pg-i ,,symbolic ,,logic ,by ,lewis ,c>roll pg-ii pg-iii pg-iv ,a ,syllogism work$ out4 ,t /ory ( y\rs1 ab\t y\r once meet+ ! sea-s]p5t1 always sets me (f yawn+2 ,i nev] yawn1 unless :5 ,i'm li/5+ to some?+ totally devoid ( int]e/4 ,! ,premisses1 sep>ately4 --------------- --------------- 7 7 7 7 ------ ------ 77 7 7 ------------ ------------ 7 7 ------ ------ --------------- --------------- ,! ,premisses1 comb9$4 --------------- 7 7 7 7 ------ 777 7 ------------ 7 7 ------ --------------- ,! ,conclusion4 ------- 777 7 ------ ------- ,t /ory ( y\rs1 ab\t y\r once meet+ ! sea-s]p5t1 is totally devoid ( int]e/4 pg-v ,,symbolic ,,logic ,,"p ,i ,,elem5t>y ,,by ,,lewis ,,c>roll ,,second ,,?\s& ,,f\r? ,,edition ,,price ,,two ,,%ill+s ,london ,,macmillan ,,& ,,co41 ,,limit$ ,,new ,,york3 ,,! ,,macmillan ,,company #ahig ,all rights res]v$ pg-vi ,,ri*>d ,,clay ,,& ,,sons1 ,,limit$1 ,,london ,,& ,,bungay pg-vii ,,adv]tisem5t4 ,an envelope1 conta9+ two blank ,diagrams 7,bilit]al & ,trilit]al7 & #i c\nt]s 7#d ,r$ & #e ,grey71 may be _h1 f ,messrs4 ,macmillan1 = #c;d41 by po/ #d;d4 99 99 99 99 99 ,i %all be grateful to any ,read] ( ?is book :o w po9t out any mi/akes or mispr9ts he may happ5 to notice 9 x1 or any passage :i* he ?9ks is n cle>ly express$4 99 99 99 99 99 ,i h a quantity ( ,,ms4 9 h& = ,p>ts ,,ii & ,,iii1 & hope to be able----%\ld life1 & heal?1 & opportunity1 be grant$ to me1 to publi% !m 9 ! c\rse ( ! next few ye>s4 ,_! cont5ts w be z foll[s3-- ,,"p ,,ii4 ,,advanc$4 ,fur!r inve/igations 9 ! subjects ( ,"p ,i4 ,propositions ( o!r =ms 7su* z ,n-all x are y74 ,trilit]al & ,multilit]al ,propositions 7su* z ,all abc are de74 ,hypo!ticals4 ,dilemmas4 c4 c4 ,"p ,,iii4 ,,transc5d5tal4 ,analysis ( a ,proposition into its ,elem5ts4 ,num]ical & ,geometrical ,problems4 ,! ,!ory ( ,inf]5ce4 ,! ,con/ruction ( ,problems4 ,& _m o!r ,curiosa ,logica4 pg-viii ,,preface ,,to ,,! ,,f\r? ,,edition4 ,! *ief alt]ations1 s9ce ! ,fir/ ,edition1 h be5 made 9 ! ,*apt] on ',classification' 7pp4 #b1 #c7 & ! ,book on ',propositions' 7pp4 #aj to #ai74 ,! *ief additions h be5 ! que/ions on words & phrases1 add$ to ! ,exam9ation-,pap]s at p4 #id1 & ! ,notes ins]t$ at pp4 #afd1 #aid4 ,9 ,book ,i1 ,*apt] ,,ii1 ,i h adopt$ a new def9ition ( ',classification'1 :i* enables me to reg>d ! :ole ,univ]se z a ',class1' & ?us to disp5se ) ! v awkw>d phrase 'a ,set ( ,?+s4' ,9 ! ,*apt] on ',propositions ( ,exi/5ce' ,i h adopt$ a new 'normal =m1' 9 :i* ! ,class1 ^: exi/5ce is affirm$ or d5i$1 is reg>d$ z ! ,pr$icate1 in/ead ( ! ,subject1 ( ! ,proposition1 ?us evad+ a v subtle difficulty :i* besets ! o!r =m4 ,^! subtle difficulties seem to lie at ! root ( e ,tree ( ,k1 & !y are f> m hopeless to grapple ) ?an any t occur 9 its high] bran*es4 ,= example1 ! difficulties ( ! ,=ty-,sev5? ,proposition ( ,euclid are m]e *ild's play comp>$ ) ! m5tal torture endur$ 9 ! ef=t to ?9k out ! ess5tial nature ( a /raight ,l9e4 ,&1 9 ! pres5t "w1 ! difficulties ( ! #e ,li>s ,problem1 at p4 #aib1 are trifles1 light z air1 comp>$ ) ! bewild]+ "q ,:at is a ,?+8 ,9 ! ,*apt] on ',propositions ( ,relation' ,i h ins]t$ a new ,section1 conta9+ ! pro( t a ,proposition1 beg9n+ ) ,all1 is a ,d\ble ,proposition 7a fact t is q indep5d5t ( ! arbitr>y rule1 laid d[n 9 ! next ,section1 t su* a ,proposition is to be und]/ood z imply+ ! actual exi/5ce ( its ,subject74 ,?is pro( 0 giv51 9 ! e>li] editions1 incid5tally1 9 ! c\rse ( ! discussion ( ! ,bilit]al ,diagram3 b its prop] place1 9 ?is treatise1 is :]e ,i h n[ introduc$ x4 pg-ix ,9 ! ,sorites-,examples1 ,i h made a good _m v]bal alt]ations1 9 ord] to evade a difficulty1 :i* ,i fe> w h p]plex$ "s ( ! ,read]s ( ! fir/ ?ree ,editions4 ,"s ( ! ,premisses 7 s word$ t _! ,t]ms 7 n ,specieses ( ! ,univ4 nam$ 9 ! ,diction>y1 b ( a l>g] ,class1 ( :i* ! ,univ4 0 only a portion4 ,9 all su* cases1 x 0 int5d$ t ! ,read] %\ld p]ceive t :at 0 ass]t$ ( ! l>g] ,class 0 !reby ass]t$ ( ! ,univ41 & %\ld ignore1 z sup]flu\s1 all t x ass]t$ ( its o!r portion4 ,?us1 9 ,ex4 #ae1 ! ,univ4 0 /at$ to be ducks 9 ?is village1 & ! ?ird ,premiss 0 ,mrs4 ,bond has no gray ducks1 i4e4 ,no gray ducks are ducks belong+ to ,mrs4 ,bond4 ,"h ! ,t]ms are n ,specieses ( ! ,univ41 b ( ! l>g] ,class ducks1 ( :i* ! ,univ4 is only a portion3 & x 0 int5d$ t ! ,read] %\ld p]ceive t :at is "h ass]t$ ( ducks is !reby ass]t$ ( ducks 9 ?is village4 & %\ld treat ?is ,premiss z if x 7 ,mrs4 ,bond has no gray ducks 9 ?is village1 & %\ld ignore1 z sup]flu\s1 :at x ass]ts z to ! o!r portion ( ! ,class ducks1 viz4 ,mrs4 ,bond has no gray ducks out ( ?is village4 ,9 ! ,app5dix ,i h giv5 a new v]sion ( ! ,problem ( ! ,five ,li>s4 ,my object1 9 do+ s1 is to escape ! subtle & my/]i\s difficulties :i* beset all attempts at reg>d+ a ,proposition z be+ its own ,subject1 or a ,set ( ,propositions z be+ ,subjects = "o ano!r4 ,x is c]ta9ly1 a mo/ bewild]+ & unsatisfactory !ory3 "o _c help feel+ t !re is a great lack ( sub/ance 9 all ?is %ad[y ho/----t1 z ! procession ( phantoms glides be=e u1 !re is n "o t we c p\nce ^u1 & say ,"h is a ,proposition t mu/ be ei!r true or false6----t x is b a ,b>mecide ,fea/1 to :i* we h be5 bidd5----& t its prototype is to be f\nd 9 t my?ical isl&1 ^: inhabitants e>n$ a prec>i\s liv+ by tak+ 9 ea* o!rs' wa%+6 ,by simply translat+ tell+ #b ,tru?s into tak+ bo? ( #b condim5ts 7salt & mu/>d71 tell+ #b ,lies into tak+ nei!r ( !m & tell+ a ,tru? & a ,lie 7ord] n specifi$7 into tak+ only "o condim5t 7x is n specifi$ :i*71 ,i h escap$ all ^? metaphysical puzzles1 & h produc$ a ,problem :i*1 :5 translat$ into a ,set ( symboliz$ ,premisses1 furni%es ! v same ,data z 7 furni%$ by ! ,problem ( ! ,five ,li>s4 pg-x ,! co9$ words1 introduc$ 9 previ\s editions1 su* z ,elim9&s & ,ret95ds1 p]haps h>dly ne$ any apology3 !y 7 indisp5sable to my sy/em3 b ! new plural1 "h us$ = ! fir/ "t1 viz4 ,soriteses1 w1 ,i fe>1 be condemn$ z bad ,engli%1 unless ,i say a ^w 9 its def5ce4 ,we h ?ree s+ul> n\ns1 9 ,engli%1 ( plural =m1 s]ies1 species1 & ,sorites3 9 all ?ree1 ! awkw>dness1 ( us+ ! same ^w = bo? s+ul> & plural1 mu/ (t5 h be5 felt3 ?is has be5 rem$i$1 9 ! case ( s]ies by co9+ ! plural s]ieses1 :i* has already f\nd its way into ! diction>ies3 s ,i am no ra% innovator1 b am m]ely foll[+ suit1 9 us+ ! new plural ,soriteses4 ,9 conclusion1 let me po9t out t ev5 ^?1 :o are oblig$ to /udy ,=mal ,logic1 ) a view to be+ able to answ] ,exam9ation-,pap]s 9 t subject1 w f9d ! /udy ( ,symbolic ,logic mo/ helpful = ?is purpose1 9 ?r[+ light ^u _m ( ! obscurities ) :i* ,=mal ,logic ab\nds1 & 9 furni%+ a delightfully easy me?od ( te/+ ! results arriv$ at by ! cumbr\s processes :i* ,=mal ,logic en=ces ^u its vot>ies4 ,?is is1 ,i believe1 ! v fir/ attempt 7) ! exception ( my own little book1 ,! ,game ( ,logic1 publi%$ 9 #ahhf1 a v incomplete p]=mance7 t has be5 made to popul>ise ?is fasc9at+ subject4 ,x has co/ me ye>s ( h>d "w3 b if x %\ld prove1 z ,i hope x may1 to be ( real s]vice to ! "y1 & to be tak5 up1 9 ,high ,s*ools & 9 private families1 z a valuable addition to _! /ock ( heal?ful m5tal recreations1 su* a result w\ld m ?an repay t5 times ! lab\r t ,i h exp5d$ on x4 ,l4 ,c4 #bi1 ,,b$=d ,,/reet1 ,,/r&4 ,*ri/mas1 #ahif4 pg-xi ,,introduction4 ,,to ,,le>n]s4 ,n4,b4 ,"s rem>ks1 address$ to ,tea*]s1 w be f\nd 9 ! ,app5dix1 at p4 #afe4 ,! ,le>n]1 :o wi%es to try ! "q fairly1 :e!r ?is little book does1 or does n1 supply ! mat]ials = a mo/ int]e/+ m5tal recreation1 is e>ne/ly advis$ to adopt ! foll[+ ,rules3-- 7#a7 ,beg9 at ! beg9n+1 & d n all[ y\rself to gratify a m]e idle curiosity by dipp+ into ! book1 "h & !re4 ,?is w\ld v likely lead to y\r ?r[+ x aside1 ) ! rem>k ,?is is mu* too h>d = me61 & ?us los+ ! *ance ( add+ a v l>ge item to y\r /ock ( m5tal delights4 ,?is ,rule 7( n dipp+7 is v desirable ) o!r k9ds ( books----su* z novels1 = in/ance1 :]e y may easily spoil mu* ( ! enjoym5t y w\ld o!rwise get f ! /ory1 by dipp+ into x fur!r on1 s t :at ! au?or meant to be a pleasant surprise comes to y z a matt] ( c\rse4 ,"s p1 ,i "k1 make a practice ( look+ into ,vol4 ,,iii fir/1 j to see h[ ! /ory ends3 & p]haps x is z well j to "k t all ends happily----t ! mu*-p]secut$ lov]s d m>ry aft] all1 t he is prov$ to be q innoc5t ( ! murd]1 t ! wick$ c\s9 is completely foil$ 9 8 plot & gets ! puni%m5t he des]ves1 & t ! ri* uncle 9 ,india 7,qu4 ,:y 9 ,india8 ,ans4 ,because1 someh[1 uncles nev] c get ri* any:]e else7 dies at exactly ! "r mom5t----be=e tak+ ! tr\ble to read ,vol4 ,i4 ,?is1 ,i say1 is j p]missible ) a novel1 :]e ,vol4 ,,iii has a mean+1 ev5 = ^? :o h n read ! e>li] "p ( ! /ory2 b1 ) a sci5tific book1 x is %e] insanity3 y w f9d ! latt] "p hopelessly un9telligible1 if y read x be=e rea*+ x 9 regul> c\rse4 pg-xii 7#b7 ,don't beg9 any fre% ,*apt]1 or ,section1 until y are c]ta9 t y ?or\ghly und]/& ! :ole book up to t po9t1 & t y h work$1 correctly1 mo/ if n all ( ! examples :i* h be5 set4 ,s long z y are consci\s t all ! l& y h pass$ ?r\gh is absolutely conqu]$1 & t y are leav+ no unsolv$ difficulties beh9d y1 :i* w be sure to turn up aga9 lat] on1 y\r triumphal progress w be easy & delightful4 ,o!rwise1 y w f9d y\r /ate ( puzzlem5t get worse & worse z y proce$1 till y give up ! :ole ?+ 9 utt] disgu/4 7#c7 ,:5 y come to any passage y don't und]/&1 read x aga93 if y /ill don't und]/& x1 read x aga93 if y fail1 ev5 aft] ?ree read+s1 v likely y\r bra9 is gett+ a little tir$4 ,9 t case1 put ! book away1 & take to o!r occupations1 & next day1 :5 y come to x fre%1 y w v likely f9d t x is q easy4 7#d7 ,if possible1 f9d "s g5ial fri5d1 :o w read ! book along ) y1 & w talk ov] ! difficulties ) y4 ,talk+ is a wond]ful smoo!r-ov] ( difficulties4 ,:5 ,i come ^u any?+----9 ,logic or 9 any o!r h>d subject----t entirely puzzles me1 ,i f9d x a capital plan to talk x ov]1 al\d1 ev5 :5 ,i am all alone4 ,"o c expla9 ?+s s cle>ly to "o's self6 ,& !n1 y "k1 "o is s pati5t ) "o's self3 "o nev] gets irritat$ at "o's own /upidity6 ,if1 de> ,read]1 y w fai?fully obs]ve ^! ,rules1 & s give my little book a really fair trial1 ,i promise y1 mo/ confid5tly1 t y w f9d ,symbolic ,logic to be "o ( ! mo/1 if n ! mo/1 fasc9at+ ( m5tal recreations6 ,9 ?is ,fir/ ,"p1 ,i h c>efully avoid$ all difficulties :i* seem$ to me to be beyond ! grasp ( an intellig5t *ild ( 7say7 twelve or f\rte5 ye>s ( age4 ,i h myself taught mo/ ( its cont5ts1 viv voce1 to _m *ildr51 & h f\nd !m take a real intellig5t int]e/ 9 ! subject4 ,= ^?1 :o succe$ 9 ma/]+ ,"p ,i1 & :o beg91 l ,oliv]1 ask+ = m1 ,i hope to provide1 9 ,"p ,,ii1 "s tol]ably h>d nuts to crack----nuts t w require all ! nut-crack]s !y happ5 to possess6 pg-xiii ,m5tal recreation is a ?+ t we all ( u ne$ = our m5tal heal?2 & y may get mu* heal?y enjoym5t1 no d\bt1 f ,games1 su* z ,back-gammon1 ,*ess1 & ! new ,game ,halma4 ,b1 aft] all1 :5 y h made y\rself a fir/-rate play] at any "o ( ^! ,games1 y h no?+ real to %[ = x1 z a result6 ,y enjoy$ ! ,game1 & ! victory1 no d\bt1 at ! "t3 b y h no result t y c treasure up & get real good out (4 ,&1 all ! :ile1 y h be5 leav+ unexplor$ a p]fect m9e ( weal?4 ,once ma/] ! ma*9]y ( ,symbolic ,logic1 & y h a m5tal occupation always at h&1 ( absorb+ int]e/1 & "o t w be ( real use to y 9 any subject y may take up4 ,x w give y cle>ness ( ?\ght----! ability to see y\r way ?r\gh a puzzle----! habit ( arrang+ y\r ideas 9 an ord]ly & get-at-able =m----&1 m valuable ?an all1 ! p[] to detect fallacies1 & to te> to pieces ! flimsy illogical argum5ts1 :i* y w s cont9ually enc\nt] 9 books1 9 newspap]s1 9 spee*es1 & ev5 9 s]mons1 & :i* s easily delude ^? :o h nev] tak5 ! tr\ble to ma/] ?is fasc9at+ ,art4 ,try x4 ,t is all ,i ask ( y6 ,l4 ,c4 #bi1 ,,b$=d ,,/reet1 ,,/r&4 ,febru>y #ba1 #ahif4 pg-xiv pg-xv ,,cont5ts4 ,,book ,i4 ,,?+s ,,& ,,_! ,,attributes4 ,,*apt] ,i4 ,,introductory4 ,,page ',?