te*nique1 a sci5ce1 an assortm5t ( g5]al ideas1 & /hetic appreciation1 & t ea* ( ^! sides ( 8 tra9+ %\ld be illum9at$ by ! o!rs4 ,lack ( "t1 ev5 = ! mo/ fav\r$ pupil1 makes x impossible to develop fully ea* curriculum4 ,always !re mu/ be a dom9ant emphasis4 ,! mo/ direct /hetic tra9+ naturally falls 9 ! te*nical curriculum 9 ^? cases :5 ! tra9+ is t requisite = "s art or arti/ic craft4 ,b x is ( high importance 9 bo? a lit]>y & a sci5tific education4 ,! educational me?od ( ! lit]>y curriculum is ! /udy ( language1 t is1 ! /udy ( our mo/ habitual me?od ( convey+ to o!rs our /ates ( m9d4 ,! te*nique :i* %\ld be acquir$ is ! te*nique ( v]bal expression1 ! sci5ce is ! /udy ( ! /ructure ( language & ! analysis ( ! relations ( language to ! /ates ( m9d convey$4 ,fur!rmore1 ! subtle relations ( language to feel+1 & ! high developm5t ( ! s5se organs to :i* writt5 & spok5 words appeal1 lead to ke5 /hetic appreciations be+ ar\s$ by ! successful employm5t ( language4 ,f9ally1 ! wisdom ( ! _w is pres]v$ 9 ! ma/]pieces ( l+ui/ic composition4 ,?is curriculum has ! m]it ( homog5eity4 ,all its v>i\s p>ts are co-ord9at$ & play into ea* o!r's h&s4 ,we c h>dly be surpris$ t su* a curriculum1 :5 once broadly e/abli%$1 %\ld h claim$ ! position ( ! sole p]fect type ( education4 ,its defect is unduly to emphasise ! importance ( language4 ,inde$ ! v>i$ importance ( v]bal expression is s ov]:elm+ t its sob] e/imation is difficult4 ,rec5t g5]ations h be5 witness+ ! retreat ( lit]ature1 & ( lit]>y =ms ( expression1 f _! position ( unique importance 9 intellectual life4 ,9 ord] truly to become a s]vant & a m9i/] ( nature some?+ m is requir$ ?an lit]>y aptitudes4 ,a sci5tific education is prim>ily a tra9+ 9 ! art ( obs]v+ natural ph5om5a1 & 9 ! k & d$uction ( laws conc]n+ ! sequ5ce ( su* ph5om5a4 ,b "h1 z 9 ! case ( a lib]al education1 we are met by ! limitations impos$ by %ortness ( "t4 ,!re are _m types ( natural ph5om5a1 & to ea* type !re corresponds a sci5ce ) its peculi> modes ( obs]vation1 & its peculi> types ( ?\ght employ$ 9 ! d$uction ( laws4 ,a /udy ( sci5ce 9 g5]al is impossible 9 education1 all t c be a*iev$ is ! /udy ( two or ?ree alli$ sci5ces4 ,h5ce ! *>ge ( n>r[ specialism urg$ aga9/ any education :i* is prim>ily sci5tific4 ,x is obvi\s t ! *>ge is apt to be well-f\nd$2 & x is wor? consid]+ h[1 )9 ! limits ( a sci5tific education & to ! advantage ( su* an education1 ! dang] c be avoid$4 ,su* a discussion requires ! consid]ation ( te*nical education4 ,a te*nical education is 9 ! ma9 a tra9+ 9 ! art ( utilis+ k = ! manufacture ( mat]ial products4 ,su* a tra9+ emphasises manual skill1 & ! co-ord9at$ action ( h& & eye1 & judgm5t 9 ! control ( ! process ( con/ruction4 ,b judgm5t necessitates k ( ^? natural processes ( :i* ! manufacture is ! utilisation4 ,?us some:]e 9 te*nical tra9+ an education 9 sci5tific k is requir$4 ,if y m9imise ! sci5tific side1 y w conf9e x to ! sci5tific exp]ts2 if y maximise x1 y w imp>t x 9 "s measure to ! m51 &--:at is ( no less importance--to ! directors & manag]s ( ! bus9esses4 ,te*nical education is n necess>ily alli$ exclusively to sci5ce on its m5tal side4 ,x may be an education = an arti/ or = appr5tices to an arti/ic craft4 ,9 t case /hetic appreciation w h to be cultivat$ 9 connection ) x4 ,an evil side ( ! ,platonic culture has be5 its total neglect ( te*nical education z an +r$i5t 9 ! complete developm5t ( ideal human be+s4 ,?is neglect has aris5 f two disa/r\s anti!ses1 namely1 t betwe5 m9d & body1 & t betwe5 ?\ght & action4 ,i w "h int]ject1 solely to avoid criticism1 t ,i am well aw>e t ! ,greeks highly valu$ physical beauty & physical activity4 ,!y _h1 h[ev]1 t p]v]t$ s5se ( values :i* is ! nemesis ( slave-own+4 ,i lay x d[n z an educational axiom t 9 tea*+ y w come to grief z soon z y =get t y\r pupils h bodies4 ,?is is exactly ! mi/ake ( ! po/-r5aissance ,platonic curriculum4 ,b nature c be kept at bay by no pit*=k2 s 9 ,engli% education1 be+ expell$ f ! classroom1 %e return$ ) a cap & bells 9 ! =m ( all-conqu]+ a?leticism4 ,! connections betwe5 intellectual activity & ! body1 ?\gh diffus$ 9 e bodily feel+1 are focuss$ 9 ! eyes1 ! e>s1 ! voice1 & ! h&s4 ,!re is a co-ord9ation ( s5ses & ?\ght1 & also a reciprocal influ5ce betwe5 bra9 activity & mat]ial creative activity4 ,9 ?is reaction ! h&s are peculi>ly important4 ,x is a moot po9t :e!r ! human h& creat$ ! human bra91 or ! bra9 creat$ ! h&4 ,c]ta9ly ! connection is intimate & reciprocal4 ,su* deep-seat$ relations are n widely atrophi$ by a few hundr$ ye>s ( disuse 9 exceptional families4 ,! disuse ( h&-craft is a contributory cause to ! bra9-le?>gy ( ari/ocracies1 :i* is only mitigat$ by sport :]e ! concurr5t bra9-activity is r$uc$ to a m9imum & ! h&-craft lacks subtlety4 ,! necessity = con/ant writ+ & vocal exposition is "s slight /imulus to ! ?\ght-p[] ( ! pr(essional classes4 ,great read]s1 :o exclude o!r activities1 are n di/+ui%$ by subtlety ( bra94 ,!y t5d to be timid conv5tional ?9k]s4 ,no d\bt ?is is p>tly due to _! excessive k outrunn+ _! p[]s ( ?\ght2 b x is p>tly due to ! lack ( bra9-/imulus f ! productive activities ( h& or voice4 ,9 e/imat+ ! importance ( te*nical education we mu/ rise above ! exclusive association ( le>n+ ) book-le>n+4 ,fir/-h& k is ! ultimate basis ( intellectual life4 ,to a l>ge ext5t book-le>n+ conveys second-h& in=mation1 & z su* c nev] rise to ! importance ( imm$iate practice4 ,our goal is to see ! imm$iate ev5t ( our lives z in/ances ( our g5]al ideas4 ,:at ! le>n$ _w t5ds to (f] is "o second-h& scrap ( in=mation illu/rat+ ideas d]iv$ f ano!r second-h& scrap ( in=mation4 ,! second-h&$ness ( ! le>n$ _w is ! secret ( its m$iocrity4 ,x is tame because x has nev] be5 sc>$ by facts4 ,! ma9 importance ( ,francis ,bacon's influ5ce does n lie 9 any peculi> !ory ( inductive reason+ :i* he happ5$ to express1 b 9 ! revolt aga9/ second-h& in=mation ( :i* he 0 a lead]4 ,! peculi> m]it ( a sci5tific education %\ld be1 t x bases ?\ght ^u fir/-h& obs]vation2 & ! correspond+ m]it ( a te*nical education is1 t x foll[s our deep natural in/9ct to translate ?\ght into manual skill1 & manual activity into ?\ght4 ,we are a ,ma!matical ,association1 & x is natural to ask3 ,:]e d we come 98 ,we come 9 j at ?is po9t4 ,! ?\ght :i* sci5ce evokes is logical ?\ght4 ,n[ logic is ( two k9ds3 ! logic ( discov]y & ! logic ( ! discov]$4 ,! logic ( discov]y consi/s 9 ! weigh+ ( probabilities1 9 disc>d+ details deem$ to be irrelevant1 9 div9+ ! g5]al rules accord+ to :i* ev5ts occur1 & 9 te/+ hypo!ses by devis+ suitable exp]im5ts4 ,?is is inductive logic4 ,! logic ( ! discov]$ is ! d$uction ( ! special ev5ts :i*1 "u c]ta9 circum/ances1 w\ld happ5 9 ob$i5ce to ! assum$ laws ( nature4 ,?us :5 ! laws are discov]$ or assum$1 _! utilisation entirely dep5ds on d$uctive logic4 ,)\t d$uctive logic sci5ce w\ld be entirely useless4 ,x is m]ely a b>r5 game to asc5d f ! p>ticul> to ! g5]al1 unless aft]w>ds we c rev]se ! process & desc5d f ! g5]al to ! p>ticul>1 asc5d+ & desc5d+ l ! angels on ,jacob's ladd]4 ,:5 ,newton _h div9$ ! law ( gravitation he at once proce$$ to calculate ! e>?'s attractions on an apple at its surface & on ! moon4 ,we may note 9 pass+ t inductive logic w\ld be impossible )\t d$uctive logic4 ,?us ,newton's calculations 7 an ess5tial /ep 9 8 inductive v]ification ( ! great law4 ,n[ ma!matics is no?+ else ?an ! m complicat$ p>ts ( ! art ( d$uctive reason+1 especially :]e x conc]ns numb]1 quantity1 & space4 ,9 ! tea*+ ( sci5ce1 ! art ( ?\ght %\ld be taught3 namely1 ! art ( =m+ cle> conceptions apply+ to fir/-h& exp]i5ce1 ! art ( div9+ ! g5]al tru?s :i* apply1 ! art ( te/+ div9ations1 & ! art ( utilis+ g5]al tru?s by reason+ to m p>ticul> cases ( "s peculi> importance4 ,fur!rmore1 a p[] ( sci5tific exposition is necess>y1 s t ! relevant issues f a confus$ mass ( ideas c be /at$ cle>ly1 ) due emphasis on important po9ts4 ,by ! "t a sci5ce1 or a small gr\p ( sci5ces1 has be5 taught ?us amply1 ) due reg>d to ! g5]al art ( ?\ght1 we h gone a long way t[>ds correct+ ! specialism ( sci5ce4 ,! wor/ ( a sci5tific education bas$1 z necess>ily mu/ be ! case1 on "o or two p>ticul> bran*es ( sci5ce1 is t ! tea*]s "u ! influ5ce ( ! exam9ation sy/em are apt m]ely to /uff _! pupils ) ! n>r[ results ( ^! special sci5ces4 ,x is ess5tial t ! g5]ality ( ! me?od be cont9ually br\ght to light & contra/$ ) ! speciality ( ! p>ticul> application4 ,a man :o only kn[s 8 own sci5ce1 z a r\t9e peculi> to t sci5ce1 does n ev5 "k t4 ,he has no f]tility ( ?\ght1 no p[] ( quickly seiz+ ! be>+ ( ali5 ideas4 ,he w discov] no?+1 & be /upid 9 practical applications4 ,?is exhibition ( ! g5]al 9 ! p>ticul> is extremely difficult to effect1 especially 9 ! case ( y\ng] pupils4 ,! art ( education is nev] easy4 ,to surm\nt its difficulties1 especially ^? ( elem5t>y education1 is a task wor?y ( ! highe/ g5ius4 ,x is ! tra9+ ( human s\ls4 ,ma!matics1 well taught1 %\ld be ! mo/ p[]ful in/rum5t 9 gradually implant+ ?is g5]ality ( idea4 ,! ess5ce ( ma!matics is p]petually to be disc>d+ m special ideas 9 fav\r ( m g5]al ideas1 & special me?ods 9 fav\r ( g5]al me?ods4 ,we express ! conditions ( a special problem 9 ! =m ( an equation1 b t equation w s]ve = a hundr$ o!r problems1 scatt]$ ?r\gh div]se sci5ces4 ,! g5]al reason+ is always ! p[]ful reason+1 because d$uctive cog5cy is ! prop]ty ( ab/ract =m4 ,"h1 aga91 we mu/ be c>eful4 ,we %all ru9 ma!matical education if we use x m]ely to impress g5]al tru?s4 ,! g5]al ideas are ! means ( connect+ p>ticul> results4 ,aft] all1 x is ! concrete special cases :i* are important4 ,?us 9 ! h&l+ ( ma!matics 9 y\r results y _c be too concrete1 & 9 y\r me?ods y _c be too g5]al4 ,! ess5tial c\rse ( reason+ is to g5]alise :at is p>ticul>1 & !n to p>ticul>ise :at is g5]al4 ,)\t g5]ality !re is no reason+1 )\t concret5ess !re is no importance4 ,concret5ess is ! /r5g? ( te*nical education4 ,i w\ld rem9d y t tru?s :i* lack ! highe/ g5]ality are n necess>ily concrete facts4 ,= example1 x y y x is an algebraic tru? m g5]al ?an #b #b #d4 ,b two & two make f\r is itself a highly g5]al proposition lack+ any elem5t ( concret5ess4 ,to obta9 a concrete proposition imm$iate intuition ( a tru? conc]n+ p>ticul> objects is requisite2 = example1 ^! two apples & ^? apples toge!r make f\r apples is a concrete proposition1 if y h direct p]ception or imm$iate memory ( ! apples4 ,9 ord] to obta9 ! full realisation ( tru?s z apply+1 & n z empty =mul1 !re is no alt]native to te*nical education4 ,m]e passive obs]vation is n suffici5t4 ,9 creation only is !re vivid insight into ! prop]ties ( ! object !reby produc$4 ,if y want to und]/& any?+1 make x y\rself1 is a s\nd rule4 ,y\r faculties w be alive1 y\r ?\ghts ga9 vividness by an imm$iate translation into acts4 ,y\r ideas ga9 t reality :i* comes f see+ ! limits ( _! application4 ,9 elem5t>y education ?is doctr9e has long be5 put into practice4 ,"y *ildr5 are taught to famili>ise !mselves ) %apes & col\rs by simple manual op]ations ( cutt+ out & ( sort+4 ,b good ?\gh ?is is1 x is n q :at ,i mean4 ,t is practical exp]i5ce be=e y ?9k1 exp]i5ce antec$5t to ?\ght 9 ord] to create ideas1 a v excell5t discipl9e4 ,b te*nical education %\ld be mu* m ?an t3 x is creative exp]i5ce :ile y ?9k1 exp]i5ce :i* realises y\r ?\ght1 exp]i5ce :i* tea*es y to co-ord9ate act & ?\ght1 exp]i5ce lead+ y to associate ?\ght ) =esight & =esight ) a*ievem5t4 ,te*nical education gives !ory1 & a %rewd insight z to :]e !ory fails4 ,a te*nical education is n to be conceiv$ z a maim$ alt]native to ! p]fect ,platonic culture3 namely1 z a defective tra9+ un=tunately made necess>y by cramp$ conditions ( life4 ,no human be+ c atta9 to any?+ b fragm5t>y k & a fragm5t>y tra9+ ( 8 capacities4 ,!re are1 h[ev]1 ?ree ma9 roads along :i* we c proce$ ) good hope ( advanc+ t[>ds ! be/ balance ( intellect & "*3 ^! are ! way ( lit]>y culture1 ! way ( sci5tific culture1 ! way ( te*nical culture4 ,no "o ( ^! me?ods c be exclusively foll[$ )\t grave loss ( intellectual activity & ( "*4 ,b a m]e me*anical mixture ( ! ?ree curricula w produce bad results 9 ! %ape ( scraps ( in=mation nev] int]connect$ or utilis$4 ,we h already not$ z "o ( ! /rong po9ts ( ! traditional lit]>y culture t all its p>ts are co-ord9at$4 ,! problem ( education is to reta9 ! dom9ant emphasis1 :e!r lit]>y1 sci5tific1 or te*nical1 & )\t loss ( co-ord9ation to infuse into ea* way ( education some?+ ( ! o!r two4 ,to make def9ite ! problem ( te*nical education fix att5tion on two ages3 "o ?irte51 :5 elem5t>y education ends2 & ! o!r sev5te51 :5 te*nical education ends s f> z x is compress$ )9 a s*ool curriculum4 ,i am aw>e t = artisans 9 junior te*nical s*ools a ?ree-ye>s' c\rse w\ld be m usual4 ,on ! o!r h&1 = naval (fic]s1 & = direct+ classes g5]ally1 a long] "t c be af=d$4 ,we want to consid] ! pr9ciples to gov]n a curriculum :i* %all l& ^! *ildr5 at ! age ( sev5te5 9 ! position ( hav+ te*nical skill useful to ! community4 ,_! te*nical manual tra9+ %\ld />t at ?irte51 be>+ a mode/ proportion to ! re/ ( _! "w1 & %\ld increase 9 ea* ye> f9ally to atta9 to a sub/antial proportion4 ,above all ?+s x %\ld n be too specialis$4 ,work%op f9i% & work%op dodges1 adapt$ to "o p>ticul> job1 %\ld be taught 9 ! comm]cial work%op1 & %\ld =m no ess5tial "p ( ! s*ool c\rse4 ,a prop]ly tra9$ work] w\ld pick !m up 9 no "t4 ,9 all education ! ma9 cause ( failure is /al5ess4 ,te*nical education is doom$ if we conceive x z a sy/em = cat*+ *ildr5 "y & = giv+ !m "o highly specialis$ manual aptitude4 ,! nation has ne$ ( a fluidity ( lab\r1 n m]ely f place to place1 b also )9 reasonable limits ( alli$ aptitudes1 f "o special type ( "w to ano!r special type4 ,i "k t "h ,i am on delicate gr\nd1 & ,i am n claim+ t m5 :ile !y are specialis+ on "o sort ( "w %\ld spasmodically be set to o!r k9ds4 ,t is a "q ( trade organisation ) :i* educationali/s h no conc]n4 ,i am only ass]t+ ! pr9ciples t tra9+ %\ld be broad] ?an ! ultimate specialisation1 & t ! result+ p[] ( adaptation to v>y+ dem&s is advantage\s to ! work]s1 to ! employ]s1 & to ! nation4 ,9 consid]+ ! intellectual side ( ! curriculum we mu/ be guid$ by ! pr9ciple ( ! co-ord9ation ( /udies4 ,9 g5]al1 ! intellectual /udies mo/ imm$iately relat$ to manual tra9+ w be "s bran*es ( sci5ce4 ,m ?an "o bran* w1 9 fact1 be conc]n$2 & ev5 if t be n ! case1 x is impossible to n>r[ d[n sci5tific /udy to a s+le ?9 l9e ( ?\ght4 ,x is possible1 h[ev]1 provid$ t we d n press ! classification too f>1 r\ghly to classify te*nical pursuits accord+ to ! dom9ant sci5ce involv$4 ,we ?us f9d a sixfold division1 namely1 7#a7 ,geometrical te*niques1 7#b7 ,me*anical te*niques1 7#c7 ,physical te*niques1 7#d7 ,*emical te*niques1 7#e7 ,biological te*niques1 7#f7 ,te*niques ( comm]ce & ( social s]vice4 ,by ?is division1 x is meant t ap>t f auxili>y sci5ces "s p>ticul> sci5ce requires emphasis 9 ! tra9+ = mo/ occupations4 ,we c1 = example1 reckon c>p5try1 ironmong]y1 & _m arti/ic crafts among geometrical te*niques4 ,simil>ly agriculture is a biological te*nique4 ,probably cook]y1 if x includes food cat]+1 w\ld fall midway betwe5 biological1 physical1 & *emical sci5ces1 ?\gh ( ?is ,i am n sure4 ,! sci5ces associat$ ) comm]ce & social s]vice w\ld be p>tly algebra1 includ+ ari?metic & /ati/ics1 & p>tly geography & hi/ory4 ,b ?is section is some:at het]og5e\s 9 its sci5tific aff9ities4 ,anyh[ ! exact way 9 :i* te*nical pursuits are classifi$ 9 relation to sci5ce is a detail4 ,! ess5tial po9t is1 t ) "s ?\ght x is possible to f9d sci5tific c\rses :i* illum9ate mo/ occupations4 ,fur!rmore1 ! problem is well und]/ood1 & has be5 brilliantly solv$ 9 _m ( ! s*ools ( te*nology & junior te*nical s*ools ?r\gh\t ! c\ntry4 ,9 pass+ f sci5ce to lit]ature1 9 our review ( ! intellectual elem5ts ( te*nical education1 we note t _m /udies hov] betwe5 ! two3 = example1 hi/ory & geography4 ,!y are bo? ( !m v ess5tial 9 education1 provid$ t !y are ! "r hi/ory & ! "r geography4 ,also books giv+ descriptive acc\nts ( g5]al results1 & tra9s ( ?\ght 9 v>i\s sci5ces fall 9 ! same category4 ,su* books %\ld be p>tly hi/orical & p>tly expository ( ! ma9 ideas :i* h f9ally aris54 ,pr(4 ,r4 ,a4 ,gregory's rec5t book1 ,discov]y1 & ! ,home ,univ]sity ,libr>y s]ies illu/rate my mean+4 ,_! value 9 education dep5ds on _! quality z m5tal /imulants4 ,!y mu/ n be inflat$ ) gas on ! wond]s ( sci5ce1 & mu/ be in=m$ ) a broad outlook4 ,x is un=tunate t ! lit]>y elem5t 9 education has r>ely be5 consid]$ ap>t f grammatical /udy4 ,! hi/orical reason is1 t :5 ! mod]n ,platonic curriculum 0 be+ =m$ ,lat9 & ,greek 7 ! sole keys :i* r5d]$ great lit]ature accessible4 ,b !re is no necess>y connection betwe5 lit]ature & gramm>4 ,! great age ( ,greek lit]ature 0 already pa/ be=e ! arrival ( ! gramm>ians ( ,alex&ria4 ,( all types ( m5 to-day exi/+1 classical s*ol>s are ! mo/ remote f ! ,greeks ( ! ,p]iclean times4 ,m]e lit]>y k is ( slight importance4 ,! only ?+ t matt]s is1 h[ x is kn[n4 ,! facts relat$ are no?+4 ,lit]ature only exi/s to express & develop t imag9ative _w :i* is our life1 ! k+dom :i* is )9 u4 ,x foll[s t ! lit]>y side ( a te*nical education %\ld consi/ 9 an ef=t to make ! pupils enjoy lit]ature4 ,x does n matt] :at !y "k1 b ! enjoym5t is vital4 ,! great ,engli% ,univ]sities1 "u ^: direct au?ority s*ool-*ildr5 are exam9$ 9 plays ( ,%akespe>e1 to ! c]ta9 de/ruction ( _! enjoym5t1 %\ld be prosecut$ = s\l-murd]4 ,n[ !re are two k9ds ( intellectual enjoym5t3 ! enjoym5t ( creation1 & ! enjoym5t ( relaxation4 ,!y are n necess>ily sep>at$4 ,a *ange ( occupation may give ! full tide ( happ9ess :i* comes f ! concurr5ce ( bo? =ms ( pleasure4 ,! appreciation ( lit]ature is really creation4 ,! writt5 ^w1 its music1 & its associations1 are only ! /imuli4 ,! vision :i* !y evoke is our own do+4 ,no "o1 no g5ius o!r ?an our own1 c make our own life live4 ,b except = ^? engag$ 9 lit]>y occupations1 lit]ature is also a relaxation4 ,x gives ex]cise to t o!r side :i* any occupation mu/ suppress dur+ ! work+ h\rs4 ,art also has ! same function 9 life z has lit]ature4 ,to obta9 ! pleasure ( relaxation requires no help4 ,! pleasure is m]ely to cease do+4 ,"s su* pure relaxation is a necess>y condition ( heal?4 ,its dang]s are notori\s1 & to ! great] "p ( ! necess>y relaxation nature has affix$1 n enjoym5t1 b ! oblivion ( sleep4 ,creative enjoym5t is ! outcome ( successful ef=t & requires help = its initiation4 ,su* enjoym5t is necess>y = high-spe$ "w & = orig9al a*ievem5t4 ,to spe$ up production ) unrefre%$ workm5 is a disa/r\s economic policy4 ,tempor>y success w be at ! exp5se ( ! nation1 :i*1 = long ye>s ( _! lives1 w h to support worn-out artisans--unemployables4 ,equally disa/r\s is ! alt]nation ( spasms ( ef=t ) p]iods ( pure relaxation4 ,su* p]iods are ! se$-times ( deg5]ation1 unless rigor\sly curtail$4 ,! normal recreation %\ld be *ange ( activity1 satisfy+ ! crav+s ( in/9cts4 ,games af=d su* activity4 ,_! disconnection emphasises ! relaxation1 b _! excess leaves u empty4 ,x is "h t lit]ature & art %\ld play an ess5tial "p 9 a heal?ily organis$ nation4 ,_! s]vices to economic production w\ld be only second to ^? ( sleep or ( food4 ,i am n n[ talk+ ( ! tra9+ ( an arti/1 b ( ! use ( art z a condition ( heal?y life4 ,x is analog\s to sun%9e 9 ! physical _w4 ,:5 we h once rid our m9ds ( ! idea t k is to be exact$1 !re is no especial difficulty or exp5se involv$ 9 help+ ! gr[? ( arti/ic enjoym5t4 ,all s*ool-*ildr5 c\ld be s5t at regul> int]vals to neighb\r+ !atres :]e suitable plays c\ld be subsidis$4 ,simil>ly = conc]ts & c9ema films4 ,pictures are m d\btful 9 _! popul> attraction2 b int]e/+ repres5tations ( sc5es or ideas :i* ! *ildr5 h read ab\t w\ld probably appeal4 ,! pupils !mselves %\ld be enc\rag$ 9 arti/ic ef=ts4 ,above all ! art ( read+ al\d %\ld be cultivat$4 ,! ,rog] de ,cov]ley essays ( ,addison are p]fect examples ( readable prose4 ,art & lit]ature h n m]ely an indirect effect on ! ma9 en]gies ( life4 ,directly1 !y give vision4 ,! _w spreads wide beyond ! deliv]ances ( mat]ial s5se1 ) subtleties ( reaction & ) pulses ( emotion4 ,vision is ! necess>y antec$5t to control & to direction4 ,9 ! conte/ ( races :i* 9 its f9al issues w be decid$ 9 ! work%ops & n on ! battle-field1 ! victory w belong to ^? :o are ma/]s ( /ores ( tra9$ n]v\s en]gy1 work+ "u conditions fav\rable to gr[?4 ,"o su* ess5tial condition is ,art4 ,if !re _h be5 "t1 !re are o!r ?+s :i* ,i %\ld l to h said3 = example1 to advocate ! inclusion ( "o =eign language 9 all education4 ,f direct obs]vation ,i "k ?is to be possible = artisan *ildr54 ,b en\gh has be5 put be=e y1 to make pla9 ! pr9ciples ) :i* we %\ld und]take national education4 ,9 conclusion1 ,i recur to ! ?\ght ( ! ,b5$ict9es1 :o sav$ = mank9d ! vani%+ civilisation ( ! anci5t _w by l9k+ toge!r k1 lab\r1 & moral en]gy4 ,our dang] is to conceive practical affairs z ! k+dom ( evil1 9 :i* success is only possible by ! extrusion ( ideal aims4 ,i believe t su* a conception is a fallacy directly negativ$ by practical exp]i5ce4 ,9 education ?is error takes ! =m ( a mean view ( te*nical tra9+4 ,our =efa!rs 9 ! d>k ages sav$ !mselves by embody+ high ideals 9 great organisations4 ,x is our task1 )\t s]vile imitation1 boldly to ex]cise our creative en]gies1 rememb]+ amid disc\ragem5ts t ! colde/ h\r imm$iately prec$es ! dawn4 ,,footnotes3 ,footnote #a3 ,cf4 ,,b]n>d ,,%aw3 ,john ,bull's ,o!r ,isl&4 ,,*apt] ,,iii ,a ,,polyte*nic ,,9 ,,w>-,,"t ,address at ! ,prize ,di/ribution1 ,bor\gh ,polyte*nic ,in/itute1 ,s\?w>k1 #af? ,febru>y1 #aiag ,i ,,w comm5ce by draw+ y\r att5tion to "s ( ! satisfactory features ( ! ,pr9cipal's report on ! "w ( ! ,in/itute dur+ ! pa/ ye>4 ,x has be5 a ye> ( great difficulties4 ,"s ( our /aff are s]v+ ) ! col\rs1 & our classes h be5 deplet$4 ,b 9 spite ( ev]y?+1 we h done v well4 ,fir/1 ! av]age result 9 ! exam9ations has be5 good1 surpris+ly good 9 view ( ! pres5t circum/ances4 ,! ,gov]nors atta* great importance to ! ma9t5ance ( a high av]age result2 x is ! be/ s+le te/ ( effici5cy4 ,aga91 our individual successes h be5 notable4 ,we h ga9$--,i say we because we are all "o 9 our pleasure at ^! successes--we h ga9$ two #hj ,l4,c4,c4 s*ol>%ips1 n9ete5 exhibitions1 9 addition to a fir/-place1 & m$als1 prizes & c]tificates4 ,all ?is is v satisfactory4 ,x tells ( effici5t tea*+1 & ( h>d "w & regul> att5dance on ! "p ( ! /ud5ts4 ,we "k t we are keep+ up ! /&>d ( effici5cy :i* 9 ! pa/ has be5 a s\rce ( pride to e "o connect$ ) ?is ,in/itute4 ,n[ all ?is good "w does n come ab\t by itself )\t any "o mak+ an ef=t4 ,su* a record requires our skill$ /aff ( tea*]s & organis]s4 ,!y h work$ v h>d dur+ ! la/ session "u great difficulties1 9 ord] to create ! successful result :i* we are "h to celebrate4 ,i "k some?+ ab\t tea*+4 ,x is v exact+ "w1 & c be made successful only by cont9ual devotion4 ,i am sure t ,i am voic+ y\r feel+s1 & ,i "k t ,i am express+ ^? ( ! ,gov]nors1 :5 ,i ?ank ! ladies & g5tlem5 ( ! /aff v he>tily = _! s]vices dur+ ! la/ session4 ,prize-giv+s are always pleasant occasions4 ,we h come "h to ?9k ab\t our successes1 & to congratulate our /ud5ts4 ,!re is no m satisfactory ,gov]nors' ,meet+ 9 ! c\rse ( ! ye> ?an :5 we meet on ?is occasion1 & face our fri5ds & tell !m h[ pleas$ we are at ! successful result ( _! h>d "w4 ,?is ev5+ ,i am 9 a d\bly happy position1 = my colleagues h ask$ me to be _! spokesman 9 t5d]+ our good wi%es to ! prize-w9n]s4 ,y h work$ h>d & y h done well1 & ,i am sure t y all des]ve y\r successes2 !y are a pleasure n only to y1 b 9 y\r homes & to y\r companions & fell[-/ud5ts4 ,successful "w "h w enable y to acquire skill 9 y\r trades1 & !reby ! bett] to e>n y\r liv+4 ,e>n+ a liv+ is on ! av]age no bad te/ ( s]vice r5d]$ to ! community4 ,a man :o has made himself skilful 9 8 trade & has done well = himself 9 8 walk ( life1 has 9 g5]al good reason to believe t he is a citiz5 :o has b5efit$ 8 c\ntry4 ,x is an evil day = a nation :5 x loses respect = success 9 indu/ry4 ,b if y /e] y\r lives by ! compass :i* po9ts /eadily to ! ,nor? ,pole ( p]sonal success1 y w h miss$ y\r greate/ *ances 9 life4 ,! g5ial climate is 9 ! s\?4 ,:at ,i mean is ?is3 y mu/ make up y\r m9d to f9d ! be/ "p ( y\r happ9ess 9 k9dly helpful relations ) o!rs4 ,x %\ld be our ambition to leave our own small corn] ( ! _w a little tidi] & a little happi] ?an :5 we ent]$ x4 ,i am well aw>e t ?is is an old /ory2 b old /ories are sometimes true1 & ?is is ! bigge/ tru? 9 ! :ole _w4 ,! w>m k9dly feel+s are ! happy feel+s4 ,! =tunate p are ^? ^: m9ds are fill$ ) ?\ghts 9 :i* !y =get !mselves & rememb] o!rs4 ,x is n true t nature is a m]e sc5e ( /ruggle 9 :i* e "o competes ) 8 neighb\r4 ,^? communities ?rive be/ & la/ longe/ :i* are fill$ ) a _s ( mutual help4 ,! future ( ! c\ntry lies ) y4 ,! cr[n ( y\r success is ! promise ( future "w1 (t5 unrecognis$ "w1 done "u disc\ragem5t1 b done /eadily & *e]fully4 ,x is on y t ! c\ntry dep5ds = ! ma9t5ance & ! gr[? ( ^? ideals )\t :i* a race )]s4 ,d n be disc\rag$ by difficulties :i* seem unsurm\ntable4 ,! conditions ( life :i* m\ld u all are modifi$ by our w1 by our en]gy1 & by ! purity ( our int5tions4 ,if we may judge ( int5sity ( feel+ by l5g? ( memory1 ! enjoym5t ( receiv+ a prize bites v deep4 ,across ! space ( m ?an =ty ye>s1 be=e _m ( y\r p>5ts 7 born1 or :5 !y 7 be+ c>ri$ ab\t 9 long clo!s1 ,i c rememb]1 z if x 7 ye/]day1 ! occasion :5 ,i receiv$ my fir/ prize at s*ool4 ,i c see ! m$ival s*ool-room1 ! headma/]1 & my companions4 ,p]haps "s ( y1 :5 a g5]ation has pass$ by1 w rememb] ! sc5e to-night--?is ,/anley ,gymnasium recall+ ! memory ( ,miss ,maude ,/anley1 :o devot$ to our welf>e s mu* ( h] en]gy & h] ?\ght--! adjo9+ ,edric ,hall associat$ ) ! "n ( ,mr4 ,edric ,bayley1 ! ,fa!r ( ! ,in/itute2 ,mr4 ,millis & ,miss ,smi?1 ! fir/ ,pr9cipal & ! fir/ ,lady ,sup]9t5d5t1 ! ar*itects ( our prosp]ity2 ,mr4 ,leon>d ,spic]1 our ,*airman & memb] ( a family & ( a firm kn[n ?r\gh\t ! _w1 & respect$ 9 proportion z !y are kn[n4 ,& ! cause :y to-night we are a small ga!r+ is "o m reason :y ?is assembly c nev] slip f y\r memory4 ,we meet at a mom5t :5 ,engl& /&s 9 z deadly a p]il z 9 any previ\s mom5t ( h] hi/ory--su* p]il z :5 ! ,spani% %ips ( ! ,armada rode 9 ! ,engli% ,*annel1 or :5 ,napoleon wat*$ our coa/ across ! ,/rait ( ,dov]4 ,! pres5t dang] c be ov]come only by ! same c\rage z t :i* sav$ our fre$om 9 ^? =m] times4 ,!re=e1 to-night1 9 recall+ ! activities ( ! v>i\s sections ( our society :i* =m ?is great ,polyte*nic ,in/itute1 our ?\ghts g fur!r afield4 ,!y travel by l& & by sea1 till !y br+ be=e our m9ds ! gallant b& :om ?is ,in/itute has s5t to ! ,front--m ?an #hjj ( our memb]s are ) ! ,col\rs4 ,:at our fight+ m5 h done = u1 = ! _w 9 g5]al1 & = ! future ( ,engl&1 is s ov]:elm+ t words _c praise !m en\gh4 ,i w j say "o ?+ to y3 ,:5 y read ( great de$s done 9 pa/ times1 ( p]ils enc\nt]$1 ( adv5tures1 ( undaunt$ c\rage1 ( patriotism1 ( self-sacrifice1 ( suff]+ endur$ = noble cause1 y ea* c say--,i1 too1 h kn[n su* h]oes2 !y are among my c\ntrym51 !y are among my fell[-work]s1 !y are among my fell[-/ud5ts & companions1 !y are among ! de> inmates ( my home4 ,& = ^? :o h fall51 x is = u to erect a monum5t suffici5t to transmit to future ages ! memory ( _! sacrifice4 ,= ?is purpose !re is only "o memorial :i* c suffice1 namely1 ! cause = :i* !y di$4 ,! greatness ( ,engl&1 ! future ( ,engl&1 has be5 left by !m to our keep+4 ,gu>d x well4 ,! greatness ( a c\ntry is no?+ else ?an ! greatness ( ! lives ( ! m5 & ( ! wom5 :o compose x4 ,d n look r\nd & ?9k :o ought to be great ,engli%m5--be great y\rselves--y are ! p to a*ieve x1 y :o are sitt+ "h to-night4 ,!re c be no sub/itute s]vice = ?is purpose4 ,x is ! collective en]gy ( ! :ole p t w be ne$$ to fa%ion a new ,engl& wor?y ( ! suff]+s :i* = its sake h be5 endur$4 ,a few days ago ,i ask$ a man :o has work$ 9 ,egypt = _m ye>s "u ,"l ,kit*5]1 :at he w\ld pick out z ! be/ sign ( ,"l ,kit*5]'s greatness4 ,he answ]$1 :atev] ,kit*5] set himself to d1 !reby became important4 ,n[ t is ! secret ( x all--take hold ( y\r opportunities & make !m important4 ,"h we are 9 ?is ,bor\gh ,polyte*nic4 ,:at an opportunity x repres5ts4 ,?is ,in/itute is a c5tre = social meet+1 a c5tre = recreation1 a c5tre = education1 a c5tre = discussion4 ,we w n sacrifice any "o ( our sides4 ,!y mu/ all be "p ( ! greatness :i* we claim4 ,make !m all fir/-rate4 ,consid] fir/ ! social & recreative sides4 ,= heav5's sake don't ?9k t y mu/ be dull 9 ord] to be great4 ,!re is no f9] te/ ( a nation ?an ! way 9 :i* x fa%ions its amusem5ts4 ,?ree c5turies ago aft] ! ,armada we made a good />t 9 ,s\?w>k4 ,%akespe>e _h 8 !atre "h & wrote 8 plays to be act$ 9 ?is bor\gh4 ,he has walk$ ^! /reets1 & if y _h met him 9 ,we/m9/] he w\ld1 q likely1 h told y t he 0 go+ d[n to ! ,elephant4 ,& ev5 n[ ! p]=mances giv5 at ! ,old ,vic are among ! be/ 9 ,london = ! purpose ( see+ 8 plays prop]ly act$4 ,:at ,s\?w>k has done = ! drama1 %e c d = ! o!r arts1 by us+ ?is ,in/itute z ! in/rum5t = h] en]gies4 ,:y %\ld we n be a c5tre = arti/ic ent]prise--,i mean = our own art & our own ent]prise1 ?\ght ( by ourselves & enjoy$ by ourselves & c>ri$ ?r\gh by ourselves8 ,we %all n always enjoy ea* o!rs' creations1 b ! great po9t is to make our own ef=ts4 ,( c\rse all ef=ts require prep>ation & /imulus & k ( :at o!rs are do+4 ,at ! pres5t "t--int]rupt$ = ! mom5t by ! w>--a great revolution 9 ! art ( pa9t+ is 9 progress ?r\gh\t ! _w4 ,its c5tres are ,p>is & ,italy & ,london & ,muni*1 & its orig9 9 ! f> ea/1 9 ,*9a & ,japan4 ,!re are two sides z 9 e revolution1 ! ,cons]vatives & ! ,revolutioni/s4 ,our own frescoes 9 a neighb\r+ room repres5t an e>ly /age ( ! movem5t 9 ,london4 ,:y %\ld we n "k all ab\t x--obta9 loans ( pictures :i* illu/rate its phases & its cross curr5ts1 & comp>e ^! ) examples ( ! old /yle8 ,b pictures are only "o phase ( art1 & n ! sort ( art :i* we ourselves c produce mo/ easily4 ,!re are music1 danc+1 recitation1 lit]ature1 c>v+ & modell+1 & ! v>i\s decorative arts1 su* z embroid]y1 bookb9d+1 dress-mak+ & uphol/]y4 ,?is li/1 incomplete z x is1 tells u two great tru?s--y _c sep>ate art & recreation1 & y _c sep>ate art & bus9ess4 ,! li/ includes items :i* we consid] z amusem5ts1 & items :i* we ?9k ( z bus9ess4 ,we began ) danc+ & end$ ) uphol/]y4 ,make !m all beautiful4 ,beautiful ?+s h dignity4 ,enjoy ! rhy?m ( y\r danc+ & admire ! beauty ( y\r embroid]y or y\r bookb9d+4 ,9 :atev] y d1 h an ideal ( excell5ce4 ,any sep>ation betwe5 art & "w is n only an error1 b x is v bad bus9ess4 ,our brave allies1 ! ,fr5*1 h made ,p>is ! art c5tre ( ! _w4 ,!y h built up & ma9ta9 _! l>ge & lucrative trade 9 ! decorative products ( ,france1 ma9ly by reason ( ?ree qualities :i* !y possess4 ,9 ! fir/ place1 !y enjoy art !mselves1 & rev]5ce x4 ,9 ! second place1 !y h a trem5d\s p[] ( h>d "w4 ,& 9 ! ?ird place1 e ,fr5*man1 & /ill m e ,fr5*woman1 h )9 !m an imm5se fund ( common s5se4 ,! ?reefold secret is1 ,love ( ,art1 ,indu/ry1 & ,common ,s5se4 ,to make available our indu/ry & common s5se 9 ! trades :]e !y are want$1 rigor\s tra9+ 9 s*ools ( design & te*nique are necess>y4 ,we h su* dep>tm5ts "h4 ,b all su* tra9+ ( y w be a failure unless y y\rselves enjoy art & beauty z a natural recreation4 ,a te*nical s*ool ( tra9+ is l a deep1 n>r[ well1 sunk ) c>eful lab\r to tap ! und]gr\nd riv] ( wat] :i* fl[s bel[ ! surface ( our natures4 ,b y\r well w be dry unless ! bright w>m sun has fir/ drawn up ! vap\r f ! wide ocean1 & ! free untrammell$ breezes h c>ri$ ! cl\ds hi!r & ?i!r1 until at l5g? !y break1 z x 7 by *ance ov] ! di/ant hills & soak ! l& ) _! d[np\r4 ,:at ,i h said ab\t art is a p>able :i* applies to o!r occupations & o!r /udies4 ,x is m ?an a p>able2 x is ! lit]al tru?4 ,! love ( art is ! love ( excell5ce1 x is ! enjoym5t ( ! triumph ( design ov] ! %apeless products ( *ance =ces4 ,an eng9e]1 :o is wor? 8 salt1 loves ! beauty ( 8 ma*9es1 %[n 9 _! adju/m5t ( p>ts & 9 _! swift1 smoo? motions4 ,he loves also ! s5se ( =esight & ( insight :i* k c give him4 ,p say t ma*9]y & comm]ce are driv+ beauty out ( ! mod]n _w4 ,i d n believe x4 ,a new beauty is be+ add$1 a m intellectual beauty1 appeal+ to ! und]/&+ z mu* z to ! eye4 ,! wond] ( ,london ev] takes ! m9d ) fre% a/oni%m5t4 ,! city possesses p>ks1 & palaces1 & ca!drals4 ,b no o!r p>ts ( x surpass 9 wond] its h\ses ( bus9ess & its work%ops & its factories4 ,9 ! next few ye>s ! future ( ! _w w be decid$ = c5turies to come4 ,! battles ( ?is w> are only ! fir/ "p ( ! conte/ betwe5 races1 & betwe5 ! ways ( life = :i* ^? races /&4 ,we believe t ,engl&1 ) its v>i\s peoples & communities scatt]$ 9 isl&s & cont95ts beyond ! seas1 /&s = ways ( life inf9itely preci\s1 ! way ( humanity1 ! way ( lib]ty1 ! way ( self-gov]nm5t1 ! way ( good ord] bas$ on tol]ation & k9dly feel+1 ! way ( peaceful indu/ry4 ,! f9al decision 9 ?is /ruggle w be f\nd 9 ! work%ops ( ! _w4 ,x lies 9 y\r h&s4 ,/atesm5 & emp]ors w only regi/] ! results :i* y h a*iev$4 ,y\r weapons w be skill1 & en]gy1 & k4 ,y w require a sane und]/&+ ( y\r own rights1 & a sane und]/&+ ( ! rights & ! difficulties ( o!r classes4 ,! greatness ( ,engl& w be y\r greatness1 & its success y\r success4 ,! ars5al = w> is at ,woolwi*4 ,?is ,polyte*nic ,in/itute is an ars5al = peace1 :]e y c f9d ! weapons = ! conque/ ( y\r lives4 ,,*apt] ,,iv ,,! ,,ma!matical ,,curriculum 7,presid5tial ,address to ! ,london ,bran* ( ! ,ma!matical ,association1 #aiab7 ,,! situation 9 reg>d to education at ! pres5t "t _c f9d its p>allel )\t go+ back = "s c5turies to ! break-up ( ! m$ival traditions ( le>n+4 ,!n1 z n[1 ! traditional intellectual outlook1 despite ! au?ority :i* x _h ju/ly acquir$ f its notable triumphs1 _h gr[n to be too n>r[ = ! int]e/s ( mank9d4 ,! result ( ?is %ift+ ( human int]e/ 0 a dem& = a p>allel %ift+ ( ! basis ( education1 s z to fit ! pupils = ! ideas :i* lat] 9 life w\ld 9 fact occupy _! m9ds4 ,any s]i\s fundam5tal *ange 9 ! intellectual outlook ( human society mu/ necess>ily be foll[$ by an educational revolution4 ,x may be delay$ = a g5]ation by ve/$ int]e/s or by ! passionate atta*m5t ( "s lead]s ( ?\ght to ! cycle ( ideas )9 :i* !y receiv$ _! own m5tal /imulus at an impressionable age4 ,b ! law is inexorable t education to be liv+ & effective mu/ be direct$ to in=m+ pupils ) ^? ideas1 & to creat+ = !m ^? capacities :i* w enable !m to appreciate ! curr5t ?\ght ( _! epo*4 ,!re is no su* ?+ z a successful sy/em ( education 9 a vacuum1 t is to say1 a sy/em :i* is divorc$ f imm$iate contact ) ! exi/+ intellectual atmosph]e4 ,education :i* is n mod]n %>es ! fate ( all organic ?+s :i* are kept too long4 ,b ! bless$ ^w mod]n does n really solve our difficulties4 ,:at we mean is1 relevant to mod]n ?\ght1 ei!r 9 ! ideas imp>t$ or 9 ! aptitudes produc$4 ,some?+ f\nd out only ye/]day may n really be mod]n 9 ?is s5se4 ,x may belong to "s bygone sy/em ( ?\ght preval5t 9 a previ\s age1 or1 :at is v mu* m likely1 x may be too recondite4 ,:5 we dem& t education %\ld be relevant to mod]n ?\ght1 we are ref]r+ to ?\ghts broadly spread ?r\gh\t cultivat$ society4 ,x is ?is "q ( ! unfitness ( recondite subjects = use 9 g5]al education :i* ,i wi% to make ! keynote ( my address ?is aft]noon4 ,x is 9 fact r a delicate subject = u ma!maticians4 ,outsid]s are apt to accuse our subject ( be+ recondite4 ,let u grasp ! nettle at once & frankly admit t 9 g5]al op9ion x is ! v typical example ( recondit5ess4 ,by ?is ^w ,i d n mean difficulty1 b t ! ideas involv$ are ( highly special application1 & r>ely influ5ce ?\ght4 ,?is liability to recondit5ess is ! *>act]i/ic evil :i* is apt to de/roy ! utility ( ma!matics 9 lib]al education4 ,s f> z x cl+s to ! educational use ( ! subject1 s f> we mu/ acquiesce 9 a mis]ably l[ level ( ma!matical atta9m5t among cultivat$ p 9 g5]al4 ,i yield to no "o 9 my anxiety to increase ! educational scope ( ma!matics4 ,! way to a*ieve ?is end is n by a m]e bl9d dem& = m ma!matics4 ,we mu/ face ! real difficulty :i* ob/ructs its ext5d$ use4 ,is ! subject recondite8 ,n[1 view$ z a :ole1 ,i ?9k x is4 ,securus judicat orbis t]r>um--! g5]al judgm5t ( mank9d is sure4 ,! subject z x exi/s 9 ! m9ds & 9 ! books ( /ud5ts ( ma!matics is recondite4 ,x proce$s by d$uc+ innum]able special results f g5]al ideas1 ea* result m recondite ?an ! prec$+4 ,x is n my task ?is aft]noon to def5d ma!matics z a subject = pr(\nd /udy4 ,x c v well take c>e ( itself4 ,:at ,i want to emphasise is1 t ! v reasons :i* make ?is sci5ce a delight to its /ud5ts are reasons :i* ob/ruct its use z an educational in/rum5t--namely1 ! b\ndless weal? ( d$uctions f ! int]play ( g5]al !orems1 _! complication1 _! app>5t remot5ess f ! ideas f :i* ! argum5t />t$1 ! v>iety ( me?ods1 & _! purely ab/ract "* :i* br+s1 z its gift1 et]nal tru?4 ,( c\rse1 all ^! *>act]i/ics are ( priceless value to /ud5ts2 = ages !y h fasc9at$ "s ( ! ke5e/ intellects4 ,my only rem>k is t1 except = a highly select$ class1 !y are fatal 9 education4 ,! pupils are bewild]$ by a multiplicity ( detail1 )\t app>5t relevance ei!r to great ideas or to ord9>y ?\ghts4 ,! ext5sion ( ?is sort ( tra9+ 9 ! direction ( acquir+ m detail is ! la/ measure to be desir$ 9 ! int]e/s ( education4 ,! conclusion at :i* we arrive is1 t ma!matics1 if x is to be us$ 9 g5]al education1 mu/ be subject$ to a rigor\s process ( selection & adaptation4 ,i d n mean1 :at is ( c\rse obvi\s1 t h[ev] mu* "t we devote to ! subject ! av]age pupil w n get v f>4 ,b t1 h[ev] limit$ ! progress1 c]ta9 *>act]i/ics ( ! subject1 natural at any /age1 mu/ be rigor\sly exclud$4 ,! sci5ce z pres5t$ to "y pupils mu/ lose its aspect ( recondit5ess4 ,x mu/1 on ! face ( x1 deal directly & simply ) a few g5]al ideas ( f>-rea*+ importance4 ,n[1 9 ?is matt] ( ! re=m ( ma!matical in/ruction1 ! pres5t g5]ation ( tea*]s may take a v legitimate pride 9 its a*ievem5ts4 ,x has %[n imm5se en]gy 9 re=m1 & has accompli%$ m ?an w\ld h be5 ?\ght possible 9 s %ort a "t4 ,x is n always recognis$ h[ difficult is ! task ( *ang+ a well-e/abli%$ curriculum entr5*$ beh9d public exam9ations4 ,b = all t1 great progress has be5 made1 &1 to put ! matt] at its l[e/1 ! old dead tradition has be5 brok5 up4 ,i want to indicate ?is aft]noon ! guid+ idea :i* %\ld direct our ef=ts at recon/ruction4 ,i h already summ$ x up 9 a phrase1 namely1 we mu/ aim at ! elim9ation ( recondit5ess f ! educational use ( ! subject4 ,our c\rses ( in/ruction %\ld be plann$ to illu/rate simply a succession ( ideas ( obvi\s importance4 ,all pretty divagations %\ld be rigor\sly exclud$4 ,! goal to be aim$ at is t ! pupil %\ld acquire famili>ity ) ab/ract ?\ght1 %\ld realise h[ x applies to p>ticul> concrete circum/ances1 & %\ld "k h[ to apply g5]al me?ods to its logical inve/igation4 ,) ?is educational ideal no?+ c be worse ?an ! aimless accretion ( !orems 9 our text-books1 :i* acquire _! position m]ely because ! *ildr5 c be made to le>n !m & exam9]s c set neat que/ions on !m4 ,! bookwork to be le>nt %\ld all be v important z illu/rat+ ideas4 ,! examples set--& let !re be z _m examples z tea*]s f9d necess>y--%\ld be direct illu/rations ( ! !orems1 ei!r by way ( ab/ract p>ticul> cases or by way ( application to concrete ph5om5a4 ,"h x is wor? rem>k+ t x is q useless to simplify ! bookwork1 if ! examples set 9 exam9ations 9 fact require an ext5d$ k ( recondite details4 ,!re is a mi/ak5 idea t problems te/ ability & g5ius1 & t bookwork te/s cram4 ,?is is n my exp]i5ce4 ,only boys :o h be5 specially cramm$ = s*ol>%ips c ev] d a problem pap] successfully4 ,bookwork prop]ly set1 n 9 m]e snippets accord+ to ! usual bad plan1 is a f> bett] te/ ( ability1 provid$ t x is supplem5t$ by direct examples4 ,b ?is is a digression on ! bad influ5ce ( exam9ations on tea*+4 ,! ma9 ideas :i* lie at ! base ( ma!matics are n at all recondite4 ,!y are ab/ract4 ,b "o ( ! ma9 objects ( ! inclusion ( ma!matics 9 a lib]al education is to tra9 ! pupils to h&le ab/ract ideas4 ,! sci5ce con/itutes ! fir/ l>ge gr\p ( ab/ract ideas :i* naturally occur to ! m9d 9 any precise =m4 ,= ! purposes ( education1 ma!matics consi/s ( ! relations ( numb]1 ! relations ( quantity1 & ! relations ( space4 ,?is is n a g5]al def9ition ( ma!matics1 :i*1 9 my op9ion1 is a mu* m g5]al sci5ce4 ,b we are n[ discuss+ ! use ( ma!matics 9 education4 ,^! ?ree gr\ps ( relations1 conc]n+ numb]1 quantity1 & space1 are int]connect$4 ,n[1 9 education we proce$ f ! p>ticul> to ! g5]al4 ,accord+ly1 *ildr5 %\ld be taught ! use ( ^! ideas by practice among simple examples4 ,my po9t is ?is3 ,! goal %\ld be1 n an aimless accumulation ( special ma!matical !orems1 b ! f9al recognition t ! prec$+ ye>s ( "w h illu/rat$ ^? relations ( numb]1 & ( quantity1 & ( space1 :i* are ( fundam5tal importance4 ,su* a tra9+ %\ld lie at ! base ( all philosophical ?\ght4 ,9 fact elem5t>y ma!matics rightly conceiv$ w\ld give j t philosophical discipl9e ( :i* ! ord9>y m9d is capable4 ,b :at at all co/s we ought to avoid1 is ! po9tless accumulation ( details4 ,z _m examples z y l2 let ! *ildr5 "w at !m = t]ms1 or = ye>s4 ,b ^! examples %\ld be direct illu/rations ( ! ma9 ideas4 ,9 ?is way1 & ?is only1 c ! fatal recondit5ess be avoid$4 ,i am n n[ speak+ 9 p>ticul> ( ^? :o are to be pr(essional ma!maticians1 or ( ^? :o = pr(essional reasons require a k ( c]ta9 ma!matical details4 ,we are consid]+ ! lib]al education ( all /ud5ts1 includ+ ^! two classes4 ,?is g5]al use ( ma!matics %\ld be ! simple /udy ( a few g5]al tru?s1 well illu/rat$ by practical examples4 ,?is /udy %\ld be conceiv$ by itself1 & completely sep>at$ 9 idea f ! pr(essional /udy m5tion$ above1 = :i* x w\ld make a mo/ excell5t prep>ation4 ,its f9al /age %\ld be ! recognition ( ! g5]al tru?s :i* ! "w done has illu/rat$4 ,z f> z ,i c make out1 at pres5t ! f9al /age is ! pro( ( "s prop]ty ( circles connect$ ) triangles4 ,su* prop]ties are imm5sely int]e/+ to ma!maticians4 ,b are !y n r recondite1 & :at is ! precise relation ( su* !orems to ! ideal ( a lib]al education8 ,! end ( all ! grammatical /udies ( ! /ud5t 9 classics is to read ,virgil & ,horace--! greate/ ?\ghts ( ! greate/ m54 ,are we cont5t1 :5 plead+ = ! adequate repres5tation 9 education ( our own sci5ce1 to say t ! end ( a ma!matical tra9+ is t ! /ud5t %\ld "k ! prop]ties ( ! n9e-po9t circle8 ,i ask y frankly1 is x n r a come d[n8 ,?is g5]ation ( ma!matical tea*]s has done s mu* /r5u\s "w 9 ! way ( reorganis+ ma!matical in/ruction t !re is no ne$ to despair ( its be+ able to elaborate a curriculum :i* %all leave 9 ! m9ds ( ! pupils some?+ ev5 nobl] ?an ! ambigu\s case4 ,let u ?9k h[ ?is f9al review1 clos+ ! elem5t>y c\rse1 might be conduct$ = ! m intellig5t pupils4 ,p>tly no d\bt x requires a g5]al ov]sight ( ! :ole "w done1 consid]$ )\t undue detail s z to emphasise ! g5]al ideas us$1 & _! possibilities ( importance :5 subject$ to fur!r /udy4 ,also ! analytical & geometrical ideas f9d imm$iate application 9 ! physical laboratory :]e a c\rse ( simple exp]im5tal me*anics %\ld h be5 work$ ?r\gh4 ,"h ! po9t ( view is tw(old1 ! physical ideas & ! ma!matical ideas illu/rate ea* o!r4 ,! ma!matical ideas are ess5tial to ! precise =mulation ( ! me*anical laws4 ,! idea ( a precise law ( nature1 ! ext5t to :i* su* laws are 9 fact v]ifi$ 9 our exp]i5ce1 & ! rle ( ab/ract ?\ght 9 _! =mulation1 !n become practically app>5t to ! pupil4 ,! :ole topic ( c\rse requires detail$ developm5t ) full p>ticul> illu/ration1 & is n sugge/$ z requir+ m]ely a few b>e ab/ract /atem5ts4 ,x w\ld1 h[ev]1 be a grave error to put too mu* emphasis on ! m]e process ( direct explanation ( ! previ\s "w by way ( f9al review4 ,my po9t is1 t ! latt] end ( ! c\rse %\ld be s select$ t 9 fact ! g5]al ideas und]ly+ all ! previ\s ma!matical "w %\ld be br\ght into prom95ce4 ,?is may well be done by app>5tly ent]+ on a new subject4 ,= example1 ! ideas ( quantity & ! ideas ( numb] are fundam5tal to all precise ?\ght4 ,9 ! previ\s /ages !y w n h be5 %>ply sep>at$2 & *ildr5 are1 rightly en\gh1 pu%$ on to algebra )\t too mu* bo!r & quantity4 ,b ! m intellig5t among !m at ! end ( _! curriculum w\ld ga9 imm5sely by a c>eful consid]ation ( ^? fundam5tal prop]ties ( quantity 9 g5]al :i* lead to ! introduction ( num]ical measurem5t4 ,?is is a topic :i* also has ! advantage t ! necess>y books are actually to h&4 ,euclid's fif? book is reg>d$ by ^? qualifi$ to judge z "o ( ! triumphs ( ,greek ma!matics4 ,x deals ) ?is v po9t4 ,no?+ c be m *>act]i/ic ( ! hopelessly illib]al "* ( ! traditional ma!matical education ?an ! fact t ?is book has always be5 omitt$4 ,x deals ) ideas1 & !re=e 0 o/racis$4 ,( c\rse a c>eful selection ( ! m important propositions & a c>eful revision ( ! argum5t are requir$4 ,?is also is to h& 9 ! publications ( my imm$iate pr$ecessor 9 ! (fice ( presid5t1 ,pr(4 ,hill4 ,fur!rmore1 9 ,sir ,t4 ,l4 ,hea?'s complete edition ( ,euclid1 !re is a full comm5t>y embody+ mo/ ( :at has be5 said & ?\ght on ! po9t4 ,?us x is p]fectly easy = tea*]s to in=m !mselves g5]ally on ! topic4 ,! :ole book w\ld n be want$1 b j ! few propositions :i* embody ! fundam5tal ideas4 ,! subject is n fit = backw>d pupils2 b c]ta9ly x c\ld be made int]e/+ to ! m advanc$ class4 ,!re w\ld be great scope = int]e/+ discussion z to ! nature ( quantity1 & ! te/s :i* we %\ld apply to asc]ta9 :5 we are deal+ ) quantities4 ,! "w w\ld n be at all 9 ! air1 b w\ld be illu/rat$ at e /age by ref]5ce to actual examples ( cases :]e ! quantitative "* is abs5t1 or obscure1 or d\btful1 or evid5t4 ,temp]ature1 heat1 electricity1 pleasure & pa91 mass & di/ance c\ld all be consid]$4 ,ano!r idea :i* requires illu/ration is t ( functionality4 ,a function 9 analysis is ! c\nt]p>t ( a law 9 ! physical univ]se1 & ( a curve 9 geometry4 ,*ildr5 h /udi$ ! relations ( functions to curves f ! fir/ beg9n+ ( _! /udy ( algebra1 namely 9 draw+ graphs4 ,( rec5t ye>s !re has be5 a great re=m 9 respect to graphs4 ,b at its pres5t /age x has ei!r gone too f> or n f> en\gh4 ,x is n en\gh m]ely to draw a graph4 ,! idea beh9d ! graph--l ! man beh9d ! gun--is ess5tial 9 ord] to make x effective4 ,at pres5t !re is "s t5d5cy m]ely to set ! *ildr5 to draw curves1 & !re to leave ! :ole "q4 ,9 ! /udy ( simple algebraic functions & ( trigonometrical functions we are initiat+ ! /udy ( ! precise expression ( physical laws4 ,curves are ano!r way ( repres5t+ ^! laws4 ,! simple fundam5tal laws--su* z ! inv]se squ>e & ! direct di/ance--%\ld be pass$ "u review1 & ! applications ( ! simple functions to express important concrete cases ( physical laws consid]$4 ,i _c help ?9k+ t ! f9al review ( ?is topic might well take ! =m ( a /udy ( "s ( ! ma9 ideas ( ! diff]5tial calculus appli$ to simple curves4 ,!re is no?+ p>ticul>ly difficult ab\t ! conception ( a rate ( *ange2 & ! diff]5tiation ( a few p[]s ( x1 su* z x#b1 x#c1 etc41 c\ld easily be effect$2 p]haps by ! aid ( geometry ev5 s9 x & cos x c\ld be diff]5tiat$4 ,if we once ab&on our fatal habit ( cramm+ ! *ildr5 ) !orems :i* !y d n und]/&1 & w nev] use1 !re w be pl5ty ( "t to conc5trate _! att5tion on really important topics4 ,we c give !m famili>ity ) conceptions :i* really influ5ce ?\ght4 ,be=e leav+ ?is topic ( physical laws & ma!matical functions1 !re are o!r po9ts to be notic$4 ,! fact t ! precise law is nev] really v]ifi$ by obs]vation 9 its full precision is capable ( easy illu/ration & ( af=d+ excell5t examples4 ,aga91 /ati/ical laws1 namely laws :i* are only satisfi$ on ! av]age by l>ge numb]s1 c easily be /udi$ & illu/rat$4 ,9 fact a slight /udy ( /ati/ical me?ods & _! application to social ph5om5a af=ds "o ( ! simple/ examples ( ! application ( algebraic ideas4 ,ano!r way 9 :i* ! /ud5ts' ideas c be g5]alis$ is by ! use ( ! ,hi/ory ( ,ma!matics1 conceiv$ n z a m]e assemblage ( ! dates & names ( m51 b z an exposition ( ! g5]al curr5t ( ?\ght :i* occasion$ ! subjects to be objects ( int]e/ at ! "t ( _! fir/ elaboration4 ,! use ( ! ,hi/ory ( ,ma!matics is to be consid]$ at a lat] /age ( our proce$+s ?is aft]noon4 ,accord+ly ,i m]ely draw att5tion to x n[1 to po9t out t p]haps x is ! v subject :i* may be/ obta9 ! results = :i* ,i am plead+4 ,we h indicat$ two ma9 topics1 namely g5]al ideas ( quantity & ( laws ( nature1 :i* %\ld be an object ( /udy 9 ! ma!matical curriculum ( a lib]al education4 ,b !re is ano!r side to ma!matics :i* mu/ n be ov]look$4 ,x is ! *ief in/rum5t = discipl9e 9 logical me?od4 ,n[1 :at is logical me?od1 & h[ c any "o be tra9$ 9 x8 ,logical me?od is m ?an ! m]e k ( valid types ( reason+ & practice 9 ! conc5tration ( m9d necess>y to foll[ !m4 ,if x 7 only ?is1 x w\ld /ill be v important2 = ! human m9d 0 n evolv$ 9 ! bygone ages = ! sake ( reason+1 b m]ely to enable mank9d ) m art to hunt betwe5 meals = fre% food supplies4 ,accord+ly few p c foll[ close reason+ )\t consid]able practice4 ,m ?an ?is is want$ to make a good reason]1 or ev5 to enlight5 ord9>y p ) k ( :at con/itutes ! ess5ce ( ! art4 ,! art ( reason+ consi/s 9 gett+ hold ( ! subject at ! "r end1 ( seiz+ on ! few g5]al ideas :i* illum9ate ! :ole1 & ( p]si/5tly m>%all+ all subsidi>y facts r\nd !m4 ,nobody c be a good reason] unless by con/ant practice he has realis$ ! importance ( gett+ hold ( ! big ideas & ( hang+ on to !m l grim dea?4 ,= ?is sort ( tra9+ geometry is1 ,i ?9k1 bett] ?an algebra4 ,! field ( ?\ght ( algebra is r obscure1 :]eas space is an obvi\s insi/5t ?+ evid5t to all4 ,!n ! process ( simplification1 or ab/raction1 by :i* all irrelevant prop]ties ( matt]1 su* z col\r1 ta/e1 & weight1 are put aside is an education 9 itself4 ,aga91 ! def9itions & ! propositions assum$ )\t pro( illu/rate ! necessity ( =m+ cle> notions ( ! fundam5tal facts ( ! subject-matt] & ( ! relations betwe5 !m4 ,all ?is belongs to ! m]e prolegom5a ( ! subject4 ,:5 we come to its developm5t1 its excell5ce increases4 ,! le>n] is n initially confront$ ) any symbolism :i* bo!rs ! memory by its rules1 h[ev] simple !y may be4 ,also1 f ! v beg9n+ ! reason+1 if prop]ly conduct$1 is dom9at$ by well-m>k$ ideas :i* guide ea* /age ( developm5t4 ,accord+ly ! ess5ce ( logical me?od receives imm$iate exemplification4 ,let u n[ put aside = ! mom5t ! limitations introduc$ by ! dullness ( av]age pupils & ! pressure on "t due to o!r subjects1 & consid] :at geometry has to (f] 9 ! way ( a lib]al education4 ,i w indicate "s /ages 9 ! subject1 )\t mean+ t necess>ily !y are to be /udi$ 9 ?is exclusive ord]4 ,! fir/ /age is ! /udy ( congru5ce4 ,our p]ception ( congru5ce is 9 practice dep5d5t on our judgm5ts ( ! inv>iability ( ! intr9sic prop]ties ( bodies :5 _! ext]nal circum/ances are v>y+4 ,b h[ev] x arises1 congru5ce is 9 ess5ce ! correlation ( two regions ( space1 po9t by po9t1 s t all homolog\s di/ances & all homolog\s angles are equal4 ,x is to be notic$ t ! def9ition ( ! equality ( l5g?s & angles is _! congru5ce1 & all te/s ( equality1 su* z ! use ( ! y>d measure1 are m]ely devices = mak+ imm$iate judgm5ts ( congru5ce easy4 ,i make ^! rem>ks to sugge/ t ap>t f ! reason+ connect$ ) x1 congru5ce1 bo? z an example ( a l>g] & v f>-rea*+ idea & also = its own sake1 is well wor?y ( att5tive consid]ation4 ,! propositions conc]n+ x elucidate ! elem5t>y prop]ties ( ! triangle1 ! p>allelogram1 & ! circle1 & ( ! relations ( two planes to ea* o!r4 ,x is v desirable to re/rict ! prov$ propositions ( ?is "p )9 ! n>r[e/ b\nds1 p>tly by assum+ r$undant axiomatic propositions1 & p>tly by introduc+ only ^? propositions ( absolutely fundam5tal importance4 ,! second /age is ! /udy ( simil>ity4 ,?is c be r$uc$ to ?ree or f\r fundam5tal propositions4 ,simil>ity is an enl>gem5t ( ! idea ( congru5ce1 &1 l t idea1 is ano!r example ( a "o-to-"o correlation ( po9ts ( spaces4 ,any ext5sion ( /udy ( ?is subject might well be 9 ! direction ( ! inve/igation ( "o or two simple prop]ties ( simil> & simil>ly situat$ rectil9e> figures4 ,! :ole subject receives its imm$iate applications 9 plans & maps4 ,x is important1 h[ev]1 to rememb] t trigonometry is really ! me?od by :i* ! ma9 !orems are made available = use4 ,! ?ird /age is ! /udy ( ! elem5ts ( trigonometry4 ,?is is ! /udy ( ! p]iodicity introduc$ by rotation & ( prop]ties pres]v$ 9 a correlation ( simil> figures4 ,"h = ! fir/ "t we introduce a slight use ( ! algebraic analysis f\nd$ on ! /udy ( numb] & quantity4 ,! importance ( ! p]iodic "* ( ! functions requires full illu/ration4 ,! simple/ prop]ties ( ! functions are ! only ones requir$ = ! solution ( triangles1 & ! consequ5t applications to survey+4 ,! weal? ( =mul1 (t5 important 9 !mselves1 b entirely useless = ?is type ( /udy1 :i* cr[d our books %\ld be rigor\sly exclud$1 except s f> z !y are capable ( be+ prov$ by ! pupils z direct examples ( ! bookwork4 ,?is "q ( ! exclusion ( =mul is be/ illu/rat$ by consid]+ ?is example ( ,trigonometry1 ?