+s' #a ',attributes' ',adjuncts' ,,*apt] ,,ii4 ,,classification4 ',classification' #a ',class' ',peculi>' ,attributes ',g5us' ',species' ',diff]5tia' ',real' & ',unreal'1 or ',imag9>y'1 ,classes #b ',individual' ,a ,class reg>d$ z a s+le ,?+ #b pg-xvi ,,*apt] ,,iii4 ,,division4 #a4 ,introductory4 ',division' #c ',codivisional' ,classes #b4 ,di*otomy4 ',di*otomy' #c ,arbitr>y limits ( ,classes ,subdivision ( ,classes #d ,,*apt] ,,iv4 ,,names4 ',"n' #d ',real' & ',unreal' ,names ,?ree ways ( express+ a ,"n ,two s5ses 9 :i* a plural ,"n may be us$ #e ,,*apt] ,v4 ,,def9itions4 ',def9ition' #f ,examples work$ z models pg-xvii ,,book ,,ii4 ,,propositions4 ,,*apt] ,i4 ,,propositions ,,g5]ally4 #a4 ,introductory4 ,te*nical mean+ ( "s #h ',proposition' ',normal =m' ( a ,proposition ',subject'1 ',pr$icate'1 & ',t]ms' #i #b4 ,normal =m ( a ,proposition4 ,its f\r p>ts3-- 7#a7 ',sign ( ,quantity' #i 7#b7 ,"n ( ,subject 7#c7 ',copula' 7#d7 ,"n ( ,pr$icate #c4 ,v>i\s k9ds ( ,propositions4 ,?ree k9ds ( ,propositions3-- 7#a7 ,beg9s ) ,"s4 ,call$ a ',p>ticul>' ,proposition3 also a ,proposition '9 ,i' #aj 7#b7 ,beg9s ) ,no4 ,call$ a ',univ]sal ,negative' ,proposition3 also a ,proposition '9 ,e' 7#c7 ,beg9s ) ,all4 ,call$ a ',univ]sal ,affirmative' ,proposition3 also a ,proposition '9 ,a' pg-xviii ,a ,proposition1 ^: ,subject is an ,individual1 is to be reg>d$ z ,univ]sal ,two k9ds ( ,propositions1 ',propositions ( ,exi/5ce'1 & ',propositions ( ,relation' ,,*apt] ,,ii4 ,,propositions ,,( ,,exi/5ce4 ',proposition ( ,exi/5ce ' #aa ,,*apt] ,,iii4 ,,propositions ,,( ,,relation4 #a4 ,introductory4 ',proposition ( ,relation' #ab ',univ]se ( ,disc\rse1' or ',univ4' #b4 ,r$uction ( a ,proposition ( ,relation to ,normal =m4 ,rules #ac ,examples work$ #c4 ,a ,proposition ( ,relation1 beg9n+ ) ,all1 is a ,d\ble ,proposition4 ,its equival5ce to two ,propositions #ag pg-xix #d4 ,:at is impli$1 9 a ,proposition ( ,relation1 z to ! ,reality ( its ,t]ms8 ,propositions beg9n+ ) ,"s #ai ,no ,all #e4 ,translation ( a ,proposition ( ,relation into "o or m ,propositions ( ,exi/5ce4 ,rules #bj ,examples work$ ,,book ,,iii4 ,,! ,,bilit]al ,,diagram4 ,,*apt] ,i4 ,,symbols ,,& ,,cells4 ,! ,diagram assign$ to a c]ta9 ,set ( ,?+s1 viz4 our ,univ4 #bb ,univ4 divid$ into '! x-,class' & '! x'-,class' #bc ,! ,nor? & ,s\? ,halves assign$ to ^! two ,classes ,! x-,class subdivid$ into '! xy-,class' & '! xy'-,class' ,! ,nor?-,we/ & ,nor?-,ea/ ,cells assign$ to ^! two ,classes ,! x'-,class simil>ly divid$ ,! ,s\?-,we/ & ,s\?-,ea/ ,cells simil>ly assign$ ,! ,we/ & ,ea/ ,halves h ?us be5 assign$ to '! y-,class' & '! y'-,class' #bd ,table ,i4 ,attributes ( ,classes1 & ,comp>tm5ts1 or ,cells1 assign$ to !m #be pg-xx ,,*apt] ,,ii4 ,,c\nt]s4 ,mean+ ( a ,r$ ,c\nt] plac$ 9 a ,cell #bf on a ,p>tition ,am]ican phrase sitt+ on ! f5ce ,mean+ ( a ,grey ,c\nt] plac$ 9 a ,cell ,,*apt] ,,iii4 ,,repres5tation ,,( ,,propositions4 #a4 ,introductory4 ,! ^w ,?+s to be h5ce=w>ds omitt$ #bg ',unilit]al' ,proposition ',bilit]al' d4 ,proposition '9 t]ms (' c]ta9 ,lett]s #b4 ,repres5tation ( ,propositions ( ,exi/5ce4 ,! ,proposition ,"s x exi/ #bh ,?ree o!r simil> ,propositions ,! ,proposition ,no x exi/ ,?ree o!r simil> ,propositions #bi ,! ,proposition ,"s xy exi/ ,?ree o!r simil> ,propositions ,! ,proposition ,no xy exi/ ,?ree o!r simil> ,propositions ,! ,proposition ,no x exi/ is ,d\ble1 & is equival5t to ! two ,propositions ,no xy exi/ & ,no xy' exi/ #cj pg-xxi #c4 ,repres5tation ( ,propositions ( ,relations4 ,! ,proposition ,"s x are y ,?ree o!r simil> ,propositions ,! ,proposition ,"s y are x #ca ,?ree o!r simil> ,propositions ,trio ( equival5t ,propositions1 viz4 ,"s xy exi/ ,"s x are y ,"s y are x ',conv]se' ,propositions1 & ',conv]sion' ,?ree o!r simil> ,trios #cb ,! ,proposition ,no x are y ,?ree o!r simil> ,propositions ,! ,proposition ,no y are x ,?ree o!r simil> ,propositions ,trio ( equival5t ,propositions1 viz4 ,no xy exi/ ,no x are y ,no y are x #cc ,?ree o!r simil> ,trios ,! ,proposition ,all x are y is ,d\ble1 & is equival5t to ! two ,propositions ,"s x are y & ,no x are y' ,sev5 o!r simil> ,propositions #cd ,tables ,,ii1 ,,iii4 ,repres5tation ( ,propositions ( ,exi/5ce & ,relation #cd1 #ce ,,*apt] ,,iv4 ,,int]pretation ,,( ,,bilit]al ,,diagram1 ,,:5 ,,m>k$ ,,) ,,c\nt]s4 ------- 747 ,int]pretation ( ------ #cf ------- ,& ( ?ree o!r simil> arrangem5ts pg-xxii ------- 7 7 ,int]pretation ( ------ ------- ,& ( ?ree o!r simil> arrangem5ts ------- 747 ,int]pretation ( ------ #cg ------- ,& ( ?ree o!r simil> arrangem5ts ------- 747747 ,int]pretation ( ------ ------- ,& ( ?ree o!r simil> arrangem5ts ------- 7 77 7 ,int]pretation ( ------ ------- ,& ( ?ree o!r simil> arrangem5ts ------- 7477 7 ,int]pretation ( ------ ------- ,& ( sev5 o!r simil> arrangem5ts #ch ,,book ,,iv4 ,,! ,,trilit]al ,,diagram4 ,,*apt] ,i4 ,,symbols ,,& ,,cells4 ,*ange ( ,bilit]al into ,trilit]al ,diagram #ci ,! xy-,class subdivid$ into '! xym-,class' & '! xym'-,class' #dj pg-xxiii ,! ,inn] & ,out] ,cells ( ! ,nor?-,we/ ,qu>t] assign$ to ^! ,classes ,! xy'-,class1 ! x'y-,class1 & ! x'y'-,class simil>ly subdivid$ ,! ,inn] & ,out] ,cells ( ! ,nor?-,ea/1 ! ,s\?-,we/1 & ! ,s\?-,ea/ ,qu>t] simil>ly assign$ ,! ,inn] ,squ>e & ! ,out] ,bord] h ?us be5 assign$ to '! m-,class' & '! m'-,class' ,rules = f9d+ readily ! ,comp>tm5t1 or ,cell1 assign$ to any giv5 ,attribute or ,attributes ,table ,,iv4 ,attributes ( ,classes1 & ,comp>tm5ts1 or ,cells1 assign$ to !m #db ,,*apt] ,,ii4 ,,repres5tation ,,( ,,propositions ,,9 ,,t]ms ,,( x ,,& m1 ,,or ,,( y ,,& m4 #a4 ,repres5tation ( ,propositions ( ,exi/5ce 9 t]ms ( x & m1 or ( y & m4 ,! ,proposition ,"s xm exi/ #dc ,sev5 o!r simil> ,propositions ,! ,proposition ,no xm exi/ #dd ,sev5 o!r simil> ,propositions #b4 ,repres5tation ( ,propositions ( ,relation 9 t]ms ( x & m1 or ( y & m4 ,! ,pair ( ,conv]se ,propositions ,"s x are m ,"s m are x ,sev5 o!r simil> ,pairs ,! ,pair ( ,conv]se ,propositions ,no x are m ,no m are x ,sev5 o!r simil> ,pairs ,! ,proposition ,all x are m #de ,fifte5 o!r simil> ,propositions ,tables ,v1 ,,vi1 ,,vii1 ,,viii4 ,repres5tations ( ,propositions 9 t]ms ( x & m1 or ( y & m #df to #di pg-xxiv ,,*apt] ,,iii4 ,,repres5tation ,,( ,,two ,,propositions ,,( ,,relation1 ,,"o ,,9 ,,t]ms ,,( x ,,& m1 ,,& ,,! ,,o!r ,,9 ,,t]ms ,,( y ,,& m1 ,,on ,,! ,,same ,,diagram4 ,! ,digits ,i & ,o to be us$ in/ead ( ,r$ & ,grey ,c\nt]s #ej ,rules ,examples work$ ,,*apt] ,,iv4 ,,int]pretation1 ,,9 ,,t]ms ,,( x ,,& y1 ,,( ,,trilit]al ,,diagram1 ,,:5 ,,m>k$ ,,) ,,c\nt]s ,,or ,,digits4 ,rules #ec ,examples work$ #ed ,,book ,v4 ,,syllogisms4 ,,*apt] ,i4 ,,introductory4 ',syllogism' #ef ',premisses' ',conclusion' ',elim9&s' #eg ',ret95ds' ',consequ5t' ,! ,symbol 4'4 ,specim5-,syllogisms pg-xxv ,,*apt] ,,ii4 ,,problems ,,9 ,,syllogisms4 #a4 ,introductory4 ',concrete' & ',ab/ract' ,propositions #ei ,me?od ( translat+ a ,proposition f concrete into ab/ract =m ,two =ms ( ,problems #b4 ,giv5 a ,pair ( ,propositions ( ,relation1 :i* conta9 betwe5 !m a ,pair ( codivisional ,classes1 & :i* are propos$ z ,premisses3 to asc]ta9 :at ,conclusion1 if any1 is consequ5t f !m4 ,rules #fj ,examples work$ fully ,! same work$ briefly1 z models #fd #c4 ,giv5 a ,trio ( ,propositions ( ,relation1 ( :i* e two conta9 a ,pair ( codivisional ,classes1 & :i* are propos$ z a ,syllogism3 to asc]ta9 :e!r ! propos$ ,conclusion is consequ5t f ! propos$ ,premisses1 &1 if s1 :e!r x is complete4 ,rules #ff ,examples work$ briefly1 z models pg-xxvi ,,book ,,vi4 ,,! ,,me?od ,,( ,,subscripts4 ,,*apt] ,i4 ,,introductory4 ,mean+ ( x#a1 xy#a1 c4 #gj ',entity' ,mean+ ( x#j1 xy#j1 c4 ',nullity' ,! ,symbols & ',l' & 'unlike' ,signs ,,*apt] ,,ii4 ,,repres5tation ,,( ,,propositions ,,( ,,relation4 ,! ,pair ( ,conv]se ,propositions ,"s x are y ,"s y are x #ga ,?ree o!r simil> ,pairs ,! ,pair ( ,conv]se ,propositions ,no x are y ,no y are x ,?ree o!r simil> ,pairs ,! ,proposition ,all x are y #gb ,! ,proposition ,all x are y is ,d\ble1 & is equival5t to ! two ,propositions ,"s x exi/ & ,no x & y' ,sev5 o!r simil> ,propositions ,rule = translat+ ,all x are y f ab/ract into subscript =m1 & vice v]s pg-xxvii ,,*apt] ,,iii4 ,,syllogisms4 #a4 ,repres5tation ( ,syllogisms4 ,rules #gc #b4 ,=mul = ,syllogisms4 ,?ree ,=mul work$ out3-- ,fig4 ,i4 xm#j ym'#j xy#j #ge its two ,v>iants 7a7 & 7b7 ,fig4 ,,ii4 xm#j ym#a x'y#a #gf ,fig4 ,,iii4 xm#j ym#j m#a x'y'#a #gg ,table ,,ix4 ,=mul & ,rules #gh ,examples work$ briefly1 z models #c4 ,fallacies4 ',fallacy' #ha ,me?od ( f9d+ ,=ms ( ,fallacies #hb ,=ms be/ /at$ 9 words ,?ree ,=ms ( ,fallacies3-- 7#a7 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/ 7#b7 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss #hc 7#c7 ,fallacy ( two ,entity-,premisses #d4 ,me?od ( proce$+ ) a giv5 ,pair ( ,propositions4 ,rules #hd pg-xxviii ,,book ,,vii4 ,,soriteses4 ,,*apt] ,i4 ,,introductory4 ',sorites' #he ',premisses' ',p>tial ,conclusion' ',complete ,conclusion' 7or ',conclusion'7 ',elim9&s' ',ret95ds' 'consequ5t' ,! ,symbol 4'4 ,specim5-,soriteses #hf ,,*apt] ,,ii4 ,,problems ,,9 ,,soriteses4 #a4 ,introductory4 ,=m ( ,problem #hg ,two ,me?ods ( ,solution #b4 ,solution by ,me?od ( ,sep>ate ,syllogisms4 ,rules #hh ,example work$ pg-xxix #c4 ,solution by ,me?od ( ,und]scor+4 ',und]scor+' #ia ,subscripts to be omitt$ ,example work$ fully #ib ,example work$ briefly1 z model #ic ,sev5te5 ,exam9ation-,pap]s #id ,,book ,,viii4 ,,examples1 ,,) ,,answ]s ,,& ,,solutions4 ,,*apt] ,i4 ,,examples4 #a4 ,propositions ( ,relation1 to be r$uc$ to normal =m #ig #b4 ,pairs ( ,ab/ract ,propositions1 "o 9 t]ms ( x & m1 & ! o!r 9 t]ms ( y & m1 to be repres5t$ on ! same ,trilit]al ,diagram #ih #c4 ,m>k$ ,trilit]al ,diagrams1 to be int]pret$ 9 t]ms ( x & y #ii #d4 ,pairs ( ,ab/ract ,propositions1 propos$ z ,premisses3 ,conclusions to be f\nd #ajj pg-xxx #e4 ,pairs ( ,concrete ,propositions1 propos$ z ,premisses3 ,conclusions to be f\nd #aja #f4 ,trios ( ,ab/ract ,propositions1 propos$ z ,syllogisms3 to be exam9$ #ajf #g4 ,trios ( ,concrete ,propositions1 propos$ z ,syllogisms3 to be exam9$ #ajg #h4 ,sets ( ,ab/ract ,propositions1 propos$ z ,premisses = ,soriteses3 ,conclusions to be f\nd #aaj #i4 ,sets ( ,concrete ,propositions1 propos$ z ,premisses = ,soriteses3 ,conclusions to be f\nd #aab ,,*apt] ,,ii4 ,,answ]s4 ,answ]s to #a #abe #b #abf #c1 #d #abg #e #abh #f #acj #g #aca #h1 #i #acb pg-xxxi ,,*apt] ,,iii4 ,,solutions4 #a4 ,propositions ( ,relation r$uc$ to normal =m4 ,solutions = #a #acd #b4 ,me?od ( ,diagrams4 ,solutions = #d ,nos4 #a to #ab #acf #e #a to #ab #ach #f #a to #aj #ada #g #a to #f #add #c4 ,me?od ( ,subscripts4 ,solutions = #d #adf #e ,nos4 #ac to #bd #adg #f1 #g1 #h1 #i #adh to #aeg ,,notes #afd ,,app5dix1 ,,address$ ,,to ,,tea*]s #afe ,,notes ,,to ,,app5dix #aie ,,index4 #a4 ,tables #aig #b4 ,words c4 expla9$ pg-xxxii pg#jja ,,book ,i4 ,,?+s ,,& ,,_! ,,attributes4 ,,*apt] ,i4 ,,introductory4 ,! ,univ]se conta9s ',?+s4' ,= example1 ,i1 ,london1 roses1 r$ness1 old ,engli% books1 ! lett] :i* ,i receiv$ ye/]day4 ,?+s h ',attributes4' ,= example1 l>ge1 r$1 old1 :i* ,i receiv$ ye/]day4 ,"o ,?+ may h _m ,attributes2 & "o ,attribute may belong to _m ,?+s4 ,?us1 ! ,?+ a rose may h ! ,attributes r$1 sc5t$1 full-bl[n1 c42 & ! ,attribute r$ may belong to ! ,?+s a rose1 a brick1 a ribbon1 c4 ,any ,attribute1 or any ,set ( ,attributes1 may be call$ an ',adjunct4' ,?is ^w is introduc$ 9 ord] to avoid ! con/ant repetition ( ! phrase ,attribute or ,set ( ,attributes4 ,?us1 we may say t a rose has ! ,attribute r$ 7or ! ,adjunct r$1 :i*ev] we pref]72 or we may say t x has ! ,adjunct r$1 sc5t$ & full-bl[n4 pg#jja ,,*apt] ,,ii4 ,,classification4 ',classification1' or ! =mation ( ,classes1 is a ,m5tal ,process1 9 :i* we imag9e t we h put toge!r1 9 a gr\p1 c]ta9 ,?+s4 ,su* a gr\p is call$ a ',class4' ,?is ,process may be p]=m$ 9 ?ree diff]5t ways1 z foll[s3-- 7#a7 ,we may imag9e t we h put toge!r all ,?+s4 ,! ,class s =m$ 7i4e4 ! ,class ,?