\gh ( c\rse ,i may well h hit on an un=tunate case 9 :i* my judgm5t is at fault4 ,a great "p ( ! educational advantage ( ! subject c be obta9$ by conf9+ /udy to ,trigonometry ( "o angle & by exclusion ( ! addition =mul = ! s9e & cos9e ( ! sum ( two angles4 ,! functions c be graph$1 & ! solution ( triangles effect$4 ,?us ! aspects ( ! sci5ce z 7#a7 embody+ analytically ! imm$iate results ( "s ( ! !orems d$uc$ f congru5ce & simil>ity1 7#b7 z a solution ( ! ma9 problem ( survey+1 7#c7 z a /udy ( ! fundam5tal functions requir$ to express p]iodicity & wave motion1 w all be impress$ on ! pupils' m9ds bo? by bookwork & example4 ,if x be desir$ to ext5d ?is c\rse1 ! addition =mul %\ld be add$4 ,b great c>e %\ld be tak5 to exclude specialis+ ! pupils 9 ! weal? ( =mul :i* comes 9 _! tra94 ,by exclude is meant t ! pupils %\ld n h sp5t "t or en]gy 9 acquir+ any facility 9 _! d$uction4 ,! tea*] may f9d x int]e/+ to "w a few su* examples be=e a class4 ,b su* results are n among ^? :i* le>n]s ne$ reta94 ,also1 ,i w\ld exclude ! :ole subject ( circumscrib$ & inscrib$ circles bo? f ,trigonometry & f ! previ\s geometrical c\rses4 ,x is all v pretty1 b ,i d n und]/& :at its function is 9 an elem5t>y non-pr(essional curriculum4 ,accord+ly1 ! actual bookwork ( ! subject is r$uc$ to v manageable proportions4 ,i 0 told ! o!r day ( an ,am]ican college :]e ! /ud5ts are expect$ to "k by he>t n9ety =mul or results 9 ,trigonometry alone4 ,we are n q s bad z t4 ,9 fact1 9 ,trigonometry we h ne>ly approa*$ ! ideal "h sket*$ out z f> z our elem5t>y c\rses are conc]n$4 ,! f\r? /age introduces ,analytical ,geometry4 ,! /udy ( graphs 9 algebra has already employ$ ! fundam5tal notions1 & all t is n[ requir$ is a rigor\sly prun$ c\rse on ! /raight l9e1 ! circle1 & ! ?ree types ( conic sections1 def9$ by ! =ms ( _! equations4 ,at ?is po9t !re are two rem>ks to be made4 ,x is (t5 desirable to give our pupils ma!matical in=mation :i* we d n prove4 ,= example1 9 co-ord9ate geometry1 ! r$uction ( ! g5]al equation ( ! second degree is probably beyond ! capacities ( mo/ ( ! type ( /ud5ts :om we are consid]+4 ,b t ne$ n prev5t u f expla9+ ! fundam5tal position ( conics1 z exhau/+ ! possible types ( su* curves4 ,! second rem>k is to advocate ! entire sweep+ away ( geometrical conics z a sep>ate subject4 ,naturally1 on suitable occasions ! analysis ( analytical geometry w be light5$ by ! use ( direct d$uction f "s simple figure4 ,b geometrical conics1 z develop$ f ! def9ition ( a conic section by ! focus & directrix prop]ty1 suff]s f gl>+ defects4 ,x is hopelessly recondite4 ,! fundam5tal def9ition ( a conic1 ,,sp e ,,pm1 usual 9 ?is subject at ?is /age1 is ?or\ghly bad4 ,x is v recondite1 & has no obvi\s importance4 ,:y %\ld su* curves be /udi$ at all1 any m ?an ^? def9$ by an indef9ite numb] ( o!r =mul8 ,b :5 we h comm5c$ ! /udy ( ! ,c>tesian me?ods1 ! equations ( ! fir/ & second degrees are naturally ! fir/ ?+s to ?9k ab\t4 ,9 ?is ideal c\rse ( ,geometry1 ! fif? /age is occupi$ ) ! elem5ts ( ,projective ,geometry4 ,! g5]al ideas ( cross ratio & ( projection are "h fundam5tal4 ,projection is yet a m g5]al in/ance ( t "o-to-"o correlation :i* we h already consid]$ "u congru5ce & simil>ity4 ,"h aga9 we mu/ avoid ! dang] ( be+ l$ into a bewild]+ weal? ( detail4 ,! intellectual idea :i* projective geometry is to illu/rate is ! importance 9 reason+ ( ! correlation ( all cases :i* c be prov$ to possess 9 common c]ta9 id5tical prop]ties4 ,! pres]vation ( ! projective prop]ties 9 projection is ! "o important educational idea ( ! subject4 ,cross ratio only ent]s z ! fundam5tal metrical prop]ty :i* is pres]v$4 ,! few propositions consid]$ are select$ to illu/rate ! two alli$ processes :i* are made possible by ?is proc$ure4 ,"o is pro( by simplification4 ,"h ! simplification is psy*ological & n logical--= ! g5]al case is logically ! simple/4 ,:at is meant is3 ,pro( by consid]+ ! case :i* is 9 fact ! mo/ famili> to u1 or ! easie/ to ?9k ab\t4 ,! o!r proc$ure is ! d$uction ( p>ticul> cases f kn[n g5]al tru?s1 z soon z we h a means ( discov]+ su* cases or a crit]ion = te/+ !m4 ,! projective def9ition ( conic sections & ! id5tity ( ! results obta9$ ) ! curves d]iv$ f ! g5]al equation ( ! second degree are capable ( simple exposition1 b lie on ! bord]-l9e ( ! subject4 ,x is ! sort ( topic on :i* in=mation c be giv51 & ! pro(s suppress$4 ,! c\rse ( geometry z "h conceiv$ 9 its complete ideal--& ideals c nev] be realis$--is n a long "o4 ,! actual am\nt ( ma!matical d$uction at ea* /age 9 ! =m ( bookwork is v slight4 ,b mu* m explanation w\ld be giv51 ! importance ( ea* proposition be+ illu/rat$ by examples1 ei!r work$ out or = /ud5ts to "w1 s select$ z to indicate ! fields ( ?\ght to :i* x applies4 ,by su* a c\rse ! /ud5t w\ld ga9 an analysis ( ! lead+ prop]ties ( space1 & ( ! *ief me?ods by :i* !y are inve/igat$4 ,! /udy ( ! elem5ts ( ma!matics1 conceiv$ 9 ?is _s1 w\ld con/itute a tra9+ 9 logical me?od toge!r ) an acquisition ( ! precise ideas :i* lie at ! base ( ! sci5tific & philosophical inve/igations ( ! univ]se4 ,w\ld x be easy to cont9ue ! excell5t re=ms 9 ma!matical in/ruction :i* ?is g5]ation has already a*iev$1 s z to include 9 ! curriculum ?is wid] & m philosophic _s8 ,frankly1 ,i ?9k t ?is result w\ld be v h>d to a*ieve z ! result ( s+le individual ef=ts4 ,= reasons :i* ,i h already briefly indicat$1 all re=ms 9 education are v difficult to effect4 ,b ! cont9u$ pressure ( comb9$ ef=t1 provid$ t ! ideal is really pres5t 9 ! m9ds ( ! mass ( tea*]s1 c d mu*1 & effects 9 ! end surpris+ modification4 ,gradually ! requisite books get writt51 /ill m gradually ! exam9ations are re=m$ s z to give weight to ! less te*nical aspects ( ! subject1 & !n all rec5t exp]i5ce has %[n t ! majority ( tea*]s are only too ready to welcome any practicable means ( rescu+ ! subject f ! reproa* ( be+ a me*anical discipl9e4 ,,*apt] ,v ,,! ,,pr9ciples ,,( ,,ma!matics ,,9 ,,relation ,,to ,,elem5t>y ,,tea*+ 7,int]national ,congress ( ,ma!maticians1 ,cambridge1 ,augu/1 #aiab7 ,,we are conc]n$ n ) ! advanc$ tea*+ ( a few speciali/ ma!matical /ud5ts1 b ) ! ma!matical education ( ! majority ( boys 9 our second>y s*ools4 ,aga9 ^! boys mu/ be divid$ into two sections3 "o section consi/s ( ^? :o desire to re/rict _! ma!matical education2 ! o!r section is made up ( ^? :o w require "s ma!matical tra9+ = _! subsequ5t pr(essional c>e]s1 ei!r 9 ! =m ( def9ite ma!matical results or 9 ! =m ( ma!matically tra9$ m9ds4 ,i %all call ! latt] ( ^! two sections ! ma!matical section1 & ! =m] ! non-ma!matical section4 ,b ,i mu/ repeat t by ! ma!matical section is meant t l>ge numb] ( boys :o desire to le>n m ?an ! m9imum am\nt ( ma!matics4 ,fur!rmore1 mo/ ( my rem>ks ab\t ^! sections ( boys apply also to elem5t>y classes ( our ,univ]sity /ud5ts4 ,! subject ( ?is pap] is ! inve/igation ( ! place :i* %\ld be occupi$ by mod]n inve/igations respect+ ma!matical pr9ciples 9 ! education ( bo? ( ^! sections ( s*ool-boys4 ,to f9d a foo?old f :i* to />t ! inquiry1 let u ask :y ! non-ma!matical section %\ld be taught any ma!matics at all beyond ! b>e/ elem5ts ( ari?metic4 ,:at are ! qualities ( m9d :i* a ma!matical tra9+ is design$ to produce :5 x is employ$ z an elem5t 9 a lib]al education8 ,my answ]1 :i* applies equally to bo? sections ( /ud5ts1 is t !re are two alli$ =ms ( m5tal discipl9e :i* %\ld be acquir$ by a well-design$ ma!matical c\rse4 ,^! two =ms ?\gh closely alli$ are p]fectly di/9ct4 ,! fir/ =m ( discipl9e is n 9 its ess5ce logical at all4 ,x is ! p[] ( cle>ly grasp+ ab/ract ideas1 & ( relat+ !m to p>ticul> circum/ances4 ,9 o!r words1 ! fir/ use ( ma!matics is to /r5g!n ! p[] ( ab/ract ?\ght4 ,i repeat t 9 its ess5ce ?is has no?+ to d ) logic1 ?\gh z a matt] ( fact a logical discipl9e is ! be/ me?od ( produc+ ! desir$ effect4 ,x is n ! philosophical !ory ( ab/ract ideas :i* is to be acquir$1 b ! habit & ! p[] ( us+ !m4 ,!re is "o & only way ( acquir+ ! habit & ! p[] ( us+ any?+1 t is by ! simple common-place me?od ( habitually us+ x4 ,!re is no o!r %ort cut4 ,if 9 education we desire to produce a c]ta9 con=mation ( m9d1 we mu/ day by day1 & ye> by ye>1 accu/om ! /ud5ts' m9ds to gr[ into ! desir$ /ructural %ape4 ,?us to tea* ! p[] ( grasp+ ab/ract ideas & ! habit ( us+ !m1 we mu/ select a gr\p ( su* ideas1 :i* are important & are also easy to ?9k ab\t because !y are cle> & def9ite4 ,! fundam5tal ma!matical tru?s conc]n+ geometry1 ratio1 quantity1 & numb]1 satisfy ^! conditions z d no o!rs4 ,h5ce1 ! fundam5tal univ]sal position held by ma!matics z an elem5t ( a lib]al education4 ,b :at are ! fundam5tal ma!matical tru?s conc]n+ geometry1 quantity & numb]8 ,at ?is po9t we come to ! great "q ( ! relation betwe5 ! mod]n sci5ce ( ! pr9ciples ( ma!matics & a ma!matical education4 ,my answ] to ! "q z to ^! fundam5tal ma!matical tru?s is1 t 9 any absolute s5se !re are none4 ,!re is no unique small body ( indep5d5t primitive unprov$ propositions :i* are ! necess>y />t+ po9ts ( all ma!matical reason+ on ^! subjects4 ,9 ma!matical reason+ ! only absolute necess>y pre-suppositions are ^? :i* make logical d$uction possible4 ,betwe5 ^! absolute logical tru?s & s-call$ fundam5tal tru?s conc]n+ geometry1 quantity & numb]1 !re is a :ole new _w ( ma!matical subjects conc]n+ ! logic ( propositions1 ( classes1 & ( relations4 ,b ?is subject is too ab/ract to =m an elem5t>y tra9+ gr\nd 9 ! difficult art ( ab/ract ?\ght4 ,x is = ?is reason t we h to make a compromise & />t f su* obvi\s g5]al ideas z naturally occur to all m5 :5 !y p]ceive objects ) _! s5ses4 ,9 geometry1 ! ideas elaborat$ by ! ,greeks & pres5t$ by ,euclid are1 r\ghly speak+1 ^? adapt$ = our purpose1 namely1 ideas ( volumes1 surfaces1 l9es1 ( /raightness & ( curvature1 ( int]section & ( congru5ce1 ( great] & less1 ( simil>ity1 %ape1 & scale4 ,9 fact1 we use 9 education ^? g5]al ideas ( spatial prop]ties :i* mu/ be habitually pres5t 9 ! m9d ( any "o :o is to obs]ve ! _w ( ph5om5a ) und]/&+4 ,?us we come back to ,plato's op9ion t = a lib]al education1 geometry1 z he knew x1 is ! que5 ( sci5ces4 ,9 addition to geometry1 !re rema9 ! ideas ( quantity1 ratio1 & ( numb]4 ,?is 9 practice means1 elem5t>y algebra4 ,"h ! prom95t ideas are ^? ( any numb]1 9 o!r words1 ! use ( ! famili> x1 y1 z1 & ( ! dep5d5ce ( v>iables on ea* o!r1 or o!rwise1 ! idea ( functionality4 ,all ?is is to be gradually acquir$ by ! cont9ual use ( ! v simple/ functions :i* we c devise3 ( l9e> functions1 graphically repres5t$ by /raight l9es2 ( quadratic functions1 graphically repres5t$ by p>abolas2 & ( ^? simple implicit functions1 graphically repres5t$ by conic sections4 ,!nce1 ) good =tune & a will+ class1 we c advance to ! ideas ( rates ( increase1 /ill conf9+ ourselves to ! simple/ possible cases4 ,i wi% "h emphatically to rem9d y t bo? 9 geometry & 9 algebra a cle> grasp ( ^! g5]al ideas is n :at ! pupil />ts f1 x is ! goal at :i* he is to arrive4 ,! me?od ( progression is cont9ual practice 9 ! consid]ation ( ! simple/ p>ticul> cases1 & ! goal is n philosophical analysis b ! p[] ( use4 ,b h[ is he to practise himself 9 _! use8 ,he _c simply sit d[n & ?9k ( ! relation y x #a1 he mu/ employ x 9 "s simple obvi\s way4 ,?is br+s u to ! second p[] ( m9d :i* is to be produc$ by a ma!matical tra9+1 namely1 ! p[] ( logical reason+4 ,"h aga91 x is n ! k ( ! philosophy ( logic :i* x is ess5tial to tea*1 b ! habit ( ?9k+ logically4 ,by logic1 ,i mean d$uctive logic4 ,d$uctive logic is ! sci5ce ( c]ta9 relations1 su* z implication1 etc41 betwe5 g5]al ideas4 ,:5 logic beg9s1 def9ite p>ticul> individual ?+s h be5 bani%$4 ,i _c relate logically ?is ?+ to t ?+1 = example ?is p5 to t p51 except by ! indirect way ( relat+ "s g5]al idea :i* applies to ?is p5 to "s g5]al idea :i* applies to t p54 ,& ! individualities ( ! two p5s are q irrelevant to ! logical process4 ,?is process is entirely conc]n$ ) ! two g5]al ideas4 ,?us ! practice ( logic is a c]ta9 way ( employ+ ! m9d 9 ! consid]ation ( su* ideas2 & an elem5t>y ma!matical tra9+ is 9 fact no?+ else b ! logical use ( ! g5]al ideas respect+ geometry & algebra :i* we h enum]at$ above4 ,x has !re=e1 z ,i />t$ ?is pap] by /at+1 a d\ble advantage4 ,x makes ! m9d capable ( ab/ract ?\ght1 & x a*ieves ?is object by tra9+ ! m9d 9 ! mo/ important k9d ( ab/ract ?\ght1 namely1 d$uctive logic4 ,i may rem9d y t o!r *oices ( a type ( ab/ract ?\ght might be made4 ,we might tra9 ! *ildr5 to contemplate directly ! beauty ( ab/ract moral ideas1 9 ! hope ( mak+ !m religi\s my/ics4 ,! g5]al practice ( education has decid$ 9 fav\r ( logic1 z exemplifi$ 9 elem5t>y ma!matics4 ,we h n[ to answ] ! fur!r "q1 :at is ! rle ( logical precision 9 ! tea*+ ( ma!matics8 ,our g5]al answ] to ! impli$ "q is obvi\s3 logical precision is "o ( ! two objects ( ! tea*+ ( ma!matics1 & x is ! only weapon by :i* ! tea*+ ( ma!matics c a*ieve its o!r object4 ,to tea* ma!matics is to tea* logical precision4 ,a ma!matical tea*] :o has n taught t has taught no?+4 ,b hav+ /at$ ?is !sis 9 ?is unqualifi$ way1 its mean+ mu/ be c>efully expla9$2 = o!rwise its real be>+ on ! problem w be entirely misund]/ood4 ,logical precision is ! faculty to be acquir$4 ,x is ! quality ( m9d :i* x is ! object ( ! tea*+ to imp>t4 ,?us ! habit ( read+ great lit]ature is ! goal at :i* a lit]>y education aims4 ,b we d n expect a *ild to />t its fir/ lesson by read+ = itself ,%akespe>e4 ,we recognise t read+ is impossible till ! pupil has le>nt its alphabet & c spell1 & !n we />t x ) books ( "o syllable4 ,9 ! same way1 a ma!matical education %\ld gr[ 9 logical precision4 ,x is folly to expect ! same c>eful logical analysis at ! comm5cem5t ( ! tra9+ z w\ld be appropriate at ! end4 ,x is an entire misconception ( my !sis to con/rue x z mean+ t a ma!matical tra9+ %\ld assume 9 ! pupil a p[] ( conc5trat$ logical ?\ght4 ,my !sis is 9 fact ! exact opposite1 namely1 t ?is p[] _c be assum$1 & has got to be acquir$1 & t a ma!matical tra9+ is no?+ else ?an ! process ( acquir+ x4 ,my :ole gr\ndwork ( assumption is t ?is p[] does n initially exi/ 9 a fully develop$ /ate4 ,( c\rse l e o!r p[] :i* is acquir$1 x mu/ be develop$ gradually4 ,! v>i\s /ages ( developm5t mu/ be guid$ by ! judgm5t & ! g5ius ( ! tea*]4 ,b :at is ess5tial is1 t ! tea*] %\ld keep cle>ly 9 8 m9d t x is j ?is p[] ( logical precise reason+ :i* is ! :ole object ( 8 ef=ts4 ,if 8 pupils h 9 any measure ga9$ ?is1 !y h ga9$ all4 ,we h n yet1 h[ev]1 fully consid]$ ?is "p ( our subject4 ,logical precision is ! full realisation ( ! /eps ( ! argum5t4 ,b :at are ! /eps ( ! argum5t8 ,! full /atem5t ( all ! /eps is f> too elaborate & difficult an op]ation to be introduc$ into ! ma!matical reason+ ( an educational curriculum4 ,su* a /atem5t involves ! introduction ( ab/ract logical ideas :i* are v difficult to grasp1 because !re is s r>ely any ne$ to make !m explicit 9 ord9>y ?\ght4 ,!y are !re=e n a fit subject-gr\nd = an elem5t>y education4 ,i d n ?9k t x is possible to draw any !oretical l9e betwe5 ^? logical /eps :i* =m a !oretically full logical inve/igation1 & ^? :i* are full en\gh = mo/ practical purposes1 includ+ t ( education4 ,! "q is "o ( psy*ology1 to be solv$ by a process ( exp]im5t4 ,! object to be atta9$ is to ga9 t am\nt ( logical al]tness :i* w enable its possessors to detect fallacy & to "k ! types ( s\nd logical d$uction4 ,! objects ( go+ fur!r are p>tly philosophical1 & also p>tly to lay b>e ab/ract ideas ^: inve/igation is 9 itself important4 ,b bo? ^! objects are =eign to education4 ,my op9ion is1 t1 on ! :ole1 ! type ( logical precision h&$ d[n to u by ! ,greek ma!maticians is1 r\ghly speak+1 :at we want4 ,9 geometry1 ?is means ! sort ( precision :i* we f9d 9 ,euclid4 ,i d n mean t we %\ld use 8 fam\s ,elem5ts z a text-book1 nor t "h & !re a c]ta9 compression 9 8 mode ( exposition is n advisable4 ,all ?is is m]e detail4 ,:at ,i d mean is1 t ! sort ( logical transition :i* he made explicit1 we %\ld make explicit1 & t ! sort ( transition :i* he omits1 we %\ld omit4 ,i d\bt1 h[ev]1 :e!r x is desirable to plunge ! /ud5t into ! full rig\r ( euclidean geometry )\t "s mitigation4 ,x is = ?is reason t ! mod]n habit1 at lea/ 9 ,engl&1 ( lay+ great /ress 9 ! initial /ages on tra9+ ! pupil 9 simple con/ructions f num]ical data is to be prais$4 ,x means t aft] a slight am\nt ( reason+ on ! euclidean basis ( accuracy1 ! m9d ( ! le>n] is reliev$ by do+ ! ?+s 9 v>i\s special cases1 & not+ by r\gh measurem5ts t ! desir$ results are actually atta9$4 ,x is important1 h[ev]1 t ! measurem5ts be n mi/ak5 = ! pro(s4 ,_! object is to make ! beg9n] appreh5d :at ! ab/ract ideas really mean4 ,aga9 9 algebra1 ! notation & ! practical use ( ! symbols %\ld be acquir$ 9 ! simple/ cases1 & ! m !oretical treatm5t ( ! symbolism res]v$ to a suitable lat] /age4 ,my rule w\ld be initially to le>n ! mean+ ( ! ideas by a crude practice 9 simple ways1 & to ref9e ! logical proc$ure 9 prep>ation = an advance to great] g5]ality4 ,9 fact ! !sis ( my pap] c be put 9 ano!r way ?us1 ! object ( a ma!matical education is1 to acquire ! p[]s ( analysis1 ( g5]alisation1 & ( reason+4 ,! two processes ( analysis & g5]alisation 7 9 my previ\s /atem5t put toge!r z ! p[] ( grasp+ ab/ract ideas4 ,b 9 ord] to analyse & to g5]alise1 we mu/ comm5ce ) ! crude mat]ial ( ideas :i* are to be analys$ & g5]alis$4 ,accord+ly x is a positive error 9 education to />t ) ! ultimate products ( ?is process1 namely ! ideas 9 _! ref9$ analys$ & g5]alis$ =ms4 ,we are !reby skipp+ an important "p ( ! tra9+1 :i* is to take ! ideas z !y actually exi/ 9 ! *ild's m9d1 & to ex]cise ! *ild 9 ! difficult art ( civilis+ !m & clo?+ !m4 ,! s*oolma/] is 9 fact a mission>y1 ! savages are ! ideas 9 ! *ild's m9d2 & ! mission>y %irks 8 ma9 task if he refuse to risk 8 body among ! cannibals4 ,at ?is po9t ,i %\ld l to turn y\r att5tion to ^? pupils =m+ ! ma!matical section4 ,!re is an idea1 widely preval5t1 t x is possible to tea* ma!matics ( a relatively advanc$ type--su* z diff]5tial calculus1 = in/ance--9 a way useful to physici/s & eng9e]s )\t any att5tion to its logic or its !ory4 ,?is seems to me to be a pr(\nd mi/ake4 ,x implies t a m]ely me*anical k )\t und]/&+ ( ways ( arriv+ at ma!matical results is useful 9 appli$ sci5ce4 ,x is ( no use :atev]4 ,! results !mselves c all be f\nd /at$ 9 ! appropriate pocket books & 9 o!r elem5t>y works ( ref]5ce4 ,no "o :5 apply+ a result ne$ bo!r himself z to :y x is true4 ,he accepts x & applies x4 ,:at is ( supreme importance 9 physics & 9 eng9e]+ is a ma!matically tra9$ m9d1 & su* a m9d c only be acquir$ by a prop] ma!matical discipl9e4 ,i fully admit t ! prop] way to />t su* a subject z ! diff]5tial calculus is to plunge quickly into ! use ( ! notation 9 a few absurdly simple cases1 ) a crude explanation ( ! idea ( rates ( increase4 ,! notation z ?us kn[n c !n be us$ by ! lectur]s 9 ! ,physical & ,eng9e]+ ,laboratories4 ,b ! ma!matical tra9+ ( ! appli$ sci5ti/s consi/s 9 mak+ ^! ideas precise & ! pro(s accurate4 ,i hope t ! !sis ( ?is pap] respect+ ! position ( logical precision 9 ! tea*+ ( ma!matics has be5 r5d]$ pla94 ,! habit ( logical precision ) its necess>y conc5tration ( ?\ght ^u ab/ract ideas is n :olly possible 9 ! initial /ages ( le>n+4 ,x is ! ideal at :i* ! tea*] %\ld aim4 ,also logical precision1 9 ! s5se ( logical explicitness1 is n an absolute ?+3 x is an affair ( m or less4 ,accord+ly ! quantity ( explicitness to be introduc$ at ea* /age ( progress mu/ dep5d ^u ! practical judgm5t ( ! tea*]4 ,la/ly1 9 a s5se1 ! in/ruct$ m9d is less explicit2 = x travels m quickly ov] a well-rememb]$ pa?1 & may save ! tr\ble ( putt+ into words tra9s ( ?\ght :i* are v obvi\s to x4 ,b on ! o!r h& x atones = ?is rapidity by a conc5tration on e subtle po9t :]e a fallacy c lurk4 ,! habit ( logical precision is ! in/9ct = ! subtle difficulty4 ,,*apt] ,,vi ,,! ,,organisation ,,( ,,?\ght 7,presid5tial ,address to ,section ,a1 ,briti% ,association1 ,newca/le1 #aiaf7 ,,! subject ( ?is address is ! organisation ( ?\ght1 a topic evid5tly capable ( _m div]se modes ( treatm5t4 ,i int5d m p>ticul>ly to give "s acc\nt ( t dep>tm5t ( logical sci5ce ) :i* "s ( my own /udies h be5 connect$4 ,b ,i am anxi\s1 if ,i c succe$ 9 s do+1 to h&le ?is acc\nt s z to exhibit ! relation ) c]ta9 consid]ations :i* und]lie g5]al sci5tific activities4 ,x is no accid5t t an age ( sci5ce has develop$ into an age ( organisation4 ,organis$ ?\ght is ! basis ( organis$ action4 ,organisation is ! adju/m5t ( div]se elem5ts s t _! mutual relations may exhibit "s pr$et]m9$ quality4 ,an epic poem is a triumph ( organisation1 t is to say1 x is a triumph 9 ! unlikely ev5t ( its be+ a good epic poem4 ,x is ! successful organisation ( multitud9\s s\nds ( words1 associations ( words1 pictorial memories ( div]se ev5ts & feel+s ord9>ily occurr+ 9 life1 comb9$ ) a special n>rative ( great ev5ts3 ! :ole s dispos$ z to excite emotions :i*1 z def9$ by ,milton1 are simple1 s5su\s1 & passionate4 ,! numb] ( successful epic poems is comm5surate1 or r1 is inv]sely comm5surate1 ) ! obvi\s difficulty ( ! task ( organisation4 ,sci5ce is ! organisation ( ?\ght4 ,b ! example ( ! epic poem w>ns u t sci5ce is n any organisation ( ?\ght4 ,x is an organisation ( a c]ta9 def9ite type :i* we w endeav\r to det]m9e4 ,sci5ce is a riv] ) two s\rces1 ! practical s\rce & ! !oretical s\rce4 ,! practical s\rce is ! desire to direct our actions to a*ieve pr$et]m9$ ends4 ,= example1 ! ,briti% nation1 fight+ = ju/ice1 turns to sci5ce1 :i* tea*es x ! importance ( comp\nds ( nitrog54 ,! !oretical s\rce is ! desire to und]/&4 ,n[ ,i am go+ to emphasise ! importance ( !ory 9 sci5ce4 ,b to avoid misconception ,i mo/ emphatically /ate t ,i d n consid] "o s\rce z 9 any s5se nobl] ?an ! o!r1 or intr9sically m int]e/+4 ,i _c see :y x is nobl] to /rive to und]/& ?an to busy oneself ) ! "r ord]+ ( "o's actions4 ,bo? h _! bad sides2 !re are evil ends direct+ actions1 & !re are ignoble curiosities ( ! und]/&+4 ,! importance1 ev5 9 practice1 ( ! !oretical side ( sci5ce arises f ! fact t action mu/ be imm$iate1 & takes place "u circum/ances :i* are excessively complicat$4 ,if we wait = ! necessities ( action be=e we comm5ce to arrange our ideas1 9 peace we %all h lo/ our trade1 & 9 w> we %all h lo/ ! battle4 ,success 9 practice dep5ds on !ori/s :o1 l$ by o!r motives ( exploration1 h be5 !re be=e1 & by "s good *ance h hit ^u ! relevant ideas4 ,by a !ori/ ,i d n mean a man :o is up 9 ! cl\ds1 b a man ^: motive = ?\ght is ! desire to =mulate correctly ! rules accord+ to :i* ev5ts occur4 ,a successful !ori/ %\ld be excessively int]e/$ 9 imm$iate ev5ts1 o!rwise he is n at all likely to =mulate correctly any?+ ab\t !m4 ,( c\rse1 bo? s\rces ( sci5ce exi/ 9 all m54 ,n[1 :at is ?is ?\ght organisation :i* we call sci5ce8 ,! fir/ aspect ( mod]n sci5ce :i* /ruck ?\ghtful obs]v]s 0 its inductive "*4 ,! nature ( induction1 its importance1 & ! rules ( inductive logic h be5 consid]$ by a long s]ies ( ?9k]s1 especially ,engli% ?9k]s3 ,bacon1 ,h]s*el1 ,j4 ,s4 ,mill1 ,v5n1 ,jevons1 & o!rs4 ,i am n go+ to plunge into an analysis ( ! process ( induction4 ,induction is ! ma*9]y & n ! product1 & x is ! product :i* ,i want to consid]4 ,:5 we und]/& ! product we %all be 9 a /rong] position to improve ! ma*9]y4 ,fir/1 !re is "o po9t :i* x is necess>y to emphasise4 ,!re is a t5d5cy 9 analys+ sci5tific processes to assume a giv5 assemblage ( concepts apply+ to nature1 & to imag9e t ! discov]y ( laws ( nature consi/s 9 select+ by means ( inductive logic "s "o out ( a def9ite set ( possible alt]native relations :i* may hold betwe5 ! ?+s 9 nature answ]+ to ^! obvi\s concepts4 ,9 a s5se ?is assumption is fairly correct1 especially 9 reg>d to ! e>li] /ages ( sci5ce4 ,mank9d f\nd itself 9 possession ( c]ta9 concepts respect+ nature--= example1 ! concept ( fairly p]man5t mat]ial bodies--& proce$$ to det]m9e laws :i* relat$ ! correspond+ p]cepts 9 nature4 ,b ! =mulation ( laws *ang$ ! concepts1 sometimes g5tly by an add$ precision1 sometimes viol5tly4 ,at fir/ ?is process 0 n mu* notic$1 or at lea/ 0 felt to be a process curb$ )9 n>r[ b\nds1 n t\*+ fundam5tal ideas4 ,at ! /age :]e we n[ are1 ! =mulation ( ! concepts c be se5 to be z important z ! =mulation ( ! empirical laws connect+ ! ev5ts 9 ! univ]se z ?us conceiv$ by u4 ,= example1 ! concepts ( life1 ( h]$ity1 ( a mat]ial body1 ( a molecule1 ( an atom1 ( an electron1 ( en]gy1 ( space1 ( "t1 ( quantity1 & ( numb]4 ,i am n dogmatis+ ab\t ! be/ way ( gett+ su* ideas /raight4 ,c]ta9ly x w only be done by ^? :o h devot$ !mselves to a special /udy ( ! facts 9 "q4 ,success is nev] absolute1 & progress 9 ! "r direction is ! result ( a sl[1 gradual process ( cont9ual comp>ison ( ideas ) facts4 ,! crit]ion ( success is t we %\ld be able to =mulate empirical laws1 t is1 /atem5ts ( relations1 connect+ ! v>i\s p>ts ( ! univ]se z ?us conceiv$1 laws ) ! prop]ty t we c int]pret ! actual ev5ts ( our lives z be+ our fragm5t>y k ( ?is conceiv$ int]relat$ :ole4 ,b1 = ! purpose ( sci5ce1 :at is ! actual _w8 ,has sci5ce to wait = ! t]m9ation ( ! metaphysical debate till x c det]m9e its own subject-matt]8 ,i sugge/ t sci5ce has a mu* m homely />t+-gr\nd4 ,its task is ! discov]y ( ! relations :i* exi/ )9 t flux ( p]ceptions1 s5sations1 & emotions :i* =ms our exp]i5ce ( life4 ,! panorama yield$ by sight1 s\nd1 ta/e1 smell1 t\*1 & by m in*oate s5sible feel+s1 is ! sole field ( activity4 ,x is 9 ?is way t sci5ce is ! ?\ght organisation ( exp]i5ce4 ,! mo/ obvi\s aspect ( ?is field ( actual exp]i5ce is its disord]ly "*4 ,x is = ea* p]son a cont9uum1 fragm5t>y1 & ) elem5ts n cle>ly diff]5tiat$4 ,! comp>ison ( ! s5sible exp]i5ces ( div]se p br+s its own difficulties4 ,i insi/ on ! radically untidy1 ill-adju/$ "* ( ! fields ( actual exp]i5ce f :i* sci5ce />ts4 ,to grasp ?is fundam5tal tru? is ! fir/ /ep 9 wisdom1 :5 con/ruct+ a philosophy ( sci5ce4 ,?is fact is conceal$ by ! influ5ce ( language1 m\ld$ by sci5ce1 :i* foi/s on u exact concepts z ?\gh !y repres5t$ ! imm$iate deliv]ances ( exp]i5ce4 ,! result is1 t we imag9e t we h imm$iate exp]i5ce ( a _w ( p]fectly def9$ objects implicat$ 9 p]fectly def9$ ev5ts :i*1 z kn[n to u by ! direct deliv]ance ( our s5ses1 happ5 at exact in/ants ( "t1 9 a space =m$ by exact po9ts1 )\t p>ts & )\t magnitude3 ! neat1 trim1 tidy1 exact _w :i* is ! goal ( sci5tific ?\ght4 ,my cont5tion is1 t ?is _w is a _w ( ideas1 & t its int]nal relations are relations betwe5 ab/ract concepts1 & t ! elucidation ( ! precise connection betwe5 ?is _w & ! feel+s ( actual exp]i5ce is ! fundam5tal "q ( sci5tific philosophy4 ,! "q :i* ,i am invit+ y to consid] is ?is3 ,h[ does exact ?\ght apply to ! fragm5t>y1 vague cont9ua ( exp]i5ce8 ,i am n say+ t x does n apply3 q ! contr>y4 ,b ,i want to "k h[ x applies4 ,! solution ,i am ask+ = is n a phrase1 h[ev] brilliant1 b a solid bran* ( sci5ce1 con/ruct$ ) sl[ pati5ce1 %[+ 9 detail h[ ! correspond5ce is effect$4 ,! fir/ great /eps 9 ! organisation ( ?\ght 7 due exclusively to ! practical s\rce ( sci5tific activity1 )\t any admixture ( !oretical impulse4 ,_! sl[ accompli%m5t 0 ! cause & also ! effect ( ! gradual evolution ( mod]ately rational be+s4 ,i mean ! =mation ( ! concepts ( def9ite mat]ial objects1 ( ! det]m9ate lapse ( "t1 ( simultaneity1 ( recurr5ce1 ( def9ite relative position1 & ( analog\s fundam5tal ideas1 accord+ to :i* ! flux ( our exp]i5ce is m5tally arrang$ = h&y ref]5ce3 9 fact1 ! :ole app>atus ( commons5se ?