+s7 conta9s ! :ole ,univ]se4 7#b7 ,we may ?9k ( ! ,class ,?+s1 & may imag9e t we h pick$ out f x all ! ,?+s :i* possess a c]ta9 ,adjunct n possess$ by ! :ole ,class4 ,?is ,adjunct is said to be 'peculi>' to ! ,class s =m$4 ,9 ?is case1 ! ,class ,?+s is call$ a ',g5us' ) reg>d to ! ,class s =m$3 ! ,class1 s =m$1 is call$ a ',species' ( ! ,class ,?+s3 & its peculi> ,adjunct is call$ its ',diff]5tia'4 pg#jjb ,z ?is ,process is entirely ,m5tal1 we c p]=m x :e!r !re is1 or is n1 an exi/+ ,?+ :i* possesses t ,adjunct4 ,if !re is1 ! ,class is said to be ',real'2 if n1 x is said to be ',unreal'1 or ',imag9>y4' ,= example1 we may imag9e t we h pick$ out1 f ! ,class ,?+s1 all ! ,?+s :i* possess ! ,adjunct mat]ial1 artificial1 consi/+ ( h\ses & /reets2 & we may ?us =m ! ,real ,class t[ns4 ,"h we may reg>d ,?+s z a ,g5us1 ,t[ns z a ,species ( ,?+s1 & mat]ial1 artificial1 consi/+ ( h\ses & /reets z its ,diff]5tia4 ,aga91 we may imag9e t we h pick$ out all ! ,?+s :i* possess ! ,adjunct weigh+ a ton1 easily lift$ by a baby2 & we may ?us =m ! ,imag9>y ,class ,?+s t weigh a ton & are easily lift$ by a baby4 7#c7 ,we may ?9k ( a c]ta9 ,class1 n ! ,class ,?+s1 & may imag9e t we h pick$ out f x all ! ,memb]s ( x :i* possess a c]ta9 ,adjunct n possess$ by ! :ole ,class4 ,?is ,adjunct is said to be 'peculi>' to ! small] ,class s =m$4 ,9 ?is case1 ! ,class ?\ght ( is call$ a ',g5us' ) reg>d to ! small] ,class pick$ out f x3 ! small] ,class is call$ a ',species' ( ! l>g]3 & its peculi> ,adjunct is call$ its ',diff]5tia'4 ,= example1 we may ?9k ( ! ,class t[ns1 & imag9e t we h pick$ out f x all ! t[ns :i* possess ! ,attribute lit ) gas2 & we may ?us =m ! ,real ,class t[ns lit ) gas4 ,"h we may reg>d ,t[ns z a ,g5us1 ,t[ns lit ) gas z a ,species ( ,t[ns1 & lit ) gas z its ,diff]5tia4 ,if1 9 ! above example1 we 7 to alt] lit ) gas into pav$ ) gold1 we %\ld get ! ,imag9>y ,class t[ns pav$ ) gold4 ,a ,class1 conta9+ only "o ,memb] is call$ an ',individual4' ,= example1 ! ,class t[ns hav+ f\r million inhabitants1 :i* ,class conta9s only "o ,memb]1 viz4 ,london4 pg#jjb ,h5ce1 any s+le ,?+1 :i* we c "n s z to di/+ui% x f all o!r ,?+s1 may be reg>d$ z a "o-,memb] ,class4 ,?us ,london may be reg>d$ z ! "o-,memb] ,class1 pick$ out f ! ,class t[ns1 :i* has1 z its ,diff]5tia1 hav+ f\r million inhabitants4 ,a ,class1 conta9+ two or m ,memb]s1 is sometimes reg>d$ z "o s+le ,?+4 ,:5 s reg>d$1 x may possess an ,adjunct :i* is n possess$ by any ,memb] ( x tak5 sep>ately4 ,?us1 ! ,class ,! soldi]s ( ! ,t5? ,regim5t1 :5 reg>d$ z "o s+le ,?+1 may possess ! ,attribute =m$ 9 squ>e1 :i* is n possess$ by any ,memb] ( x tak5 sep>ately4 pg#jjc ,,*apt] ,,iii4 ,,division4 #a4 ,introductory4 ',division' is a ,m5tal ,process1 9 :i* we ?9k ( a c]ta9 ,class ( ,?+s1 & imag9e t we h divid$ x into two or m small] ,classes4 ,?us1 we might ?9k ( ! ,class books1 & imag9e t we _h divid$ x into ! two small] ,classes b\nd books & unb\nd books1 or into ! ?ree ,classes1 books pric$ at less ?an a %ill+1 %ill+-books1 books pric$ at m ?an a %ill+1 or into ! tw5ty-six ,classes1 books ^: names beg9 ) ,a1 books ^: names beg9 ) ,b1 c4 ,a ,class1 t has be5 obta9$ by a c]ta9 ,division1 is said to be 'codivisional' ) e ,class obta9$ by t ,division4 ,?us1 ! ,class b\nd books is codivisional ) ea* ( ! two ,classes1 b\nd books & unb\nd books4 ,simil>ly1 ! ,battle ( ,wat]loo may be said to h be5 contempor>y ) e ev5t t happ5$ 9 #ahae4 ,h5ce a ,class1 obta9$ by ,division1 is codivisional ) itself4 ,?us1 ! ,class b\nd books is codivisional ) itself4 ,simil>ly1 ! ,battle ( ,wat]loo may be said to h be5 contempor>y ) itself4 pg#jjc #b4 ,di*otomy4 ,if we ?9k ( a c]ta9 ,class1 & imag9e t we h pick$ out f x a c]ta9 small] ,class1 x is evid5t t ! ,rema9d] ( ! l>ge ,class does n possess ! ,diff]5tia ( t small] ,class4 ,h5ce x may be reg>d$ z ano!r small] ,class1 ^: ,diff]5tia may be =m$1 f t ( ! ,class fir/ pick$ out1 by prefix+ ! ^w n2 & we may imag9e t we h divid$ ! ,class fir/ ?\ght ( into two small] ,classes1 ^: ,diff]5ti are contradictory4 ,?is k9d ( ,division is call$ ',di*otomy'4 ,= example1 we may divide books into ! two ,classes ^: ,diff]5ti are old & n-old4 ,9 p]=m+ ?is ,process1 we may sometimes f9d t ! ,attributes we h *os5 are us$ s loosely1 9 ord9>y conv]sation1 t x is n easy to decide :i* ( ! ,?+s belong to ! "o ,class & :i* to ! o!r4 ,9 su* a case1 x w\ld be necess>y to lay d[n "s arbitr>y rule1 z to :]e ! "o ,class %\ld end & ! o!r beg94 ,?us1 9 divid+ books into old & n-old1 we may say ,let all books pr9t$ be=e ,a4,d4 #ahja1 be reg>d$ z 'old1' & all o!rs z 'n-old'4 ,h5ce=w>ds let x be und]/ood t1 if a ,class ( ,?+s be divid$ into two ,classes1 ^: ,diff]5ti h contr>y mean+s1 ea* ,diff]5tia is to be reg>d$ z equival5t to ! o!r ) ! ^w n prefix$4 ,?us1 if books be divid$ into old & new ! ,attribute old is to be reg>d$ z equival5t to n-new1 & ! ,attribute new z equival5t to n-old4 pg#jjd ,aft] divid+ a ,class1 by ! ,process ( ,di*otomy1 into two small] ,classes1 we may sub-divide ea* ( ^! into two /ill small] ,classes2 & ?is ,process may be repeat$ ov] & ov] aga91 ! numb] ( ,classes be+ d\bl$ at ea* repetition4 ,= example1 we may divide books into old & new 7i4e4 n-old73 we may !n sub-divide ea* ( ^! into ,engli% & =eign 7i4e4 n-,engli%71 ?us gett+ f\r ,classes1 viz4 7#a7 old ,engli%2 7#b7 old =eign2 7#c7 new ,engli%2 7#d7 new =eign4 ,if we _h begun by divid+ into ,engli% & =eign1 & _h !n sub-divid$ into old & new1 ! f\r ,classes w\ld h be5 7#a7 ,engli% old2 7#b7 ,engli% new2 7#c7 =eign old2 7#d7 =eign new4 ,! ,read] w easily see t ^! are ! v same f\r ,classes :i* we _h be=e4 pg#jjd ,,*apt] ,,iv4 ,,names4 ,! ^w ,?+1 :i* conveys ! idea ( a ,?+1 )\t any idea ( an ,adjunct1 repres5ts any s+le ,?+4 ,any o!r ^w 7or phrase71 :i* conveys ! idea ( a ,?+1 ) ! idea ( an ,adjunct repres5ts any ,?+ :i* possesses t ,adjunct2 i4e41 x repres5ts any ,memb] ( ! ,class to :i* t ,adjunct is peculi>4 ,su* a ^w 7or phrase7 is call$ a ',"n'2 &1 if !re be an exi/+ ,?+ :i* x repres5ts1 x is said to be a ,"n ( t ,?+4 ,= example1 ! words ,?+1 ,treasure1 ,t[n1 & ! phrases valuable ,?+1 mat]ial artificial ,?+ consi/+ ( h\ses & /reets1 ,t[n lit ) gas1 ,t[n pav$ ) gold1 old ,engli% ,book4 ,j z a ,class is said to be ,real1 or ,unreal1 accord+ z !re is1 or is n1 an exi/+ ,?+ 9 x1 s also a ,"n is said to be ,real1 or ,unreal1 accord+ z !re is1 or is n1 an exi/+ ,?+ repres5t$ by x4 ,?us1 ,t[n lit ) gas is a ,real ,"n3 ,t[n pav$ ) gold is an ,unreal ,"n4 ,e ,"n is ei!r a ,sub/antive only1 or else a phrase consi/+ ( a ,sub/antive & "o or m ,adjectives 7or phrases us$ z ,adjectives74 ,e ,"n1 except ,?+1 may usually be express$ 9 ?ree diff]5t =ms3-- 7a7 ,! ,sub/antive ,?+1 & "o or m ,adjectives 7or phrases us$ z ,adjectives7 convey+ ! ideas ( ! ,attributes2 pg#jje 7b7 ,a ,sub/antive1 convey+ ! idea ( a ,?+ ) ! ideas ( "s ( ! ,attributes1 & "o or m ,adjectives 7or phrases us$ z ,adjectives7 convey+ ! ideas ( ! o!r ,attributes2 7c7 ,a ,sub/antive convey+ ! idea ( a ,?+ ) ! ideas ( all ! ,attributes4 ,?us1 ! phrase mat]ial liv+ ,?+1 belong+ to ! ,animal ,k+dom1 hav+ two h&s & two feet is a ,"n express$ 9 ,=m 7a74 ,if we *oose to roll up toge!r ! ,sub/antive ,?+ & ! ,adjectives mat]ial1 liv+1 belong+ to ! ,animal ,k+dom1 s z to make ! new ,sub/antive ,animal1 we get ! phrase ,animal hav+ two h&s & two feet1 :i* is a ,"n 7repres5t+ ! same ,?+ z be=e7 express$ 9 ,=m 7b74 ,&1 if we *oose to roll up ! :ole phrase into "o ^w1 s z to make ! new ,sub/antive ,man1 we get a ,"n 7/ill repres5t+ ! v same ,?+7 express$ 9 ,=m 7c74 ,a ,"n1 ^: ,sub/antive is 9 ! plural numb]1 may be us$ to repres5t ei!r 7#a7 ,memb]s ( a ,class1 reg>d$ z sep>ate ,?+s2 or 7#b7 a :ole ,class1 reg>d$ z "o s+le ,?+4 ,?us1 :5 ,i say ,"s soldi]s ( ! ,t5? ,regim5t are tall1 or ,! soldi]s ( ! ,t5? ,regim5t are brave1 ,i am us+ ! ,"n soldi]s ( ! ,t5? ,regim5t 9 ! fir/ s5se2 & x is j ! same z if ,i 7 to po9t to ea* ( !m sep>ately1 & to say ,?is soldi] ( ! ,t5? ,regim5t is tall1 ,t soldi] ( ! ,t5? ,regim5t is tall1 & s on4 ,b1 :5 ,i say ,! soldi]s ( ! ,t5? ,regim5t are =m$ 9 squ>e1 ,i am us+ ! phrase 9 ! second s5se2 & x is j ! same z if ,i 7 to say ,! ,t5? ,regim5t is =m$ 9 squ>e4 pg#jjf ,,*apt] ,v4 ,,def9itions4 ,x is evid5t t e ,memb] ( a ,species is also a ,memb] ( ! ,g5us out ( :i* t ,species has be5 pick$1 & t x possesses ! ,diff]5tia ( t ,species4 ,h5ce x may be repres5t$ by a ,"n consi/+ ( two p>ts1 "o be+ a ,"n repres5t+ any ,memb] ( ! ,g5us1 & ! o!r be+ ! ,diff]5tia ( t ,species4 ,su* a ,"n is call$ a ',def9ition' ( any ,memb] ( t ,species1 & to give x su* a ,"n is to 'def9e' x4 ,?us1 we may def9e a ,treasure z a valuable ,?+4 ,9 ?is case we reg>d ,?+s z ! ,g5us1 & valuable z ! ,diff]5tia4 ,! foll[+ ,examples1 ( ?is ,process1 may be tak5 z models = work+ o!rs4 ,note t1 9 ea* ,def9ition1 ! ,sub/antive1 repres5t+ a ,memb] 7or ,memb]s7 ( ! ,g5us1 is pr9t$ 9 ,capitals4 #a4 ,def9e a ,treasure4 ,ans4 a valuable ,,?+4 #b4 ,def9e ,treasures4 ,ans4 valuable ,,?+s4 #c4 ,def9e a ,t[n4 ,ans4 a mat]ial artificial ,,?+1 consi/+ ( h\ses & /reets4 pg#jjg #d4 ,def9e ,m54 ,ans4 mat]ial1 liv+ ,,?+s1 belong+ to ! ,animal ,k+dom1 hav+ two h&s & two feet2 or else ,,animals hav+ two h&s & two feet4 #e4 ,def9e ,london4 ,ans4 ! mat]ial artificial ,,?+1 :i* consi/s ( h\ses & /reets1 & has f\r million inhabitants2 or else ! ,,t[n :i* has f\r million inhabitants4 ,note t we "h use ! article ! in/ead ( a1 because we happ5 to "k t !re is only "o su* ,?+4 ,! ,read] c set himself any numb] ( ,examples ( ?is ,process1 by simply *oos+ ! ,"n ( any common ,?+ 7su* z h\se1 tree1 knife71 mak+ a ,def9ition = x1 & !n te/+ 8 answ] by ref]r+ to any ,engli% ,diction>y4 pg#jjh ,,book ,,ii4 ,,propositions4 ,,*apt] ,i4 ,,propositions ,,g5]ally4 #a4 ,introductory4 ,note t ! ^w "s is to be reg>d$1 h5ce=w>d1 z mean+ "o or m4 ,! ^w ',proposition1' z us$ 9 ord9>y conv]sation1 may be appli$ to any ^w1 or phrase1 :i* conveys any in=mation :atev]4 ,?us ! words yes & no are ,propositions 9 ! ord9>y s5se ( ! ^w2 & s are ! phrases y owe me five f>?+s & ,i don't6 ,su* words z oh6 or nev]61 & su* phrases z fet* me t book6 :i* book d y mean8 d n seem1 at fir/ sight1 to convey any in=mation2 b !y c easily be turn$ into equival5t =ms :i* d s1 viz4 ,i am surpris$1 ,i w nev] cons5t to x1 ,i ord] y to fet* me t book1 ,i want to "k :i* book y mean4 ,b a ',proposition1' z us$ 9 ?is ,fir/ ,"p ( ,symbolic ,logic1 has a peculi> =m1 :i* may be call$ its ',normal =m'2 & if any ,proposition1 :i* we wi% to use 9 an argum5t1 is n 9 normal =m1 we mu/ r$uce x to su* a =m1 be=e we c use x4 pg#jji ,a ',proposition1' :5 9 normal =m1 ass]ts1 z to c]ta9 two ,classes1 :i* are call$ its ',subject' & ',pr$icate1' ei!r 7#a7 t "s ,memb]s ( its ,subject are ,memb]s ( its ,pr$icate2 or 7#b7 t no ,memb]s ( its ,subject are ,memb]s ( its ,pr$icate2 or 7#c7 t all ,memb]s ( its ,subject are ,memb]s ( its ,pr$icate4 ,! ,subject & ! ,pr$icate ( a ,proposition are call$ its ',t]ms4' ,two ,propositions1 :i* convey ! same in=mation1 are said to be 'equival5t'4 ,?us1 ! two ,propositions1 ,i see ,john & ,john is se5 by me1 are equival5t4 #b4 ,normal =m ( a ,proposition4 ,a ,proposition1 9 normal =m1 consi/s ( f\r p>ts1 viz4-- 7#a7 ,! ^w "s1 or no1 or all4 7,?is ^w1 :i* tells u h[ _m ,memb]s ( ! ,subject are also ,memb]s ( ! ,pr$icate1 is call$ ! ',sign ( ,quantity4'7 7#b7 ,"n ( ,subject4 7#c7 ,! v]b are 7or is74 7,?is is call$ ! ',copula4'7 7#d7 ,"n ( ,pr$icate4 pg#jaj #c4 ,v>i\s k9ds ( ,propositions4 ,a ,proposition1 t beg9s ) ,"s1 is said to be ',p>ticul>4' ,x is also call$ 'a ,proposition 9 ,i4' ,note1 t x is call$ ',p>ticul>1' because x ref]s to a "p only ( ! ,subject4 ,a ,proposition1 t beg9s ) ,no1 is said to be ',univ]sal ,negative4' ,x is also call$ 'a ,proposition 9 ,e4' ,a ,proposition1 t beg9s ) ,all1 is said to be ',univ]sal ,affirmative4' ,x is also call$ 'a ,proposition 9 ,a4' ,note1 t !y are call$ ',univ]sal'1 because !y ref] to ! :ole ( ! ,subject4 ,a ,proposition1 ^: ,subject is an ,individual1 is to be reg>d$ z ,univ]sal4 ,let u take1 z an example1 ! ,proposition ,john is n well4 ,?is ( c\rse implies t !re is an ,individual1 to :om ! speak] ref]s :5 he m5tions ,john1 & :om ! li/5] kn[s to be ref]r$ to4 ,h5ce ! ,class m5 ref]r$ to by ! speak] :5 he m5tions ',john' is a "o-,memb] ,class1 & ! ,proposition is equival5t to ,all ! m51 :o are ref]r$ to by ! speak] :5 he m5tions ',john'1 are n well4 ,propositions are ( two k9ds1 ',propositions ( ,exi/5ce' & ',propositions ( ,relation4' ,^! %all be discuss$ sep>ately4 pg#jaa ,,*apt] ,,ii4 ,,propositions ,,( ,,exi/5ce4 ,a ',proposition ( ,exi/5ce'1 :5 9 normal =m1 has1 = its ,subject1 ! ,class exi/+ ,?+s4 ,its ,sign ( ,quantity is ,"s or ,no4 ,note t1 ?\gh its ,sign ( ,quantity tells u h[ _m exi/+ ,?+s are ,memb]s ( its ,pr$icate1 x does n tell u ! exact numb]3 9 fact1 x only deals ) two numb]s1 :i* are1 9 asc5d+ ord]1 #j & #a or m4 ,x is call$ a ,proposition ( ,exi/5ce because its effect is to ass]t ! ,reality 7i4e4 ! real exi/5ce71 or else ! ,imag9>9ess1 ( its ,pr$icate4 ,?us1 ! ,proposition ,"s exi/+ ,?+s are hone/ m5 ass]ts t ! ,class hone/ m5 is ,real4 ,?is is ! normal =m2 b x may also be express$ 9 any "o ( ! foll[+ =ms3-- 7#a7 ,hone/ m5 exi/2 7#b7 ,"s hone/ m5 exi/2 7#c7 ,! ,class 'hone/ m5' exi/s2 7#d7 ,!re are hone/ m52 7#e7 ,!re are "s hone/ m54 ,simil>ly1 ! ,proposition ,no exi/+ ,?+s are m5 fifty feet high ass]ts t ! ,class m5 #ej feet high is ,imag9>y4 ,?is is ! normal =m2 b x may also be express$ 9 any "o ( ! foll[+ =ms3-- 7#a7 ,m5 #ej feet high d n exi/2 7#b7 ,no m5 #ej feet high exi/2 7#c7 ,! ,class 'm5 #ej feet high' does n exi/2 7#d7 ,!re are n any m5 #ej feet high2 7#e7 ,!re are no m5 #ej feet high4 pg#jab ,,*apt] ,,iii4 ,,propositions ,,( ,,relation4 #a4 ,introductory4 ,a ,proposition ( ,relation1 ( ! k9d to be "h discuss$1 has1 = its ,t]ms1 two ,specieses ( ! same ,g5us1 su* t ea* ( ! two ,names conveys ! idea ( "s ,attribute n convey$ by ! o!r4 ,?us1 ! ,proposition ,"s m]*ants are mis]s is ( ! "r k9d1 s9ce m]*ants & mis]s are ,specieses ( ! same ,g5us m52 & s9ce ! ,"n m]*ants conveys ! idea ( ! ,attribute m]cantile1 & ! "n mis]s ! idea ( ! ,attribute mis]ly1 ea* ( :i* ideas is n convey$ by ! o!r ,"n4 ,b ! ,proposition ,"s dogs are sett]s is n ( ! "r k9d1 s9ce1 al?\gh x is true t dogs & sett]s are ,specieses ( ! same ,g5us animals1 x is n true t ! ,"n dogs conveys ! idea ( any ,attribute n convey$ by ! ,"n sett]s4 ,su* ,propositions w be discuss$ 9 ,"p ,,ii4 ,! ,g5us1 ( :i* ! two ,t]ms are ,specieses1 is call$ ! ',univ]se ( ,disc\rse1' or 7m briefly7 ! ',univ4' ,! ,sign ( ,quantity is ,"s or ,no or ,all4 ,note t1 ?\gh its ,sign ( ,quantity tells u h[ _m ,memb]s ( its ,subject are also ,memb]s ( its ,pr$icate1 x does n tell u ! exact numb]3 9 fact1 x only deals ) ?ree numb]s1 :i* are1 9 asc5d+ ord]1 #j1 #a or m1 ! total numb] ( ,memb]s ( ! ,subject4 ,x is call$ a ,proposition ( ,relation because its effect is to ass]t t a c]ta9 relation%ip exi/s betwe5 its ,t]ms4 pg#jac #b4 ,r$uction ( a ,proposition ( ,relation to ,normal =m4 ,! ,rules1 = do+ ?is1 are z foll[s3-- 7#a7 ,asc]ta9 :at is ! ,subject 7i4e41 asc]ta9 :at ,class we are talk+ ab\t72 7#b7 ,if ! v]b1 gov]n$ by ! ,subject1 is n ! v]b are 7or is71 sub/itute = x a phrase beg9n+ ) are 7or is72 7#c7 ,asc]ta9 :at is ! ,pr$icate 7i4e41 asc]ta9 :at ,class x is1 :i* is ass]t$ to conta9 "s1 or none1 or all1 ( ! ,memb]s ( ! ,subject72 7#d7 ,if ! ,"n ( ea* ,t]m is completely express$ 7i4e4 if x conta9s a ,sub/antive71 !re is no ne$ to det]m9e ! ',univ4'2 b1 if ei!r ,"n is incompletely express$1 & conta9s ,attributes only1 x is !n necess>y to det]m9e a ',univ4'1 9 ord] to ins]t its ,"n z ! ,sub/antive4 7#e7 ,asc]ta9 ! ,sign ( ,quantity2 7#f7 ,arrange 9 ! foll[+ ord]3-- ,sign ( ,quantity1 ,subject1 ,copula1 ,pr$icate4 ,let u "w a few ,examples1 to illu/rate ^! ,rules4 7#a7 ,"s apples are n ripe4 7#a7 ,! ,subject is apples4 7#b7 ,! ,v]b is are4 7#c7 ,! ,pr$icate is n-ripe 99 99 994 7,z no ,sub/antive is express$1 & we h n yet settl$ :at ! ,univ4 is to be1 we are =c$ to leave a blank47 7#d7 ,let ,univ4 be fruit4 7#e7 ,! ,sign ( ,quantity is "s4 7#f7 ,! ,proposition n[ becomes ,"s apples are n-ripe fruit4 pg#jad 7#b7 ,none ( my speculations h br\ght me z mu* z #e p] c5t4 7#a7 ,! ,subject is my speculations4 7#b7 ,! ,v]b is h br\ght1 = :i* we sub/itute ! phrase are 99 99 99 t h br\ght4 7#c7 ,! ,pr$icate is 99 99 99 t h br\ght c4 7#d7 ,let ,univ4 be transactions4 7#e7 ,! ,sign ( ,quantity is none (4 7#f7 ,! ,proposition n[ becomes ,none ( my speculations are transactions t h br\ght me z mu* z #e p] c5t4 7#c7 ,none b ! brave des]ve ! fair4 ,to beg9 )1 we note t ! phrase none b ! brave is equival5t to no n-brave4 7#a7 ,! ,subject has = its ,attribute n-brave4 ,b no ,sub/antive is suppli$4 ,s we express ! ,subject z n-brave 99 99 994 7#b7 ,! ,v]b is des]ve1 = :i* we sub/itute ! phrase are des]v+ (4 7#c7 ,! ,pr$icate is 99 99 99 des]v+ ( ! fair4 7#d7 ,let ,univ4 be p]sons4 7#e7 ,! ,sign ( ,quantity is no4 7#f7 ,! ,proposition n[ becomes ,no n-brave p]sons are p]sons des]v+ ( ! fair4 7#d7 ,a lame puppy w\ld n say ?ank y if y (f]$ to l5d x a skipp+-rope4 7#a7 ,! ,subject is evid5tly lame puppies1 & all ! re/ ( ! s5t5ce mu/ someh[ be pack$ into ! ,pr$icate4 7#b7 ,! ,v]b is w\ld n say1 c41 = :i* we may sub/itute ! phrase are n grateful =4 7#c7 ,! ,pr$icate may be express$ z 99 99 99 n grateful = ! loan ( a skipp+-rope4 7#d7 ,let ,univ4 be puppies4 7#e7 ,! ,sign ( ,quantity is all4 7#f7 ,! ,proposition n[ becomes ,all lame puppies are puppies n grateful = ! loan ( a skipp+-rope4 pg#jae 7#e7 ,no "o takes 9 ! ,times1 unless he is well-educat$4 7#a7 ,! ,subject is evid5tly p]sons :o are n well-educat$ 7no "o evid5tly means no p]son74 7#b7 ,! ,v]b is takes 91 = :i* we may sub/itute ! phrase are p]sons tak+ 94 7#c7 ,! ,pr$icate is p]sons tak+ 9 ! ,times4 7#d7 ,let ,univ4 be p]sons4 7#e7 ,! ,sign ( ,quantity is no4 7#f7 ,! ,proposition n[ becomes ,no p]sons :o are n well-educat$ are p]sons tak+ 9 ! ,times4 7#f7 ,my c>riage w meet y at ! /ation4 7#a7 ,! ,subject is my c>riage4 ,?is1 be+ an ',individual1' is equival5t to ! ,class my c>riages4 7,note t ?is ,class conta9s only "o ,memb]47 7#b7 ,! ,v]b is w meet1 = :i* we may sub/itute ! phrase are 99 99 99 t w meet4 7#c7 ,! ,pr$icate is 99 99 99 t w meet y at ! /ation4 7#d7 ,let ,univ4 be ?+s4 7#e7 ,! ,sign ( ,quantity is all4 7#f7 ,! ,proposition n[ becomes ,all my c>riages are ?+s t w meet y at ! /ation4 7#g7 ,happy is ! man :o does n "k :at 'too?a*e' means6 7#a7 ,! ,subject is evid5tly ! man c4 7,note t 9 ?is s5t5ce1 ! ,pr$icate comes fir/47 ,at fir/ sight1 ! ,subject seems to be an ',individual'2 b on fur!r consid]ation1 we see t ! article ! does n imply t !re is only "o su* man4 ,h5ce ! phrase ! man :o is equival5t to all m5 :o4 7#b7 ,! ,v]b is are4 7#c7 ,! ,pr$icate is happy 99 99 994 7#d7 ,let ,univ4 be m54 7#e7 ,! ,sign ( ,quantity is all4 7#f7 ,! ,proposition n[ becomes ,all m5 :o d n "k :at 'too?a*e' means are happy m54 pg#jaf 7#h7 ,"s f>m]s always grumble at ! wea!r1 :atev] x may be4 7#a7 ,! ,subject is f>m]s4 7#b7 ,! ,v]b is grumble1 = :i* we sub/itute ! phrase are 99 99 99 :o grumble4 7#c7 ,! ,pr$icate is 99 99 99 :o always grumble c4 7#d7 ,let ,univ4 be p]sons4 7#e7 ,! ,sign ( ,quantity is "s4 7#f7 ,! ,proposition n[ becomes ,"s f>m]s are p]sons :o always grumble at ! wea!r1 :atev] x may be4 7#i7 ,no lambs are accu/om$ to smoke cig>s4 7#a7 ,! ,subject is lambs4 7#b7 ,! ,v]b is are4 7#c7 ,! ,pr$icate is 99 99 99 accu/om$ c4 7#d7 ,let ,univ4 be animals4 7#e7 ,! ,sign ( ,quantity is no4 7#f7 ,! ,proposition n[ becomes ,no lambs are animals accu/om$ to smoke cig>s4 7#aj7 ,i ca'n't und]/& examples t are n arrang$ 9 regul> ord]1 l ^? ,i am us$ to4 7#a7 ,! ,subject is examples t1 c4 7#b7 ,! ,v]b is ,i ca'n't und]/&1 :i* we mu/ alt]1 s z to h examples1 in/ead ( ,i1 z ! nom9ative case4 ,x may be express$ z are n und]/ood by me4 7#c7 ,! ,pr$icate is 99 99 99 n und]/ood by me4 7#d7 ,let ,univ4 be examples4 7#e7 ,! ,sign ( ,quantity is all4 7#f7 ,! ,proposition n[ becomes ,all examples t are n arrang$ 9 regul> ord] l ^? ,i am us$ to are examples n und]/ood by me4 pg#jag #c4 ,a ,proposition ( ,relation1 beg9n+ ) ,all1 is a ,d\ble ,proposition4 ,a ,proposition ( ,relation1 beg9n+ ) ,all1 ass]ts 7z we already "k7 t ,all ,memb]s ( ! ,subject are ,memb]s ( ! ,pr$icate4 ,?is evid5tly conta9s1 z a "p ( :at x tells u1 ! small] ,proposition ,"s ,memb]s ( ! ,subject are ,memb]s ( ! ,pr$icate4 ,?us1 ! ,proposition ,all bank]s are ri* m5 evid5tly conta9s ! small] ,proposition ,"s bank]s are ri* m54 ,! "q n[ arises ,:at is ! re/ ( ! in=mation :i* ?is ,proposition gives u8 ,9 ord] to answ] ?is "q1 let u beg9 ) ! small] ,proposition1 ,"s ,memb]s ( ! ,subject are ,memb]s ( ! ,pr$icate1 & suppose t ?is is all we h be5 told2 & let u proce$ to inquire :at else we ne$ to be told1 9 ord] to "k t ,all ,memb]s ( ! ,subject are ,memb]s ( ! ,pr$icate4 ,?us1 we may suppose t ! ,proposition ,"s bank]s are ri* m5 is all ! in=mation we possess2 & we may proce$ to inquire :at o!r ,proposition ne$s to be add$ to x1 9 ord] to make up ! entire ,proposition ,all bank]s are ri* m54 ,let u also suppose t ! ',univ4' 7i4e4 ! ,g5us1 ( :i* bo? ! ,subject & ! ,pr$icate are ,specieses7 has be5 divid$ 7by ! ,process ( ,di*otomy7 into two small] ,classes1 viz4 7#a7 ! ,pr$icate2 7#b7 ! ,class ^: ,diff]5tia is contradictory to t ( ! ,pr$icate4 ,?us1 we may suppose t ! ,g5us m51 7( :i* bo? bank]s & ri* m5 are ,specieses7 has be5 divid$ into ! two small] ,classes1 ri* m51 poor m54 pg#jah ,n[ we "k t e ,memb] ( ! ,subject is 7z %[n at p4 #f7 a ,memb] ( ! ,univ4 ,h5ce e ,memb] ( ! ,subject is ei!r 9 ,class 7#a7 or else 9 ,class 7#b74 ,?us1 we "k t e bank] is a ,memb] ( ! ,g5us m54 ,h5ce1 e bank] is ei!r 9 ! ,class ri* m51 or else 9 ! ,class poor m54 ,also we h be5 told t1 9 ! case we are discuss+1 "s ,memb]s ( ! ,subject are 9 ,class 7#a74 ,:at else d we ne$ to be told1 9 ord] to "k t all ( !m are !re8 ,evid5tly we ne$ to be told t none ( !m are 9 ,class 7#b72 i4e4 t none ( !m are ,memb]s ( ! ,class ^: ,diff]5tia is contradictory to t ( ! ,pr$icate4 ,?us1 we may suppose we h be5 told t "s bank]s are 9 ! ,class ri* m54 ,:at else d we ne$ to be told1 9 ord] to "k t all ( !m are !re8 ,evid5tly we ne$ to be told t none ( !m are 9 ! ,class poor m54 ,h5ce a ,proposition ( ,relation1 beg9n+ ) ,all1 is a ,d\ble ,proposition1 & is 'equival5t' to 7i4e4 gives ! same in=mation z7 ! two ,propositions 7#a7 ,"s ,memb]s ( ! ,subject are ,memb]s ( ! ,pr$icate2 7#b7 ,no ,memb]s ( ! ,subject are ,memb]s ( ! ,class ^: ,diff]5tia is contradictory to t ( ! ,pr$icate4 ,?us1 ! ,proposition ,all bank]s are ri* m5 is a ,d\ble ,proposition1 & is equival5t to ! two ,propositions 7#a7 ,"s bank]s are ri* m52 7#b7 ,no bank]s are poor m54 pg#jai #d4 ,:at is impli$1 9 a ,proposition ( ,relation1 z to ! ,reality ( its ,t]ms8 ,note t ! rules1 "h laid d[n1 are arbitr>y1 & only apply to ,"p ,i ( my ,symbolic ,logic4 ,a ,proposition ( ,relation1 beg9n+ ) ,"s1 is h5ce=w>d to be und]/ood z ass]t+ t !re are "s exi/+ ,?+s1 :i*1 be+ ,memb]s ( ! ,subject1 are also ,memb]s ( ! ,pr$icate2 i4e4 t "s exi/+ ,?+s are ,memb]s ( bo? ,t]ms at once4 ,h5ce x is to be und]/ood z imply+ t ea* ,t]m1 tak5 by itself1 is ,real4 ,?us1 ! ,proposition ,"s ri* m5 are invalids is to be und]/ood z ass]t+ t "s exi/+ ,?+s are ri* invalids4 ,h5ce x implies t ea* ( ! two ,classes1 ri* m5 & invalids1 tak5 by itself1 is ,real4 ,a ,proposition ( ,relation1 beg9n+ ) ,no1 is h5ce=w>d to be und]/ood z ass]t+ t !re are no exi/+ ,?+s :i*1 be+ ,memb]s ( ! ,subject1 are also ,memb]s ( ! ,pr$icate2 i4e4 t no exi/+ ,?+s are ,memb]s ( bo? ,t]ms at once4 ,b ?is implies no?