\ght4 ,consid] 9 y\r m9d "s def9ite *air4 ,! concept ( t *air is simply ! concept ( all ! int]relat$ exp]i5ces connect$ ) t *air--namely1 ( ! exp]i5ce ( ! folk :o made x1 ( ! folk :o sold x1 ( ! folk :o h se5 x or us$ x1 ( ! man :o is n[ exp]i5c+ a com=table s5se ( support1 comb9$ ) our expectations ( an analog\s future1 t]m9at$ f9ally by a diff]5t set ( exp]i5ces :5 ! *air collapses & becomes firewood4 ,! =mation ( t type ( concept 0 a trem5d\s job1 & zoologi/s & geologi/s tell u t x took _m t5s ( millions ( ye>s4 ,i c well believe x4 ,i n[ emphasise two po9ts4 ,9 ! fir/ place1 sci5ce is root$ 9 :at ,i h j call$ ! :ole app>atus ( commons5se ?\ght4 ,t is ! datum f :i* x />ts1 & to :i* x mu/ recur4 ,we may speculate1 if x amuses u1 ( o!r be+s 9 o!r planets :o h arrang$ analog\s exp]i5ces accord+ to an entirely diff]5t conceptual code--namely1 :o h direct$ _! *ief att5tion to diff]5t relations betwe5 _! v>i\s exp]i5ces4 ,b ! task is too complex1 too gigantic1 to be revis$ 9 its ma9 outl9es4 ,y may poli% up commons5se1 y may contradict x 9 detail1 y may surprise x4 ,b ultimately y\r :ole task is to satisfy x4 ,9 ! second place1 nei!r commons5se nor sci5ce c proce$ ) _! task ( ?\ght organisation )\t dep>t+ 9 "s respect f ! /rict consid]ation ( :at is actual 9 exp]i5ce4 ,?9k aga9 ( ! *air4 ,among ! exp]i5ces ^u :i* its concept is bas$1 ,i includ$ our expectations ( its future hi/ory4 ,i %\ld h gone fur!r & includ$ our imag9ation ( all ! possible exp]i5ces :i* 9 ord9>y language we %\ld call p]ceptions ( ! *air :i* might h occurr$4 ,?is is a difficult "q1 & ,i d n see my way ?r\gh x4 ,b1 at pres5t1 9 ! con/ruction ( a !ory ( space & ( "t !re seem insup]able difficulties if we refuse to admit ideal exp]i5ces4 ,?is imag9ative p]ception ( exp]i5ces1 :i*1 if !y occurr$1 w\ld be coh]5t ) our actual exp]i5ces1 seems fundam5tal 9 our lives4 ,x is nei!r :olly arbitr>y1 nor yet fully det]m9$4 ,x is a vague backgr\nd :i* is only made 9 "p def9ite by isolat$ activities ( ?\ght4 ,consid]1 = example1 our ?\ghts ( ! unse5 flora ( ,brazil4 ,ideal exp]i5ces are closely connect$ ) our imag9ative reproduction ( ! actual exp]i5ces ( o!r p1 & also ) our almo/ inevitable conception ( ourselves z receiv+ our impressions f an ext]nal complex reality beyond ourselves4 ,x may be t an adequate analysis ( e s\rce & e type ( exp]i5ce yields demon/rative pro( ( su* a reality & ( its nature4 ,inde$1 x is h>dly to be d\bt$ t ?is is ! case4 ,! precise elucidation ( ?is "q is ! problem ( metaphysics4 ,"o ( ! po9ts :i* ,i am urg+ 9 ?is address is1 t ! basis ( sci5ce does n dep5d on ! assumption ( any ( ! conclusions ( metaphysics2 b t bo? sci5ce & metaphysics />t f ! same giv5 gr\ndwork ( imm$iate exp]i5ce1 & 9 ! ma9 proce$ 9 opposite directions on _! div]se tasks4 ,= example1 metaphysics inquires h[ our p]ceptions ( ! *air relate u to "s true reality4 ,sci5ce ga!rs up ^! p]ceptions into a det]m9ate class1 adds to !m ideal p]ceptions ( analog\s sort1 :i* "u assignable circum/ances w\ld be obta9$1 & ?is s+le concept ( t set ( p]ceptions is all t sci5ce ne$s2 unless inde$ y pref] t ?\ght f9d its orig9 9 "s leg5d ( ^? great tw9 bre?r51 ! ,cock & ,bull4 ,my imm$iate problem is to inquire into ! nature ( ! texture ( sci5ce4 ,sci5ce is ess5tially logical4 ,! nexus betwe5 its concepts is a logical nexus1 & ! gr\nds = its detail$ ass]tions are logical gr\nds4 ,k+ ,james said1 ,no bi%ops1 no k+4 ,) great] confid5ce we c say1 ,no logic1 no sci5ce4 ,! reason = ! in/9ctive dislike :i* mo/ m5 ( sci5ce feel t[>ds ! recognition ( ?is tru? is1 ,i ?9k1 ! b>r5 failure ( logical !ory dur+ ! pa/ ?ree or f\r c5turies4 ,we may trace ?is failure back to ! wor%ip ( au?ority1 :i* 9 "s respects increas$ 9 ! le>n$ _w at ! "t ( ! ,r5aissance4 ,mank9d !n *ang$ its au?ority1 & ?is fact temporally act$ z an emancipation4 ,b ! ma9 fact1 & we c f9d compla9ts#b ( x at ! v comm5cem5t ( ! mod]n movem5t1 0 ! e/abli%m5t ( a rev]5tial attitude t[>ds any /atem5t made by a classical au?or4 ,s*ol>s became comm5tators on tru?s too fragile to be> translation4 ,a sci5ce :i* hesitates to =get its f\nd]s is lo/4 ,to ?is hesitation ,i ascribe ! b>r5ness ( logic4 ,ano!r reason = di/ru/ ( logical !ory & ( ma!matics is ! belief t d$uctive reason+ c give y no?+ new4 ,y\r conclusions are conta9$ 9 y\r premises1 :i* by hypo!sis are kn[n to y4 ,9 ! fir/ place ?is la/ condemnation ( logic neglects ! fragm5t>y1 disconnect$ "* ( human k4 ,to "k "o premise on ,monday1 & ano!r premise on ,tuesday1 is useless to y on ,w$nesday4 ,sci5ce is a p]man5t record ( premises1 d$uctions1 & conclusions1 v]ifi$ all along ! l9e by its correspond5ce ) facts4 ,secondly1 x is untrue t :5 we "k ! premises we also "k ! conclusions4 ,9 ari?metic1 = example1 mank9d are n calculat+ boys4 ,any !ory :i* proves t !y are conv]sant ) ! consequ5ces ( _! assumptions mu/ be wrong4 ,we c imag9e be+s :o possess su* insight4 ,b we are n su* creatures4 ,bo? ^! answ]s are1 ,i ?9k1 true & relevant4 ,b !y are n satisfactory4 ,!y are too mu* 9 ! nature ( bludgeons1 too ext]nal4 ,we want some?+ m explanatory ( ! v real difficulty :i* ! "q sugge/s4 ,9 fact1 ! true answ] is emb$d$ 9 ! discussion ( our ma9 problem ( ! relation ( logic to natural sci5ce4 ,x w be necess>y to sket* 9 broad outl9e "s relevant features ( mod]n logic4 ,9 do+ s ,i %all try to avoid ! pr(\nd g5]al discussions & ! m9ute te*nical classifications :i* occupy ! ma9 "p ( traditional logic4 ,x is *>act]i/ic ( a sci5ce 9 its e>li] /ages--& logic has become fossilis$ 9 su* a /age--to be bo? ambiti\sly pr(\nd 9 its aims & trivial 9 its h&l+ ( details4 ,we c disc]n f\r dep>tm5ts ( logical !ory4 ,by an analogy :i* is n s v remote ,i w call ^! dep>tm5ts or sections ! ari?metic section1 ! algebraic section1 ! section ( g5]al-function !ory1 ! analytical section4 ,i d n mean t ari?metic arises 9 ! fir/ section1 algebra 9 ! second section1 & s on2 b ! names are sugge/ive ( c]ta9 qualities ( ?\ght 9 ea* section :i* are rem9isc5t ( analog\s qualities 9 ari?metic1 9 algebra1 9 ! g5]al !ory ( a ma!matical function1 & 9 ! ma!matical analysis ( ! prop]ties ( p>ticul> functions4 ,! fir/ section--namely1 ! ari?metic /age--deals ) ! relations ( def9ite propositions to ea* o!r1 j z ari?metic deals ) def9ite numb]s4 ,consid] any def9ite proposition2 call x p4 ,we conceive t !re is always ano!r proposition :i* is ! direct contradictory to p2 call x n-p4 ,:5 we h got two propositions1 p & q1 we c =m d]ivative propositions f !m1 & f _! contradictories4 ,we c say1 ,at la/ "o ( p or q is true1 & p]haps bo?4 ,let u call ?is proposition p or q4 ,i may m5tion z an aside t "o ( ! greate/ liv+ philosoph]s has /at$ t ?is use ( ! ^w or--namely1 p or q 9 ! s5se t ei!r or bo? may be true--makes him despair ( exact expression4 ,we mu/ brave 8 wra?1 :i* is un9telligible to me4 ,we h ?us got hold ( f\r new propositions1 namely1 p or q1 & n-p or q1 & p or n-q1 & n-p or n-q4 ,call ^! ! set ( disjunctive d]ivatives4 ,!re are1 s f>1 9 all eight propositions1 p1 n-p1 q1 n-q1 & ! f\r disjunctive d]ivatives4 ,any pair ( ^! eight propositions c be tak51 & sub/itut$ = p & q 9 ! =ego+ treatm5t4 ,?us ea* pair yields eight propositions1 "s ( :i* may h be5 obta9$ be=e4 ,by proce$+ 9 ?is way we arrive at an un5d+ set ( propositions ( gr[+ complexity1 ultimately d]iv$ f ! two orig9al propositions p or q4 ,( c\rse1 only a few are important4 ,simil>ly we c />t f ?ree propositions1 p1 q1 r1 or f f\r propositions1 p1 q1 r1 s1 & s on4 ,any "o ( ! propositions ( ^! aggregates may be true or false4 ,x has no o!r alt]native4 ,:i*ev] x is1 true or false1 call x ! tru?-value ( ! proposition4 ,! fir/ section ( logical inquiry is to settle :at we "k ( ! tru?-values ( ^! propositions1 :5 we "k ! tru?-values ( "s ( !m4 ,! inquiry1 s f> z x is wor? :ile c>ry+ x1 is n v ab/ruse1 & ! be/ way ( express+ its results is a detail :i* ,i w n n[ consid]4 ,?is inquiry =ms ! ari?metic /age4 ,! next section ( logic is ! algebraic /age4 ,n[1 ! diff]5ce betwe5 ari?metic & algebra is1 t 9 ari?metic def9ite numb]s are consid]$1 & 9 algebra symbols--namely1 lett]s--are introduc$ :i* /& = any numb]s4 ,! idea ( a numb] is also enl>g$4 ,^! lett]s1 /&+ = any numb]s1 are call$ sometimes v>iables & sometimes p>amet]s4 ,_! ess5tial *>act]i/ic is t !y are undet]m9$1 unless1 inde$1 ! algebraic conditions :i* !y satisfy implicitly det]m9e !m4 ,!n !y are sometimes call$ unkn[ns4 ,an algebraic =mula ) lett]s is a blank =m4 ,x becomes a det]m9ate ari?metic /atem5t :5 def9ite numb]s are sub/itut$ = ! lett]s4 ,! importance ( algebra is a tribute to ! /udy ( =m4 ,consid] n[ ! foll[+ proposition-- ,! specific heat ( m]cury is #jjcc4 ,?is is a def9ite proposition :i*1 ) c]ta9 limitations1 is true4 ,b ! tru?-value ( ! proposition does n imm$iately conc]n u4 ,in/ead ( m]cury put a m]e lett] :i* is ! "n ( "s undet]m9$ ?+3 we get-- ,! specific heat ( x is #jjcc4 ,?is is n a proposition2 x has be5 call$ by ,russell a propositional function4 ,x is ! logical analogy ( an algebraic expression4 ,let u write 7x7 = any propositional function4 ,we c\ld also g5]alise /ill fur!r1 & say1 ,! specific heat ( x is y4 ,we ?us get ano!r propositional function1 ,f7x1 y71 ( two argum5ts x & y1 & s on = any numb] ( argum5ts4 ,n[1 consid] 7x74 ,!re is ! range ( values ( x1 = :i* 7x7 is a proposition1 true or false4 ,= values ( x outside ?is range1 7x7 is n a proposition at all1 & is nei!r true nor false4 ,x may h vague sugge/ions = u1 b x has no unit mean+ ( def9ite ass]tion4 ,= example1 ,! specific heat ( wat] is #jjcc is a proposition :i* is false2 &-- ,! specific heat ( virtue is #jjcc is1 ,i %\ld imag9e1 n a proposition at all2 s t x is nei!r true nor false1 ?\gh its compon5t p>ts raise v>i\s associations 9 our m9ds4 ,?is range ( values1 = :i* 7x7 has s5se1 is call$ ! type ( ! argum5t x4 ,b !re is also a range ( values ( x = :i* 7x7 is a true proposition4 ,?is is ! class ( ^? values ( ! argum5t :i* satisfy 7x74 ,?is class may h no memb]s1 or1 9 ! o!r extreme1 ! class may be ! :ole type ( ! argum5ts4 ,we ?us conceive two g5]al propositions respect+ ! indef9ite numb] ( propositions :i* %>e 9 ! same logical =m1 t is1 :i* are values ( ! same propositional function4 ,"o ( ^! propositions is1 7x7 yields a true proposition = ea* value ( x ( ! prop] type2 ! o!r proposition is1 ,!re is a value ( x = :i* 7x7 is true4 ,giv5 two1 or m1 propositional functions 7x7 & 7x7 ) ! same argum5t x1 we =m d]ivative propositional functions1 namely1 7x7 or 7x71 7x7 or n-7x71 & s on ) ! contradictories1 obta9+1 z 9 ! ari?metical /age1 an un5d+ aggregate ( propositional functions4 ,also ea* propositional function yields two g5]al propositions4 ,! !ory ( ! int]connection betwe5 ! tru?-values ( ! g5]al propositions aris+ f any su* aggregate ( propositional functions =ms a simple & elegant *apt] ( ma!matical logic4 ,9 ?is algebraic section ( logic ! !ory ( types crops up1 z we h already not$4 ,x _c be neglect$ )\t ! introduction ( error4 ,its !ory has to be settl$ at lea/ by "s safe hypo!sis1 ev5 if x does n g to ! philosophic basis ( ! "q4 ,?is "p ( ! subject is obscure & difficult1 & has n be5 f9ally elucidat$1 ?\gh ,russell's brilliant "w has op5$ out ! subject4 ,! f9al impulse to mod]n logic comes f ! indep5d5t discov]y ( ! importance ( ! logic v>iable by ,frege & ,peano4 ,frege w5t fur!r ?an ,peano1 b by an un=tunate symbolism r5d]$ 8 "w s obscure t no "o fully recognis$ 8 mean+ :o _h n f\nd x out = himself4 ,b ! movem5t has a l>ge hi/ory rea*+ back to ,leibniz & ev5 to ,ari/otle4 ,among ,engli% contributors are ,de ,morgan1 ,boole1 & ,sir ,alfr$ ,kempe2 _! "w is ( ! fir/ rank4 ,! ?ird logical section is ! /age ( g5]al-function !ory4 ,9 logical language1 we p]=m 9 ?is /age ! transition f int5sion to ext5sion1 & inve/igate ! !ory ( d5otation4 ,take ! propositional function1 7x74 ,!re is ! class1 or range ( values = x1 ^: memb]s satisfy 7x74 ,b ! same range may be ! class ^: memb]s satisfy ano!r propositional function 7x74 ,x is necess>y to inve/igate h[ to indicate ! class by a way :i* is indiff]5t z betwe5 ! v>i\s propositional functions :i* are satisfi$ by any memb] ( x1 & ( x only4 ,:at has to be done is to analyse ! nature ( propositions ab\t a class--namely1 ^? propositions ^: tru?-values dep5d on ! class itself & n on ! p>ticul> mean+ by :i* ! class is indicat$4 ,fur!rmore1 !re are propositions ab\t alleg$ individuals indicat$ by descriptive phrases3 = example1 propositions ab\t ! pres5t ,k+ ( ,engl&1 :o does exi/1 & ! pres5t ,emp]or ( ,brazil1 :o does n exi/4 ,m complicat$1 b analog\s1 que/ions involv+ propositional functions ( two v>iables involve ! notion ( correlation1 j z functions ( "o argum5t involve classes4 ,simil>ly functions ( ?ree argum5ts yield ?ree-corn]$ correlations1 & s on4 ,?is logical section is "o :i* ,russell has made peculi>ly 8 own by "w :i* mu/ always rema9 fundam5tal4 ,i h call$ ?is ! section ( functional !ory1 because its ideas are ess5tial to ! con/ruction ( logical d5ot+ functions :i* include z a special case ord9>y ma!matical functions1 su* z s9e1 log>i?m1 etc4 ,9 ea* ( ^! ?ree /ages x w be necess>y gradually to introduce an appropriate symbolism1 if we are to pass on to ! f\r? /age4 ,! f\r? logical section1 ! analytic /age1 is conc]n$ ) ! inve/igation ( ! prop]ties ( special logical con/ructions1 t is1 ( classes & correlations ( special sorts4 ,! :ole ( ma!matics is includ$ "h4 ,s ! section is a l>ge "o4 ,9 fact1 x is ma!matics1 nei!r m nor less1 b x includes an analysis ( ma!matical ideas n hi!rto includ$ 9 ! scope ( t sci5ce1 nor1 inde$1 contemplat$ at all4 ,! ess5ce ( ?is /age is con/ruction4 ,x is by means ( suitable con/ructions t ! great framework ( appli$ ma!matics1 compris+ ! !ories ( numb]1 quantity1 "t1 & space1 is elaborat$4 ,x is impossible1 ev5 9 brief outl9e1 to expla9 h[ ma!matics is develop$ f ! concepts ( class & correlation1 includ+ _m-corn]$ correlations1 :i* are e/abli%$ 9 ! ?ird section4 ,i c only allude to ! head+s ( ! process1 :i* is fully develop$ 9 ! "w1 ,pr9cipia ,ma!matica1 by ,mr4 ,russell & myself4 ,!re are 9 ?is process ( developm5t sev5 special sorts ( correlations :i* are ( peculi> int]e/4 ,! fir/ sort comprises "o-to-_m1 _m-to-"o1 & "o-to-"o correlations4 ,! second sort comprises s]ial relations1 t is1 correlations by :i* ! memb]s ( "s field are arrang$ 9 s]ial ord]1 s t1 9 ! s5se def9$ by ! relation1 any memb] ( ! field is ei!r be=e or aft] any o!r memb]4 ,! ?ird class comprises inductive relations1 t is1 correlations on :i* ! !ory ( ma!matical induction dep5ds4 ,! f\r? class comprises selective relations1 :i* are requir$ = ! g5]al !ory ( ari?metic op]ations1 & else:]e4 ,x is 9 connection ) su* relations t ! fam\s multiplicative axiom arises = consid]ation4 ,! fif? class comprises vector relations1 f :i* ! !ory ( quantity arises4 ,! six? class comprises ratio relations1 :i* int]connect numb] & quantity4 ,! sev5? class comprises ?ree-corn]$ & f\r-corn]$ relations :i* occur 9 geometry4 ,a b>e enum]ation ( te*nical names1 su* z ! above1 is n v illum9at+1 ?\gh x may help to a compreh5sion ( ! dem>cations ( ! subject4 ,please rememb] t ! names are te*nical names1 meant1 no d\bt1 to be sugge/ive1 b us$ 9 /rictly def9$ s5ses4 ,we h suff]$ mu* f critics :o consid] x suffici5t to criticise our proc$ure on ! sl5d] basis ( a k ( ! diction>y mean+s ( su* t]ms4 ,= example1 a "o-to-"o correlation dep5ds on ! notion ( a class ) only "o memb]1 & ?is notion is def9$ )\t appeal to ! concept ( ! numb] "o4 ,! notion ( div]sity is all t is want$4 ,?us ! class has only "o memb]1 if 7#a7 ! class ( values ( x :i* satisfies ! propositional function1 x is n a memb] ( 1 is n ! :ole type ( relevant values ( x1 & if 7#b7 ! propositional function1 x & y are memb]s ( 1 & x is div]se f y is false1 :atev] be ! values ( x & y 9 ! relevant type4 ,analog\s proc$ures are obvi\sly possible = high] f9ite c>d9al memb]s4 ,?us1 /ep by /ep1 ! :ole cycle ( curr5t ma!matical ideas is capable ( logical def9ition4 ,! process is detail$ & labori\s1 &1 l all sci5ce1 kn[s no?+ ( a royal road ( airy phrases4 ,! ess5ce ( ! process is1 fir/1 to con/ruct ! notion 9 t]ms ( ! =ms ( propositions1 t is1 9 t]ms ( ! relevant propositional functions1 & secondly1 to prove ! fundam5tal tru?s :i* hold ab\t ! notion by ref]5ce to ! results obta9$ 9 ! algebraic section ( logic4 ,x w be se5 t 9 ?is process ! :ole app>atus ( special indef9able ma!matical concepts1 & special a priori ma!matical premises1 respect+ numb]1 quantity1 & space1 has vani%$4 ,ma!matics is m]ely an app>atus = analys+ ! d$uctions :i* c be drawn f any p>ticul> premises1 suppli$ by commons5se1 or by m ref9$ sci5tific obs]vation1 s f> z ^! d$uctions dep5d on ! =ms ( ! propositions4 ,propositions ( c]ta9 =ms are cont9ually occurr+ 9 ?\ght4 ,our exi/+ ma!matics is ! analysis ( d$uctions :i* conc]n ^? =ms & 9 "s way are important1 ei!r f practical utility or !oretical int]e/4 ,"h ,i am speak+ ( ! sci5ce z x 9 fact exi/s4 ,a !oretical def9ition ( ma!matics mu/ include 9 its scope any d$uctions dep5d+ on ! m]e =ms ( propositions4 ,b1 ( c\rse no "o w\ld wi% to develop t "p ( ma!matics :i* 9 no s5se is ( importance4 ,?is ha/y summ>y ( logical ideas sugge/s "s reflections4 ,! "q arises1 ,h[ _m =ms ( propositions are !re8 ,! answ] is1 ,an un5d+ numb]4 ,! reason = ! suppos$ /]ility ( logical sci5ce c ?us be disc]n$4 ,ari/otle f\nd$ ! sci5ce by conceiv+ ! idea ( ! =m ( a proposition1 & by conceiv+ d$uction z tak+ place 9 virtue ( ! =ms4 ,b he conf9$ propositions to f\r =ms1 n[ nam$ ,a1 ,i1 ,e1 ,o4 ,s long z logicians 7 obsess$ by ?is un=tunate re/riction1 real progress 0 impossible4 ,aga91 9 _! !ory ( =m1 bo? ,ari/otle & subsequ5t logicians came v ne> to ! !ory ( ! logical v>iable4 ,b to come v ne> to a true !ory1 & to grasp its precise application1 are two v diff]5t ?+s1 z ! hi/ory ( sci5ce tea*es u4 ,ev]y?+ ( importance has be5 said be=e by somebody :o did n discov] x4 ,aga91 "o reason :y logical d$uctions are n obvi\s is1 t logical =m is n a subject :i* ord9>ily ent]s into ?\ght4 ,commons5se d$uction probably moves by bl9d in/9ct f concrete proposition to concrete proposition1 guid$ by "s habitual association ( ideas4 ,?us commons5se fails 9 ! pres5ce ( a weal? ( mat]ial4 ,a m important "q is ! relation ( induction1 bas$ on obs]vation1 to d$uctive logic4 ,!re is a tradition ( opposition betwe5 adh]5ts ( induction & ( d$uction4 ,9 my view1 x w\ld be j z s5sible = ! two ends ( a worm to qu>rel4 ,bo? obs]vation & d$uction are necess>y = any k wor? hav+4 ,we _c get at an inductive law )\t hav+ rec\rse to a propositional function4 ,= example1 take ! /atem5t ( obs]v$ fact1 ,?is body is m]cury1 & its specific heat is #jjcc4 ,! propositional function is =m$1 ,ei!r x is n m]cury1 or its specific heat is #jjcc4 ,! inductive law is ! assumption ( ! tru? ( ! g5]al proposition1 t ! above propositional function is true = e value ( x 9 ! relevant type4 ,b x is object$ t ?is process & its consequ5ces are s simple t an elaborate sci5ce is out ( place4 ,9 ! same way1 a ,briti% sailor kn[s ! salt sea :5 he sails ov] x4 ,:at1 !n1 is ! use ( an elaborate *emical analysis ( sea-wat]8 ,!re is ! g5]al answ]1 t y _c "k too mu* ( me?ods :i* y always employ2 & !re is ! special answ]1 t logical =ms & logical implications are n s v simple1 & t ! :ole ( ma!matics is evid5ce to ?is effect4 ,"o great use ( ! /udy ( logical me?od is n 9 ! region ( elaborate d$uction1 b to guide u 9 ! /udy ( ! =mation ( ! ma9 concepts ( sci5ce4 ,consid] geometry1 = example4 ,:at are ! po9ts :i* compose space8 ,euclid tells u t !y are )\t p>ts & )\t magnitude4 ,b h[ is ! notion ( a po9t d]iv$ f ! s5se-p]ceptions f :i* sci5ce />ts8 ,c]ta9ly po9ts are n direct deliv]ances ( ! s5ses4 ,"h & !re we may see or unpleasantly feel some?+ sugge/ive ( a po9t4 ,b ?is is a r>e ph5om5on1 & c]ta9ly does n w>rant ! conception ( space z compos$ ( po9ts4 ,our k ( space prop]ties is n bas$ on any obs]vations ( relations betwe5 po9ts4 ,x arises f exp]i5ce ( relations betwe5 bodies4 ,n[ a fundam5tal space-relation betwe5 bodies is t "o body may be "p ( ano!r4 ,we are tempt$ to def9e ! :ole & "p relation by say+ t ! po9ts occupi$ by ! "p are "s ( ! po9ts occupi$ by ! :ole4 ,b :ole & "p be+ m fundam5tal ?an ! notion ( po9t1 ?is def9ition is really circul> & vici\s4 ,we accord+ly ask :e!r any o!r def9ition ( spatial :ole & "p c be giv54 ,i ?9k t x c be done 9 ?is way1 ?\gh1 if ,i be mi/ak51 x is uness5tial to my g5]al argum5t4 ,we h come to ! conclusion t an ext5d$ body is no?+ else ?an ! class ( p]ception ( x by all its p]cipi5ts1 actual or ideal4 ,( c\rse1 x is n any class ( p]ceptions1 b a c]ta9 def9ite sort ( class :i* ,i h n def9$ "h1 except by ! vici\s me?od ( say+ t !y are p]ceptions ( body4 ,n[1 ! p]ceptions ( a "p ( a body are among ! p]ceptions :i* compose ! :ole body4 ,?us two bodies a & b are bo? classes ( p]ceptions2 & b is "p ( a :5 ! class :i* is b is conta9$ 9 ! class :i* is a4 ,x imm$iately foll[s f ! logical =m ( ?is def9ition t if b is "p ( a1 & c is "p ( b1 !n c is "p ( a4 ,?us ! relation :ole to "p is transitive4 ,aga91 x w be conv5i5t to all[ t a body is "p ( itself4 ,?is is a m]e "q ( h[ y draw ! def9ition4 ,) ?is und]/&+1 ! relation is reflexive4 ,f9ally1 if a is "p ( b1 & b is "p ( a1 !n a & b mu/ be id5tical4 ,^! prop]ties ( :ole & "p are n fre% assumptions1 !y foll[ f ! logical =m ( our def9ition4 ,"o assumption has to be made if we assume ! ideal inf9ite divisibility ( space4 ,namely1 we assume t e class ( p]ceptions :i* is an ext5d$ body conta9s o!r classes ( p]ceptions :i* are ext5d$ bodies div]se f itself4 ,?is assumption makes r a l>ge draft on ! !ory ( ideal p]ceptions4 ,geometry vani%es unless 9 "s =m y make x4 ,! assumption is n peculi> to my exposition4 ,x is !n possible to def9e :at we mean by a po9t4 ,a po9t is ! class ( ext5d$ objects :i*1 9 ord9>y language1 conta9 t po9t4 ,! def9ition1 )\t presuppos+ ! idea ( a po9t1 is r elaborate1 & ,i h n n[ "t = its /atem5t4 ,! advantage ( introduc+ po9ts into geometry is ! simplicity ( ! logical expression ( _! mutual relations4 ,= sci5ce1 simplicity ( def9ition is ( slight importance1 b simplicity ( mutual relations is ess5tial4 ,ano!r example ( ?is law is ! way physici/s & *emi/s h dissolv$ ! simple idea ( an ext5d$ body1 say ( a *air1 :i* a *ild und]/&s1 into a bewild]+ notion ( a complex dance ( molecules & atoms & electrons & waves ( light4 ,!y h !reby ga9$ notions ) simpl] logical relations4 ,space z ?us conceiv$ is ! exact =mulation ( ! prop]ties ( ! app>5t space ( ! commons5se _w ( exp]i5ce4 ,x is n necess>ily ! be/ mode ( conceiv+ ! space ( ! physici/4 ,! "o ess5tial requisite is t ! correspond5ce betwe5 ! commons5se _w 9 its space & ! physici/s' _w 9 its space %\ld be def9ite & reciprocal4 ,i w n[ break (f ! exposition ( ! function ( logic 9 connection ) ! sci5ce ( natural ph5om5a4 ,i h endeav\r$ to exhibit x z ! organis+ pr9ciple1 analys+ ! d]ivation ( ! concepts f ! imm$iate ph5om5a1 exam9+ ! /ructure ( ! g5]al propositions :i* are ! assum$ laws ( nature1 e/abli%+ _! relations to ea* o!r 9 respect to reciprocal implications1 d$uc+ ! ph5om5a we may expect "u giv5 circum/ances4 ,logic1 prop]ly us$1 does n %ackle ?\ght4 ,x gives fre$om1 & above all1 boldness4 ,illogical ?\ght hesitates to draw conclusions1 because x nev] kn[s ei!r :at x means1 or :at x assumes1 or h[ f> x tru/s its own assumptions1 or :at w be ! effect ( any modification ( assumptions4 ,also ! m9d untra9$ 9 t "p ( con/ructive logic :i* is relevant to ! subject 9 h& w be ignorant ( ! sort ( conclusions :i* foll[ f v>i\s sorts ( assumptions1 & w be correspond+ly dull 9 div9+ ! inductive laws4 ,! fundam5tal tra9+ 9 ?is relevant logic is1 und\bt$ly1 to pond] ) an active m9d ov] ! kn[n facts ( ! case1 directly obs]v$4 ,b :]e elaborate d$uctions are possible1 ?is m5tal activity requires = its full ex]cise ! direct /udy ( ! ab/ract logical relations4 ,?is is appli$ ma!matics4 ,nei!r logic )\t obs]vation1 nor obs]vation )\t logic1 c move "o /ep 9 ! =mation ( sci5ce4 ,we may conceive humanity z engag$ 9 an int]nec9e conflict betwe5 y\? & age4 ,y\? is n def9$ by ye>s b by ! creative impulse to make some?+4 ,! ag$ are ^? :o1 be=e all ?+s1 desire n to make a mi/ake4 ,logic is ! olive bran* f ! old to ! "y1 ! w& :i* 9 ! h&s ( y\? has ! magic prop]ty ( creat+ sci5ce4 ,,footnotes3 ,footnote #b3 ,e4g4 9 #aeea by ,italian s*oolm52 cf4 ,s>pi's ,hi/ory ( ! ,c\ncil ( ,tr5t1 "u t date4 ,,*apt] ,,vii ,,! ,,anatomy ,,( ,,"s ,,sci5tific ,,ideas ,i4 ,fact ,,! *>act]i/ic ( physical sci5ce is1 t x ignores all judgm5ts ( value3 = example1 /hetic or moral judgm5ts4 ,x is purely matt]-(-fact1 & ?is is ! s5se 9 :i* we mu/ int]pret ! sonor\s phrase1 ,man1 ! s]vant & ! m9i/] ( ,nature4 ,! sph]e ( ?\ght :i* is ?us left is ev5 !n too wide = physical sci5ce4 ,x w\ld include ,ontology1 namely1 ! det]m9ation ( ! nature ( :at truly exi/s2 9 o!r words1 ,metaphysics4 ,f an ab/ract po9t ( view ?is exclusion ( metaphysical inquiry is a pity4 ,su* an inquiry is a necess>y critique ( ! wor? ( sci5ce1 to tell u :at x all comes to4 ,! reasons = its c>eful sep>ation f sci5tific ?\ght are purely practical2 namely1 because we c agree ab\t sci5ce--aft] due debate--:]eas 9 respect to metaphysics debate has hi!rto acc5tuat$ disagreem5t4 ,^! *>act]i/ics ( sci5ce & metaphysics 7 unexpect$ 9 ! e>ly days ( civilis$ ?\ght4 ,! ,greeks ?\ght t metaphysics 0 easi] ?an physics1 & t5d$ to d$uce sci5tific pr9ciples f a priori conceptions ( ! nature ( ?+s4 ,!y 7 re/ra9$ 9 ?is disa/r\s t5d5cy by _! vivid naturalism1 _! delight 9 fir/-h& p]ception4 ,m$ival ,europe %>$ ! t5d5cy )\t ! re/ra9t4 ,x is possible t "s di/ant g5]ations may arrive at unanim\s conclusions on ontological que/ions1 :]eas sci5tific progress may h l$ to +ra9$ oppos+ ve9s ( ?\ght :i* c nei!r be reconcil$ nor ab&on$4 ,9 su* times metaphysics & physical sci5ce w ex*ange _! rles4 ,mean:ile we mu/ take ! case z we f9d x4 ,b a problem rema9s4 ,h[ c mank9d agree ab\t sci5ce )\t a prelim9>y det]m9ation ( :at really is8 ,! answ] mu/ be f\nd 9 an analysis ( ! facts :i* =m ! field ( sci5tific activity4 ,mank9d p]ceives1 & f9ds itself ?9k+ ab\t its p]ceptions4 ,x is ! ?\ght t matt]s & n t elem5t ( p]ception :i* is n ?\ght4 ,:5 ! imm$iate judgm5t has be5 =m$--,hullo1 r$6--x does n matt] if we c imag9e t 9 o!r circum/ances--9 bett] circum/ances1 p]haps--! judgm5t w\ld h be5--,hullo1 blue6--or ev5--,hullo1 no?+6 ,= all int5ts & purposes1 at ! "t x 0 r$4 ,ev]y?+ else is hypo!tical recon/ruction4 ,! field ( physical sci5ce is compos$ ( ^! prim>y ?\ghts1 & ( ?\ghts ab\t ^! ?\ghts4 ,b--to avoid confusion--a false simplicity has be5 introduc$ above into ! example giv5 ( a prim>y p]ceptive ?\ght4 ,hullo1 r$6 is n really a prim>y p]ceptive ?\ght1 ?\gh x (t5 is ! fir/ ?\ght :i* f9ds v]bal expression ev5 sil5tly 9 ! m9d4 ,no?+ is 9 isolation4 ,! p]ception ( r$ is ( a r$ object 9 its relations to ! :ole cont5t ( ! p]ceiv+ consci\sness4 ,among ! mo/ easily analys$ ( su* relations are ! space relations4 ,aga9 ! r$ object is 9 imm$iate p]ception no?