+ z to ! ,reality ( ei!r ,t]m tak5 by itself4 ,?us1 ! ,proposition ,no m]maids are mill9]s is to be und]/ood z ass]t+ t no exi/+ ,?+s are m]maid-mill9]s4 ,b ?is implies no?+ z to ! ,reality1 or ! ,unreality1 ( ei!r ( ! two ,classes1 m]maids & mill9]s1 tak5 by itself4 ,9 ?is case z x happ5s1 ! ,subject is ,imag9>y1 & ! ,pr$icate ,real4 ,a ,proposition ( ,relation1 beg9n+ ) ,all1 conta9s 7see #c7 a simil> ,proposition beg9n+ ) ,"s4 ,h5ce x is to be und]/ood z imply+ t ea* ,t]m1 tak5 by itself1 is ,real4 ,?us1 ! ,proposition ,all hynas are savage animals conta9s ! ,proposition ,"s hynas are savage animals4 ,h5ce x implies t ea* ( ! two ,classes1 hynas & savage animals1 tak5 by itself1 is ,real4 pg#jbj #e4 ,translation ( a ,proposition ( ,relation into "o or m ,propositions ( ,exi/5ce4 ,we h se5 t a ,proposition ( ,relation1 beg9n+ ) ,"s1 ass]ts t "s exi/+ ,?+s1 be+ ,memb]s ( its ,subject1 are also ,memb]s ( its ,pr$icate4 ,h5ce1 x ass]ts t "s exi/+ ,?+s are ,memb]s ( bo?2 i4e4 x ass]ts t "s exi/+ ,?+s are ,memb]s ( ! ,class ( ,?+s :i* h all ! ,attributes ( ! ,subject & ! ,pr$icate4 ,h5ce1 to translate x into a ,proposition ( ,exi/5ce1 we take exi/+ ,?+s z ! new ,subject1 & ,?+s1 :i* h all ! ,attributes ( ! ,subject & ! ,pr$icate1 z ! new ,pr$icate4 ,simil>ly = a ,proposition ( ,relation beg9n+ ) ,no4 ,a ,proposition ( ,relation1 beg9n+ ) ,all1 is 7z %[n 9 #c7 equival5t to two ,propositions1 "o beg9n+ ) ,"s & ! o!r ) ,no1 ea* ( :i* we n[ "k h[ to translate4 ,let u "w a few ,examples1 to illu/rate ^! ,rules4 7#a7 ,"s apples are n ripe4 ,"h we arrange ?us3-- ,"s ,sign ( ,quantity4 exi/+ ,?+s ,subject4 are ,copula4 n-ripe apples ,pr$icate4 or ?us3-- ,"s exi/+ ,?+s are n-ripe apples4 pg#jba 7#b7 ,"s f>m]s always grumble at ! wea!r1 :atev] x may be4 ,"h we arrange ?us3-- ,"s exi/+ ,?+s are f>m]s :o always grumble at ! wea!r1 :atev] x may be4 7#c7 ,no lambs are accu/om$ to smoke cig>s4 ,"h we arrange ?us3-- ,no exi/+ ,?+s are lambs accu/om$ to smoke cig>s4 7#d7 ,none ( my speculations h br\ght me z mu* z #e p] c5t4 ,"h we arrange ?us3-- ,no exi/+ ,?+s are speculations ( m9e1 :i* h br\ght me z mu* z #e p] c5t4 7#e7 ,none b ! brave des]ve ! fair4 ,"h we note1 to beg9 )1 t ! phrase none b ! brave is equival5t to no n-brave m54 ,we !n arrange ?us3-- ,no exi/+ ,?+s are n-brave m5 des]v+ ( ! fair4 7#f7 ,all bank]s are ri* m54 ,?is is equival5t to ! two ,propositions ,"s bank]s are ri* m5 & ,no bank]s are poor m54 ,"h we arrange ?us3-- ,"s exi/+ ,?+s are ri* bank]s2 & ,no exi/+ ,?+s are poor bank]s4 ,"w ,examples #a1 #a-d 7p4 #ig74 pg#jbb ,,book ,,iii4 ,,! ,,bilit]al ,,diagram4 ------------- xy xy' ------------ x'y x'y' ------------- ,,*apt] ,i4 ,,symbols ,,& ,,cells4 ,fir/1 let u suppose t ! above ,diagram is an enclosure assign$ to a c]ta9 ,class ( ,?+s1 :i* we h select$ z our ',univ]se ( ,disc\rse4' or1 m briefly1 z our ',univ'4 ,= example1 we might say ,let ,univ4 be 'books'2 & we might imag9e ! ,diagram to be a l>ge table1 assign$ to all books4 ,! ,read] is /rongly advis$1 9 read+ ?is ,*apt]1 n to ref] to ! above ,diagram1 b to draw a l>ge "o = himself1 )\t any lett]s1 & to h x by him :ile he reads1 & keep 8 f+] on t p>ticul> "p ( x1 ab\t :i* he is read+4 pg#jbc ,secondly1 let u suppose t we h select$ a c]ta9 ,adjunct1 :i* we may call x1 & h divid$ ! l>ge ,class1 to :i* we h assign$ ! :ole ,diagram1 into ! two small] ,classes ^: ,diff]5ti are x & n-x 7:i* we may call x'71 & t we h assign$ ! ,nor? ,half ( ! ,diagram to ! "o 7:i* we may call ! ,class ( x-,?+s1 or ! x-,class71 & ! ,s\? ,half to ! o!r 7:i* we may call ! ,class ( x'-,?+s1 or ! x'-,class74 ,= example1 we might say ,let x mean 'old1' s t x' w mean 'new'1 & we might suppose t we _h divid$ books into ! two ,classes ^: ,diff]5ti are old & new1 & _h assign$ ! ,nor? ,half ( ! table to old books & ! ,s\? ,half to new books4 ,?irdly1 let u suppose t we h select$ ano!r ,adjunct1 :i* we may call y1 & h subdivid$ ! x-,class into ! two ,classes ^: ,diff]5ti are y & y'1 & t we h assign$ ! ,nor?-,we/ ,cell to ! "o 7:i* we may call ! xy-,class71 & ! ,nor?-,ea/ ,cell to ! o!r 7:i* we may call ! xy'-,class74 ,= example1 we might say ,let y mean ',engli%1' s t y' w mean '=eign'1 & we might suppose t we _h subdivid$ old books into ! two ,classes ^: ,diff]5ti are ,engli% & =eign1 & _h assign$ ! ,nor?-,we/ ,cell to old ,engli% books1 & ! ,nor?-,ea/ ,cell to old =eign books4 ,f\r?ly1 let u suppose t we h subdivid$ ! x'-,class 9 ! same mann]1 & h assign$ ! ,s\?-,we/ ,cell to ! x'y-,class1 & ! ,s\?-,ea/ ,cell to ! x'y'-,class4 ,= example1 we might suppose t we _h subdivid$ new books into ! two ,classes new ,engli% books & new =eign books1 & _h assign$ ! ,s\?-,we/ ,cell to ! "o1 & ! ,s\?-,ea/ ,cell to ! o!r4 ,x is evid5t t1 if we _h begun by divid+ = y & y'1 & _h !n subdivid$ = x & x'1 we %\ld h got ! same f\r ,classes4 ,h5ce we see t we h assign$ ! ,we/ ,half to ! y-,class1 & ! ,ea/ ,half to ! y'-,class4 pg#jbd ,?us1 9 ! above ,example1 we %\ld f9d t we _h assign$ ! ,we/ ,half ( ! table to ,engli% books & ! ,ea/ ,half to =eign books4 ------------------- old old ,engli% =eign books books ------------------ new new ,engli% =eign books books ------------------- ,we h1 9 fact1 assign$ ! f\r ,qu>t]s ( ! table to f\r diff]5t ,classes ( books1 z "h %[n4 ,! ,read] %\ld c>efully rememb] t1 9 su* a phrase z ! x-,?+s1 ! ^w ,?+s means t p>ticul> k9d ( ,?+s1 to :i* ! :ole ,diagram has be5 assign$4 ,?us1 if we say ,let ,univ4 be 'books'1 we mean t we h assign$ ! :ole ,diagram to books4 ,9 t case1 if we took x to mean old1 ! phrase ! x-,?+s w\ld mean ! old books4 ,! ,read] %\ld n g on to ! next ,*apt] until he is q famili> ) ! blank ,diagram ,i h advis$ him to draw4 ,he ought to be able to "n1 in/antly1 ! ,adjunct assign$ to any ,comp>tm5t nam$ 9 ! "r-h& column ( ! foll[+ ,table4 ,also he ought to be able to "n1 in/antly1 ! ,comp>tm5t assign$ to any ,adjunct nam$ 9 ! left-h& column4 ,to make sure ( ?is1 he _h bett] put ! book into ! h&s ( "s g5ial fri5d1 :ile he himself has no?+ b ! blank ,diagram1 & get t g5ial fri5d to "q him on ?is ,table1 dodg+ ab\t z mu* z possible4 ,! ,que/ions & ,answ]s %\ld be some?+ l ?is3-- pg#jbe ,,table ,i4 ---------------------------------------- ,adjuncts ,comp>tm5ts1 or ,cells1 ( assign$ to !m4 ,classes4 --------------------------------------- x ,nor? ,half4 x' ,s\? y ,we/ y' ,ea/ --------------------------------------- xy ,nor?-,we/ ,cell4 xy' ,ea/ x'y ,s\?-,we/ x'y' ,ea/ ---------------------------------------- ,q4 ,adjunct = ,we/ ,half8 ,a4 y4 ,q4 ,comp>tm5t = xy'8 ,a4 ,nor?-,ea/ ,cell4 ,q4 ,adjunct = ,s\?-,we/ ,cell8 ,a4 x'y4 c41 c4 ,aft] a little practice1 he w f9d himself able to d )\t ! blank ,diagram1 & w be able to see x m5tally 79 my m9d's eye1 ,horatio67 :ile answ]+ ! que/ions ( 8 g5ial fri5d4 ,:5 ?is result has be5 rea*$1 he may safely g on to ! next ,*apt]4 pg#jbf ,,*apt] ,,ii4 ,,c\nt]s4 ,let u agree t a ,r$ ,c\nt]1 plac$ )9 a ,cell1 %all mean ,?is ,cell is occupi$ 7i4e4 ,!re is at lea/ "o ,?+ 9 x74 ,let u also agree t a ,r$ ,c\nt]1 plac$ on ! p>tition betwe5 two ,cells1 %all mean ,! ,comp>tm5t1 made up ( ^! two ,cells1 is occupi$2 b x is n kn[n :]eab\ts1 9 x1 its occupants are4 ,h5ce x may be und]/ood to mean ,at lea/ "o ( ^! two ,cells is occupi$3 possibly bo? are4 ,our +5i\s ,am]ican c\s9s h inv5t$ a phrase to describe ! condition ( a man :o has n yet made up 8 m9d :i* ( two political p>ties he w jo93 su* a man is said to be sitt+ on ! f5ce4 ,?is phrase exactly describes ! condition ( ! ,r$ ,c\nt]4 ,let u also agree t a ,grey ,c\nt]1 plac$ )9 a ,cell1 %all mean ,?is ,cell is empty 7i4e4 ,!re is no?+ 9 x74 ,! ,read] _h bett] provide himself ) #d ,r$ ,c\nt]s & #e ,grey ones4 pg#jbg ,,*apt] ,,iii4 ,,repres5tation ,,( ,,propositions4 #a4 ,introductory4 ,h5ce=w>ds1 9 /at+ su* ,propositions z ,"s x-,?+s exi/ or ,no x-,?+s are y-,?+s1 ,i %all omit ! ^w ,?+s1 :i* ! ,read] c supply = himself1 & %all write !m z ,"s x exi/ or ,no x are y4 ,note t ! ^w ,?+s is "h us$ ) a special mean+1 z expla9$ at p4 #bc4 ,a ,proposition1 conta9+ only "o ( ! ,lett]s us$ z ,symbols = ,attributes1 is said to be ',unilit]al'4 ,= example1 ,"s x exi/1 ,no y' exi/1 c4 ,a ,proposition1 conta9+ two ,lett]s1 is said to be ',bilit]al'4 ,= example1 ,"s xy' exi/1 ,no x' are y1 c4 ,a ,proposition is said to be '9 t]ms (' ! ,lett]s x conta9s1 :e!r ) or )\t acc5ts4 ,?us1 ,"s xy' exi/1 ,no x' are y1 c41 are said to be 9 t]ms ( x & y4 pg#jbh #b4 ,repres5tation ( ,propositions ( ,exi/5ce4 ,let u take1 fir/1 ! ,proposition ,"s x exi/4 ,note t ?is ,proposition is 7z expla9$ at p4 #ab7 equival5t to ,"s exi/+ ,?+s are x-,?+s4 ,?is tells u t !re is at lea/ "o ,?+ 9 ! ,nor? ,half2 t is1 t ! ,nor? ,half is occupi$4 ,& ?is we c evid5tly repres5t by plac+ a ,r$ ,c\nt] 7"h repres5t$ by a dott$ circle7 on ! p>tition :i* divides ! ,nor? ,half4 ------- 747 ------ ------- ,9 ! books example1 ?is ,proposition w\ld be ,"s old books exi/4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,"s x' exi/1 ,"s y exi/1 & ,"s y' exi/4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ,propositions w\ld be ,"s new books exi/1 c4 ,let u take1 next1 ! ,proposition ,no x exi/4 ,?is tells u t !re is no?+ 9 ! ,nor? ,half2 t is1 t ! ,nor? ,half is empty2 t is1 t ! ,nor?-,we/ ,cell & ! ,nor?-,ea/ ,cell are bo? ( !m empty4 ,& ?is we c repres5t by plac+ two ,grey ,c\nt]s 9 ! ,nor? ,half1 "o 9 ea* ,cell4 ------- 7 77 7 ------ ------- ,! ,read] may p]haps ?9k t x w\ld be en\gh to place a ,grey ,c\nt] on ! p>tition 9 ! ,nor? ,half1 & t1 j z a ,r$ ,c\nt]1 s plac$1 w\ld mean ,?is ,half is occupi$1 s a ,grey "o w\ld mean ,?is ,half is empty4 ,?is1 h[ev]1 w\ld be a mi/ake4 ,we h se5 t a ,r$ ,c\nt]1 s plac$1 w\ld mean ,at lea/ "o ( ^! two ,cells is occupi$3 possibly bo? are4 ,h5ce a ,grey "o w\ld m]ely mean ,at lea/ "o ( ^! two ,cells is empty3 possibly bo? are4 ,b :at we h to repres5t is1 t bo? ,cells are c]ta9ly empty3 & ?is c only be done by plac+ a ,grey ,c\nt] 9 ea* ( !m4 ,9 ! books example1 ?is ,proposition w\ld be ,no old books exi/4 pg#jbi ,simil>ly we may repres5t ! ?ree simil> ,propositions ,no x' exi/1 ,no y exi/1 & ,no y' exi/4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,no new books exi/1 c4 ,let u take1 next1 ! ,proposition ,"s xy exi/4 ,?is tells u t !re is at lea/ "o ,?+ 9 ! ,nor?-,we/ ,cell2 t is1 t ! ,nor?-,we/ ,cell is occupi$4 ,& ?is we c repres5t by plac+ a ,r$ ,c\nt] 9 x4 ------- 747 ------ ------- ,9 ! books example1 ?is ,proposition w\ld be ,"s old ,engli% books exi/4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,"s xy' exi/1 ,"s x'y exi/1 & ,"s x'y' exi/4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,"s old =eign books exi/1 c4 ,let u take1 next1 ! ,proposition ,no xy exi/4 ,?is tells u t !re is no?+ 9 ! ,nor?-,we/ ,cell2 t is1 t ! ,nor?-,we/ ,cell is empty4 ,& ?is we c repres5t by plac+ a ,grey ,c\nt] 9 x4 ------- 7 7 ------ ------- ,9 ! books example1 ?is ,proposition w\ld be ,no old ,engli% books exi/4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,no xy' exi/1 ,no x'y exi/1 & ,no x'y' exi/4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,no old =eign books exi/1 c4 pg#jcj ,we h se5 t ! ,proposition ,no x exi/ may be repres5t$ by plac+ two ,grey ,c\nt]s 9 ! ,nor? ,half1 "o 9 ea* ,cell4 ------- 7 77 7 ------ ------- ,we h also se5 t ^! two ,grey ,c\nt]s1 tak5 sep>ately1 repres5t ! two ,propositions ,no xy exi/ & ,no xy' exi/4 ,h5ce we see t ! ,proposition ,no x exi/ is a ,d\ble ,proposition1 & is equival5t to ! two ,propositions ,no xy exi/ & ,no xy' exi/4 ,9 ! books example1 ?is ,proposition w\ld be ,no old books exi/4 ,h5ce ?is is a ,d\ble ,proposition1 & is equival5t to ! two ,propositions ,no old ,engli% books exi/ & ,no old =eign books exi/4 #c4 ,repres5tation ( ,propositions ( ,relation4 ,let u take1 fir/1 ! ,proposition ,"s x are y4 ,?is tells u t at lea/ "o ,?+1 9 ! ,nor? ,half1 is also 9 ! ,we/ ,half4 ,h5ce x mu/ be 9 ! space common to !m1 t is1 9 ! ,nor?-,we/ ,cell4 ,h5ce ! ,nor?-,we/ ,cell is occupi$4 ,& ?is we c repres5t by plac+ a ,r$ ,c\nt] 9 x4 ------- 747 ------ ------- ,note t ! ,subject ( ! ,proposition settles :i* ,half we are to use2 & t ! ,pr$icate settles 9 :i* portion ( x we are to place ! ,r$ ,c\nt]4 ,9 ! books example1 ?is ,proposition w\ld be ,"s old books are ,engli%4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,"s x are y'1 ,"s x' are y1 & ,"s x' are y'4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,"s old books are =eign1 c4 pg#jca ,let u take1 next1 ! ,proposition ,"s y are x4 ,?is tells u t at lea/ "o ,?+1 9 ! ,we/ ,half1 is also 9 ! ,nor? ,half4 ,h5ce x mu/ be 9 ! space common to !m1 t is1 9 ! ,nor?-,we/ ,cell4 ,h5ce ! ,nor?-,we/ ,cell is occupi$4 ,& ?is we c repres5t by plac+ a ,r$ ,c\nt] 9 x4 ------- 747 ------ ------- ,9 ! books example1 ?is ,proposition w\ld be ,"s ,engli% books are old4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,"s y are x'1 ,"s y' are x1 & ,"s y' are x'4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,"s ,engli% books are new1 c4 ,we see t ?is "o ,diagram has n[ s]v$ to repres5t no less ?an ?ree ,propositions1 viz4 7#a7 ,"s xy exi/2 7#b7 ,"s x are y2 7#c7 ,"s y are x4 ------- 747 ------ ------- ,h5ce ^! ?ree ,propositions are equival5t4 ,9 ! books example1 ^! ,propositions w\ld be 7#a7 ,"s old ,engli% books exi/2 7#b7 ,"s old books are ,engli%2 7#c7 ,"s ,engli% books are old4 ,! two equival5t ,propositions1 ,"s x are y & ,"s y are x1 are said to be ',conv]se' to ea* o!r2 & ! ,process1 ( *ang+ "o into ! o!r1 is call$ ',conv]t+'1 or ',conv]sion'4 ,= example1 if we 7 told to conv]t ! ,proposition ,"s apples are n ripe1 we %\ld fir/ *oose our ,univ4 7say fruit71 & !n complete ! ,proposition1 by supply+ ! ,sub/antive fruit 9 ! ,pr$icate1 s t x w\ld be ,"s apples are n-ripe fruit2 & we %\ld !n conv]t x by int]*ang+ its ,t]ms1 s t x w\ld be ,"s n-ripe fruit are apples4 pg#jcb ,simil>ly we may repres5t ! ?ree simil> ,trios ( equival5t ,propositions2 ! :ole ,set ( f\r ,trios be+ z foll[s3-- 7#a7 ,"s xy exi/ ,"s x are y ,"s y are x4 7#b7 ,"s xy' exi/ ,"s x are y' ,"s y' are x4 7#c7 ,"s x'y exi/ ,"s x' are y ,"s y are x'4 7#d7 ,"s x'y' exi/ ,"s x' are y' ,"s y' are x'4 ,let u take1 next1 ! ,proposition ,no x are y4 ,?is tell u t no ,?+1 9 ! ,nor? ,half1 is also 9 ! ,we/ ,half4 ,h5ce !re is no?+ 9 ! space common to !m1 t is1 9 ! ,nor?-,we/ ,cell4 ,h5ce ! ,nor?-,we/ ,cell is empty4 ,& ?is we c repres5t by plac+ a ,grey ,c\nt] 9 x4 ------- 7 7 ------ ------- ,9 ! books example1 ?is ,proposition w\ld be ,no old books are ,engli%4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,no x are y'1 & ,no x' are y1 & ,no x' are y'4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,no old books are =eign1 c4 ,let u take1 next1 ! ,proposition ,no y are x4 ,?is tells u t no ,?+1 9 ! ,we/ ,half1 is also 9 ! ,nor? ,half4 ,h5ce !re is no?+ 9 ! space common to !m1 t is1 9 ! ,nor?-,we/ ,cell4 ,t is1 ! ,nor?-,we/ ,cell is empty4 ,& ?is we c repres5t by plac+ a ,grey ,c\nt] 9 x4 ------- 7 7 ------ ------- ,9 ! books example1 ?is ,proposition w\ld be ,no ,engli% books are old4 ,simil>ly we may repres5t ! ?ree simil> ,propositions ,no y are x'1 ,no y' are x1 & ,no y' are x'4 ,! ,read] %\ld make out all ^! = himself4 ,9 ! books example1 ^! ?ree ,propositions w\ld be ,no ,engli% books are new1 c4 pg#jcc ------- 7 7 ------ ------- ,we see t ?is "o ,diagram has n[ s]v$ to pres5t no less ?an ?ree ,propositions1 viz4 7#a7 ,no xy exi/2 7#b7 ,no x are y2 7#c7 ,no y are x4 ,h5ce ^! ?ree ,propositions are equival5t4 ,9 ! books example1 ^! ,propositions w\ld be 7#a7 ,no old ,engli% books exi/2 7#b7 ,no old books are ,engli%2 7#c7 ,no ,engli% books are old4 ,! two equival5t ,propositions1 ,no x are y & ,no y are x1 are said to be ',conv]se' to ea* o!r4 ,= example1 if we 7 told to conv]t ! ,proposition ,no porcup9es are talkative1 we %\ld fir/ *oose our ,univ4 7say animals71 & !n complete ! ,proposition1 by supply+ ! ,sub/antive animals 9 ! ,pr$icate1 s t x w\ld be ,no porcup9es are talkative animals1 & we %\ld !n conv]t x1 by int]*ang+ its ,t]ms1 s t x w\ld be ,no talkative animals are porcup9es4 ,simil>ly we may repres5t ! ?ree simil> ,trios ( equival5t ,propositions2 ! :ole ,set ( f\r ,trios be+ z foll[s3-- 7#a7 ,no xy exi/ ,no x are y ,no y are x4 7#b7 ,no xy' exi/ ,no x are y' ,no y' are x4 7#c7 ,no x'y exi/ ,no x' are y ,no y are x'4 7#d7 ,no x'y' exi/ ,no x' are y' ,no y' are x'4 ,let u take1 next1 ! ,proposition ,all x are y4 ,we "k 7see p4 #ag7 t ?is is a ,d\ble ,proposition1 & equival5t to ! two ,propositions ,"s x are y & ,no x are y'1 ea* ( :i* we already "k h[ to repres5t4 ------- 7477 7 ------ ------- ,note t ! ,subject ( ! giv5 ,proposition settles :i* ,half we are to use2 & t its ,pr$icate settles 9 :i* portion ( t ,half we are to place ! ,r$ ,c\nt]4 pg#jcd ,,table ,,ii4 ---------------------------------------- ------------- ------- ------- 747 7 77 7 ,"s x exi/ ------ ,no x exi/ ------ ------- ------- ---------------------------------------- ---------- ------- ------- ,"s x' exi/ ------ ,no x' exi/ ------ 747 7 77 7 ------- ------- ---------------------------------------- ---------- ------- ------- 7 7 ,"s y exi/ 747--- ,no y exi/ ------ 7 7 ------- ------- ---------------------------------------- ---------- ------- ------- 7 7 ,"s y' exi/ ---747 ,no y' exi/ ------ 7 7 ------- ------- ---------------------------------------- ------------- ,simil>ly we may repres5t ! sev5 simil> ,propositions ,all x are y'1 ,all x' are y1 ,all x' are y'1 ,all y are x1 ,all y are x'1 ,all y' are x1 & ,all y' are x'4 ,let u take1 la/ly1 ! ,d\ble ,proposition ,"s x are y & "s are y'1 ea* "p ( :i* we already "k h[ to repres5t4 ------- 747747 ------ ------- ,simil>ly we may repres5t ! ?ree simil> ,propositions1 ,"s x' are y & "s are y'1 ,"s y are x & "s are x'1 ,"s y' are x & "s are x'4 ,! ,read] %\ld n[ get 8 g5ial fri5d to "q him1 sev]ely1 on ^! two ,tables4 ,! ,inquisitor %\ld h ! ,tables be=e him3 b ! ,victim %\ld h no?+ b a blank ,diagram1 & ! ,c\nt]s ) :i* he is to repres5t ! v>i\s ,propositions nam$ by 8 fri5d1 e4g4 ,"s y exi/1 ,no y' are x1 ,all x are y1 c4 c4 pg#jce ,,table ,,iii4 ---------------------------------------- --------------------- ------- ------- ,"s xy exi/ 747 7477 7 ,"s x are y ------ ,all x are y ------ ,"s y are x ------- ------- ---------------------------------------- ------------------ ------- ------- ,"s xy' exi/ 747 7 7747 ,"s x are y' ------ ,all x are y' ------ ,"s y' are x ------- ------- ---------------------------------------- ------------------ ------- ------- ,"s x'y exi/ ,"s x' are y ------ ,all x' are y ------ ,"s y are x' 747 7477 7 ------- ------- ---------------------------------------- ------------------ ------- ------- ,"s x'y' exi/ ,"s x' are y' ------ ,all x' are y' ------ ,"s y' are x' 747 7 7747 ------- ------- ---------------------------------------- --------------------- ---------------------------------------- --------------------- ------- ------- ,no xy exi/ 7 7 747 ,no x are y ------ ,all y are x ------ ,no y are x 7 7 ------- ------- ---------------------------------------- ------------------ ------- ------- ,no xy' exi/ 7 7 7 7 ,no x are y' ------ ,all y are x' ------ ,no y' are x 747 ------- ------- ---------------------------------------- ------------------ ------- ------- ,no x'y exi/ 747 ,no x' are y ------ ,all y' are x ------ ,no y are x' 7 7 7 7 ------- ------- ---------------------------------------- ------------------ ------- ------- ,no x'y' exi/ 7 7 ,no x' are y' ------ ,all y' are x' ------ ,no y' are x' 7 7 747 ------- ------- ---------------------------------------- --------------------- ---------------------------------------- --------------------- ------- ------- 747747 747 ,"s x are y1 ------ ,"s y are x ------ & "s are y' & "s are x' 747 ------- ------- ---------------------------------------- ------------------ ------- ------- 747 ,"s x' are y1 ------ ,"s y' are x ------ & "s are y' 747747 & "s are x' 747 ------- ------- ---------------------------------------- --------------------- pg#jcf ,,*apt] ,,iv4 ,,int]pretation ,,( ,,bilit]al ,,diagram ,,:5 ,,m>k$ ,,) ,,c\nt]s4 ,! ,diagram is suppos$ to be set be=e u1 ) c]ta9 ,c\nt]s plac$ ^u x2 & ! problem is to f9d out :at ,proposition1 or ,propositions1 ! ,c\nt]s repres5t4 ,z ! process is simply ! rev]se ( t discuss$ 9 ! previ\s ,*apt]1 we c avail ourselves ( ! results !re obta9$1 z f> z !y g4 ,fir/1 let u suppose t we f9d a ,r$ ,c\nt] plac$ 9 ! ,nor?-,we/ ,cell4 ------- 747 ------ ------- ,we "k t ?is repres5ts ea* ( ! ,trio ( equival5t ,propositions ,"s xy exi/ ,"s x are y ,"s y are x4 ,simil>ly we may int]pret a ,r$ ,c\nt]1 :5 plac$ 9 ! ,nor?-,ea/1 or ,s\?-,we/1 or ,s\?-,ea/ ,cell4 ,next1 let u suppose t we f9d a ,grey ,c\nt] plac$ 9 ! ,nor?-,we/ ,cell4 ------- 7 7 ------ ------- ,we "k t ?is repres5ts ea* ( ! ,trio ( equival5t ,propositions ,no xy exi/ ,no x are y ,no y are x4 ,simil>ly we may int]pret a ,grey ,c\nt]1 :5 plac$ 9 ! ,nor?-,ea/1 or ,s\?-,we/1 or ,s\?-,ea/ ,cell4 pg#jcg ,next1 let u suppose t we f9d a ,r$ ,c\nt] plac$ on ! p>tition :i* divides ! ,nor? ,half4 ------- 747 ------ ------- ,we "k t ?is repres5ts ! ,proposition ,"s x exi/4 ,simil>ly we may int]pret a ,r$ ,c\nt]1 :5 plac$ on ! p>tition :i* divides ! ,s\?1 or ,we/1 or ,ea/ ,half4 99 99 99 99 99 ,next1 let u suppose t we f9d two ,r$ ,c\nt]s plac$ 9 ! ,nor? ,half1 "o 9 ea* ,cell4 ------- 747747 ------ ------- ,we "k t ?is repres5ts ! ,d\ble ,proposition ,"s x are y & "s are y'4 ,simil>ly we may int]pret two ,r$ ,c\nt]s1 :5 plac$ 9 ! ,s\?1 or ,we/1 or ,ea/ ,half4 99 99 99 99 99 ,next1 let u suppose t we f9d two ,grey ,c\nt]s plac$ 9 ! ,nor? ,half1 "o 9 ea* ,cell4 ------- 7 77 7 ------ ------- ,we "k t ?is repres5ts ! ,proposition ,no x exi/4 ,simil>ly we may int]pret two ,grey ,c\nt]s1 :5 plac$ 9 ! ,s\?1 or ,we/1 or ,ea/ ,half4 99 99 99 99 99 ,la/ly1 let u suppose t we f9d a ,r$ & a ,grey ,c\nt] plac$ 9 ! ,nor? ,half1 ! ,r$ 9 ! ,nor?-,we/ ,cell1 & ! ,grey 9 ! ,nor?-,ea/ ,cell4 ------- 7477 7 ------ ------- ,we "k t ?is repres5ts ! ,proposition1 ,all x are y4 ,note t ! ,half1 occupi$ by ! two ,c\nt]s1 settles :at is to be ! ,subject ( ! ,proposition1 & t ! ,cell1 occupi$ by ! ,r$ ,c\nt]1 settles :at is to be its ,pr$icate4 pg#jch ,simil>ly we may int]pret a ,r$ & a ,grey c\nt]1 :5 plac$ 9 any "o ( ! sev5 simil> positions ,r$ 9 ,nor?-,ea/1 ,grey 9 ,nor?-,we/2 ,r$ 9 ,s\?-,we/1 ,grey 9 ,s\?-,ea/2 ,r$ 9 ,s\?-,ea/1 ,grey 9 ,s\?-,we/2 ,r$ 9 ,nor?-,we/1 ,grey 9 ,s\?-,we/2 ,r$ 9 ,s\?-,we/1 ,grey 9 ,nor?-,we/2 ,r$ 9 ,nor?-,ea/1 ,grey 9 ,s\?-,ea/2 ,r$ 9 ,s\?-,ea/1 ,grey 9 ,nor?-,ea/4 ,once m ! g5ial fri5d mu/ be appeal$ to1 & reque/$ to exam9e ! ,read] on ,tables ,,ii & ,,iii1 & to make him n only repres5t ,propositions1 b also int]pret ,diagrams :5 m>k$ ) ,c\nt]s4 ,! ,que/ions & ,answ]s %\ld be l ?is3-- ,q4 ,repres5t ,no x' are y'4 ,a4 ,grey ,c\nt] 9 ,s4,e4 ,cell4 ,q4 ,int]pret ,r$ ,c\nt] on ,e4 p>tition4 ,a4 ,"s y' exi/4 ,q4 ,repres5t ,all y' are x4 ,a4 ,r$ 9 ,n4,e4 ,cell2 ,grey 9 ,s4,e4 ,q4 ,int]pret ,grey ,c\nt] 9 ,s4,w4 ,cell4 ,a4 ,no x'y exi/ ,no x' are y ,no y are x'4 c41 c4 ,at fir/ ! ,exam9ee w ne$ to h ! ,bo>d & ,c\nt]s be=e him2 b he w soon le>n to disp5se ) ^!1 & to answ] ) 8 eyes %ut or gaz+ into vacancy4 ,"w ,examples #a1 #e-h 7p4 #ig74 pg#jci ,,book ,,iv4 ,,! ,,trilit]al ,,diagram4 ----------------- ----------------- xy xy' m' m' xy xy' -------- xy xy' m m ---------------- -------------- x'y x'y' m m x'y x'y' -------- x'y x'y' m' m' ----------------- ----------------- ,,*apt] ,i4 ,,symbols ,,& ,,cells4 ,fir/1 let u suppose t ! above left-h& ,diagram is ! ,bilit]al ,diagram t we h be5 us+ 9 ,book ,,iii41 & t we *ange x into a ,trilit]al ,diagram by draw+ an ,inn] ,squ>e1 s z to divide ea* ( its #d ,cells into #b portions1 ?us mak+ #h ,cells altoge!r4 ,! "r-h& ,diagram %[s ! result4 ,! ,read] is /rongly advis$1 9 read+ ?is ,*apt]1 n to ref] to ! above ,diagrams1 b to make a l>ge copy ( ! "r-h& "o = himself1 )\t any lett]s1 & to h x by him :ile he reads1 & keep 8 f+] on t p>ticul> "p ( x1 ab\t :i* he is read+4 pg#jdj ,secondly1 let u suppose t we h select$ a c]ta9 ,adjunct1 :i* we may call m1 & h subdivid$ ! xy-,class into ! two ,classes ^: ,diff]5ti are m & m'1 & t we h assign$ ! ,n4,w4 ,inn] ,cell to ! "o 7:i* we may call ! ,class ( xym-,?