+ else ?an a r$ object4 ,x is bett] t]m$ an object ( r$ness4 ,?us a bett] approximation to an imm$iate p]ceptive judgm5t is1 ,hullo1 object ( r$ness !re6 ,b1 ( c\rse1 9 ?is =mulation o!r m complex relations are omitt$4 ,?is t5d5cy t[>ds a false simplicity 9 sci5tific analysis1 to an excessive ab/raction1 to an ov]-univ]salis+ ( univ]sals1 is d]iv$ f ! e>li] metaphysical /age4 ,x arises f ! implicit belief t we are endeav\r+ to qualify ! real ) appropriate adjectives4 ,9 con=mity ) ?is t5d5cy we ?9k1 ?is real ?+ is r$4 ,:]eas our true goal is to make explicit our p]ception ( ! app>5t 9 t]ms ( its relations4 ,:at we p]ceive is r$ness relat$ to o!r app>5ts4 ,our object is ! analysis ( ! relations4 ,"o aim ( sci5ce is ! h>mony ( ?\ght1 t is1 to secure t judgm5ts :i* are logical contr>ies %\ld n be ?\ght-expressions ( consci\sness4 ,ano!r aim is ! ext5sion ( su* h>monis$ ?\ght4 ,"s ?\ghts arise directly f s5se-pres5tation1 & are "p ( ! /ate ( consci\sness :i* is p]ception4 ,su* a ?\ght is1 ,an object ( r$ness is !re4 ,b 9 g5]al ! ?\ght is n v]bal1 b is a direct appreh5sion ( qualities & relations )9 ! cont5t ( consci\sness4 ,amid su* ?\ghts !re c be no lack ( h>mony4 ,= direct appreh5sion is 9 its ess5ce unique1 & x is impossible to appreh5d an object z bo? r$ & blue4 ,subsequ5tly x may be judg$ t if o!r elem5ts ( ! consci\sness _h be5 diff]5t1 ! appreh5sion w\ld h be5 ( a blue object4 ,!n--"u c]ta9 circum/ances--! orig9al appreh5sion w be call$ an error4 ,b = all t ! fact rema9s1 !re 0 an appreh5sion ( a r$ object4 ,:5 we speak ( s5se-pres5tation1 we mean ^! prim>y ?\ghts ess5tially involv$ 9 its p]ception4 ,b !re are ?\ghts ab\t ?\ghts1 & ?\ghts d]iv$ f o!r ?\ghts4 ,^! are second>y ?\ghts4 ,at ?is po9t x is well explicitly to discrim9ate betwe5 an actual ?\ght-expression1 namely1 a judgm5t actually made1 & a m]e proposition :i* is a hypo!tical ?\ght-expression1 namely1 an imag9$ possibility ( ?\ght-expression4 ,note t ! actual complete ?\ght-cont5t ( ! consci\sness is explicitly nei!r affirm$ or d5i$4 ,x is j :at is ?\ght4 ,?us1 to ?9k two & two make f\r is di/9ct f affirm+ t two & two make f\r4 ,9 ! fir/ case ! proposition is ! ?\ght-expression1 9 ! second case ! affirmation ( ! proposition is ! ?\ght-expression1 & ! proposition has be5 degrad$ to a m]e proposition1 namely1 to a hypo!tical ?\ght-expression :i* is reflect$ ^u4 ,a di/9ction is sometimes made betwe5 facts & ?\ghts4 ,s f> z physical sci5ce is conc]n$1 ! facts are ?\ghts1 & ?\ghts are facts4 ,namely1 ! facts ( s5se-pres5tation z !y affect sci5ce are ^? elem5ts 9 ! imm$iate appreh5sions :i* are ?\ghts4 ,also1 actual ?\ght-expressions1 prim>y or second>y1 are ! mat]ial facts :i* sci5ce int]prets4 ,! di/9ction t facts are giv51 b ?\ghts are free1 is n absolute4 ,we c select & modify our s5se-pres5tation1 s t facts--9 ! n>r[] s5se ( imm$iate appreh5sion ( s5se-pres5tation--are to "s degree subject to volition4 ,aga91 our /ream ( ?\ght-expression is only p>tially modifi$ by explicit volition4 ,we c *oose our physical exp]i5ce1 & we f9d ourselves ?9k+2 namely1 on ! "o h& !re is selection amid ! dom9ant necessity ( s5se1 & on ! o!r h&1 ! ?\ght-cont5t ( consci\sness 7s f> z second>y ?\ghts are conc]n$7 is n :olly con/itut$ by ! selection ( w4 ,?us1 on ! :ole !re is a l>ge prim>y region ( second>y ?\ght1 z well z ( ! prim>y ?\ghts ( s5se-pres5tation1 :i* is giv5 9 type4 ,t is ! way 9 :i* we d ?9k ( ?+s1 n :olly f any ab/ract necessity1 s f> z we "k1 b because we h inh]it$ ! me?od f an environm5t4 ,x is ! way we f9d ourselves ?9k+1 a way :i* c only be fundam5tally laid aside by an imm5se ef=t1 & !n only = isolat$ %ort p]iods ( "t4 ,?is is :at ,i h call$ ! :ole app>atus ( commons5se ?\ght4 ,x is ?is body ( ?\ght :i* is assum$ 9 sci5ce4 ,x is a way ( ?9k+ r ?an a set ( axioms4 ,x is1 9 fact1 ! set ( concepts :i* commons5se has f\nd useful 9 sort+ out human exp]i5ce4 ,x is modifi$ 9 detail1 b assum$ 9 gross4 ,! explanations ( sci5ce are direct$ to f9d+ conceptions & propositions conc]n+ nature :i* expla9 ! importance ( ^! common s5se notions4 ,= example1 a *air is a common s5se notion1 molecules & electrons expla9 our vision ( *airs4 ,n[ sci5ce aims at h>monis+ our reflective & d]ivative ?\ghts ) ! prim>y ?\ghts involv$ 9 ! imm$iate appreh5sion ( s5se-pres5tation4 ,x also aims at produc+ su* d]ivative ?\ghts1 logically knit toge!r4 ,?is is sci5tific !ory2 & ! h>mony to be a*iev$ is ! agreem5t ( !ory ) obs]vation1 :i* is ! appreh5sion ( s5se-pres5tation4 ,?us !re is a tw(old sci5tific aim3 7#a7 ! production ( !ory :i* agrees ) exp]i5ce2 & 7#b7 ! explanation ( commons5se concepts ( nature1 at lea/ 9 _! ma9 outl9es4 ,?is explanation consi/s 9 ! pres]vation ( ! concepts 9 a sci5tific !ory ( h>monis$ ?\ght4 ,x is n ass]t$ t ?is is :at sci5ti/s 9 ! pa/ meant to a*ieve1 or ?\ght t !y c\ld a*ieve4 ,x is sugge/$ z ! actual result ( sci5tific ef=t1 s f> z t ef=t has _h any measure ( success4 ,9 %ort1 we are "h discuss+ ! natural hi/ory ( ideas & n volitions ( sci5ti/s4 ,,ii4 ,objects ,we p]ceive ?+s 9 space4 ,= example1 among su* ?+s are dogs1 *airs1 curta9s1 drops ( wat]1 gu/s ( air1 flames1 ra9b[s1 *imes ( bells1 od\rs1 a*es & pa9s4 ,!re is a sci5tific explanation ( ! orig9 ( ^! p]ceptions4 ,?is explanation is giv5 9 t]ms ( molecules1 atoms1 electrons1 & _! mutual relations1 9 p>ticul> ( _! space-relations1 & waves ( di/urbance ( ^! space-relations :i* are propagat$ ?r\gh space4 ,! prim>y elem5ts ( ! sci5tific explanation--molecules1 etc4--are n ! ?+s directly p]ceiv$4 ,= example1 we d n p]ceive a wave ( light2 ! s5sation ( sight is ! resultant effect ( ! impact ( millions ( su* waves ?r\gh a /ret* ( "t4 ,?us ! object directly p]ceiv$ corresponds to a s]ies ( ev5ts 9 ! physical _w1 ev5ts :i* are prolong$ ?r\gh a /ret* ( "t4 ,nor is x true t a p]ceiv$ object always corresponds to ! same gr\p ( molecules4 ,aft] a few ye>s we recognise ! same cat1 b we are !reby relat$ to diff]5t molecules4 ,aga91 neglect+ = a mom5t ! sci5tific explanation1 ! p]ceiv$ object is l>gely ! supposition ( our imag9ation4 ,:5 we recognis$ ! cat1 we also recognis$ t x 0 glad to see u4 ,b we m]ely he>d its mew+1 saw x ar* its back1 & felt x rubb+ itself aga9/ u4 ,we mu/ di/+ui%1 !re=e1 betwe5 ! _m direct objects ( s5se1 & ! s+le indirect object ( ?\ght :i* is ! cat4 ,?us1 :5 we say t we p]ceiv$ ! cat & und]/ood its feel+s1 we mean t we he>d a s5se-object ( s\nd1 t we saw a s5se-object ( sight1 t we felt a s5se-object ( t\*1 & t we ?\ght ( a cat & imag9$ its feel+s4 ,s5se-objects are correlat$ by "t-relations & space-relations4 ,?ree simultane\s s5se-objects :i* are also spatially co9cid5t1 are comb9$ by ?\ght into ! p]ception ( "o cat4 ,su* comb9ation ( s5se-objects is an in/9ctive imm$iate judgm5t 9 g5]al )\t ef=t ( reason+4 ,sometimes only "o s5se-object is pres5t4 ,= example1 we he> mew+ & say !re mu/ be a cat 9 ! room4 ,! transition f ! s5se-object to ! cat has !n be5 made1 by delib]ate ratioc9ation4 ,ev5 ! concurr5ce ( s5se-objects may provoke su* a self-consci\s ef=t4 ,= example1 9 ! d>k we feel some?+1 & he> mew+ f ! same place1 & ?9k1 ,surely ?is is a cat4 ,sight is m bold2 :5 we see a cat1 we d n ?9k fur!r4 ,we id5tify ! sight ) ! cat1 :]eas ! cat & ! mew are sep>ate4 ,b su* imm$iate id5tification ( a sight object & an object ( ?\ght may lead to error2 ! birds peck$ at ! grapes ( ,apelles4 ,a s+le s5se-object is a complex entity4 ,! sight-object ( a tile on ! he>? may rema9 un*ang$ z we wat* x 9 a /eady light1 rema9+ ourselves un*ang$ 9 position4 ,ev5 !n x is prolong$ 9 "t1 & has p>ts 9 space4 ,also x is some:at arbitr>ily di/+ui%$ f a l>g] :ole ( :i* x =ms "p4 ,b ! glanc+ fire-light & a *ange 9 our position alt]s ! sight-object4 ,we judge t ! tile ?\ght-object rema9s un*ang$4 ,! sight-object ( ! coal on ! fire gradually modifies1 ?\gh )9 %ort int]vals x rema9s un*ang$4 ,we judge t ! coal ?\ght-object is *ang+4 ,! flame is nev] ! same1 & its %ape is only vaguely di/+ui%able4 ,we conclude t a s+le self-id5tical sight-object is already a phantasy ( ?\ght4 ,consid] ! un*ang+ sight-object ( ! tile1 z we rema9 /ill 9 a /eady light4 ,n[ a s5se-object p]ceiv$ at "o "t is a di/9ct object f a s5se-object se5 at ano!r "t4 ,?us ! sight ( ! tile at noon is di/9ct f its sight at #ab4cj4 ,b !re is no su* ?+ z a s5se-object at an in/ant4 ,z we />e at ! tile1 a m9ute1 or a second1 or a t5? ( a second1 has fl[n by3 ess5tially !re is a duration4 ,!re is a /ream ( sight1 & we c di/+ui% its p>ts4 ,b ! p>ts also are /reams1 & x is only 9 ?\ght t ! /ream sep>ates into a succession ( elem5ts4 ,! /ream may be /eady z 9 ! case ( ! un*ang+ sight-tile1 or may be turbul5t z 9 ! case ( ! glanc+ sight-flame4 ,9 ei!r case a sight-object is "s arbitr>ily small "p ( ! /ream4 ,aga91 ! /ream :i* =ms ! succession ( sight-tiles is m]ely a di/+ui%able "p ( ! :ole /ream ( sight-pres5tation4 ,s1 f9ally1 we conceive ourselves ea* exp]i5c+ a complete "t-flux 7or /ream7 ( s5se-pres5tation4 ,?is /ream is di/+ui%able into p>ts4 ,! gr\nds ( di/9ction are diff]5ces ( s5se--includ+ )9 t t]m1 diff]5ces ( types ( s5se1 & diff]5ces ( quality & ( int5sity )9 ! same type ( s5se--& diff]5ces ( "t-relations1 & diff]5ces ( space-relations4 ,also ! p>ts are n mutually exclusive & exi/ 9 unb\nd$ v>iety4 ,! "t-relation betwe5 ! p>ts raises ! que/ions ( memory & recognition1 subjects too complex = discussion "h4 ,"o rem>k mu/ be made4 ,if x be admitt$1 z /at$ above1 t we live 9 durations & n 9 in/ants1 namely1 t ! pres5t ess5tially occupies a /ret* ( "t1 ! di/9ction betwe5 memory & imm$iate pres5tation _c be q fundam5tal2 = always we h ) u ! fad+ pres5t z x becomes ! imm$iate pa/4 ,?is region ( our consci\sness is nei!r pure memory nor pure imm$iate pres5tation4 ,anyh[1 memory is also a pres5tation 9 consci\sness4 ,ano!r po9t is to be not$ 9 connection ) memory4 ,!re is no directly p]ceiv$ "t-relation betwe5 a pres5t ev5t & a pa/ ev5t4 ,! pres5t ev5t is only relat$ to ! memory ( ! pa/ ev5t4 ,b ! memory ( a pa/ ev5t is itself a pres5t elem5t 9 consci\sness4 ,we ass]t ! pr9ciple t directly p]ceiv$ relations c only exi/ betwe5 elem5ts ( consci\sness1 bo? 9 t pres5t dur+ :i* ! p]ception occurs4 ,all o!r relations betwe5 elem5ts ( p]ception are inf]5tial con/ructions4 ,x ?us becomes necess>y to expla9 h[ ! "t /ream ( ev5ts e/abli%es itself 9 ?\ght1 & h[ ! app>5t _w fails to collapse into "o s+le pres5t4 ,! solution ( ! difficulty is arriv$ at by obs]v+ t ! pres5t is itself a duration1 & !re=e includes directly p]ceiv$ "t-relations betwe5 ev5ts conta9$ )9 x4 ,9 o!r words we put ! pres5t on ! same foot+ z ! pa/ & ! future 9 respect to ! inclusion )9 x ( antec$5t & succe$+ ev5ts1 s t pa/1 pres5t1 & future are 9 ?is respect exactly analog\s ideas4 ,?us !re w be two ev5ts a & b1 bo? 9 ! same pres5t1 b ! ev5t a w be directly p]ceiv$ to prec$e ! ev5t b4 ,aga9 "t fl[s on1 & ! ev5t a fades into ! pa/1 & 9 ! new pres5t duration ev5ts b & c occur1 ev5t b prec$+ ev5t c1 also 9 ! same pres5t duration !re is ! memory ( ! "t-relation betwe5 a & b4 ,!n by an inf]5tial con/ruction ! ev5t a 9 ! pa/ prec$es ! ev5t c 9 ! pres5t4 ,by proce$+ accord+ to ?is pr9ciple ! "t-relations betwe5 elem5ts ( consci\sness1 n 9 ! same pres5t1 are e/abli%$4 ,! me?od ( proc$ure "h expla9$ is a fir/ example ( :at we w call ! ,pr9ciple ( ,aggregation4 ,?is is "o ( ! fundam5tal pr9ciples ( m5tal con/ruction accord+ to :i* our conception ( ! ext]nal physical _w is con/ruct$4 ,o!r examples w lat] on be met )4 ,! space-relations betwe5 ! p>ts are confus$ & fluctuat+1 & 9 g5]al lack det]m9ate precision4 ,! ma/]-key by :i* we conf9e our att5tion to su* p>ts z possess mutual relations suffici5tly simple = our intellects to consid] is ! pr9ciple ( conv]g5ce to simplicity ) dim9ution ( ext5t4 ,we w call x ! pr9ciple ( conv]g5ce4 ,?is pr9ciple ext5ds ?r\gh\t ! :ole field ( s5se-pres5tation4 ,! fir/ application ( ! pr9ciple occurs 9 respect to "t4 ,! %ort] ! /ret* ( "t1 ! simpl] are ! aspects ( ! s5se-pres5tation conta9$ )9 x4 ,! p]plex+ effects ( *ange are dim9i%$ & 9 _m cases c be neglect$4 ,nature has re/rict$ ! acts ( ?\ght :i* endeav\r to realise ! cont5t ( ! pres5t1 to /ret*es ( "t suffici5tly %ort to secure ?is /atic simplicity ov] ! great] "p ( ! s5se-/ream4 ,spatial relations become simplifi$ )9 ! approximately /atic s5se-_w ( ! %ort "t4 ,a fur!r simplicity is ga9$ by p>tition+ ?is /atic _w into p>ts ( re/rict$ space-cont5t4 ,! v>i\s p>ts ?us obta9$ h simpl] mutual space-relations1 & aga9 ! pr9ciple ( conv]g5ce holds4 ,f9ally1 ! la/ simplicity is obta9$ by p>tition+ ! p>ts1 already re/rict$ z to space & "t1 into fur!r p>ts *>act]is$ by homog5eity 9 type ( s5se1 & homog5eity 9 quality & int5sity ( s5se4 ,^! ?ree processes ( re/riction yield1 f9ally1 ! s5se-objects :i* h be5 m5tion$ above4 ,?us ! s5se-object is ! result ( an active process ( discrim9ation made 9 virtue ( ! pr9ciple ( conv]g5ce4 ,x is ! result ( ! que/ = simplicity ( relations )9 ! complete /ream ( s5se-pres5tation4 ,! ?\ght-objects ( p]ception are in/ances ( a fundam5tal law ( nature1 ! law ( objective /ability4 ,x is ! law ( ! coh]5ce ( s5se-objects4 ,?is law ( /ability has an application to "t & an application to space2 also x mu/ be appli$ 9 conjunction ) t o!r law1 ! pr9ciple ( conv]g5ce to simplicity f :i* s5se-objects are d]iv$4 ,"s composite p>tial /reams ( s5se-pres5tation c be di/+ui%$ ) ! foll[+ *>act]i/ics3 7#a7 ! "t-succession ( s5se-objects1 belong+ to a s+le s5se1 involv$ 9 any su* a composite p>tial /ream1 is compos$ ( v simil> objects ^: modifications increase only gradually1 & ?us =ms a homog5e\s compon5t /ream )9 ! composite /ream2 7#b7 ! space-relations ( ^? s5se-objects 7( v>i\s s5ses7 ( su* a composite /ream :i* are conf9$ )9 any suffici5tly %ort "t are id5tical s f> z !y are def9itely appreh5d$1 & ?us ^! v>i\s compon5t /reams1 ea* homog5e\s1 coh]e to =m ! :ole composite p>tial /ream2 7#c7 !re are o!r s5se-pres5tations occurr+ 9 association ) t composite p>tial /ream :i* c be det]m9$ by rules d]iv$ f analog\s composite p>tial /reams1 ) o!r space & "t relations1 provid$ t ! analogy be suffici5tly close4 ,call ^! ! associat$ s5se-pres5tations4 ,a p>tial /ream ( ?is sort1 view$ z a :ole1 is "h call$ a fir/ crude ?\ght-object ( p]ception4 ,= example1 we look at an orange = half a m9ute1 h&le x1 & smell x1 note its position 9 ! fruit-basket1 & !n turn away4 ,! /ream ( s5se-pres5tation ( ! orange dur+ t half-m9ute is a fir/ crude ?\ght-object ( p]ception4 ,among ! associat$ s5se pres5tations are ^? ( ! fruit-basket :i* we conceive z support+ ! orange4 ,! ess5tial gr\nd ( ! association ( s5se-objects ( v>i\s types1 p]ceiv$ )9 "o %ort duration1 into a fir/ crude ?\ght-object ( p]ception is ! co9cid5ce ( _! space-relations1 t is1 9 g5]al an approximate co9cid5ce ( su* relations p]haps only vaguely appreh5d$4 ,?us co9cid5t space-relations associate s5se-objects into a fir/ crude ?\ght-object1 & div]se space-relations dissociate s5se-objects f aggregation into a fir/ crude ?\ght-object4 ,9 respect to "s gr\ps ( s5se-objects ! association may be an imm$iate judgm5t devoid ( all inf]5ce1 s t ! prim>y p]ceptual ?\ght is t ( ! fir/ crude ?\ght-object1 & ! sep>ate s5se-objects are ! result ( reflective analysis act+ on memory4 ,= example s5se-objects ( sight & s5se-objects ( t\* are (t5 ?us prim>ily associat$ & only second>ily dissociat$ 9 ?\ght4 ,b sometimes ! association is wav]+ & indet]m9ate1 = example1 t betwe5 ! s\nd-object ( ! mew ( ! cat & ! sight-object ( ! cat4 ,?us to sum up1 ! p>tial /ream ( s5se-p]ceptions coalesces into t fir/ crude ?\ght-object ( p]ception :i* is ! mom5t>y cat because ! s5se-p]ceptions belong+ to ?is /ream are 9 ! same place1 b equally x w\ld be true to say t !y are 9 ! same place because !y belong to ! same mom5t>y cat4 ,?is analysis ( ! complete /ream ( s5se-pres5tation 9 any small pres5t duration into a v>iety ( fir/ crude ?\ght-objects only p>tially fits ! facts2 = "o reason because _m s5se-objects1 su* z s\nd = in/ance1 h vague & indet]m9ate space-relations1 = example vaguely ^? space-relations :i* we associate ) our organs ( s5se & also vaguely ^? ( ! orig9 f :i* 79 ! sci5tific explanation7 !y proce$4 ,! proc$ure by :i* ! orange ( half a m9ute is elaborat$ into ! orange 9 ! ord9>y s5se ( ! t]m involves 9 addition ! two pr9ciples ( aggregation & ( hypo!tical s5se-pres5tation4 ,! pr9ciple ( aggregation1 z "h employ$1 takes ! =m t _m di/9ct fir/ crude ?\ght-objects ( p]ception are conceiv$ z "o ?\ght-object ( p]ception1 if ! _m p>tial /reams =m+ ^! objects are suffici5tly analog\s1 if _! times ( occurr5ce are di/9ct1 & if ! associat$ s5se-pres5tations are suffici5tly analog\s4 ,= example1 aft] leav+ ! orange1 9 five m9utes we return4 ,a new fir/ crude ?\ght-object ( p]ception pres5ts itself to u1 indi/+ui%able f ! half-m9ute orange we previ\sly exp]i5c$2 x is 9 ! same fruit-basket4 ,we aggregate ! two pres5tations ( an orange into ! same orange4 ,by su* aggregations we obta9 second crude ?\ght-objects ( p]ception4 ,b h[ev] f> we c proce$ ) aggregation ( ?is type1 ! orange is m ?an t4 ,= example1 :at d we mean :5 we say1 ,! orange is 9 ! cupbo>d1 if ,tom has n eat5 x8 ,! _w ( pres5t fact is m ?an a /ream ( s5se-pres5tation4 ,we f9d ourselves ) emotions1 volitions1 imag9ations1 conceptions1 & judgm5ts4 ,no factor :i* ent]s into consci\sness is by itself or ev5 c exi/ 9 isolation4 ,we are analys+ c]ta9 relations betwe5 s5se-pres5tation & o!r factors ( consci\sness4 ,hi!rto we h tak5 into acc\nt m]ely ! factors ( concept & judgm5t4 ,imag9ation is necess>y to complete ! orange1 namely1 ! imag9ation ( hypo!tical s5se-pres5tations4 ,x is beside ! po9t to argue :e!r we ought to h su* imag9ations1 or to discuss :at are ! metaphysical tru?s conc]n+ reality to :i* !y correspond4 ,we are "h only conc]n$ ) ! fact t su* imag9ations exi/ & ess5tially ent] into ! =mation ( ! concepts ( ! ?\ght-objects ( p]ception :i* are ! fir/ data ( sci5ce4 ,we conceive ! orange z a p]man5t collection ( s5se-pres5tations exi/+ z if !y 7 an actual elem5t 9 our consci\sness1 :i* !y are n4 ,! orange is ?us conceiv$ z 9 ! cupbo>d ) its %ape1 od\r1 col\r1 & o!r qualities4 ,namely1 we imag9e hypo!tical possibilities ( s5se-pres5tation1 & conceive _! want ( actuality 9 our consci\sness z immat]ial to _! exi/5ce 9 fact4 ,! fact :i* is ess5tial = sci5ce is our conception2 its mean+ 9 reg>d to ! metaphysics ( reality is ( no sci5tific importance1 s f> z physical sci5ce is conc]n$4 ,! orange complet$ 9 ?is way is ! ?\ght-object ( p]ception4 ,x mu/ be rememb]$ t ! judgm5ts & concepts aris+ 9 ! =mation ( ?\ght-objects ( p]ception are 9 ! ma9 in/9ctive judgm5ts1 & in/9ctive concepts1 & are n concepts & judgm5ts consci\sly s\ght = & consci\sly criticis$ be=e adoption4 ,_! adoption is facilitat$ by & int]wov5 ) ! expectation ( ! future 9 :i* ! hypo!tical passes into ! actual1 & also ) ! fur!r judgm5t ( ! exi/5ce ( o!r consci\snesses1 s t mu* t is hypo!tical to "o consci\sness is judg$ to be actual to o!rs4 ,! ?\ght-object ( p]ception is1 9 fact1 a device to make pla9 to our reflective consci\sness relations :i* hold )9 ! complete /ream ( s5se-pres5tation4 ,conc]n+ ! utility ( ?is weapon !re c be no "q2 x is ! rock ^u :i* ! :ole /ructure ( commons5se ?\ght is erect$4 ,b :5 we consid] ! limits ( its application ! evid5ce is confus$4 ,a great "p ( our s5se-pres5tation c be con/ru$ z p]ception ( v>i\s p]si/5t ?\ght-objects4 ,b h>dly at any "t c ! s5se-pres5tations be con/ru$ :olly 9 t way4 ,sights l5d !mselves easily to ?is con/ruction1 b sight c be baffl$3 = example1 consid] reflections 9 look+-glasses1 app>5tly b5t /icks half 9 & half out ( wat]1 ra9b[s1 brilliant pat*es ( light :i* conceal ! object f :i* !y emanate1 & _m analog\s ph5om5a4 ,s\nd is m difficult2 x t5ds l>gely to dis5gage itself f any su* object4 ,= example1 we see ! bell1 b we he> ! s\nd :i* comes f ! bell2 yet we also say t we he> ! bell4 ,aga91 a too?a*e is l>gely by itself1 & is only indirectly a p]ception ( ! n]ve ( ! too?4 ,illu/rations to ! same effect c be accumulat$ f e type ( s5sation4 ,ano!r difficulty arises f ! fact ( *ange4 ,! ?\ght-object is conceiv$ z "o ?+1 :olly actual at ea* in/ant4 ,b s9ce ! meat has be5 b\ght x has be5 cook$1 ! grass gr[s & !n )]s1 ! coal burns 9 ! fire1 ! pyramids ( ,egypt rema9 un*ang$ = ages1 b ev5 ! pyramids are n :olly un*ang$4 ,! difficulty ( *ange is m]ely evad$ by affix+ a te*nical ,lat9 "n to a suppos$ logical fallacy4 ,a slight cook+ leaves ! meat ! same object1 b two days 9 ! ov5 burns x to a c9d]4 ,:5 does ! meat cease to be8 ,n[ ! *ief use ( ! ?\ght-object is ! concept ( x z "o ?+1 "h & n[1 :i* lat] c be recognis$1 !re & !n4 ,?is concept applies suffici5tly well to mo/ ?+s = %ort times1 & to _m ?+s = long times4 ,b s5se-pres5tation z a :ole entirely refuses to be pati5t ( ! concept4 ,we h n[ come to ! reflective region ( explanation1 :i* is sci5ce4 ,a great "p ( ! difficulty is at once remov$ by apply+ ! pr9ciple ( conv]g5ce to simplicity4 ,we habitually make our ?\ght-objects too l>ge2 we %\ld ?9k 9 small] p>ts4 ,= example1 ! ,sph9x has *ang$ by its nose becom+ *ipp$1 b by prop] inquiry we c\ld f9d ! miss+ "p 9 "s private h\se ( ,we/]n ,europe or ,nor!rn ,am]ica4 ,?us1 ei!r "p1 ! re/ ( ! ,sph9x or ! *ip1 rega9s its p]man5ce4 ,fur!rmore1 we enl>ge ?is explanation by conceiv+ p>ts s small t !y c only be obs]v$ "u ! mo/ fav\rable circum/ances4 ,?is is a wide ext5sion ( ! pr9ciple ( conv]g5ce 9 its application to nature2 b x is a pr9ciple amply support$ by ! hi/ory ( exact obs]vation4 ,?us1 *ange 9 ?\ght-objects ( p]ception is l>gely expla9$ z a dis9tegration into small] p>ts1 !mselves ?\ght-objects ( p]ception4 ,! ?\ght-objects ( p]ception :i* are presuppos$ 9 ! common ?\ght ( civilis$ be+s are almo/ :olly hypo!tical4 ,! mat]ial univ]se is l>gely a concept ( ! imag9ation :i* re/s on a sl5d] basis ( direct s5se-pres5tation4 ,b none ! less x is a fact2 = x is a fact t actually we imag9e x4 ,?us x is actual 9 our consci\sness j z s5se-pres5tation also is actual !re4 ,! ef=t ( reflective criticism is to make ^! two factors 9 our consci\sness agree :]e !y are relat$1 namely1 to con/rue our s5se-pres5tation z actual realisation ( ! hypo!tical ?\ght-objects ( p]ception4 ,! :olesale employm5t ( purely hypo!tical ?\ght-objects ( p]ception enables sci5ce to expla9 "s ( ! /ray s5se-objects :i* _c be con/ru$ z p]ceptions ( a ?\ght-object ( p]ception3 = example1 s\nds4 ,b ! ph5om5a z a :ole defy explanation on ^! l9es until a fur!r fundam5tal /ep is tak51 :i* trans=ms ! :ole concept ( ! mat]ial univ]se4 ,namely1 ! ?\ght-object ( p]ception is sup]s$$ by ! ?\ght-object ( sci5ce4 ,! ?\ght-objects ( sci5ce are molecules1 atoms1 & electrons4 ,! peculi>ity ( ^! objects is t !y h %$ all ! qualities :i* are capable ( direct s5se-repres5tation 9 consci\sness4 ,!y are kn[n to u only by _! associat$ ph5om5a1 namely1 s]ies ( ev5ts 9 :i* !y are implicat$ are repres5t$ 9 our consci\sness by s5se-pres5tations4 ,9 ?is way1 ! ?\ght-objects ( sci5ce are conceiv$ z ! causes ( s5se-repres5tation4 ,! transition f ?\ght-objects ( p]ception to ?\ght-objects ( sci5ce is dec5tly veil$ by an elaborate !ory conc]n+ prim>y & second>y qualities ( bodies4 ,?is device1 by :i* s5se-pres5tations are repres5t$ 9 ?\ght z our p]ception ( ev5ts 9 :i* ?\ght-objects ( sci5ce are implicat$1 is ! fundam5tal means by :i* a bridge is =m$ betwe5 ! fluid vagu5ess ( s5se & ! exact def9ition ( ?\ght4 ,9 ?\ght a proposition is ei!r true or false1 an entity is exactly :at x is1 & relations betwe5 entities are expressible 79 idea7 by def9ite propositions ab\t di/9ctly conceiv$ entities4 ,s5se-p]ception kn[s none ( ^! ?+s1 except by c\rtesy4 ,accuracy ess5tially collapses at "s /age ( inquiry4 ,,iii4 ,"t & ,space ,recapitulation4--,relations ( "t & relations ( space hold betwe5 s5se-objects ( p]ception4 ,^! s5se-objects are di/+ui%$ z sep>ate objects by ! recognition ( ei!r 7#a7 diff]5ces ( s5se-cont5t1 or 7#b7 "t-relations betwe5 !m o!r ?an simultaneity1 or 7#c7 space-relations betwe5 !m o!r ?an co9cid5ce4 ,?us s5se-objects arise f ! recognition ( contra/ )9 ! complete /ream ( s5se-pres5tation1 namely1 f ! recognition ( ! objects z relat$ t]ms1 by relations :i* contra/ !m4 ,diff]5ces ( s5se-cont5t are inf9itely complex 9 _! v>iety4 ,_! analysis "u ! head+ ( g5]al ideas is ! un5d+ task ( physical sci5ce4 ,"t-relations & space-relations are comp>atively simple1 & ! g5]al ideas accord+ to :i* _! analysis %\ld proce$ are obvi\s4 ,?is simplicity ( "t & space is p]haps ! reason :y ?\ght *ooses !m z ! p]man5t gr\nd = objectival di/9ction1 ?r[+ ! v>i\s s5se-objects ?us obta9able into "o heap1 z a fir/ crude ?\ght-object ( p]ception1 & !nce1 z describ$ above1 obta9+ a ?\ght-object ( p]ception4 ,?us a ?\ght-object ( p]ception conceiv$ z 9 ! pres5t ( a %ort duration is a fir/ crude ?\ght-object ( p]ception ei!r actual or hypo!tical4 ,su* a ?\ght-object ( p]ception1 conf9$ )9 a %ort duration1 takes on ! space-relations ( its compon5t s5se-objects )9 t same duration4 ,accord+ly ?\ght-objects ( p]ception1 conceiv$ 9 _! :ole ext5ts1 h to ea* o!r ! "t-relation%ips ( _! complete exi/5ces1 & )9 any small duration h to ea* o!r ! space-relation%ips ( _! compon5t s5se-objects :i* lie )9 t duration4 ,relations b9d toge!r3 ?us ?\ght-objects ( p]ception are connect$ 9 "t & 9 space4 ,! g5esis ( ! objectival analysis ( s5se-pres5tation is ! recognition ( s5se-objects z di/9ct t]ms 9 "t-relations & space-relations3 ?us ?\ght-objects ( p]ception are sep>at$ by "t & by space4 ,:ole & ,"p4--,a s5se-object is "p ( ! complete /ream ( pres5tation4 ,?is concept ( be+ a "p is m]ely ! /atem5t ( ! relation ( ! s5se-object to ! complete s5se-pres5tation = t consci\sness4 ,also a s5se-object c be "p ( ano!r s5se-object4 ,x c be a "p 9 two ways1 namely1 a "p 9 "t & a "p 9 space4 ,x seems probable t bo? ^! concepts ( "t-"p & space-"p are fundam5tal2 t is1 are concepts express+ relations :i* are directly pres5t$ to u1 & are n concepts ab\t concepts4 ,9 t case no fur!r def9ition ( ! actual pres5tation is possible4 ,x may ev5 !n be possible to def9e an adequate crit]ion ( ! occurr5ce ( su* a pres5tation4 ,= example1 adopt+ = ! mom5t a reali/ metaphysic z to ! exi/5ce ( ! physical _w ( molecules & electrons1 ! vision ( a *air z occurr+ = "s def9ite p]son at "s def9ite "t is ess5tially indef9able4 ,x is 8 vision1 ?\gh ea* ( u guesses t x mu/ be uncommonly l our vision "u analog\s circum/ances4 ,b ! exi/5ce ( ! def9able molecules & waves ( light 9 c]ta9 def9able relations to 8 bodily organs ( s5se1 8 body also be+ 9 a c]ta9 def9able /ate1 =ms an adequate crit]ion ( ! occurr5ce ( ! vision1 a crit]ion :i* is accept$ 9 ,c\rts ( ,law & = physical sci5ce is tacitly sub/itut$ = ! vision4 ,! connection betwe5 ! relations :ole & "p & all & "s is intimate4 ,x c be expla9$ ?us s f> z conc]ns directly pres5t$ s5se-objects4 ,call two s5se-objects sep>at$ if !re is no ?ird s5se-object :i* is a "p ( bo? ( !m4 ,!n an object ,a is compos$ ( ! two objects ,b & ,c1 if 7#a7 ,b & ,c are bo? p>ts ( ,a1 7#b7 ,b & ,c are sep>at$1 & 7#c7 !re is no "p ( ,a :i* is sep>at$ bo? f ,b & f ,c4 ,9 su* a case ! class :i* is compos$ ( ! two objects ,b & ,c is (t5 sub/itut$ 9 ?\ght = ! s5se-object ,a4 ,b ?is process presupposes ! fundam5tal relation :ole & "p4 ,conv]sely ! objects ,b & ,c may be actual s5se-objects1 b ! s5se-object ,a :i* corresponds to ! class may rema9 hypo!tical4 ,= example1 ! r\nd _w on :i* we live rema9s a conception correspond+ to no s+le s5se-object at any "t pres5t$ 9 any human be+'s consci\sness4 ,x is possible1 h[ev]1 t "s mode ( conceiv+ ! :ole-&-"p relation betwe5 ext5d$ objects z ! all-&-"s relation ( logical classes c be f\nd4 ,b 9 ?is case ! ext5d$ objects z "h conceiv$ _c be ! true s5se-objects :i* are pres5t to consci\sness4 ,= z "h conceiv$ a "p ( a s5se-object is ano!r s5se-object ( ! same type2 & !re=e "o s5se-object _c be a class ( o!r s5se-objects1 j z a tea-spoon _c be a class ( o!r tea-spoons4 ,! ord9>y way 9 ?\ght by :i* :ole-&-"p is r$uc$ to all-&-"s is by ! device ( po9ts1 namely1 ! "p ( an object occupies "s ( ! po9ts occupi$ by ! :ole object4 ,if any "o holds t 9 8 consci\sness ! s5se-pres5tation is a pres5tation ( po9t-objects1 & t an ext5d$ object is m]ely a class ( su* po9t-objects collect$ toge!r 9 ?\ght1 !n ?is ord9>y me?od is completely satisfactory4 ,we %all proce$ on ! assumption t ?is conception ( directly p]ceiv$ po9t-objects has no relation to ! facts4 ,9 ! prec$+ address on ,! ,organisation ( ,?\ght1 ano!r mode is sugge/$4 ,b ?is me?od w\ld apply only to ! ?\ght-object ( p]ception1 & has no ref]5ce to ! prim>y s5se-objects "h consid]$4 ,accord+ly x mu/ reckon z a subord9ate device = a lat] /age ( ?\ght4 ,?us ! po9t-object 9 "t & ! po9t-object 9 space1 & ! d\ble po9t-object bo? 9 "t & space1 mu/ be conceiv$ z intellectual con/ructions4 ,! fundam5tal fact is ! s5se-object1 ext5d$ bo? 9 "t & space1 ) ! fundam5tal relation ( :ole-to-"p to o!r su* objects1 & subject to ! law ( conv]g5ce to simplicity z we proce$ 9 ?\ght ?r\gh a s]ies ( successively conta9$ p>ts4 ,! relation :ole-to-"p is a temporal or spatial relation1 & is !re=e prim>ily a relation hold+ betwe5 s5se-objects ( p]ception1 & x is only d]ivatively ascrib$ to ! ?\ght-objects ( p]ception ( :i* !y are compon5ts4 ,m g5]ally1 space & "t relations hold prim>ily betwe5 s5se-objects ( p]ception & d]ivatively betwe5 ?\ght-objects ( p]ception4 ,def9ition ( ,po9ts4--,! g5esis ( po9ts ( "t & ( space c n[ be /udi$4 ,we mu/ di/+ui% 7#a7 s5se-"t & s5se-space1 & 7#b7 ?\ght-"t ( p]ception & ?\ght-space ( p]ception4 ,s5se-"t & s5se-space are ! actually obs]v$ "t-relations & space-relations betwe5 s5se-objects4 ,s5se-"t & s5se-space h no po9ts except1 p]haps1 a few sp>se in/ances1 suffici5t to sugge/ ! logical idea2 also1 s5se-"t & s5se-space are discont9u\s & fragm5t>y4 ,?\ght-"t ( p]ception & ?\ght-space ( p]ception are ! "t & space relations :i* hold betwe5 ?\ght-objects ( p]ception4 ,?\ght-"t ( p]ception & ?\ght-space ( p]ception are ea* cont9u\s4 ,by cont9u\s is "h meant t all ?\ght-objects ( p]ception h to ea* o!r a "t 7or space7 relation4 ,! orig9 ( po9ts is ! ef=t to take full advantage ( ! pr9ciple ( conv]g5ce to simplicity4 ,9 s f> z ?is pr9ciple does n apply1 a po9t is m]ely a cumbr\s way ( direct+ att5tion to a set ( relations betwe5 a c]ta9 set ( ?\ght-objects ( p]ception1 :i* set ( relations1 ?\gh actual s f> z a ?\ght-object is actual1 is 7"u ?is supposition7 ( no p>ticul> importance4 ,?us ! prov$ importance 9 physical sci5ce ( ! concepts ( po9ts 9 "t & po9ts 9 space is a tribute to ! wide applicability ( ?is pr9ciple ( conv]g5ce4 ,euclid def9es a po9t z )\t p>ts & )\t magnitude4 ,9 mod]n language a po9t is (t5 describ$ z an ideal limit by indef9itely cont9u+ ! process ( dim9i%+ a volume 7or area74 ,po9ts z ?us conceiv$ are (t5 call$ conv5i5t fictions4 ,?is language is ambigu\s4 ,:at is meant by a fiction8 ,if x means a conception :i* does n correspond to any fact1 !re is "s difficulty 9 und]/&+ h[ x c be ( any use 9 physical sci5ce4 ,= example1 ! fiction ( a r$ man 9 a gre5 coat inhabit+ ! moon c nev] be ( ! slighte/ sci5tific s]vice1 simply because--z we may presume--x corresponds to no fact4 ,by call+ ! concept ( po9ts a conv5i5t fiction1 x mu/ be meant t ! concept does correspond to "s important facts4 ,x is1 !n1 requisite1 9 ! place ( su* vague allusiv5ess1 to expla9 exactly :at are ! facts to :i* ! concept corresponds4 ,we are n mu* help$ by expla9+ t a po9t is an ideal limit4 ,:at is a limit8 ,! idea ( a limit has a precise mean+ 9 ! !ory ( s]ies1 & 9 ! !ory ( ! values ( functions2 b nei!r ( ^! mean+s apply "h4 ,x may be obs]v$ t1 be=e ! ord9>y ma!matical mean+s ( limit _h receiv$ a precise explanation1 ! idea ( a po9t z a limit might be consid]$ z "o among o!r examples ( an idea only to be appreh5d$ by direct intuition4 ,?is view is n n[ op5 to u4 ,?us1 aga91 we are confront$ ) ! "q3 ,:at are ! precise prop]ties meant :5 a po9t is describ$ z an ideal limit8 ,! discussion :i* n[ foll[s is an attempt to express ! concept ( a po9t 9 t]ms ( ?\ght-objects ( p]ception relat$ toge!r by ! :ole-&-"p relation1 consid]$ ei!r z a "t-relation or z a space-relation4 ,if x is s pref]r$1 x may be consid]$ t ! discussion is direct$ t[>ds a precise elucidation ( ! t]m ideal limit z (t5 us$ 9 ?is connection4 ,! subsequ5t explanations c be made easi] to foll[ by a small piece ( symbolism3 ,let a,eb mean t b is "p ( a4 ,we ne$ n decide :e!r we are talk+ ( "t-p>ts or space-p>ts1 b :i*ev] *oice is suppos$ to be made mu/ be conceiv$ z adh]$ to ?r\gh\t any connect$ discussion4 ,! symbol ,e may be consid]$ z ! initial lett] ( encloses1 s we read a,eb z a encloses b4 ,aga9 ! field ( ,e is ! set ( ?+s :i* ei!r enclose or are enclos$1 i4 e4 ev]y?+ a1 :i* is su* t x c be f\nd s t ei!r a,ex or x,ea4 ,a memb] ( ! field ( ,e is call$ an enclosure-object4 ,n[1 we assume t ?is relation ( :ole-to-"p1 :i* 9 ! future we w call enclosure1 always satisfies ! conditions 9 t ! relation ,e is 7#a7 transitive1 7#b7 asymmetrical1 & 7#c7 ) its doma9 includ+ its conv]se doma94 ,^! f\r conditions des]ve "s slight consid]ation2 only ! fir/ two ( !m embody hypo!ses :i* ent] vitally into ! reason+4 ,condition 7#a7 may be /at$ z ! condition t a,eb & b,ec always implies a,ec4 ,! fact t an entity b c be f\nd su* t a,eb & b,ec may be conceiv$ z a relation betwe5 a & c4 ,x is natural to write ,e#b = ?is relation4 ,?us ! condition is n[ writt53 ,if a,e#b;c1 !n a,ec4 ,?is c be /ill o!rwise express$ by say+ t ! relation ,e#b implies1 :5ev] x holds1 t ! relation ,e also holds4 ,condition 7#b7 is p>tly a m]e "q ( trivial def9ition1 & p>tly a sub/antial assumption4 ,! asymmetrical relation 7,e7 is su* t a,eb & b,ea c nev] hold simultane\sly4 ,?is prop]ty splits up into two p>ts3 7#a7 t no in/ance ( a,eb & b,ea & a div]se f b1 c occur1 & 7#b7 t a,ea _c occur4 ,! fir/ "p is a sub/antial assumption1 ! second "p 7s f> z we are conc]n$7 r$uces to ! trivial conv5tion t we %all n consid] an object z "p ( itself1 b w conf9e att5tion to prop] p>ts4 ,condition 7#c7 means t a,eb always implies t c c be f\nd su* t b,ec4 ,?is condition1 tak5 9 conjunction ) ! fact t we are only consid]+ prop] p>ts1 is ! ass]tion ( ! pr9ciple ( ! indef9ite divisibility ( ext5d$ objects1 bo? 9 space & 9 "t4 ,an indivisible "p w lack duration 9 "t1 & ext5sion 9 space1 & is ?us an entity ( ess5tially a diff]5t "* to a divisible "p4 ,if we admit su* indivisibles z ! only true s5se-objects1 our subsequ5t proc$ure is an unnecess>y elaboration4 ,x w be f\nd t a f\r? condition is necess>y ow+ to logical difficulties connect$ ) ! !ory ( an inf9ite numb] ( *oices4 ,x w n be necess>y = u to ent] fur!r on ?is "q1 :i* involves difficult consid]ations ( ab/ract logic4 ,! outcome is1 t ap>t f hypo!sis we _c prove ! exi/5ce ( ! sets1 ea* conta9+ an inf9ite numb] ( objects1 :i* are "h call$ po9ts1 z w be expla9$ imm$iately4 ,n[ consid] a set ( enclosure objects :i* is su* t 7#a7 ( any two ( its memb]s "o encloses ! o!r1 & 7#b7 !re is no memb] :i* is enclos$ by all ! o!rs1 & 7#c7 !re is no enclosure-object1 n a memb] ( ! set :i* is enclos$ by e memb] ( ! set4 ,call su* a set a conv]g5t set ( enclosure-objects4 ,z we pass along ! s]ies f l>g] to small] memb]s1 evid5tly we conv]ge t[>ds an ideal simplicity to any degree ( approximation to :i* we l to proce$1 & ! s]ies z a :ole embodies ! complete ideal along t r\te ( approximation4 ,9 fact1 to repeat1 ! s]ies is a r\te ( approximation4 ,we h n[ to inquire if ! pr9ciple ( conv]g5ce to simplicity may be expect$ to yield ! same type ( simplicity = e su* conv]g5t r\te4 ,! answ] is1 z we might expect1 namely1 t ?is dep5ds ^u ! nature ( ! prop]ties :i* are to be simplifi$4 ,= example1 consid] ! application to "t4 ,n[1 "t is "o-dim5sional2 s :5 ?is prop]ty ( "o-dim5sionality has be5 express$ by ! prop] conditions1 n "h /at$1 a conv]g5t set ( enclosure-objects mu/1 consid]$ z a r\te ( approximation1 exhibit ! prop]ties ( "o unique in/ant ( "t1 z ord9>ily conceiv$ by ! euclidean def9ition4 ,accord+ly1 :atev] simplicity is to be a*iev$ by ! application to "t ( ! pr9ciple ( conv]g5ce to simplicity mu/ be exhibit$ among ! prop]ties ( any su* r\te ( approximation4 ,= space1 diff]5t consid]ations arise4 ,ow+ to its multiple dim5sions1 we c %[ t diff]5t conv]g5t sets ( enclosure-objects1 indicat+ diff]5t r\tes ( approximation1 may exhibit conv]g5ce to diff]5t types ( simplicity1 "s m complex ?an o!rs4 ,= example1 consid] a rectangul> box ( height h ft41 bread? b ft41 & ?ickness c ft4 ,n[1 keep h & b con/ant1 & let ! c5tral plane 7height h1 bread? b7 p]p5dicul> to ! ?ickness be fix$1 !n make c dim9i% indef9itely4 ,we ?us obta9 a conv]g5t s]ies ( an indef9itely l>ge numb] ( boxes1 & !re is no smalle/ box4 ,?us ?is conv]g5t s]ies exhibits ! r\te ( approximation t[>ds ! type ( simplicity express$ z be+ a plane area ( height h1 bread? b1 & no ?ickness4 ,aga91 by keep+ ! c5tral l9e ( height h fix$1 & by mak+ b & c dim9i% indef9itely1 ! s]ies conv]ges to ! segm5t ( a /raight l9e ( l5g? h4 ,f9ally1 by keep+ only ! c5tral po9t fix$1 & by mak+ h1 b1 & c dim9i% indef9itely1 ! s]ies conv]ges to a po9t4 ,fur!rmore1 we h introduc$ z yet no concept :i* w\ld prev5t an enclosure-object be+ =m$ ( deta*$ fragm5ts 9 space4 ,?us we c easily imag9e a conv]g5t set :i* conv]ges to a numb] ( po9ts 9 space4 ,= example1 ea* object ( ! set might be =m$ ( two n ov]lapp+ sph]es ( radius r1 ) c5tres ,a & ,b4 ,!n by dim9i%+ r indef9itely1 & keep+ ,a & ,b fix$1 we h conv]g5ce to ! pair ( po9ts ,a & ,b4 ,x rema9s n[ to consid] h[ ^? conv]g5t sets :i* conv]ge to a s+le po9t c be discrim9at$ f all ! o!r types ( su* sets1 m]ely by utilis+ concepts f\nd$ on ! relation ( enclosure4 ,let u "n conv]g5t sets by ,greek lett]s2 by proce$+ =w>d along any su* set let u und]/& ! process ( cont9ually pass+ f ! l>g] to ! small] enclosure-objects :i* =m ! set4 ,! conv]g5t set w be said to cov] ! conv]g5t set 1 if e memb] ( encloses "s memb]s ( 4 ,we notice t if an enclosure-object x encloses any memb] 7y7 ( 1 !n e memb] ( ! tail-end ( 1 f\nd by proce$+ =w>d along f y1 mu/ be enclos$ by x4 ,?us if cov]s 1 e memb] ( encloses e memb] ( ! tail-end ( 1 />t+ f ! l>ge/ memb] ( :i* is enclos$ by t memb] ( 4 ,x is possible = ea* ( two conv]g5t sets to cov] ! o!r4 ,= example1 let "o set 77 be a set ( conc5tric sph]es conv]g+ to _! c5tre ,a1 & ! o!r set 77 be a set ( conc5tric cubes1 simil>ly situat$1 conv]g+ to ! same c5tre ,a4 ,!n & w ea* cov] ! o!r4 ,let two conv]g5t sets :i* are su* t ea* cov]s ! o!r be call$ equal4 ,!n x is a suffici5t condition to secure t a conv]g5t set possesses ! po9t type ( conv]g5ce1 if e conv]g5t set cov]$ by x is also equal to x1 namely1 is a conv]g5t set ) ! punctual type ( conv]g5ce1 if cov]s always implies t cov]s 4 ,x c easily be se5 by simple examples t ! o!r types ( conv]g5ce to surfaces or l9es or sets ( po9ts _c possess ?is prop]ty4 ,consid]1 = example1 ! ?ree conv]g5t sets ( boxes 9 ! prec$+ illu/ration1 :i* conv]ge respectively to a c5tral plane1 a c5tral l9e 9 ! c5tral plane1 & ! c5tral po9t 9 ! c5tral l9e4 ,! fir/ set cov]s ! second & ?ird sets1 & ! second set cov]s ! ?ird set1 b no two ( ! sets are equal4 ,x is a m difficult "q to det]m9e :e!r ! condition "h indicat$ z suffici5t to secure ! punctual type ( conv]g5ce is also necess>y4 ,! "q turns on h[ f> ?\ght-objects ( p]ception possess exact b\nd>ies prior to ! elaboration ( exact ma!matical concepts ( space4 ,if !y are to be conceiv$ z possess+ su* exact b\nd>ies1 !n conv]g5t sets conv]g+ to po9ts on su* b\nd>ies mu/ be all[$ =4 ,! proc$ure necess>y = ! specification ( ! complete punctual condition becomes !n v elaborate1#c & w n be consid]$ "h4 ,b su* exact det]m9ation z is involv$ 9 ! conception ( an exact spatial b\nd>y does n seem to belong to ! true ?\ght-object ( p]ception4 ,! ascription ( an exact b\nd>y really belongs to ! transition /age ( ?\ght z x passes f ! ?\ght-object ( p]ception to ! ?\ght-object ( sci5ce4 ,! transition f ! s5se-object imm$iately pres5t$ to ! ?\ght-object ( p]ception is hi/orically made 9 a wav]+ indet]m9ate l9e ( ?\ght4 ,! def9ite /ages "h m>k$ out simply s]ve to prove t a logically explicable transition is possible4 ,we accord+ly assume t ! condition laid d[n above to secure ! punctual conv]g5ce ( a conv]g5t set ( enclosure-objects is n only suffici5t1 b necess>y4 ,x c be prov$ t1 if two conv]g5t sets ( enclosure-objects are bo? equal to a ?ird conv]g5t set1 !y are equal to ea* o!r4 ,consid] n[ any punctual conv]g5t set 774 ,we want to def9e ! po9t to :i* is a r\te ( approximation 9 a way :i* is neutral betwe5 & all ! conv]g5t sets :i* are equal to 4 ,ea* ( ^! sets is a r\te ( approximation to ! same po9t z 4 ,?is def9ition is secur$ if we def9e ! po9t z ! class =m$ by all ! enclosure-objects :i* belong ei!r to or to any conv]g5t set :i* is equal to 4 ,let ,p be ?is class ( enclosure-objects4 ,!n any conv]g5t set 77 :i* consi/s ( enclosure-objects entirely select$ f memb]s ( ! class ,p mu/ be a r\te ( approximation to ! same po9t z does ! orig9al punctual set 2 namely1 provid$ t we *oose a small en\gh enclosure-object 9 1 we c always f9d a memb] ( :i* encloses x2 & provid$ t we *oose a small en\gh enclosure-object 9 1 we c always f9d a memb] ( :i* encloses x4 ,?us ,p only includes conv]g5t sets ( ! punctual type1 & ! r\te ( approximation indicat$ by any two conv]g5t sets select$ f ,p conv]ges to id5tical results4 ,! ,uses ( ,po9ts4--,! sole use ( po9ts is to facilitate ! employm5t ( ! pr9ciple ( ,conv]g5ce to ,simplicity4 ,by ?is pr9ciple "s simple relations 9 appropriate circum/ances become true1 :5 objects are consid]$ :i* are suffici5tly re/rict$ 9 "t or 9 space4 ,! introduction ( po9ts enables ?is pr9ciple to be c>ri$ ?r\gh to its ideal limit4 ,= example1 suppose g 7a1 b1 c7 repres5ts "s /atem5t conc]n+ ?ree enclosure-objects1 a1 b1 c1 :i* may be true if ! objects are suffici5tly re/rict$ 9 ext5t4 ,let ,a1 ,b1 ,c be ?ree giv5 po9ts1 !n we def9e g 7,a1 ,b1 ,c7 to mean t :atev] ?ree enclosure-objects a1 b1 c are *os51 su* t a is a memb] ( ,a1 b ( ,b1 & c ( ,c1 x is always possible to f9d ?ree o!r memb]s ( ,a1 ,b1 ,c1 namely1 x a memb] ( ,a1 y ( ,b1 & z ( ,c1 su* t a,ex1 b,ey1 c,ez1 & g 7x1 y1 z74 ,s by go+ f> en\gh d[n 9 ! tail-ends ( ,a1 ,b1 ,c we c always secure ?ree objects x1 y1 z = :i* g 7x1 y1 z7 is true4 ,= example1 let g 7,a1 ,b1 ,c7 mean ,a1 ,b1 ,c are ?ree po9ts 9 a l9e> r[4 ,?is mu/ be con/ru$ to mean t :atev] ?ree objects a1 b1 c we *oose1 memb]s ( ,a1 ,b1 ,c respectively1 we c always f9d ?ree objects x1 y1 z1 also memb]s ( ,a1 ,b1 ,c respectively1 & su* t a encloses x1 b encloses y1 c encloses z1 & also su* t x1 y1 z are 9 a l9e> r[4 ,sometimes a d\ble conv]g5ce is necess>y1 namely1 a conv]g5ce ( conditions z well z a conv]g5ce ( objects4 ,= example1 consid] ! /atem5t1 ! po9ts ,a & ,b are two feet ap>t4 ,n[1 ! exact /atem5t two feet ap>t does n apply to objects4 ,= objects x & y we mu/ sub/itute ! /atem5t1 ! di/ance betwe5 x & y lies betwe5 ! limits 7#b e7 feet4 ,"h e is "s numb]1 less ?an two1 :i* we h *os5 = ?is /atem5t4 ,!n ! po9ts ,a & ,b are two feet ap>t2 if1 h[ev] we *oose ! numb] e1 :atev] enclosure-objects a & b1 memb]s ( ,a & ,b respectively1 we consid]1 we c always f9d enclosure-objects x & y1 memb]s ( ,a & ,b respectively1 su* t a encloses x & b encloses y1 & also su* t ! di/ance betwe5 x & y lies betwe5 ! limits 7#b e7 feet4 ,x is evid5t1 s9ce e c be *os5 z small z we please1 t ?is /atem5t exactly expresses ! condition t ,a & ,b are two feet ap>t4 ,/raight ,l9es & ,planes4--,b ! problem ( ! intellectual con/ruction ( /raight l9es & planes is n yet suffici5tly analys$4 ,we h int]pret$ ! mean+ ( ! /atem5t t ?ree or m po9ts are coll9e>1 & c simil>ly see h[ to int]pret ! mean+ ( ! /atem5t t f\r or m po9ts are coplan>1 9 ei!r case d]iv+ ! exact geometrical /atem5ts f vagu] /atem5ts respect+ ext5d$ objects4 ,?is proc$ure only contemplates gr\ps ( f9ite numb]s ( po9ts4 ,b /raight l9es & planes are conceiv$ z conta9+ inf9ite numb]s ( po9ts4 ,?is completion ( l9es & planes is obta9$ by a r5ew$ application ( ! pr9ciple ( aggregation1 j z a set ( fir/ crude ?\ght-objects ( p]ception are aggregat$ into "o complete ?\ght-object ( p]ception4 ,9 ?is way repeat$ judgm5ts ( ! coll9e>ity ( sets ( po9ts are f9ally1 :5 c]ta9 conditions ( int]lac+ are fulfill$1 aggregat$ 9 ! s+le judgm5t ( all ! po9ts ( ! gr\ps z =m+ "o :ole coll9e> gr\p4 ,simil>ly = judgm5ts ( coplan>ity4 ,?is process ( logical aggregation c be exhibit$ 9 its exact logical analysis4 ,b x is unnecess>y "h to proce$ to su* details4 ,?us we conceive our po9ts z sort$ into planes & /raight l9es1 conc]n+ :i* ! v>i\s axioms ( geometry hold4 ,^! axioms1 9 s f> z !y ess5tially require ! conception ( po9ts1 are capable ( be+ exhibit$ z ! outcome ( vagu]1 less exact judgm5ts respect+ ! relations ( ext5d$ objects4 ,empty ,space4--,x mu/ be obs]v$ t ! po9ts1 hi!rto def9$1 necess>ily involve ?\ght-objects ( p]ception1 & lie )9 ! space-ext5sion occupi$ by su* objects4 ,x is true t su* objects are l>gely hypo!tical1 & t we c br+ into our hypo!ses suffici5t objects to complete our l9es & planes4 ,b e su* hypo!sis weak5s ! connection betwe5 our sci5tific concept ( nature & ! actual obs]v$ facts :i* are involv$ 9 ! actual s5se-pres5tations4 ,occam's razor1 ,entia non multiplic&a prt] necessitatem1 is n an arbitr>y rule bas$ on m]e logical elegancy4 ,nor is its application purely conf9$ to metaphysical speculation4 ,i am ignorant ( ! precise reason = its metaphysical validity1 b its sci5tific validity is obvi\s1 namely1 e use ( hypo!tical entities dim9i%es ! claim ( sci5tific reason+ to be ! necess>y outcome ( a h>mony betwe5 ?\ght & s5se-pres5tation4 ,z hypo!sis increases1 necessity dim9i%es4 ,commons5se ?\ght also supports ?is refusal to conceive ( all space z ess5tially dep5d+ on hypo!tical objects :i* fill x4 ,we ?9k ( mat]ial objects z fill+ space1 b we ask :e!r any objects exi/ betwe5 ! ,e>? & ! ,sun1 betwe5 ! />s1 or beyond ! />s4 ,= u1 space is !re2 ! only "q is :e!r or n x be full4 ,b ?is =m ( "q presupposes ! mean+ ( empty space1 namely1 ( space n conta9+ hypo!tical objects4 ,?is br+s up a wid] use ( ! concept ( po9ts1 necessitat+ a wid] def9ition4 ,hi!rto we h conceiv$ po9ts z indicat+ relations ( enclosure betwe5 objects4 ,we ?us arrive at :at n[ we w t]m mat]ial po9ts4 ,b ! idea ( po9ts c n[ be trans=m$ s z to indicate ! possibilities ( ext]nal relations n ^? ( enclosure4 ,?is is effect$ by an enl>gem5t ( ! concept ( ideal po9ts1 already kn[n to geomet]s4 ,def9e mat]ial l9es to be complete coll9e> classes ( coll9e> po9ts4 ,consid] n[ ! set ( mat]ial l9es :i* conta9 a c]ta9 mat]ial po9t4 ,call su* a set ( l9es an ideal po9t4 ,?is set ( l9es indicates a possibility ( position1 :i* is 9 fact occupi$ by t mat]ial po9t common to all ! mat]ial l9es4 ,s ?is ideal po9t is an occupi$ ideal po9t4 ,n[ consid] a set ( ?ree mat]ial l9es1 su* t any two are coplan>1 b n ! :ole ?ree1 & fur!r consid] ! complete set ( mat]ial l9es su* t ea* is coplan> ) ea* ( ! ?ree mat]ial l9es fir/ *os54 ,! axioms :i* hold = ! mat]ial l9es w enable u to prove t any two l9es ( ?is set are coplan>4 ,!n ! :ole set ( l9es1 includ+ ! ?ree orig9al l9es1 =ms an ideal po9t1 accord+ to ! def9ition 9 its full g5]ality4 ,su* an ideal po9t may be occupi$4 ,9 t case !re is a mat]ial po9t common to all ! l9es ( ! set1 b x may be unoccupi$4 ,!n ! ideal po9t m]ely indicates a possibility ( spatial relations :i* has n be5 realis$4 ,x is ! po9t ( empty space4 ,?us ! ideal po9ts1 :i* may or may n be occupi$1 are ! po9ts ( geometry view$ z an appli$ sci5ce4 ,^! po9ts are di/ribut$ into /raight l9es & planes4 ,b any fur!r discussion ( ?is "q w lead u into ! te*nical subject ( ! axioms ( geometry & _! imm$iate consequ5ces4 ,en\gh has be5 said to %[ h[ geometry arises accord+ to ! relational !ory ( space4 ,space z ?us conceiv$ is ! ?\ght-space ( ! mat]ial _w4 ,,iv4 ,fields ( ,=ce ,! ?\ght-objects ( sci5ce are conceiv$ z directly relat$ to ?is ?\ght-space4 ,_! spatial relations are among ^? indicat$ by ! po9ts ( ! ?\ght-space4 ,_! em]g5ce 9 sci5ce has be5 m]ely a fur!r developm5t ( processes already inh]5t 9 commons5se ?\ght4 ,relations )9 ! complete s5se-pres5tation 7 repres5t$ 9 ?\ght by ! concept ( ?\ght-objects ( p]ception4 ,all s5se-pres5tation c\ld n be repres5t$ 9 ?is way2 also ! *ange & disappe>ance ( ?\ght-objects occasion$ confusion ( ?\ght4 ,a r$uction to ord] ( ?is confusion 0 attempt$ by ! concepts ( p]man5t matt] ) prim>y & second>y qualities4 ,f9ally1 ?is has issu$ 9 ! second>y qualities be+ trac$ z p]ception ( ev5ts g5]at$ by ! objects1 b--z p]ceiv$--entirely disconnect$ ) !m4 ,also ! ?\ght-objects ( p]ception h be5 replac$ by molecules & electrons & e!r-waves1 until at l5g? x is nev] ! ?\ght-object ( sci5ce :i* is p]ceiv$1 b complicat$ s]ies ( ev5ts 9 :i* !y are implicat$4 ,if sci5ce be "r1 nobody ev] p]ceiv$ a ?+1 b only an ev5t4 ,! result is1 t ! old] language ( philosophy :i* /ill survives 9 _m qu>t]s is n[ ?or\ghly confus+ :5 br\ght into connection ) ! mod]n concepts ( sci5ce4 ,philosophy--t is1 ! old] philosophy--conceives ! ?+ z directly p]ceiv$4 ,accord+ to sci5tific ?\ght1 ! ultimate ?+ is nev] p]ceiv$1 p]ception ess5tially issu+ f a s]ies ( ev5ts4 ,x is impossible to reconcile ! two po9ts ( view4 ,! advantage ( ! mod]n sci5tific concept is t x is enabl$ to expla9 ! fluid vague outl9es ( s5se-pres5tation4 ,! ?\ght-object ( p]ception is n[ conceiv$ z a fairly /able /ate ( motion ( a huge gr\p ( molecules1 con/antly *ang+1 b pres]v+ a c]ta9 id5tity ( *>act]i/ics4 ,also /ray s5se-objects1 n imm$iately giv5 z "p ( a ?\ght-object ( p]ception1 are n[ explicable3 ! danc+ light-reflection1 ! vaguely he>d s\nd1 ! smell4 ,9 fact1 ! p]ceiv$ ev5ts ( ! sci5tific _w h ! same g5]al def9ition & lack ( def9ition1 & ! same g5]al /ability & lack ( /ability1 z ! s5se-objects ( ! complete s5se-pres5tation or z ! ?\ght-objects ( p]ception4 ,! ?\ght-objects ( sci5ce1 namely1 molecules1 atoms1 & electrons1 h ga9$ 9 p]man5ce4 ,! ev5ts are r$uc$ to *anges 9 space-configuration4 ,! laws det]m9+ ^! *anges are ! ultimate laws ( nature4 ,! laws ( *ange 9 ! physical univ]se proce$ on ! assumption t ! prec$+ /ates ( ! univ]se det]m9e ! "* ( ! *ange4 ,?us1 to "k ! configurations & ev5ts ( ! univ]se up to & includ+ any in/ant w\ld involve suffici5t data f :i* to det]m9e ! succession ( ev5ts ?r\gh\t all "t4 ,b 9 trac+ ! antec$5ts ( ev5ts1 commons5se ?\ght1 deal+ ) ! _w ( ?\ght-objects ( p]ception1 habitually assumes t ! great] numb] ( antec$5t ev5ts c be neglect$ z irrelevant4 ,consid]ation ( causes is re/rict$ to a few ev5ts dur+ a %ort prec$+ int]val4 ,f9ally1 9 sci5tific ?\ght x has be5 assum$ t ! ev5ts 9 an arbitr>ily small prec$+ duration are suffici5t4 ,?us physical quantities & _! successive diff]5tial co-effici5ts up to any ord] at ! in/ant1 b ) _! limit+ values j be=e t in/ant1 are on ?is !ory suffici5t to det]m9e ! /ate ( ! univ]se at all times aft] ! in/ant4 ,m p>ticul> laws are assum$4 ,b ! se>* = !m is guid$ by ?is g5]al pr9ciple4 ,also x is assum$ t ! great] numb] ( ev5ts 9 ! physical univ]se are irrelevant to ! production ( any p>ticul> effect1 :i* is assum$ to issue f relatively few antec$5ts4 ,^! assumptions h gr[n out ( ! exp]i5ce ( mank9d4 ,! fir/ lesson ( life is to conc5trate att5tion on few factors ( s5se-pres5tations1 & on /ill few] ( ! univ]se ( ?\ght-objects ( p]ception4 ,! pr9ciple by :i*--consci\sly or unconsci\sly--?\ght has be5 guid$ is t 9 se>*+ = p>ticul> causes1 remot5ess 9 "t & remot5ess 9 space are evid5ces ( comp>ative disconnection ( influ5ce4 ,! extreme =m ( ?is pr9ciple is ! d5ial ( any action at a di/ance ei!r 9 "t or space4 ,! difficulty 9 accept+ ?is pr9ciple 9 its crude =m is1 t s9ce !re are no contigu\s po9ts1 only co9cid5t bodies c act on ea* o!r4 ,i c see no answ] to ?is difficulty--namely1 ei!r bodies h ! same location & are ?us co9cid5t1 or !y h diff]5t locations & are ?us at a di/ance & d n act on ea* o!r4 ,?is difficulty is n evad$ by ! hypo!sis ( an e!r1 cont9u\sly di/ribut$4 ,= two reasons3 9 ! fir/ place1 ! cont9uity ( ! e!r does n avoid ! dilemma2 & secondly1 ! difficulty applies to "t z well z to space1 & ! dilemma w\ld prove t causation produc+ *ange is impossible1 namely1 no *ang$ condition c\ld be ! result ( antec$5t circum/ances4 ,on ! o!r h&1 a direct int]action betwe5 two bodies sep>at$ 9 space und\bt$ly (f5ds ! conception ( di/ance z imply+ physical disconnection z well z spatial relation4 ,!re is no logical difficulty 9 ! assumption ( action at a di/ance z 9 ! case ( its d5ial1 b x is contradictory to p]si/5t assumptions ( t app>atus ( commons5se ?\ght :i* x is ! ma9 bus9ess ( sci5ce to h>monise ) s5se-pres5tation1 employ+ only ! m9imum ( modification4 ,mod]n sci5ce is really unconc]n$ ) ?is debate4 ,its 7unackn[l$g$7 conceptions are really q diff]5t1 ?\gh ! v]bal explanations reta9 ! =m ( a previ\s epo*4 ,! po9t ( ! *ange 9 conception is t ! old ?\ght-object ( sci5ce 0 conceiv$ z possess+ a simplicity n belong+ to ! mat]ial univ]se z a :ole4 ,x 0 seclud$ )9 a f9ite region ( space1 & *anges 9 its circum/ances c\ld only arise f =ces :i* =m$ no ess5tial "p ( its nature4 ,an e!r 0 call$ into exi/5ce to expla9 ! active relations betwe5 ^! passive ?\ght-objects4 ,! :ole conception suff]s f ! logical difficulties not$ above4 ,also no cle> conception c be =m$ ( ! s5se 9 :i* ! e!r is explanatory4 ,x is to possess a type ( activity d5i$ to ! orig9al ?