+s1 or ! xym-,class71 & ! ,n4,w4 ,out] ,cell to ! o!r 7:i* we may call ! ,class ( xym'-,?+s1 or ! xym'-,class74 ,?us1 9 ! books example1 we might say ,let m mean 'b\nd'1 s t m' w mean 'unb\nd'1 & we might suppose t we _h subdivid$ ! ,class old ,engli% books into ! two ,classes1 old ,engli% b\nd books & old ,engli% unb\nd books1 & _h assign$ ! ,n4,w4 ,inn] ,cell to ! "o1 & ! ,n4,w4 ,out] ,cell to ! o!r4 ,?irdly1 let u suppose t we h subdivid$ ! xy'-,class1 ! x'y-,class1 & ! x'y'-,class 9 ! same mann]1 & h1 9 ea* case1 assign$ ! ,inn] ,cell to ! ,class possess+ ! ,attribute m1 & ! ,out] ,cell to ! ,class possess+ ! ,attribute m'4 ,?us1 9 ! books example1 we might suppose t we _h subdivid$ ! new ,engli% books into ! two ,classes1 new ,engli% b\nd books & new ,engli% unb\nd books1 & _h assign$ ! ,s4,w4 ,inn] ,cell to ! "o1 & ! ,s4,w4 ,out] ,cell to ! o!r4 ,x is evid5t t we h n[ assign$ ! ,inn] ,squ>e to ! m-,class1 & ! ,out] ,bord] to ! m'-,class4 ,?us1 9 ! books example1 we h assign$ ! ,inn] ,squ>e to b\nd books & ! ,out] ,bord] to unb\nd books4 ,:5 ! ,read] has made himself famili> ) ?is ,diagram1 he ought to be able to f9d1 9 a mom5t1 ! ,comp>tm5t assign$ to a p>ticul> pair ( ,attributes1 or ! ,cell assign$ to a p>ticul> trio ( ,attributes4 ,! foll[+ ,rules w help him 9 do+ ?is3-- 7#a7 ,arrange ! ,attributes 9 ! ord] x1 y1 m4 pg#jda 7#b7 ,take ! fir/ ( !m & f9d ! ,comp>tm5t assign$ to x4 7#c7 ,!n take ! second1 & f9d :at portion ( t comp>tm5t is assign$ to x4 7#d7 ,treat ! ?ird1 if !re is "o1 9 ! same way4 ,= example1 suppose we h to f9d ! ,comp>tm5t assign$ to ym4 ,we say to ourselves y has ! ,we/ ,half2 & m has ! ,inn] portion ( t ,we/ ,half4 ,aga91 suppose we h to f9d ! ,cell assign$ to x'ym'4 ,we say to ourselves x' has ! ,s\? ,half2 y has ! ,we/ portion ( t ,s\? ,half1 i4e4 has ! ,s\?-,we/ ,qu>t]2 & m' has ! ,out] portion ( t ,s\?-,we/ ,qu>t]4 ,! ,read] %\ld n[ get 8 g5ial fri5d to "q him on ! ,table giv5 on ! next page1 9 ! /yle ( ! foll[+ specim5-,dialogue4 ,q4 ,adjunct = ,s\? ,half1 ,inn] ,portion8 ,a4 x'm4 ,q4 ,comp>tm5t = m'8 ,a4 ,! ,out] ,bord]4 ,q4 ,adjunct = ,nor?-,ea/ ,qu>t]1 ,out] ,portion8 ,a4 xy'm'4 ,q4 ,comp>tm5t = ym8 ,a4 ,we/ ,half1 ,inn] ,portion4 ,q4 ,adjunct = ,s\? ,half8 ,a4 x'4 ,q4 ,comp>tm5t = x'y'm8 ,a4 ,s\?-,ea/ ,qu>t]1 ,inn] ,portion4 c4 c4 pg#jdb ,,table ,,iv4 ---------------------------------------- ------- ,adjunct ( ,comp>tm5ts1 or ,cells1 assign$ ,classes4 to !m4 ---------------------------------------- ------ x ,nor? ,half4 x' ,s\? y ,we/ y' ,ea/ m ,inn] ,squ>e4 m' ,out] ,bord]4 ---------------------------------------- ------ xy ,nor?-,we/ ,qu>t]4 xy' ,ea/ x'y ,s\?-,we/ x'y' ,ea/ xm ,nor? ,half1 ,inn] ,portion4 xm' ,out] x'm ,s\? ,inn] x'm' ,out] ym ,we/ ,inn] ym' ,out] y'm ,ea/ ,inn] y'm' ,out] ---------------------------------------- ------ xym ,nor?-,we/ ,qu>t]1 ,inn] ,portion4 xym' ,out] xy'm ,ea/ ,inn] xy'm' ,out] x'ym ,s\?-,we/ ,inn] x'ym' ,out] x'y'm ,ea/ ,inn] x'y'm' ,out] ---------------------------------------- ------- pg#jdc ,,*apt] ,,ii4 ,,repres5tation ,,( ,,propositions ,,9 ,,t]ms ,,( x ,,& m1 ,,or ,,( y ,,& m4 #a4 ,repres5tation ( ,propositions ( ,exi/5ce 9 t]ms ( x & m1 or ( y & m4 ,let u take1 fir/1 ! ,proposition ,"s xm exi/4 ,note t ! full mean+ ( ?is ,proposition is 7z expla9$ at p4 #ab7 ,"s exi/+ ,?+s are xm-,?+s4 ,?is tells u t !re is at lea/ "o ,?+ 9 ! ,inn] portion ( ! ,nor? ,half2 t is1 t ?is ,comp>tm5t is occupi$4 ,& ?is we c evid5tly repres5t by plac+ a ,r$ ,c\nt] on ! p>tition :i* divides x4 --------------- ------ 747 ------------ ------ --------------- ,9 ! books example1 ?is ,proposition w\ld mean ,"s old b\nd books exi/ 7or ,!re are "s old b\nd books74 ,simil>ly we may repres5t ! sev5 simil> ,propositions1 ,"s xm' exi/1 ,"s x'm exi/1 ,"s x'm' exi/1 ,"s ym exi/1 ,"s ym' exi/1 ,"s y'm exi/1 & ,"s y'm' exi/4 pg#jdd ,let u take1 next1 ! ,proposition ,no xm exi/4 ,?is tells u t !re is no?+ 9 ! ,inn] portion ( ! ,nor? ,half2 t is1 t ?is ,comp>tm5t is empty4 ,& ?is we c repres5t by plac+ two ,grey ,c\nt]s 9 x1 "o 9 ea* ,cell4 --------------- ------ 7 77 7 ------------ ------ --------------- ,simil>ly we may repres5t ! sev5 simil> ,propositions1 9 t]ms ( x & m1 or ( y & m1 viz4 ,no xm' exi/1 ,no x'm exi/1 c4 99 99 99 99 99 ,^! sixte5 ,propositions ( ,exi/5ce are ! only ones t we %all h to repres5t on ?is ,diagram4 #b4 ,repres5tation ( ,propositions ( ,relation 9 t]ms ( x & m1 or ( y & m4 ,let u take1 fir/1 ! ,pair ( ,conv]se ,propositions ,"s x are m ,"s m are x4 ,we "k t ea* ( ^! is equival5t to ! ,proposition ( ,exi/5ce ,"s xm exi/1 :i* we already "k h[ to repres5t4 --------------- ------ 747 ------------ ------ --------------- ,simil>ly = ! sev5 simil> ,pairs1 9 t]ms ( x & m1 or ( y & m4 ,let u take1 next1 ! ,pair ( ,conv]se ,propositions ,no x are m ,no m are x4 ,we "k t ea* ( ^! is equival5t to ! ,proposition ( ,exi/5ce ,no xm exi/1 :i* we already "k h[ to repres5t4 --------------- ------ 7 77 7 ------------ ------ --------------- ,simil>ly = ! sev5 simil> ,pairs1 9 t]ms ( x & m1 or ( y & m4 pg#jde ,let u take1 next1 ! ,proposition ,all x are m4 --------------- 7 7 7 7 ------ 747 ------------ ------ --------------- ,we "k 7see p4 #ah7 t ?is is a ,d\ble ,proposition1 & equival5t to ! two ,propositions ,"s x are m & ,no x are m' 1 ea* ( :i* we already "k h[ to repres5t4 ,simil>ly = ! fifte5 simil> ,propositions1 9 t]ms ( x & m1 or ( y & m4 ,^! ?irty-two ,propositions ( ,relation are ! only ones t we %all h to repres5t on ?is ,diagram4 ,! ,read] %\ld n[ get 8 g5ial fri5d to "q him on ! foll[+ f\r ,tables4 ,! ,victim %\ld h no?+ be=e him b a blank ,trilit]al ,diagram1 a ,r$ ,c\nt]1 & #b ,grey ones1 ) :i* he is to repres5t ! v>i\s ,propositions nam$ by ! ,inquisitor1 e4g4 ,no y' are m1 ,"s xm' exi/1 c41 c4 pg#jdf ,,table ,v4 ---------------------------------------- ----------------- --------------- ,"s xm exi/ --------------- ,"s x are m ------ ,"s m are x ------ 747 7 77 7 ------------ ----------------- ------------ ,no xm exi/ ------ ,no x are m ------ ,no m are x --------------- --------------- ---------------------------------------- ----------------- --------------- ,"s xm' exi/ --------------- 747 ,"s x are m' 7 7 7 7 ------ ,"s m' are x ------ ------------ ----------------- ------------ ,no xm' exi/ ------ ,no x are m' ------ ,no m' are x --------------- --------------- ---------------------------------------- ----------------- --------------- ,"s x'm exi/ --------------- ,"s x' are m ------ ,"s m are x' ------ ------------ ----------------- ------------ 747 ,no x'm exi/ 7 77 7 ------ ,no x' are m ------ ,no m are x' --------------- --------------- ---------------------------------------- ----------------- --------------- ,"s x'm' exi/ --------------- ,"s x' are m' ------ ,"s m' are x' ------ ------------ ----------------- ------------ ,no x'm' exi/ ------ ,no x' are m' ------ 747 ,no m' are x' 7 7 7 7 --------------- --------------- ---------------------------------------- ----------------- pg#jdg ,,table ,,vi4 ---------------------------------------- ----------------- --------------- ,"s ym exi/ --------------- ,"s y are m ------ ,"s m are y ------ 7 7 ---747------ ----------------- ------------ ,no ym exi/ 7 7 ------ ,no y are m ------ ,no m are y --------------- --------------- ---------------------------------------- ----------------- --------------- ,"s ym' exi/ --------------- ,"s y are m' 7 7 ------ ,"s m' are y ------ 747--------- ----------------- ------------ ,no ym' exi/ ------ ,no y are m' ------ ,no m' are y 7 7 --------------- --------------- ---------------------------------------- ----------------- --------------- ,"s y'm exi/ --------------- ,"s y' are m ------ ,"s m are y' ------ 7 7 ------747--- ----------------- ------------ ,no y'm exi/ 7 7 ------ ,no y' are m ------ ,no m are y' --------------- --------------- ---------------------------------------- ----------------- --------------- ,"s y'm' exi/ --------------- ,"s y' are m' 7 7 ------ ,"s m' are y' ------ ---------747 ----------------- ------------ ,no y'm' exi/ ------ ,no y' are m' ------ ,no m' are y' 7 7 --------------- --------------- ---------------------------------------- ----------------- pg#jdh ,,table ,,vii4 ---------------------------------------- ----------------- --------------- --------------- 7 7 7 7 ,all x are m 747 ------ ------ 747 7 77 7 ------------ ----------------- ------------ ------ ,all x are m' ------ --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- ,all x' are m ------ ------ ------------ ----------------- ------------ 747 7 77 7 ------ ,all x' are m' ------ 7 7 7 7 747 --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- ,all m are x ------ ------ 747 7 77 7 ------------ ----------------- ------------ 7 77 7 747 ------ ,all m are x' ------ --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- 747 ,all m' are x 7 7 7 7 ------ ------ ------------ ----------------- ------------ ------ ,all m' are x' ------ 7 7 7 7 747 --------------- --------------- ---------------------------------------- ----------------- pg#jdi ,,table ,,viii4 ---------------------------------------- ----------------- --------------- --------------- 7 7 ,all y are m ------ ------ 7 7 ---747------ ----------------- 747--------- 7 7 ------ ,all y are m' ------ 7 7 --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- 7 7 ,all y' are m ------ ------ 7 7 ------747--- ----------------- ---------747 7 7 ------ ,all y' are m' ------ 7 7 --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- ,all m are y ------ ------ 7 7 7 7 ---747------ ----------------- ------747--- 7 7 7 7 ------ ,all m are y' ------ --------------- --------------- ---------------------------------------- ----------------- --------------- --------------- 7 7 ,all m' are y 7 7 ------ ------ 747--------- ----------------- ---------747 ------ ,all m' are y' ------ 7 7 7 7 --------------- --------------- ---------------------------------------- ----------------- pg#jej ,,*apt] ,,iii4 ,,repres5tation ,,( ,,two ,,propositions ,,( ,,relation1 ,,"o ,,9 ,,t]ms ,,( x ,,& m1 ,,& ,,! ,,o!r ,,9 ,,t]ms ,,( y ,,& m1 ,,on ,,! ,,same ,,diagram4 ,! ,read] _h bett] n[ beg9 to draw little ,diagrams = himself1 & to m>k !m ) ! ,digits ,i & ,o1 in/ead ( us+ ! ,bo>d & ,c\nt]s3 he may put a ,i to repres5t a ,r$ ,c\nt] 7?is may be int]pret$ to mean ,!re is at lea/ "o ,?+ "h71 & a ,o to repres5t a ,grey ,c\nt] 7?is may be int]pret$ to mean ,!re is no?