\ght-object1 namely1 x c>ries pot5tial en]gy1 :]eas ! atom possess$ only k9etic en]gy1 ! s-call$ pot5tial en]gy ( an atom belong+ really to ! surr\nd+ e!r4 ,! tru? is1 t e!r is really except$ f ! axiom no action at a di/ance1 & ! axiom !reby is robb$ ( all its =ce4 ,! mod]n ?\ght-object ( sci5ce--n yet explicitly ackn[l$g$--has ! complexity ( ! :ole mat]ial univ]se4 ,9 physics1 z else:]e1 ! hopeless endeav\r to d]ive complexity f simplicity has be5 tacitly ab&on$4 ,:at is aim$ at is n simplicity1 b p]si/5ce & regul>ity4 ,9 a s5se regul>ity is a sort ( simplicity4 ,b x is ! simplicity ( /able mutual relations1 & n ! simplicity ( abs5ce ( types ( int]nal /ructure or ( type ( relation4 ,?is ?\ght-object fills all space4 ,x is a field2 t is to say1 x is a c]ta9 di/ribution ( scal> & vector quantities ?r\gh\t space1 ^! quantities hav+ ea* its value = ea* po9t ( space at ea* po9t ( "t1 be+ cont9u\sly di/ribut$ ?r\gh\t space & ?r\gh\t "t1 possibly ) "s exceptional discont9uities4 ,! v>i\s types ( quantity :i* =m ! field h fix$ relations to ea* o!r at ea* po9t ( "t & space4 ,^! relations are ! ultimate laws ( nature4 ,= example1 consid] an electron4 ,!re is a scal> di/ribution ( electricity1 :i* is :at is ord9>ily call$ ! electron4 ,?is scal> di/ribution has a volume-d5sity at ! "t t at any po9t 7x1 y1 z74 ,?us is a function ( 7x1 y1 z1 t71 :i* is z]o except )9 a re/rict$ region4 ,fur!rmore1 at any "t t1 z an ess5tial adjunct1 !re is a cont9u\s space di/ribution at ea* po9t ( ! two vectors 7,x1 ,y1 ,z71 :i* is ! electric =ce1 & 71 1 71 :i* is ! magnetic =ce4 ,la/ly1 individuality is ascrib$ to ! scal> electric di/ribution1 s t 9 addition to its cons]vation ( quantity--involv$ 9 ! assum$ laws--x is also possible to assign ! velocities ) :i* ! v>i\s individual p>ts ( ! di/ribution are mov+4 ,let 7u1 v1 w7 be ?is velocity at 7x1 y1 z1 t74 ,?is :ole s*eme ( scal> & vector quantities1 namely1 1 7,x1 ,y1 ,z71 71 1 71 7u1 v1 w7 is int]connect$ by ! electromagnetic laws4 ,x foll[s f ^! laws t ! electron1 9 ! s5se ( ! scal> di/ribution 1 is to be conceiv$ z at ea* in/ant propagat+ f itself an emanation :i* travels outw>ds ) ! velocity ( light 9 vacuo1 & f :i* 7,x1 ,y1 ,z7 & 71 1 7 c be calculat$1 s f> z !y are due to t electron4 ,?us ! field1 at any "t1 due to ! electron z a :ole dep5ds on ! previ\s hi/ory ( ! electron1 ! ne>] to ! electron ! m rec5t be+ ! relevant hi/ory4 ,! :ole s*eme ( su* a field is "o s+le ?\ght-object ( sci5ce3 ! electron & its emanations =m "o ess5tial :ole1 namely "o ?\ght-object ( sci5ce1 ess5tially complex & ess5tially fill+ all space4 ,! electron prop]1 namely1 ! scal> di/ribution 1 is ! focus ( ! :ole1 ! ess5tial focal prop]ty be+ t ! field at any in/ant is completely det]m9$ by ! previ\s hi/ory ( ! focus & ( its space relations ?r\gh all previ\s "t4 ,b ! field & ! focus are n indep5d5t concepts1 !y are ess5tially correlat$ 9 "o organis$ unity1 namely1 !y are ess5tially correlat$ t]ms 9 ! field ( "o relation 9 virtue ( :i* ! entities ent] into our ?\ghts4 ,! fields ( a gr\p ( electrons are sup]pos$ accord+ to ! l9e> law = aggregation1 namely1 pure addition = analog\s scal> quantities & ! p>allelogram law = analog\s vectors4 ,! *anges 9 motion ( ea* electron dep5d entirely on ! resultant field 9 ! region x occupies4 ,?us a field c be view$ z a possibility ( action1 b a possibility :i* repres5ts an actuality4 ,x is to be not$ t ! two alt]native views ( causation are "h bo? includ$4 ,! complete field )9 any region ( space dep5ds on ! pa/ hi/ories ( all ! electrons1 hi/ories ext5d+ backw>ds 9 proportion to _! di/ances4 ,also ?is dep5d5ce c be conceiv$ z a transmission4 ,b view+ ! cause :i* effects *anges on ! electron )9 t region1 x is solely t field )9 ! region1 :i* field is co9cid5t ) t electron bo? 9 "t & 9 space4 ,?is process ( conceiv+ ! actuality und]ly+ a possibility is ! uni=m process by :i* regul>ity & p]man5ce is introduc$ into sci5tific ?\ght1 namely1 we proce$ f ! actuality ( ! fact to ! actuality ( possibility4 ,9 con=mity ) ?is pr9ciple1 propositions are ! outgr[? f actual ?\ght-expressions1 ?\ght-objects ( p]ceptions f crude s5se-objects1 hypo!tical ?\ght-objects ( p]ception f actual ?\ght-objects ( p]ception1 mat]ial po9ts f hypo!tical inf9ite suites ( hypo!tical ?\ght-objects ( p]ception1 ideal po9ts f mat]ial po9ts1 ?\ght-objects ( sci5ce f ?\ght-objects ( p]ception1 fields ( electrons f actual mutual reactions ( actual electrons4 ,! process is a rese>* = p]man5ce1 uni=mity1 & simplicity ( logical relation4 ,b x does n issue 9 simplicity ( int]nal /ructure4 ,ea* ultimate ?\ght-object ( sci5ce reta9s e quality attribut$ to ! :ole sci5tific univ]se1 b reta9s !m 9 a =m *>act]is$ by p]man5ce & uni=mity4 ,v4 ,conclusion ,we comm5c$ by exclud+ judgm5ts ( wor? & ontological judgm5ts4 ,we conclude by recall+ !m4 ,judgm5ts ( wor? are no "p ( ! texture ( physical sci5ce1 b !y are "p ( ! motive ( its production4 ,mank9d h rais$ ! edifice ( sci5ce1 because !y h judg$ x wor? :ile4 ,9 o!r words1 ! motives involve innum]able judgm5ts ( value4 ,aga91 !re has be5 consci\s selection ( ! p>ts ( ! sci5tific field to be cultivat$1 & ?is consci\s selection involves judgm5ts ( value4 ,^! values may be /hetic1 or moral1 or utilit>ian1 namely1 judgm5ts z to ! beauty ( ! /ructure1 or z to ! duty ( explor+ ! tru?1 or z to utility 9 ! satisfaction ( physical wants4 ,b :atev] ! motive1 )\t judgm5ts ( value !re w\ld h be5 no sci5ce4 ,aga91 ontological judgm5ts 7 n exclud$ by reason ( any lack ( int]e/4 ,!y are 9 fact presuppos$ 9 e act ( life3 9 our affections1 9 our self-re/ra9ts1 & 9 our con/ructive ef=ts4 ,!y are presuppos$ 9 moral judgm5ts4 ,! difficulty ab\t !m is ! abs5ce ( agreem5t z to ! me?od ( h>monis+ ! crude judgm5ts ( commons5se4 ,sci5ce does n dim9i% ! ne$ ( a metaphysic4 ,:]e ?is ne$ is mo/ insi/5t is 9 connection ) :at above has be5 t]m$ ! actuality und]ly+ a possibility4 ,a few words ( explanation may r5d] ! argum5t cle>]1 al?\gh !y involve a ra% approa* to metaphysical heights :i* x is n ! purpose ( ?is pap] to explore4 ,! conception ( subject & object 9 c>eless discussion cov]s two di/9ct relations4 ,!re is ! relation ( ! :ole p]ceiv+ consci\sness to "p ( its own cont5t1 = example1 ! relation ( a p]ceiv+ consci\sness to an object ( r$ness app>5t to x4 ,!re is also ! relation ( a p]ceiv+ consci\sness to an entity :i* does n exi/ 9 virtue ( be+ "p ( ! cont5t ( t consci\sness4 ,su* a relation1 s f> z kn[n to ! p]ceiv+ consci\sness1 mu/ be an inf]r$ relation1 ! inf]5ce be+ d]iv$ f an analysis ( ! cont5t ( ! p]ceiv+ consci\sness4 ,! bases = su* inf]5ces mu/ be elem5ts 9 consci\sness directly kn[n z transc5d+ _! imm$iate pres5tation 9 consci\sness4 ,su* elem5ts are univ]sal logical tru?s1 moral & /hetic tru?s1 & tru?s embodi$ 9 hypo!tical propositions4 ,^! are ! imm$iate objects ( p]ception :i* are o!r ?an ! m]e affections ( ! p]ceiv+ subject4 ,!y h ! prop]ty ( be+ p>ts ( ! imm$iate pres5tations = individual subjects & yet m ?an su* p>ts4 ,all o!r exi/5ce is inf]r$ exi/5ce4 ,9 ?is *apt] we are m directly conc]n$ ) tru?s embodi$ 9 hypo!tical propositions4 ,su* tru?s mu/ n be confus$ ) any d\btfulness :i* atta*es to our judgm5ts ( ! future c\rse ( natural ph5om5a4 ,a hypo!tical proposition1 l a categorical judgm5t1 may or may n be d\btful4 ,also l a categorial judgm5t1 x expresses a fact4 ,?is fact is tw(old3 z a pres5tation 9 consci\sness1 x is j ?is hypo!tical judgm5t2 z express+ a categorical fact1 x /ates a relation :i* lies beyond consci\sness1 hold+ betwe5 entities !reby inf]r$4 ,b ?is metaphysical analysis1 %ort ?\gh x be1 is probably wrong1 & at ! be/ w only comm& v p>tial ass5t4 ,c]ta9ly2 & ?is admission br+s out ! v po9t :i* ,i wi%$ to make4 ,physical sci5ce is bas$ on elem5ts ( ?\ght1 su* z judgm5ts regi/]+ actual p]ceptions1 & judgm5ts regi/]+ hypo!tical p]ceptions :i* "u c]ta9 circum/ances w\ld be realis$4 ,^! elem5ts =m ! agre$ cont5t ( ! app>atus ( commons5se ?\ght4 ,!y require metaphysical analysis2 b !y are among ! data f :i* metaphysics />ts4 ,a metaphysic :i* rejects !m has fail$1 9 ! same way z physical sci5ce has fail$ :5 x is unable to h>monise !m into its !ory4 ,sci5ce only r5d]s ! metaphysical ne$ m urg5t4 ,9 itself x contributes little directly to ! solution ( ! metaphysical problem4 ,b x does contribute some?+1 namely1 ! exposition ( ! fact t our exp]i5ce ( s5sible app>5t ?+s is capable ( be+ analys$ into a sci5tific !ory1 a !ory n inde$ complete1 b giv+ e promise ( indef9ite expansion4 ,?is a*ievem5t emphasises ! intimate relation betwe5 our logical ?\ght & ! facts ( s5sible appreh5sion4 ,also ! special =m ( sci5tific !ory is b\nd to h "s influ5ce4 ,9 ! pa/ false sci5ce has be5 ! p>5t ( bad metaphysics4 ,aft] all1 sci5ce embodies a rigor\s scrut9y ( "o "p ( ! :ole evid5ce f :i* metaphysicians d$uce _! conclusions4 ,,footnotes3 ,footnote #c3 ,cf4 ,rvue de ,mtaphysique et de ,morale1 ,may #aiaf1 :]e ?is "q is dealt ) by ! au?or at ! end ( an article1 ,la ?orie relationni/e de l'espace4 ,,*apt] ,,viii ,,space1 ,,"t1 ,,& ,,relativity 7,pap] read to ,section ,a at ! ,man*e/] ,meet+ ( ! ,briti% ,association1 #aiae1 & lat] be=e ! ,ari/otelian ,society7 ,,fundam5tal ,problems conc]n+ space & "t h be5 consid]$ f ! /&po9ts creat$ by _m diff]5t sci5ces4 ,! object ( ?is pap] is ! humble "o ( br++ "s ( ^! /&po9ts into relation ) ea* o!r4 ,?is necessitates a v cursory treatm5t ( ea* po9t ( view4 ,ma!matical physici/s h evolv$ _! !ory ( relativity to expla9 ! negative results ( ! ,morley-,mi*elson exp]im5t & ( ! ,tr\ton exp]im5t4 ,exp]im5tal psy*ologi/s h consid]$ ! evolution ( spatial ideas f ! crude s5se-data ( exp]i5ce4 ,metaphysicians h consid]$ ! maje/ic uni=mity ( space & "t1 )\t beg9n+ & )\t end1 )\t b\nd>ies1 & )\t exception 9 ! tru?s conc]n+ !m2 all ^! qualities ! m arre/+ to our att5tion f ! confus$ accid5tal nature ( ! empirical univ]se :i* is condition$ by !m4 ,ma!maticians h /udi$ ! axioms ( geometry1 & c n[ d$uce all t is believ$ to be univ]sally true ( space & ( "t by ! /ricte/ logic f a limit$ numb] ( assumptions4 ,^! v>i\s l9es ( ?\ght h be5 evolv$ ) surpris+ly little int]connection4 ,p]haps x is z well4 ,! results ( sci5ce are nev] q true4 ,by a heal?y indep5d5ce ( ?\ght p]haps we sometimes avoid add+ o!r p's errors to our own4 ,b !re c be no d\bt t ! normal me?od ( cross-f]tilis+ ?\ght is by consid]+ ! same1 or alli$ problems to our own1 9 ! =m :i* !y assume 9 o!r sci5ces4 ,"h ,i d n propose to ent] into a sy/ematic /udy ( ^! v>i\s *apt]s ( sci5ce4 ,i h nei!r ! k nor ! "t4 ,fir/1 let u take ! ultimate basis ( any !ory ( relativity4 ,all space measurem5t is f /uff 9 space to /uff 9 space4 ,! geometrical entities ( empty space nev] appe>4 ,! only geometrical prop]ties ( :i* we h any direct k are prop]ties ( ^? %ift+1 *angeable appe>ances :i* we call ?+s 9 space4 ,x is ! sun :i* is di/ant1 & ! ball :i* is r\nd1 & ! lamp-po/s :i* are 9 l9e> ord]4 ,:]ev] mank9d may h got its idea ( an inf9ite un*angeable space f1 x is safe to say t x is n an imm$iate deliv]ance ( direct obs]vation4 ,!re are two antagoni/ic philosophical ways ( recognis+ ?is conclusion4 ,"o is to affirm t space & "t are conditions = s5sible exp]i5ce1 t )\t projection into space & "t s5sible exp]i5ce w\ld n exi/4 ,?us1 al?\gh x may be true to say t our k ( space & "t is giv5 9 exp]i5ce1 x is n true to say t x is d$uc$ f exp]i5ce 9 ! same s5se t ! ,law ( ,gravitation is s d$uc$4 ,x is n d$uc$1 because 9 ! act ( exp]i5c+ we are necess>ily made aw>e ( space z an inf9ite giv5 :ole1 & ( "t z an un5d+ uni=m succession4 ,?is philosophical position is express$ by say+ t space & "t are a priori =ms ( s5sibility4 ,! oppos$ philosophical me?od ( deal+ ) ! "q is to affirm t our concepts ( "t & space are d$uctions f exp]i5ce1 9 exactly ! same way z ! ,law ( ,gravitation is su* a d$uction4 ,if we =m exact concepts ( po9ts1 l9es & surfaces1 & ( successive in/ants ( "t1 & assume !m to be relat$ z express$ by ! axioms ( geometry & ! axioms = "t1 !n we f9d t we h fram$ a concept :i*1 ) all ! exactness ( :i* our obs]vations are capable1 expresses ! facts ( exp]i5ce4 ,^! two philosophic positions are ea* design$ to expla9 a c]ta9 difficulty4 ,! a priori !ory expla9s ! absolute univ]sality ascrib$ to ! laws ( space & "t1 a univ]sality n ascrib$ to any d$uction f exp]i5ce4 ,! exp]i5tial !ory expla9s ! d]ivation ( ! space-"t concepts )\t introduc+ any o!r factors beyond ^? :i* are admitt$ly pres5t 9 fram+ ! o!r concepts ( physical sci5ce4 ,b we h n yet done ) ! di/9ctions :i* 9 any discussion ( space or "t mu/ ess5tially be kept 9 m9d4 ,put aside ! above "q z to h[ ^! space-"t concepts are relat$ to exp]i5ce--,:at are !y :5 !y are =m$8 ,we may conceive ( ! po9ts ( space z self-subsi/5t entities :i* h ! indef9able relation ( be+ occupi$ by ! ultimate /uff 7matt]1 ,i w call x7 :i* is !re4 ,?us1 to say t ! sun is !re 7:]ev] x is7 is to affirm ! relation ( occupation betwe5 ! set ( positive & negative electrons :i* we call ! sun & a c]ta9 set ( po9ts1 ! po9ts hav+ an exi/5ce ess5tially indep5d5t ( ! sun4 ,?is is ! absolute !ory ( space4 ,! absolute !ory is n popul> j n[1 b x has v respectable au?ority on its side--,newton1 = "o--s treat x t5d]ly4 ,! o!r !ory is associat$ ) ,leibniz4 ,our space concepts are concepts ( relations betwe5 ?+s 9 space4 ,?us !re is no su* entity z a self-subsi/5t po9t4 ,a po9t is m]ely ! "n = "s peculi>ity ( ! relations betwe5 ! matt] :i* is1 9 common language1 said to be 9 space4 ,x foll[s f ! relative !ory t a po9t %\ld be def9able 9 t]ms ( ! relations betwe5 mat]ial ?+s4 ,s f> z ,i am aw>e1 ?is outcome ( ! !ory has escap$ ! notice ( ma!maticians1 :o h inv>iably assum$ ! po9t z ! ultimate />t+ gr\nd ( _! reason+4 ,_m ye>s ago ,i expla9$ "s types ( ways 9 :i* we might a*ieve su* a def9ition1 & m rec5tly h add$ "s o!rs4 ,simil> explanations apply to "t4 ,be=e ! !ories ( space & "t h be5 c>ri$ to a satisfactory conclusion on ! relational basis1 a long & c>eful scrut9y ( ! def9itions ( po9ts ( space & in/ants ( "t w h to be und]tak51 & _m ways ( effect+ ^! def9itions w h to be tri$ & comp>$4 ,?is is an unwritt5 *apt] ( ma!matics1 9 mu* ! same /ate z 0 ! !ory ( p>allels 9 ! eighte5? c5tury4 ,9 ?is connection ,i %\ld l to draw att5tion to ! analogy betwe5 "t & space4 ,9 analys+ our exp]i5ce we di/+ui% ev5ts1 & we also di/+ui% ?+s ^: *ang+ relations =m ! ev5ts4 ,if ,i _h "t x w\ld be int]e/+ to consid] m closely ^! concepts ( ev5ts & ( ?+s4 ,x mu/ suffice n[ to po9t out t ?+s h c]ta9 relations to ea* o!r :i* we consid] z relations betwe5 ! space ext5sions ( ! ?+s2 = example1 "o space c conta9 ! o!r1 or exclude x1 or ov]lap x4 ,a po9t 9 space is no?+ else ?an a c]ta9 set ( relations betwe5 spatial ext5sions4 ,analog\sly1 !re are c]ta9 relations betwe5 ev5ts :i* we express by say+ t !y are relations betwe5 ! temporal durations ( ^! ev5ts1 t is1 betwe5 ! temporal ext5sions ( ! ev5ts4 ,! durations ( two ev5ts ,a & ,b may "o prec$e ! o!r1 or may p>tially ov]lap1 or may "o conta9 ! o!r1 giv+ 9 all six possibilities4 ,! prop]ties ( ! ext5sion ( an ev5t 9 "t are l>gely analog\s to ! ext5sion ( an object 9 space4 ,spatial ext5sions are express$ by relations betwe5 objects1 temporal ext5sions by relations betwe5 ev5ts4 ,! po9t 9 "t is a set ( relations betwe5 temporal ext5sions4 ,x ne$s v little reflection to conv9ce u t a po9t 9 "t is no direct deliv]ance ( exp]i5ce4 ,we live 9 durations1 & n 9 po9ts4 ,b :at community1 beyond ! m]e "n1 is !re betwe5 ext5sion 9 "t & ext5sion 9 space8 ,9 view ( ! intimate connection betwe5 "t & space reveal$ by ! mod]n !ory ( relativity1 ?is "q has tak5 on a new importance4 ,i h n ?\ght out an answ] to ?is "q4 ,i sugge/1 h[ev]1 t "t & space embody ^? relations betwe5 objects on :i* dep5ds our judgm5t ( _! ext]nality to ourselves4 ,namely1 location 9 space & location 9 "t bo? embody & p]haps necessitate a judgm5t ( ext]nality4 ,?is sugge/ion is v vague1 & ,i mu/ leave x 9 ?is crude =m4 ,div]se ,euclidean ,measure ,sy/ems ,turn+ n[ to ! ma!matical inve/igations on ! axioms ( geometry1 ! outcome1 :i* is mo/ important = u to rememb]1 is ! great sep>ation :i* x discloses betwe5 non-metrical projective geometry1 & metrical geometry4 ,non-metrical projective geometry is by f> ! m fundam5tal4 ,/>t+ ) ! concepts ( po9ts1 /raight l9es1 & planes 7( :i* n all ?ree ne$ be tak5 z indef9able71 & ) c]ta9 v simple non-metrical prop]ties ( ^! entities--su* z1 = in/ance1 t two po9ts uniquely det]m9e a /raight l9e--ne>ly ! :ole ( geometry c be con/ruct$4 ,ev5 quantitative coord9ates c be introduc$1 to facilitate ! reason+4 ,b no m5tion ( di/ance1 area1 or volume1 ne$ h be5 introduc$4 ,po9ts w h an ord] on ! l9e1 b ord] does n imply any settl$ di/ance4 ,:5 we n[ inquire :at measurem5ts ( di/ance are possible1 we f9d t !re are diff]5t sy/ems ( measurem5t all equally possible4 ,!re are ?ree ma9 types ( sy/em3 any sy/em ( "o type gives ,euclidean geometry1 any sy/em ( ano!r type gives ,hyp]bolic 7or ,lobat*ewskian7 geometry1 any sy/em ( ! ?ird type gives ,elliptic geometry4 ,also diff]5t be+s1 or ! same be+ if he *ooses1 may reckon 9 diff]5t sy/ems ( ! same type1 or 9 sy/ems ( diff]5t types4 ,consid] ! example :i* w int]e/ u lat]4 ,two be+s1 ,a & ,b1 agree to use ! same ?ree int]sect+ l9es z axes ( x1 y1 z4 ,!y bo? employ a sy/em ( measurem5t ( ! ,euclidean type1 & 7:at is n necess>ily ! case7 agree z to ! plane at inf9ity4 ,t is1 !y agree z to ! l9es :i* are p>allel4 ,!n ) ! usual me?od ( rectangul> ,c>tesian axes1 !y agree t ! coord9ates ( ,p are ! l5g?s ,,on1 ,,nm1 ,,mp4 ,s f> all is h>mony4 ,a fixes on ! segm5t ,,ou#a1 on ,ox1 z be+ ! unit l5g?1 & ,b on ! segm5t ,,ov#a1 on ,ox4 ,a calls 8 coord9ates 7x1 y1 z71 & ,b calls !m 7,x1 ,y1 ,z74 ,!n x is f\nd s9ce bo? sy/ems are ,euclidean t1 :atev] po9t ,p be tak51 ,x x1 ,y y1 ,z z4 4 ,!y proce$ to adju/ _! diff]5ces1 & fir/ take ! x-coord9ates4 ,obvi\sly !y h tak5 diff]5t units ( l5g? along ,ox4 ,! l5g? ,,ou#a1 :i* ,a calls "o unit1 ,b calls units4 ,b *anges 8 unit l5g? to ,,ou#a1 f its orig9al l5g? ,,ov#a1 & obta9s ,x x4 ,b n[1 z he mu/ use ! same unit = all 8 measurem5ts1 8 o!r coord9ates are alt]$ 9 ! same ratio4 ,?us we n[ h ,x x1 ,y y_/1 ,z z_/4 ,! fundam5tal div]g5ce is n[ evid5t4 ,a & ,b agree z to _! units along ,ox4 ,!y settl$ t by tak+ along t axis a giv5 segm5t ,,ou#a z hav+ ! unit l5g?4 ,b !y _c agree z to :at segm5t along ,oy is equal to ,,ou#a4 ,a says x is ,,ou#b1 & ,b t x is ,,ou#b4 ,simil>ly = l5g?s along ,,oz4 ,! result is t ,a's sph]es x#b y#b z#b r#b1 are ,b's ellipsoids1 ,x#b #b,y#b_/b #b,z#b_/b r#b1 i4 e4 ,x#b_/b ,y#b_/b ,z#b_/b r#b_/b4 ,?us ! measurem5t ( angles by ! two is hopelessly at v>iance4 ,if 1 !re is "o1 & only "o1 set ( common rectangul> axes at ,o1 namely t f :i* !y />t$4 ,if 1 b 1 !n !re are a s+ly inf9ite numb] ( common rectangul> axes f\nd by rotat+ ! axes r\nd ,ox4 ,?is is1 = u1 ! int]e/+ case4 ,! same ph5om5a are reproduc$ by transf]r+ to any p>allel axes4 ,! root ( ! difficulty is1 t ,a's measur+ rod1 :i* = him is a rigid inv>iable body1 appe>s to ,b z *ang+ 9 l5g? :5 turn$ 9 diff]5t directions4 ,simil>ly all measur+ rods1 satisfactory to ,a1 violate ,b's imm$iate judgm5t ( inv>iability1 & *ange accord+ to ! same law4 ,!re is no way out ( ! difficulty4 ,two rods & co9cide :5ev] laid "o on ! o!r2 is held /ill1 & bo? m5 agree t x does n *ange4 ,b is turn$ r\nd4 ,a says x is inv>iable1 ,b says x *anges4 ,to te/ ! matt]1 is turn$ r\nd to measure x1 & exactly fits x4 ,b :ile ,a is satisfi$1 ,b decl>es t has *ang$ 9 exactly ! same way z did 4 ,mean:ile ,b has procur$ two mat]ial rods satisfactory to him z inv>iable1 & ,a makes exactly ! same objections4 ,we %all say t ,a & ,b employ div]se ,euclidean metrical sy/ems4 ,! mo/ extraord9>y fact ( human life is t all be+s seem to =m _! judgm5ts ( spatial quantity accord+ to ! same metrical sy/em4 ,relativity 9 ,mod]n ,physics ,ow+ to ! fact t po9ts ( space are incapable ( direct recognition1 !re is a difficulty--ap>t f any ab/ract "q ( ! nature ( space--9 decid+ on ! motion to be ascrib$ to any body4 ,ev5 if !re be su* a ?+ z absolute position1 x is impossible 9 practice to decide directly :e!r a body's absolute position has *ang$4 ,all spatial measurem5t is relative to matt]4 ,newton's laws ( motion 9 _! mod]n dress evade ?is difficulty by ass]t+ t a framework ( axes ( coord9ates c be def9$ by _! relations to matt] su* t1 assum+ ^! axes to be at re/1 & all velocities to be measur$ relatively to !m1 ! laws hold4 ,! same exp$i5t has to be employ$ = "t1 namely1 ! laws hold :5 ! measurem5t ( ! fl[ ( "t is made by ! prop] ref]5ce to p]iodic ev5ts4 ,?us ! laws ass]t t ! framework & ! natural clock adapt$ = _! use h be5 successfully f\nd4 ,b1 if "o framework w d1 an inf9ity ( o!rs s]ve equally well2 namely1 n only--z is ( c\rse ! case--all ^? at re/ relatively to ! fir/ framework1 b also all ^? :i* move )\t relative rotation ) uni=m velocity relatively to ! fir/4 ,?is :ole set ( frameworks is on a level 9 respect to ,newton's laws4 ,we w call !m ,dynamical frameworks4 ,n[1 suppose !re are two obs]v]s1 ,a & ,b4 ,!y agree 9 _! non-metrical projective geometry1 e4g41 :at ,a calls a /raight l9e s does ,b4 ,!y also bo? apply a ,euclidean metrical sy/em ( measurem5t to ?is space4 ,_! two metrical sy/ems also agree 9 hav+ ! same plane at inf9ity1 t is1 l9es :i* are p>allel = ,a are also p>allel = ,b4 ,fur!rmore1 !y h bo? successfully appli$ ,newton's laws to ! movem5t ( matt]1 & agree 9 hav+ ! same sets ( dynamical axes4 ,b ! framework 7among ^! sets7 :i* ,a *ooses to reg>d z at re/ is diff]5t f ! frame 7among ! same sets7 :i* ,b s reg>ds4 ,)\t alt]ation ( _! respective judgm5t ( re/1 !y *oose _! co-ord9ate axes s t ! orig9s 7,o = ,a1 & ,o = ,b7 are 9 relative motion along ,,oo1 :i* is ! axis ( x = bo?4 ,fur!r1 s9ce ,,oo is ! l9e ( symmetry ( _! div]se ,euclidean sy/ems1 we assume t ! two measure-sy/ems agree = planes p]p5dicul> to ,,oo1 i4e41 we assume a symmetry r\nd ,,oo4 ,!n if1 = ,a at ,o1 ! di/ance ,,oo be 1 ! relations at any in/ant betwe5 ,a's coord9ates 7x1 y1 z7 & ,b's coord9ates 7x1 y1 z7 = ! same po9t ,p are giv5 by x 7x - 71 y y1 z z4 ,also1 accord+ to ,a's clock1 ,o is mov+ =w>d ) a uni=m velocity v1 & we measure ,a's "t f ! in/ant ( ! co9cid5ce ( ,o & ,o4 ,?us vt1 & x 7x - vt71 y y1 z z4 ,we n[ consid] ,b's clock1 & ask = ! mo/ g5]al supposition :i* is consi/5t ) ! fact t _! judgm5ts z to ! fact ( uni=m motion are 9 agreem5t4 ,we d n assume t ev5ts 9 v>i\s p>ts ( space :i* ,a consid]s to be simultane\s are s consid]$ by ,b4 ,b we assume t at any po9t ,p1 ) coord9ates 7x1 y1 z7 = ,a1 !re is a det]m9ate relation betwe5 ,b's "t ,t & x1 y1 z1 t4 ,put ,t 7x1 y1 z1 t74 ,write ,p ,t_/x1 ,q ,t_/y1 ,r ,t_/z1 ,s ,t_/t4 ,n[ suppose t ! po9t ,p is mov+1 & t 7u#a1 u#b1 u#c7 is its set ( compon5t velocities along ! axes accord+ to ,a's space & clock sy/em1 & 7,u#a1 ,u#b1 ,u#c7 is its set ( compon5t velocities accord+ to ,b's space & clock sy/em4 ,!n by m]e diff]5tiation x foll[s aft] a %ort ma!matical d$uction t ,u#a 7d_/dt77x - vt7 7u#a - v7_/,pu#a ,qu#b ,ru#c ,s1 ,u#b u#b_/,pu#a ,qu#b ,ru#c ,s1 ,u#c u#c_/,pu#a ,qu#b ,ru#c ,s4 ,b we h assum$ t1 :atev] ! direction ( ! resultant velocity 7u#a1 u#b1 u#c71 ! velocities 7,u#a1 ,u#b1 ,u#c7 & 7u#a1 u#b1 u#c7 are bo? uni=m :5 ei!r is uni=m4 ,h5ce x is easily prov$ t 1 ,p1 ,q1 ,r1 ,s are indep5d5t ( ! coord9ates 7x1 y1 z7 & ( ! "t t4 ,9 o!r words1 !y are con/ant4 ,h5ce we obta9 ,u#a 7u#a - v7_/,pu#a ,qu#b ,ru#c ,s1 & ,t ,px ,qy ,rz ,st4 ,b we assum$ t ,,oo1 i4e41 ,ox1 is an axis ( symmetry4 ,x foll[s f ?is assumption t ,q ,r #j4 ,we ?us obta9 ! simplifi$ results ,t ,px ,st1 ,u#a 7u#a - v7_/7,pu#a ,s71 7,i7 ,u#b u#b_/7,pu#a ,s71 ,u#c u#c_/7,pu#a ,s74 ,"h we rememb] t 7u#a1 u#b1 u#c7 are ! velocities ( any p>ticle accord+ to ,a's space & clock sy/em1 & t 7,u#a1 ,u#b1 ,u#c7 are ! velocities ( ! same po9t accord+ to ,b's space & clock sy/em4 ,we h obta9$ ! mo/ g5]al relations consi/5t ) ! facts t 7#a7 !y bo? employ ,euclidean sy/ems1 relat$ z describ$ above1 & 7#b7 !y agree 9 _! judgm5ts on ! uni=mity ( velocity4 ,we n[ comp>e _! judgm5ts on ! magnitudes ( velocities4 ,let ! magnitude ( ! velocity ( ,p be ,v accord+ to ,a's judgm5t1 & ,v accord+ to ,b's' judgm5t4 ,!n ,v#b u#ab u#bb u#cb1 ,v#b ,u#ab ,u#bb ,u#cb4 ,also we c put u#a l,v1 u#b m,v1 u#c n,v1 :]e 7l1 m1 n7 h no?+ to d ) ! magnitude ,v1 b simply dep5d on ! direction ( motion4 ,9 fact 7l1 m1 n7 are ! direction cos9es ( ! velocity accord+ to ,a's judgm5t4 ,by sub/itut+ 9 ! above equation = ,v#b we see t l#b m#b n#b #a4 ,n[1 sub/itut+ = 7u#a1 u#b1 u#c7 9 ! equations 7,i7 above1 & squ>+ & add+1 & elim9at+ m#b n#b by ! relation j f\nd1 we at once f9d ,v#b 77#b - #a7,v#bl#b - #bb,vvl #bv#b ,v#b7_/7,,pvl ,s7#b4 ,x is ?us se5 t 9 g5]al ! relation ( ,v to ,v dep5ds on ! direction cos9e l4 ,n[ l is ! cos9e ( ! angle :i* ! direction ( ! velocity ,v makes ) ,ox1 accord+ to ,a's judgm5t4 ,! mean+ ( ?is relation is1 t if ,a dis*>ges1 f guns at ! po9t ,p1 %ells ) a giv5 muzzle velocity ,v accord+ to 8 judgm5t1 ,b w consid] t _! muzzle velocities are diff]5t f ea* o!r1 except 9 ! case ( pairs ( guns equally incl9$ to ! axis ,,oo4 ,in/ances ( ?is type ( div]sity ( judgm5t c be not$ any day by any "o :o looks out ( ! w9d[ ( a railway c>riage1 & =gets t he is travell+4 ,n[1 suppose ! velocity ,v be>s a relation to ! velocity ,v1 :i* is indep5d5t ( l4 ,!n l mu/ disappe> f ! above =mula4 ,!re are two conditions to be satisfi$ ,"o condition is ,v#b #bv#b_/7b - #a71 or 9 a m conv5i5t =m #b #a_/7a - v#b_/,v#b74 ,! mean+ ( ?is condition is1 t !re is "o1 & only "o1 muzzle velocity ,v 7accord+ to ,a's judgm5t71 namely1 ! muzzle velocity giv5 by ! above =mula1 :i* c h ! prop]ty t ,b w judge t all ! guns are fir+ 9 _! div]se directions ) "o common muzzle velocity4 ,let u n[ suppose t ,v has ?is peculi> value3 t is1 if we look on ?is value ,v z kn[n1 we mu/ suppose t is giv5 by ! second ( ! above =mul4 ,! o!r condition all[s ,p & ,s to be put 9 ! =ms ,p -v_/,v#b1 ,s _/1 :]e ,v ,v4 ,?us we h ! bundle ( =mul #b #a_/7a - v#b_/,v#b71 ,t t - vx_/,v#b_/1 ,v ,v4 ,! value :i* we give to is purely a matt] = ! adju/m5t ( units4 ,if we want ,a & ,b to agree 9 _! judgm5ts ( ! magnitude ( ?is peculi> muzzle-velocity1 we put #a4 ,we !n get ! =mul usually adopt$1 namely #b #a_/7a - v#b_/,v#b71 ,t t - vx_/,v#b1 7,,ii7 ,v ,v4 ,b if we pref] t ,a & ,b %\ld reckon 7accord+ to ,a's judgm5t7 9 ! same units ( "t1 we put 1 & obta9 #b #a_/7a - v#b_/,v#b71 ,t 7t - vx7_/,v#b1 ,v ,v4 ,b ,a & ,b are 9 any case 9 su* hopeless difficulties ov] _! comp>isons ( "t-judgm5ts t ! detail ( us+ ! same units does n help !m mu*4 ,accord+ly ! =mul m>k$ 7,,ii7 are ^? us$4 ,?us ,a & ,b agree 9 _! judgm5ts z to ! magnitude ( "o special velocity ,v1 :atev] may be ! direction 9 :i* ! entity possess+ x is mov+4 ,9 ord] to rea* ?is measure ( agreem5t1 !y h to disagree z to _! space judgm5ts & _! "t judgm5ts4 ,! root cause ( _! disagreem5t is _! div]se judgm5t z to :i* axis sy/em is to be tak5 at re/ = ! purpose ( measur+ velocities4 ,be=e discuss+ ! nature ( ! disagreem5t disclos$ 9 =mula 7,,ii71 let u ask :y we %\ld br+ ^! difficulties on our heads by suppos+ t two p 9 relative motion1 :o bo? 7= ! purpose ( measur+ velocities7 assume t !y are at re/1 %\ld agree 9 _! judgm5ts 9 respect to ?is special velocity ,v4 ,su* an agreem5t has no c\nt]p>t 9 any ( our obvi\s judgm5ts made f railway c>riages4 ,surely we c wait till ! cont+5cy occurs be=e discuss+ ! confusion :i* x creates4 ,b ! cont+5cy has occurr$4 ,x occurs :5 we consid] ! velocity ( light4 ,p]haps ,i may v5ture to rem9d a philosophical society t light moves s v quickly t x is difficult to consid] its velocity at all4 ,s we ne$ n be surpris$ t ?is peculi> fact conc]n+ its velocity is n m obvi\s4 ,n[ ,v be+ ! velocity ( light1 unless v is l>ge1 v_/,v 7& /ill m v#b_/,v#b7 w be q inappreciable4 ,! only velocity ready to h& :i* is big en\gh to give v_/,v an appreciable value is ! velocity ( ! e>? 9 its orbit4 ,_m div]se exp]im5ts h be5 made1 & !y all agree 9 conclud+ t a man :o assumes ! e>? to be at re/ w f9d by measurem5t t ! velocity ( light is ! same 9 all directions4 ,fur!rmore1 :5 ! same man turns 8 att5tion to int]/ell> or int]planet>y ph5om5a1 & assumes ! sun to be at re/1 he w aga9 f9d ! velocity ( light to be ! same 9 all directions4 ,^! are well-atte/$ exp]im5ts made at long int]vals ( "t4 ,?is is ! exact cont+5cy contemplat$ above4 ,aga9 ! velocity ( light 9 vacuo has rec5tly tak5 on a new dignity4 ,x us$ to be "o among o!r wave velocities su* z ! velocity ( s\nd 9 air1 or 9 wat]1 or ! velocity ( surface waves 9 wat]4 ,b ,cl]k ,maxwell discov]$ t all electromagnetic influ5ces are propagat$ ) ! velocity ( light1 & n[ mod]n physical sci5ce half suspects t electromagnetic influ5ces are ! only physical influ5ces :i* relate ! *anges 9 ! physical _w4 ,accord+ly ! velocity ( light becomes ! fundam5tal natural velocity1 & exp]im5t %[s t our judgm5t ( its magnitude is n affect$ by our *oice ( ! framework at re/1 s long z we keep to a set ( dynamical axes4 ,^! exp]im5ts on light h be5 confirm$ by o!r electromagnetic exp]im5ts n involv+ light4 ,?us we are driv5 to equations 7,,ii71 :]e ,v is ! velocity ( light4 ,! fir/ conclusion to be drawn f equations 7,,ii7 is t two p :o make diff]5t *oices ( bodies at re/ w disagree z to _! measur+ rods 9 ! way describ$ above4 ,!re is no peculi> difficulty ab\t t4 ,! only wond] is t all p agree s well 9 _! judgm5ts z to metrical sy/ems4 ,a ma!matical angel w\ld naturally expect inc>nate m5 to be 9 viol5t disagreem5t on ?is subject4 ,b ! case ( "t is diff]5t4 ,= simplicity ( /atem5t we speak ( ,a z at ,o1 & ,b z at ,o4 ,we rememb] t ,o is mov+ relatively to ,o ) velocity v 9 direction ,,oo4 ,suppose ,a & ,b are look+ 9 ?is direction2 & !y bo? measure _! "t f ! in/ant :5 !y met1 z ,o pass$ ov] ,o4 ,!n we h ,t 77t - vx7_/,v#b7_/77a - v#b7_/,v#b74 ,n[1 suppose we consid] all ! ev5ts all ov] space :i* ,a consid]s to h happ5$ simultane\sly at ! "t t4 ,! ev5ts ( ?is set :i* occurr$ any:]e on a plane p]p5dicul> to ,,oo at a di/ance x 9 front ( ,o 7accord+ to ,a's reckon+71 w h occurr$ accord+ to ,b's reckon+ at ! "t ,t z giv5 above4 ,let u fix our att5tion on ! fact t ,b does n consid] all ^! ev5ts to be simultane\s4 ,= let ,t#a1 & ,t#b be ,b's times = su* ev5ts on planes x#a1 & x#b4 ,!n ,t#a - ,t#b v7x#b - x#a7_/7,v#b - v#b74 ,?us if x#b be great] ?an x#a1 ,t#b is less ?an ,t#a4 ,?us ,b judges ! m di/ant ev5ts 9 front ( him to h happ5$ e>li] ?an ! ne>] ev5ts 9 front ( him1 & vice v]sa = ! ev5ts beh9d4 ,?is di/urbance ( ! judgm5t ( simultaneity is ! fundam5tal fact4 ,obvi\sly ! measurem5t ( "t int]vals is a detail comp>$ to simultaneity4 ,a may ?9k a s]mon long1 & ,b may ?9k x %ort1 b at lea/ !y %\ld bo? agree t x /opp$ :5 ! clock h& po9t$ at ! h\r4 ,! wor/ ( ! matt] is t s f> z any te/ c be appli$ !re is no me?od ( discrim9at+ betwe5 ! validities ( _! judgm5ts4 ,?us we are confront$ ) two di/9ct concepts ( ! common _w1 ,a's space-"t concept1 & ,b's space-"t concept4 ,:o is "r8 ,x is no use /ay+ = an answ]4 ,we mu/ foll[ ! example ( ! wise old ,roman1 & pass on to o!r ?+s4 ,?us e/imates ( quantity 9 space & "t1 &1 to "s ext5t1 ev5 e/imates ( ord]1 dep5d on ! individual obs]v]4 ,b :at are ! crude deliv]ances ( s5sible exp]i5ce1 ap>t f t _w ( imag9ative recon/ruction :i* = ea* ( u has ! be/ claim to be call$ our real _w8 ,"h ! exp]im5tal psy*ologi/ /eps 94 ,we _c get away f him4 ,i wi% we c\ld1 = he is frightfully difficult to und]/&4 ,also1 sometimes 8 k ( ! pr9ciples ( ma!matics is r weak1 & ,i sometimes suspect---- ,no1 ,i w n say :at ,i sometimes ?9k3 probably he1 ) equal reason1 is ?9k+ ! same sort ( ?+ ( u4 ,i w1 h[ev]1 v5ture to summ>ise conclusions1 :i* are1 ,i believe1 9 h>mony ) ! exp]im5tal evid5ce1 bo? physical & psy*ological1 & :i* are c]ta9ly sugge/$ by ! mat]ials = t unwritt5 *apt] 9 ma!matical logic :i* ,i h already comm5d$ to y\r notice4 ,! concepts ( space & "t & ( quantity are capable ( analysis into bundles ( simpl] concepts4 ,9 any giv5 s5sible exp]i5ce x is n necess>y1 or ev5 usual1 t ! :ole complete bundle ( su* concepts apply4 ,= example1 ! concept ( ext]nality may apply )\t t ( l9e> ord]1 & ! concept ( l9e> ord] may apply )\t t ( l9e> di/ance4 ,aga91 ! ab/ract ma!matical concept ( a space-relation may confuse toge!r di/9ct concepts :i* apply to ! giv5 p]ceptions4 ,= example1 l9e> ord] 9 ! s5se ( a l9e> projection f ! obs]v] is di/9ct f l9e> ord] 9 ! s5se ( a r[ ( objects /ret*+ across ! l9e ( sight4 ,ma!matical physics assumes a giv5 _w ( def9itely relat$ objects1 & ! v>i\s space-"t sy/ems are alt]native ways ( express+ ^? relations z concepts 9 a =m :i* also applies to ! imm$iate exp]i5ce ( obs]v]s4 ,yet !re mu/ be "o way ( express+ ! relations betwe5 objects 9 a common ext]nal _w4 ,alt]native me?ods c only arise z ! result ( alt]native /&po9ts2 t is to say1 z ! result ( leav+ some?+ add$ by ! obs]v] /ick+ 7z x 77 9 ! univ]se4 ,b ?is way ( conceiv+ ! _w ( physical sci5ce1 z compos$ ( hypo!tical objects1 leaves x z a m]e fairy tale4 ,:at is really actual are ! imm$iate exp]i5ces4 ,! task ( d$uctive sci5ce is to consid] ! concepts :i* apply to ^! data ( exp]i5ce1 & !n to consid] ! concepts relat+ to ^! concepts1 & s on to any necess>y degree ( ref9em5t4 ,z our concepts become m ab/ract1 _! logical relations become m g5]al1 & less liable to exception4 ,by ?is logical con/ruction we f9ally arrive at conceptions1 7i7 :i* h det]m9ate exemplifications 9 ! exp]i5ce ( ! individuals1 & 7ii7 ^: logical relations h a peculi> smoo?ness4 ,= example1 conceptions ( ma!matical "t1 ( ma!matical space1 are su* smoo? conceptions4 ,no "o lives 9 an inf9ite giv5 :ole1 b 9 a set ( fragm5t>y exp]i5ces4 ,! problem is to exhibit ! concepts ( ma!matical space & "t z ! necess>y outcome ( ^! fragm5ts by a process ( logical build+ up4 ,simil>ly = ! o!r physical concepts4 ,?is process builds a common _w ( conceptions out ( fragm5t>y worlds ( exp]i5ce4 ,! mat]ial pyramids ( ,egypt are a conception1 :at is actual are ! fragm5t>y exp]i5ces ( ! races :o h gaz$ on !m4 ,s f> z sci5ce seeks to rid itself ( hypo!sis1 x _c g beyond ^! g5]al logical con/ructions4 ,= sci5ce1 z ?us conceiv$1 ! div]g5t "t ord]s consid]$ above pres5t no difficulty4 ,! diff]5t "t sy/ems simply regi/] ! diff]5t relations ( ! ma!matical con/ruct to ^? individual exp]i5ces 7actual or hypo!tical7 :i* c\ld exi/ z ! crude mat]ial f :i* ! con/ruct is elaborat$4 ,b aft] all x %\ld be possible s to elaborate ! ma!matical con/ruct s z to elim9ate specific ref]5ce to p>ticul> exp]i5ces4 ,:atev] be ! data ( exp]i5ce1 !re mu/ be some?+ :i* c be said ( !m z a :ole1 & t some?+ is a /atem5t ( ! g5]al prop]ties ( ! common _w4 ,x is h>d to believe t ) prop] g5]alisation "t & space w n be f\nd among su* prop]ties4 ,comm5t>y add$ on read+ ! ,pap] be=e ! ,ari/otelian ,society ,! fir/ six pages ( ! pap] consi/ ( a summ>y ( ideas :i* ought to be 9 our m9ds :ile consid]+ problems ( "t & space4 ,! ideas are mo/ly philosophical1 & ! summ>y has be5 made by an amateur 9 t sci5ce2 s !re is no reason to ascribe to x any importance except t ( a mode/ rem9d]4 ,!re are only two po9ts 9 ?is summ>y to :i* ,i w\ld draw att5tion4 ,on pp4 #aib & #aic !re occurs-- ,:]ev] mank9d 444 un5d+ uni=m succession4 ,if ,i und]/& ,kant rightly--:i* ,i admit to be v problematical--he holds t 9 ! act ( exp]i5ce we are aw>e ( space & "t z +r$i5ts necess>y = ! occurr5ce ( exp]i5ce4 ,i w\ld sugge/--r timidly--t ?is doctr9e %\ld be giv5 a diff]5t twi/1 :i* 9 fact turns x 9 ! opposite direction--namely1 t 9 ! act ( exp]i5ce we p]ceive a :ole =m$ ( relat$ diff]5tiat$ p>ts4 ,! relations betwe5 ^! p>ts possess c]ta9 *>act]i/ics1 & "t & space are ! expressions ( "s ( ! *>act]i/ics ( ^! relations4 ,!n ! g5]ality & uni=mity :i* are ascrib$ to "t & space express :at may be t]m$ ! uni=mity ( ! texture ( exp]i5ce4 ,! success ( mank9d--mode/ ?\gh x is--9 d$uc+ uni=m laws ( nature is1 s f> z x goes1 a te/imony t ?is uni=mity ( texture goes beyond ^? *>act]i/ics ( ! data ( exp]i5ce :i* are express$ z "t & space4 ,"t & space are necess>y to exp]i5ce 9 ! s5se t !y are *>act]i/ics ( our exp]i5ce2 &1 ( c\rse1 no "o c h our exp]i5ce )\t runn+ into !m4 ,i _c see t ,kant's d$uction am\nts to mu* m ?an say+ t :at is1 is--true en\gh1 b n v helpful4 ,b ,i admit t :at ,i h t]m$ ! uni=mity ( ! texture ( exp]i5ce is a mo/ curi\s & arre/+ fact4 ,i am q ready to believe t x is a m]e illusion2 & lat] on 9 ! pap] ,i sugge/ t ?is uni=mity does n belong to ! imm$iate relations ( ! crude data ( exp]i5ce1 b is ! result ( sub/itut+ = !m m ref9$ logical entities1 su* z relations betwe5 relations1 or classes ( relations1 or classes ( classes ( relations4 ,by ?is means x c be demon/rat$--,i ?9k--t ! uni=mity :i* mu/ be ascrib$ to exp]i5ce is ( a mu* m ab/ract att5uat$ "* ?an is usually all[$4 ,?is process ( lift+ ! uni=m "t & space ( ! physical _w into ! /atus ( logical ab/ractions has also ! advantage ( recognis+ ano!r fact1 namely1 ! extremely fragm5t>y nature ( all direct individual exp]i5ce4 ,my po9t 9 ?is respect is t fragm5t>y individual exp]i5ces are all t we "k1 & t all speculation mu/ />t f ^! disjecta membra z its sole datum4 ,x is n true t we are directly aw>e ( a smoo? runn+ _w1 :i* 9 our speculations we are to conceive z giv54 ,9 my view ! creation ( ! _w is ! fir/ unconsci\s act ( speculative ?\ght2 & ! fir/ task ( a self-consci\s philosophy is to expla9 h[ x has be5 done4 ,!re are r\ghly two rival explanations4 ,"o is to ass]t ! _w z a po/ulate4 ,! o!r way is to obta9 x z a d$uction1 n a d$uction ?r\gh a *a9 ( reason+1 b a d$uction ?r\gh a *a9 ( def9itions :i*1 9 fact1 lifts ?\ght on to a m ab/ract level 9 :i* ! logical ideas are m complex1 & _! relations are m univ]sal4 ,9 ?is way ! brok5 limit$ exp]i5ces su/a9 t connect$ inf9ite _w 9 :i* 9 our ?\ghts we live4 ,!re are ?ree m rem>ks :ile on ?is po9t ,i wi% to make-- 7i7 ,! fact t imm$iate exp]i5ce is capable ( ?is d$uctive sup]/ructive mu/ mean t x itself has a c]ta9 uni=mity ( texture4 ,s ?is great fact /ill rema9s4 7ii7 ,i d n wi% to d5y ! _w z a po/ulate4 ,speak+ )\t prejudice1 ,i d n see h[ 9 our pres5t elem5t>y /ate ( philosophical advance we c get on )\t middle axioms1 :i*1 9 fact1 we habitually assume4 ,my position is1 t by c>eful scrut9y we %\ld extrude su* po/ulates f e "p ( our organis$ k 9 :i* x is possible to d )\t !m4 ,n[1 physical sci5ce organises our k ( ! relations betwe5 ! deliv]ances ( our v>i\s s5ses4 ,i hold t 9 ?is dep>tm5t ( k su* po/ulates1 ?\gh n entirely to be extrud$1 c be r$uc$ to a m9imum 9 ! way :i* ,i h describ$4 ,i h n ! slighte/ k ( !ories respect+ our emotions1 affections1 & moral s5tim5ts1 & ,i c well believe t 9 deal+ ) !m fur!r po/ulates are requir$4 ,& 9 practice ,i recognise t we all make su* po/ulates1 uncritically4 7iii7 ,! next p>agraphs on pp4 #aic & #aid are z foll[s-- ,! oppos$ philosophical me?od 444 physical sci5ce4 ,x w be not$ t1 9 ! light ( :at has j be5 /at$1 ! fir/ ( ^! p>agraphs 7:i*1 ,i hope1 fai?fully expresses ! exp]im5tal way ( approa*+ ! problem7 really obscures ! po9t :i* ,i h be5 endeav\r+ to make4 ,! phrase1 ,if we =m ! exact concepts ( po9ts1 etc41 is fatally ambigu\s z betwe5 ! me?od ( po/ulat+ entities ) assign$ relations1 & ! me?od ( =m+ logical con/ructions1 & ?us rea*+ po9ts1 etc41 z ! result ( a *a9 ( def9itions4 ,turn+ n[ to pp4 #aid-aie1 we come to ! foll[+ p>agraphs-- ,! o!r !ory 444 eighte5? c5tury4 ,we note aga9 t ! relational !ory ( space f ano!r po9t ( view br+s u back to ! idea ( ! fundam5tal space-entities z be+ logical con/ructs f ! relations betwe5 ?+s4 ,! diff]5ce is1 t ?is p>agraph is writt5 f a m develop$ po9t ( view1 z x implicitly assumes ! ?+s 9 space1 & conceives space z an expression ( c]ta9 ( _! relations4 ,comb9+ ?is p>agraph ) :at has gone be=e1 we see t ! sugge/$ proc$ure is fir/ to def9e ?+s 9 t]ms ( ! data ( exp]i5ce1 & !n to def9e space 9 t]ms ( ! relations betwe5 ?+s4 ,?is proc$ure is explicitly assum$ 9 ! next %ort p>agraph3 ,9 ?is connection 444 f ! ev5ts4 ,! gi/ ( ! rema9+ p>agraphs ( ?is section is conta9$ 9 ! p>agraph at ! bottom ( p4 #aif3 ,! po9t 9 "t 444 new importance4 ,! s5t5ce1 ,we live 9 durations1 & n 9 po9ts1 c be amplifi$ by ! addition1 ,we live 9 space-ext5sions & n 9 space-po9ts4 ,x mu/ be not$ t :ole & "p z appli$ to ext5sions 9 space or "t mu/ be diff]5t f ! all & "s ( logic1 unless we admit po9ts to be ! fundam5tal entities4 ,= spatial :ole & spatial "p c only mean all & "s if !y really mean all ! po9ts & "s ( ! po9ts4 ,b if ext5sions & _! relations are m fundam5tal ?an po9ts1 ?is int]pretation is preclud$4 ,i sugge/ t spatial :ole & spatial "p is intimately connect$ ) ! fundam5tal relation betwe5 ?+s f :i* our space ideas spr+4 ,! relation ( space :ole to space "p has _m =mal prop]ties :i* are id5tical ) ! prop]ties ( all & "s4 ,also :5 po9ts h be5 def9$1 we c replace x by ! conception ( all ! po9ts & "s ( ! po9ts4 ,b ! confusion betwe5 ! two relations is fatal to s\nd views on ! subject4 ,div]se ,euclidean ,measure ,sy/ems ,! next section deals ) ! measure sy/ems applicable to space4 ,a measure sy/em is a gr\p ( congru5t trans=mations ( space into itself4 ,consid] a rigid body occupy+ all space4 ,let ?is body be mov$ 9 any way s t ! p>ticles ( ! body :i* occupi$ po9ts ,p#a1 ,p#b1 ,p#c1 etc41 n[ occupy po9ts ,q#a1 ,q#b1 ,q#c1 etc4 ,!n any po9t ,p#a 9 space is uniquely relat$ to ! correspond+ po9t ,q#a 9 space by a "o-to-"o trans=mation ) c]ta9 *>act]i/ics4 ,by ! aid ( ^! trans=mations we c a*ieve ! def9ition ( di/ance 9 a way :i* def9itely det]m9es ! di/ance betwe5 any two po9ts1 provid$ t we c def9e :at we mean by a congru5t trans=mation )\t introduc+ ! idea ( di/ance4 ,if we introduc$ ! idea ( di/ance1 we %\ld simply say t a congru5t trans=mation is "o :i* leaves all di/ances un*ang$1 i4 e41 if ,p#a1 ,p#b are trans=m$ into ,q#a1 ,q#b !n ! di/ance ,p#a,p#b is equal to ! di/ance ,q#a,q#b4 ,b ma!maticians h succe$$ 9 def9+ congru5t trans=mations )\t any ref]5ce to di/ance4 ,!re are alt]native gr\ps ( su* congru5t trans=mations1 & ea* gr\p gives a diff]5t measure sy/em = space4 ,! di/ance ,p#a,p#b may equal ! di/ance ,q#a,q#b = "o measure sy/em1 & w n equal x = ano!r measure sy/em4 ,all ^! diff]5t measure sy/ems are on ! same level1 equally applicable4 ,a be+ ) a /rong en\gh head c\ld ?9k ( !m all at once z apply+ to space4 ,! result s f> z x int]e/s u 9 respect to ! !ory ( relativity is expla9$ on pp4 #aig-bjj1 end+ ) ,! mo/ extraord9>y fact 444 same metrical sy/em4 ,?is f9al s5t5ce be>s on ,po9c>'s ass]tion t ! measure sy/em adopt$ is purely conv5tional4 ,i presume t by conv5tional a c]ta9 arbitr>9ess ( *oice is meant2 & 9 t case1 ,i mu/ express entire diss5t4 ,x is true t )9 ! circle ( geometrical ideas !re is no means ( giv+ any pref]5ce to any "o measure sy/em1 & any "o is z good z any o!r4 ,b x is n true t if we look at a normal c>riage :eel1 & at an oval curve "o foot broad & t5 feet long1 we exp]i5ce any arbitr>9ess ( judgm5t 9 decid+ :i* has approximately ! =m ( a circle4 ,accord+ly to ,po9c> ! *oice betwe5 !m1 z repres5t+ a circle1 is entirely conv5tional4 ,aga91 we equally =m imm$iate judgm5ts z to :e!r a body is approximately rigid4 ,we "k t a pav+ /one is rigid1 & t a conc]t9a is n rigid4 ,?is aga9 necessitates a det]m9ate measure sy/em1 select$ f among ! o!rs4 ,accord+ly we conclude t 7i7 ea* be+ does1 9 fact1 employ a det]m9ate measure sy/em1 :i* rema9s ! same1 except possibly = v small v>iations1 & 7ii7 ! measure sy/ems ( diff]5t human be+s agree1 to )9 ! limits ( our obs]vations4 ,^! conclusions are n ! less extraord9>y because no pla9 man has ev] d\bt$ !m4 ,x is an int]e/+ subject to inve/igate exactly :at are ! fundam5tal uni=mities ( exp]i5ce :i* necessitate ?is conclusion4 ,x is n s easy z x looks1 s9ce we h to dive/ ourselves ( all aid ( sci5tific hypo!sis if our conclusions are to be demon/rative4 ,relativity 9 ,mod]n ,physics ,pp4 #bja-bjb1 ,ow+ to ! fact 444 :i* ,b s reg>ds4 ,! fundam5tal =mul = ! !ory ( relativity are ! relations betwe5 div]se co-ord9ate sy/ems giv5 on p4 #bjc1 & =mul ,,ii at ! bottom ( p4 #bjg4 ,! g5]al explanation ( "o me?od 9 :i* ^! =mul arise--namely1 ,e9/e9's me?od--is giv5 on pp4 #bja-baa4 ,namely1 we seek ! condition t = all dynamical axes ! velocity ( light %\ld be ! same1 & ! same 9 all directions4 ,x %\ld be not$ t ! exp]im5ts :i*1 s f> z !y g1 confirm ^! =mul1 c also be expla9$ 9 ano!r way :i* makes ! !ory ( relativity unnecess>y4 ,we ne$ only ascribe to ! e!r a c]ta9 prop]ty ( contraction 9 ! direction ( motion1 & ! ?+ is done4 ,s no "o ne$ be bludgeon$ into accept+ ! r biz>re doctr9e ( relativity1 nor inde$ any o!r sci5tific g5]alisation4 ,! good old homely e!r1 :i* we all "k1 c 9 ?is case s]ve ! purpose4 ,j z an au?or ( g5ius1 if he lives long en\gh1 survives ! inevitable accusation ( immorality1 s ! e!r by d9t ( p]si/5ce has outliv$ all reputation ( extravagance4 ,b if we deta* ourselves f ! glib phraseology conc]n+ x1 ! sci5tific e!r is uncommonly l ! primitive explanation ( ! s\l1 z a little man inside u1 :i* c sometimes be caught escap+ 9 ! =m ( a butt]fly4 ,z soon z ! e!r has to be pat*$ up ) special prop]ties to expla9 special exp]im5ts1 its sci5tific use is problematical1 & its philosophic use is nil4 ,philosophically ! e!r seems to me to be an ambiti\s attempt to give a complete explanation ( ! physical univ]se by mak+ an elephant /& on a tortoise4 ,sci5tifically x has a p]fectly adequate use by veil+ ! extremely ab/ract "* ( sci5tific g5]alisations "u a my?1 :i* enables our imag9ations to "w m freely4 ,i am n advocat+ ! extrusion ( e!r f our sci5tific phraseology1 ev5 ?\gh at special po9ts we h to ab&on x4 ,b ! key to ! reasons :y x is wor? :ile to consid] s]i\sly ! doctr9e ( relativity is to be f\nd on pp4 #bji1 #baj3 ,aga9 ! velocity ( light 444 n involv+ light4 ,namely1 we h begun to suspect t all physical influ5ces require "t = _! propagation 9 space4 ,?is g5]alisation is a long way f be+ prov$4 ,gravitation /&s l a lion 9 ! pa?4 ,b if x be ! case1 !n all idea ( an imm$iate pres5tation to u ( an aspect ( ! _w z x 9 fact is1 mu/ necess>ily be ab&on$4 ,:at we p]ceive at any in/ant is already anci5t hi/ory1 ) ! dates ( ! v>i\s p>ts hopelessly mix$4 ,we mu/ add to ?is ! difficulty ( det]m9+ :at is at re/ & :at is 9 motion1 & ! fur!r difficulty ( det]m9+ a def9ite uni=m fl[ ( "t4 ,x is no use discuss+ ?is matt] z ?\gh1 b = ! silly extravagant doctr9e ( relativity1 ev]y?+ w\ld be pla9 sail+4 ,x isn't4 ,y may be q sure t :51 aft] prolong$ /udy1 y endeav\r to give ! simple/ explanation ( a grave difficulty1 y w be accus$ ( extravagance4 ,i h no responsibility = ! doctr9e ( relativity1 & hold no brief = x1 b x has "s claim to be consid]$ z a comp>atively simple way out ( a sci5tific maze4 ,9 ! fir/ place1 we use ! ,newtonian dynamical sets ( axes1 & ! ,newtonian clock to extricate ourselves p>tially f ! difficulties ( re/1 motion1 & "t4 ,^! h prov$ capable ( sci5tific det]m9ation )9 ! limits ( our exp]im5tal accuracy4 ,?us ! only ?+ left ov] is ! *oice ( ! axes at re/1 :i* is a completely indet]m9ate problem on ,newtonian pr9ciples4 ,aga91 s f> z we c at pres5t guess by adopt+ ! !ory t all metrical influ5ce is electromagnetic1 all influ5ces are propagat$ ) ! velocity ( light 9 vacuo4 ,?is electromagnetic hypo!sis is by no means e/abli%$1 b x gives ! simple/ ( all possible results 9 respect to ! propagation ( influ5ce1 :i* we !re=e adopt4 ,b :at dynamical axes are we tak+ z at re/8 ,n[ our practical *oice gives a range ( relative velocities small comp>$ to t ( light4 ,s except = c]ta9 ref9$ exp]im5ts x does n matt]4 ,!re are two possibilities-- 7i7 ,we may assume t "o set ( axes are at re/1 & t ! o!rs w %[ traces ( motion 9 respect to ! velocity ( light2 or-- 7ii7 ,t ! velocity ( light is ! same 9 all directions :i*ev] be ! dynamical axes assum$4 ,! fir/ supposition is negativ$ by exp]im5t1 & h5ce we are driv5 to ! second supposition2 :i* imm$iately l&s u 9 ! :ole !ory ( relativity4 ,b if we w n h ?is !ory we mu/ reject ! e>li] supposition t ! velocity ( light 9 vacuo is ! same 9 all directions4 ,?is we d1 9 fact1 by assum+ an e!r1 & assum+ a c]ta9 law = its modification4 ,!n we1 9 fact1 adopt ! fir/ supposition s f> z to hold t !re are dynamical axes specially at re/1 namely1 at re/ relatively to ! undi/urb$ e!r4 ,!n an assum$ law = ! modification ( ! e!r s alt]s ! velocity ( light t we expla9 :y no dynamical axes %[ traces ( motion4 ,i wi% n[ to g back to ! po9t :i* ,i made a few m9utes ago1 t :at we p]ceive at any in/ant is anci5t hi/ory ) its dates hopelessly mix$4 ,9 ! e>li] "p ( my comm5ts ,i emphasis$ ! po9t t our only data z to ! physical _w are our s5sible p]ceptions4 ,we mu/ n slip into ! fallacy ( assum+ t we are comp>+ a giv5 _w ) giv5 p]ceptions ( x4 ,! physical _w is 9 "s g5]al s5se ( ! t]m a d$uc$ concept4 ,our problem is1 9 fact1 to fit ! _w to our p]ceptions1 & n our p]ceptions to ! _w4 ,,pr9t$ ,,9 ,,great ,,brita9 ,,by ,,ri*>d ,,clay ,,sons1 ,,limit$1 ,,brunswick ,,/41 ,,/am=d ,,/41 ,s4,e41 ,,& ,,bungay1 ,,suffolk4 ,f ,,williams ,,norgate',s ,,li/ ,a ,,spiritual ,,pilgrimage4 ,by ! ,rev4 ,r4 ,j4 ,,campbell4 7,! ,rev4 ,r4 ,j4 ,campbell's own ,/ory ( 8 ,religi\s ,life47 #bnd ,impression4 ,demy #hvo4 #gs4 #f;d4 net4 ,?is is em95tly a book = :i* to be ?ankful--simple1 /raight=w>d1 k9dly4 ,nei!r does x lack ! sav+ grace ( hum\r4--,gu>dian4 ,mr4 ,campbell devotes a *apt] to 8 re-ord9ation1 & x mu/ be admitt$ t 8 def5ce ( ?is act is effective4--,me?odi/ ,times4 ,,ed9burgh4 ,by ! ,"r ,hon4 ,sir ,,h]b]t ,,maxwell1 ,b>t41 ,d4,c4,l41 ,au?or ( ,life ( ! ,duke ( ,well+ton1 ,scotti% ,g>d5s1 etc4 ,presid5t ( ! ,society ( ,antiqu>ies ( ,scotl&1 #aiaj-ac1 & ,*airman ( ! ,royal ,commission on ,scotti% ,hi/orical ,monum5ts4 ,) a ,col\r$ ,frontispiece & #fd pages ( ,illu/rations ( ! pa/ & pres5t city4 ,m$ium #hvo4 #ajs4 #f;d4 net4 ,a ,hi/ory ( ! ,scotti% ,capital f ! e>lie/ times to ! n9ete5? c5tury4 ,,fur!r ,,pages ,,( ,,my ,,life4 ,by ! ,"r ,rev4 ,w4 ,,boyd ,,c>p5t]1 ,k4,c4,v4,o41 ,d4,d41 ,d4,c4,l41 ,=m]ly ,bi%op ( ,ripon1 ,au?or ( ,"s ,pages ( ,my ,life1 ,! ,witness ( ,religi\s ,exp]i5ce1 etc4 ,) ,illu/rations4 ,m$ium #hvo4 #ajs4 #f;d4 net4 ,reflections m+l$ ) intimate rem9isc5ces & recollections ( ,royal p]sonages & ( m5 em95t 9 _m sph]es4 ,,"s ,,pages ,,( ,,my ,,life4 ,by ! ,"r ,rev4 ,w4 ,,boyd ,,c>p5t]4 ,new & ,*eap] ,edition4 ,l>ge po/ #hvo4 #es4 net4 ,all :o h li/5$ to 8 eloqu5t prea*+ w read ) delight 8 mus+ on :at life has br\ght ! au?or4 ,,raphael ,,meldola1 ,hon4 ,d4,sc4 7,oxon471 ,hon4 ,,ll4,d4 7,/4 ,&471 ,f4,r4,s41 ,pr(essor ( ,*emi/ry 9 ! ,city & ,guilds ( ,london ,te*nical ,college4 ,rem9isc5ces ( 8 wor? & "w1 by ^? :o knew him1 toge!r ) a ,*ronological ,li/ ( 8 ,publications 7#ahfh-aiae74 ,edit$ by ,,james ,,m>*ant4 ,) a ,preface by ! ,"r ,hon4 ,,"l ,,m\lton1 ,k4,c4,b41 ,f4,r4,s4 ,) a ,portrait4 ,cr[n #hvo4 #es4 net4 ,! book is "o ( ! mo/ delightful biographies ( sci5tific m5 t h be5 publi%$ dur+ rec5t ye>s4--,*emi/ & ,druggi/4 ,,! ,,manufacture ,,( ,,hi/orical ,,mat]ial4 ,an ,elem5t>y ,/udy 9 ! ,s\rces ( ,/ory4 ,by ,j4 ,w4 ,,jeudw9e1 ,,ll4,b4 7,camb471 ( ,l9coln's ,inn1 ,b>ri/]-at-,law1 ,au?or ( ,! ,fir/ ,twelve ,c5turies ( ,briti% ,/ory1 & o!r works4 ,cr[n #hvo4 #fs4 net4 ,a consid]ation ( ! successive phases ( ,hi/orical ,rese>*2 x expla9s necess>y processes ?r\gh :i* all ! mat]ial has to pass be=e x is plac$ be=e u z hi/ory4 ,,london3 ,,williams ,,& ,,norgate ,,"s ,,books ,,on ,,russia ,,& ,,pol& ,) a ,col\r$ ,frontispiece1 #ab ,photogravure ,plates1 #bh ,illu/rations 9 ! text1 & #h ,maps4 ,demy #hvo4 #gs4 #f;d4 net 7po/age #f;d4 extra74 ,a ,?\s& ,ye>s ( ,russian ,hi/ory ,by ,,sonia ,e4 ,,h[e4 ,we c recomm5d ! volume z an excell5t1 c>eful1 & well-writt5 hi/ory ( a great nation4--,daily ,telegraph4 ,demy #hvo4 ,clo?1 #fs4 net4 ,! ,false ,dmitri ,a ,russian ,romance & ,trag$y4 ,describ$ by ,briti% ,eye-witnesses1 #afjd-afab4 ,edit$ ) a ,preface by ,,sonia ,e4 ,,h[e4 ,illu/rat$ by reproduction ( contempor>y portraits4 ,) m ?an a :iff ( ! atmosph]e ,hakluyt got into 8 fam\s volume4--,nor!rn ,:ig4 ,( special int]e/ at ! pres5t "t4--,ox=d ,*ronicle4 ,) #af ,plates & #bh ,illu/rations 9 ! text4 ,demy #hvo4 #gs4 #f;d4 net4 ,"s ,russian ,h]oes1 ,sa9ts & ,s9n]s ,a portrait gall]y ( out/&+ figures 9 ,russian hi/ory :o 7 typical ( _! times & _! c\ntry4 ,by ,,sonia ,e4 ,,h[e4 ,x gives a vivid /udy ( ,russia 444 & int]e/+ book4--,l& & ,wat]4 ,fcap4 #hvo4 ,clo?1 #as4 #c;d4 net4 ,9 full lea!r pres5tation b9d+1 #bs4 #f;d4 net4 ,an ,outl9e ( ,russian ,lit]ature ,by ! ,hon4 ,,maurice ,,b>+1 ,au?or ( ,) ! ,russians 9 ,man*uria1 ,a ,ye> 9 ,russia1 ,! ,russian ,p1 etc4 ,gives a cle> & int]e/+ acc\nt ( ! gr[? ( ,russian lit]ature4 ,fcap4 #hvo4 ,clo?1 #as4 #c;d4 net4 ,9 full lea!r b9d+1 #bs4 #f;d4 net4 ,pol& ,by ,w4 ,,alison ,,phillips1 ,m4,a41 ,lecky ,pr(essor ( ,mod]n ,hi/ory 9 ! ,univ]sity ( ,dubl94 ,a concise survey ( ! ,hi/ory ( ,pol& up to #aiae4 ,,london3 ,,williams ,,& ,,norgate #ad ,,h5rietta ,,/reet1 ,,cov5t ,,g>d51 ,w4,c4 ,,transcrib]',s ,,notes ,simple typographical errors h be5 sil5tly correct$2 unbalanc$ quotation m>ks 7 rem$i$ :5 ! *ange 0 obvi\s1 & o!rwise left unbalanc$4 ,punctuation1 hyph5ation1 & spell+ 7 made consi/5t :5 a pr$om9ant pref]5ce 0 f\nd 9 ! orig9al book2 o!rwise !y 7 n *ang$4