+ "h74 ,! ,pair ( ,propositions1 t we %all h to repres5t1 w always be1 "o 9 t]ms ( x & m1 & ! o!r 9 t]ms ( y & m4 ,:5 we h to repres5t a ,proposition beg9n+ ) ,all1 we break x up into ! two ,propositions to :i* x is equival5t4 ,:5 we h to repres5t1 on ! same ,diagram1 ,propositions1 ( :i* "s beg9 ) ,"s & o!rs ) ,no1 we repres5t ! negative ones fir/4 ,?is w sometimes save u f hav+ to put a ,i on a f5ce & aft]w>ds hav+ to %ift x into a ,cell4 ,let u "w a few examples4 7#a7 ,no x are m'2 ,no y' are m4 ,let u fir/ repres5t ,no x are m'4 ,?is gives u ,diagram a4 ,!n1 repres5t+ ,no y' are m on ! same ,diagram1 we get ,diagram b4 pg#jea a b --------------- --------------- 7,o7 7,o7 7,o7 7,o7 ------ ------ 7,o7 ------------ ------------ 7,o7 ------ ------ --------------- --------------- 7#b7 ,"s m are x2 ,no m are y4 ,if1 neglect+ ! ,rule1 we 7 beg9 ) ,"s m are x1 we %\ld get ,diagram a4 ,& if we 7 !n to take ,no m are y1 :i* tells u t ! ,inn] ,n4,w4 ,cell is empty1 we %\ld be oblig$ to take ! ,i (f ! f5ce 7z x no long] has ! *oice ( two ,cells71 & to put x into ! ,inn] ,n4,e4 ,cell1 z 9 ,diagram c4 ,?is tr\ble may be sav$ by beg9n+ ) ,no m are y1 z 9 ,diagram b4 ,& n[1 :5 we take ,"s m are x1 !re is no f5ce to sit on6 ,! ,i has to g1 at once1 into ! ,n4,e4 ,cell1 z 9 ,diagram c4 a b c --------------- --------------- --------------- ------ ------ ------ 7,i7 7,o7 7,o77,i7 ------------ ------------ ------------ 7,o7 7,o7 ------ ------ ------ --------------- --------------- --------------- 7#c7 ,no x' are m'2 ,all m are y4 ,"h we beg9 by break+ up ! ,second into ! two ,propositions to :i* x is equival5t4 ,?us we h ?ree ,propositions to repres5t1 viz4-- 7#a7 ,no x' are m'2 7#b7 ,"s m are y2 7#c7 ,no m are y'4 ,^! we w take 9 ! ord] #a1 #c1 #b4 ,fir/ we take ,no4 7#a71 viz4 ,no x' are m'4 ,?is gives u ,diagram a4 pg#jeb ,add+ to ?is1 ,no4 7#c71 viz4 ,no m are y'1 we get ,diagram b4 ,?is "t ! ,i1 repres5t+ ,no4 7#b71 viz4 ,"s m are y1 has to sit on ! f5ce1 z !re is no ,o to ord] x (f6 ,?is gives u ,diagram c4 a b c --------------- --------------- --------------- ------ ------ ------ 7,o7 7,o7 ------------ ------------ ---7,i7------ 7,o7 7,o7 ------ ------ ------ 7,o7 7,o7 7,o7 7,o7 7,o7 7,o7 --------------- --------------- --------------- 7#d7 ,all m are x2 ,all y are m4 ,"h we break up bo? ,propositions1 & ?us get f\r to repres5t1 viz4-- 7#a7 ,"s m are x2 7#b7 ,no m are x'2 7#c7 ,"s y are m2 7#d7 ,no y are m'4 ,^! we w take 9 ! ord] #b1 #d1 #a1 #c4 ,fir/ we take ,no4 7#b71 viz4 ,no m are x'4 ,?is gives u ,diagram a4 ,to ?is we add ,no4 7#d71 viz4 ,no y are m'1 & ?us get ,diagram b4 ,if we 7 to add to ?is ,no4 7#a71 viz4 ,"s m are x1 we %\ld h to put ! ,i on a f5ce3 s let u try ,no4 7#c7 in/ead1 viz4 ,"s y are m4 ,?is gives u ,diagram c4 ,& n[ !re is no ne$ to tr\ble ab\t ,no4 7#a71 z x w\ld n add any?+ to our in=mation to put a ,i on ! f5ce4 ,! ,diagram already tells u t ,"s m are x4 a b c --------------- --------------- --------------- 7,o7 7,o7 ------ ------ ------ 7,i7 ------------ ------------ ------------ 7,o77,o7 7,o77,o7 7,o77,o7 ------ ------ ------ 7,o7 7,o7 --------------- --------------- --------------- ,"w ,examples #a1 #i-ab 7p4 #ig72 #b1 #a-bj 7p4 #ih74 pg#jec ,,*apt] ,,iv4 ,,int]pretation1 ,,9 ,,t]ms ,,( x ,,& y1 ,,( ,,trilit]al ,,diagram1 ,,:5 ,,m>k$ ,,) ,,c\nt]s ,,or ,,digits4 ,! problem be=e u is1 giv5 a m>k$ ,trilit]al ,diagram1 to asc]ta9 :at ,propositions ( ,relation1 9 t]ms ( x & y1 are repres5t$ on x4 ,! be/ plan1 = a beg9n]1 is to draw a ,bilit]al ,diagram alongside ( x1 & to transf]1 f ! "o to ! o!r1 all ! in=mation he c4 ,he c !n read (f1 f ! ,bilit]al ,diagram1 ! requir$ ,propositions4 ,aft] a little practice1 he w be able to disp5se ) ! ,bilit]al ,diagram1 & to read (f ! result f ! ,trilit]al ,diagram itself4 ,to transf] ! in=mation1 obs]ve ! foll[+ ,rules3-- 7#a7 ,exam9e ! ,n4,w4 ,qu>t] ( ! ,trilit]al ,diagram4 7#b7 ,if x conta9s a ,i1 9 ei!r ,cell1 x is c]ta9ly occupi$1 & y may m>k ! ,n4,w4 ,qu>t] ( ! ,bilit]al ,diagram ) a ,i4 7#c7 ,if x conta9s two ,os1 "o 9 ea* ,cell1 x is c]ta9ly empty1 & y may m>k ! ,n4,w4 ,qu>t] ( ! ,bilit]al ,diagram ) a ,o4 pg#jed 7#d7 ,deal 9 ! same way ) ! ,n4,e41 ! ,s4,w41 & ! ,s4,e4 ,qu>t]4 ,let u take1 z examples1 ! results ( ! f\r ,examples work$ 9 ! previ\s ,*apt]s4 7#a7 --------------- 7,o7 7,o7 ------ 7,o7 ------------ 7,o7 ------ --------------- ,9 ! ,n4,w4 ,qu>t]1 only "o ( ! two ,cells is m>k$ z empty3 s we d n "k :e!r ! ,n4,w4 ,qu>t] ( ! ,bilit]al ,diagram is occupi$ or empty3 s we _c m>k x4 ------- 7,o7 ------ ------- ,9 ! ,n4,e4 ,qu>t]1 we f9d two ,os3 s ?is ,qu>t] is c]ta9ly empty2 & we m>k x s on ! ,bilit]al ,diagram4 ,9 ! ,s4,w4 ,qu>t]1 we h no in=mation at all4 ,9 ! ,s4,e4 ,qu>t]1 we h n en\gh to use4 ,we may read (f ! result z ,no x are y'1 or ,no y' are x1 :i*ev] we pref]4 7#b7 --------------- ------ 7,o77,i7 ------------ 7,o7 ------ --------------- ,9 ! ,n4,w4 ,qu>t]1 we h n en\gh in=mation to use4 ,9 ! ,n4,e4 ,qu>t]1 we f9d a ,i4 ,?is %[s u t x is occupi$3 s we may m>k ! ,n4,e4 ,qu>t] on ! ,bilit]al ,diagram ) a ,i4 ------- 7,i7 ------ ------- ,9 ! ,s4,w4 ,qu>t]1 we h n en\gh in=mation to use4 ,9 ! ,s4,e4 ,qu>t]1 we h none at all4 ,we may read (f ! result z ,"s x are y'1 or ,"s y' are x1 :i*ev] we pref]4 pg#jee 7#c7 --------------- ------ 7,o7 ---7,i7------ 7,o7 ------ 7,o7 7,o7 --------------- ,9 ! ,n4,w4 ,qu>t]1 we h no in=mation4 7,! ,i1 sitt+ on ! f5ce1 is ( no use to u until we "k on :i* side he means to jump d[n67 ,9 ! ,n4,e4 ,qu>t]1 we h n en\gh in=mation to use4 ,nei!r h we 9 ! ,s4,w4 ,qu>t]4 ------- ------ 7,o7 ------- ,! ,s4,e4 ,qu>t] is ! only "o t yields en\gh in=mation to use4 ,x is c]ta9ly empty3 s we m>k x z su* on ! ,bilit]al ,diagram4 ,we may read (f ! results z ,no x' are y'1 or ,no y' are x'1 :i*ev] we pref]4 7#d7 --------------- 7,o7 ------ 7,i7 ------------ 7,o77,o7 ------ 7,o7 --------------- ,! ,n4,w4 ,qu>t] is occupi$1 9 spite ( ! ,o 9 ! ,out] ,cell4 ,s we m>k x ) a ,i on ! ,bilit]al ,diagram4 ,! ,n4,e4 ,qu>t] yields no in=mation4 ------- 7,i7 ------ ------- ,! ,s4,w4 ,qu>t] is c]ta9ly empty4 ,s we m>k x z su* on ! ,bilit]al ,diagram4 ------- 7,i7 ------ 7,o7 ------- ,! ,s4,e4 ,qu>t] does n yield en\gh in=mation to use4 ,we read (f ! result z ,all y are x4 ,review ,tables ,v1 ,,vi 7pp4 #df1 #dg74 ,"w ,examples #a1 #ac-af 7p4 #ig72 #b1 #ba-cb 7p4 #ih72 #c1 #a-bj 7p4 #ii74 pg#jef ,,book ,v4 ,,syllogisms4 ,,*apt] ,i4 ,,introductory ,:5 a ,trio ( ,bilit]al ,propositions ( ,relation is su* t 7#a7 all _! six ,t]ms are ,species ( ! same ,g5us1 7#b7 e two ( !m conta9 betwe5 !m a ,pair ( codivisional ,classes1 7#c7 ! ?ree ,propositions are s relat$ t1 if ! fir/ two 7 true1 ! ?ird w\ld be true1 ! ,trio is call$ a ',syllogism'2 ! ,g5us1 ( :i* ea* ( ! six ,t]ms is a ,species1 is call$ its ',univ]se ( ,disc\rse'1 or1 m briefly1 its ',univ4'2 ! fir/ two ,propositions are call$ its ',premisses'1 & ! ?ird its ',conclusion'2 also ! ,pair ( codivisional ,t]ms 9 ! ,premisses are call$ its ',elim9&s'1 & ! o!r two its ',ret95ds'4 ,! ,conclusion ( a ,syllogism is said to be 'consequ5t' f its ,premisses3 h5ce x is usual to prefix to x ! ^w ,!re=e 7or ! ,symbol 4'474 pg#jeg ,note t ! ',elim9&s' are s call$ because !y are elim9at$1 & d n appe> 9 ! ,conclusion2 & t ! ',ret95ds' are s call$ because !y are reta9$1 & d appe> 9 ! ,conclusion4 ,note also t ! "q1 :e!r ! ,conclusion is or is n consequ5t f ! ,premisses1 is n affect$ by ! actual tru? or falsity ( any ( ! ,trio1 b dep5ds entirely on _! relation%ip to ea* o!r4 ,z a specim5-,syllogism1 let u take ! ,trio ,no x-,?+s are m-,?+s2 ,no y-,?+s are m'-,?+s4 ,no x-,?+s are y-,?+s4 :i* we may write1 z expla9$ at p4 #bf1 ?us3-- ,no x are m2 ,no y are m'4 ,no x are y4 ,"h ! fir/ & second conta9 ! ,pair ( codivisional ,classes m & m'2 ! fir/ & ?ird conta9 ! ,pair x & x2 & ! second & ?ird conta9 ! ,pair y & y4 ,also ! ?ree ,propositions are 7z we %all see h]eaft]7 s relat$ t1 if ! fir/ two 7 true1 ! ?ird w\ld also be true4 ,h5ce ! ,trio is a ,syllogism2 ! two ,propositions1 ,no x are m & ,no y are m'1 are its ,premisses2 ! ,proposition ,no x are y is its ,conclusion2 ! ,t]ms m & m' are its ,elim9&s2 & ! ,t]ms x & y are its ,ret95ds4 ,h5ce we may write x ?us3-- ,no x are m2 ,no y are m'4 4'4 ,no x are y4 ,z a second specim51 let u take ! ,trio ,all cats und]/& ,fr5*2 ,"s *ick5s are cats4 ,"s *ick5s und]/& ,fr5*4 ,^!1 put into normal =m1 are ,all cats are creatures und]/&+ ,fr5*2 ,"s *ick5s are cats4 ,"s *ick5s are creatures und]/&+ ,fr5*4 ,"h all ! six ,t]ms are ,species ( ! ,g5us creatures4 ,also ! fir/ & second ,propositions conta9 ! ,pair ( codivisional ,classes cats & cats2 ! fir/ & ?ird conta9 ! ,pair creatures und]/&+ ,fr5* & creatures und]/&+ ,fr5*2 & ! second & ?ird conta9 ! ,pair *ick5s & *ick5s4 pg#jeh ,also ! ?ree ,propositions are 7z we %all see at p4 #fd7 s relat$ t1 if ! fir/ two 7 true1 ! ?ird w\ld be true4 7,! fir/ two are1 z x happ5s1 n /rictly true 9 our planet4 ,b !re is no?+ to h9d] !m f be+ true 9 "s o!r planet1 say ,m>s or ,jupit]--9 :i* case ! ?ird w\ld also be true 9 t planet1 & its inhabitants w\ld probably engage *ick5s z nurs]y-gov]nesses4 ,!y w\ld ?us secure a s+ul> cont+5t privilege1 unkn[n 9 ,engl&1 namely1 t !y w\ld be able1 at any "t :5 provisions ran %ort1 to utilise ! nurs]y-gov]ness = ! nurs]y-d9n]67 ,h5ce ! ,trio is a ,syllogism2 ! ,g5us creatures is its ',univ4'2 ! two ,propositions1 ,all cats und]/& ,fr5* & ,"s *ick5s are cats1 are its ,premisses1 ! ,proposition ,"s *ick5s und]/& ,fr5* is its ,conclusion2 ! ,t]ms cats & cats are its ,elim9&s2 & ! ,t]ms1 creatures und]/&+ ,fr5* & *ick5s1 are its ,ret95ds4 ,h5ce we may write x ?us3-- ,all cats und]/& ,fr5*2 ,"s *ick5s are cats2 4'4 ,"s *ick5s und]/& ,fr5*4 pg#jei ,,*apt] ,,ii4 ,,problems ,,9 ,,syllogisms4 #a4 ,introductory4 ,:5 ! ,t]ms ( a ,proposition are repres5t$ by words1 x is said to be 'concrete'2 :5 by lett]s1 'ab/ract4' ,to translate a ,proposition f concrete into ab/ract =m1 we fix on a ,univ41 & reg>d ea* ,t]m z a ,species ( x1 & we *oose a lett] to repres5t its ,diff]5tia4 ,= example1 suppose we wi% to translate ,"s soldi]s are brave into ab/ract =m4 ,we may take m5 z ,univ41 & reg>d soldi]s & brave m5 z ,species ( ! ,g5us m52 & we may *oose x to repres5t ! peculi> ,attribute 7say milit>y7 ( soldi]s1 & y to repres5t brave4 ,!n ! ,proposition may be writt5 ,"s milit>y m5 are brave m52 i4e4 ,"s x-m5 are y-m52 i4e4 7omitt+ m51 z expla9$ at p4 #bf7 ,"s x are y4 ,9 practice1 we %\ld m]ely say ,let ,univ4 be m51 x soldi]s1 y brave1 & at once translate ,"s soldi]s are brave into ,"s x are y4 ,! ,problems we %all h to solve are ( two k9ds1 viz4 7#a7 ,giv5 a ,pair ( ,propositions ( ,relation1 :i* conta9 betwe5 !m a pair ( codivisional ,classes1 & :i* are propos$ z ,premisses3 to asc]ta9 :at ,conclusion1 if any1 is consequ5t f !m4 7#b7 ,giv5 a ,trio ( ,propositions ( ,relation1 ( :i* e two conta9 a pair ( codivisional ,classes1 & :i* are propos$ z a ,syllogism3 to asc]ta9 :e!r ! propos$ ,conclusion is consequ5t f ! propos$ ,premisses1 &1 if s1 :e!r x is complete4 ,^! ,problems we w discuss sep>ately4 pg#jfj #b4 ,giv5 a ,pair ( ,propositions ( ,relation1 :i* conta9 betwe5 !m a pair ( codivisional ,classes1 & :i* are propos$ z ,premisses3 to asc]ta9 :at ,conclusion1 if any1 is consequ5t f !m4 ,! ,rules1 = do+ ?is1 are z foll[s3-- 7#a7 ,det]m9e ! ',univ]se ( ,disc\rse'4 7#b7 ,con/ruct a ,diction>y1 mak+ m & m 7or m & m'7 repres5t ! pair ( codivisional ,classes1 & x 7or x'7 & y 7or y'7 ! o!r two4 7#c7 ,translate ! propos$ ,premisses into ab/ract =m4 7#d7 ,repres5t !m1 toge!r1 on a ,trilit]al ,diagram4 7#e7 ,asc]ta9 :at ,proposition1 if any1 9 t]ms ( x & y1 is also repres5t$ on x4 7#f7 ,translate ?is into concrete =m4 ,x is evid5t t1 if ! propos$ ,premisses 7 true1 ?is o!r ,proposition w\ld also be true4 ,h5ce x is a ,conclusion consequ5t f ! propos$ ,premisses4 ,let u "w "s examples4 7#a7 ,no son ( m9e is di%one/2 ,p always treat an hone/ man ) respect4 ,tak+ m5 z ,univ41 we may write ^! z foll[s3-- ,no sons ( m9e are di%one/ m52 ,all hone/ m5 are m5 treat$ ) respect4 ,we c n[ con/ruct our ,diction>y1 viz4 m hone/2 x sons ( m9e2 y treat$ ) respect4 7,note t ! expression x sons ( m9e is an abbreviat$ =m ( x ! ,diff]5tia ( 'sons ( m9e'1 :5 reg>d$ z a ,species ( 'm5'47 ,! next ?+ is to translate ! propos$ ,premisses into ab/ract =m1 z foll[s3-- ,no x are m'2 ,all m are y4 pg#jfa ,next1 by ! process describ$ at p4 #ej1 we repres5t ^! on a ,trilit]al ,diagram1 ?us3-- --------------- 7,o7 7,o7 ------ 7,o7 ---7,i7------ 7,o7 ------ --------------- ,next1 by ! process describ$ at p4 #ec1 we transf] to a ,bilit]al ,diagram all ! in=mation we c4 ------- 7,o7 ------ ------- ,! result we read z ,no x are y' or z ,no y' are x1 :i*ev] we pref]4 ,s we ref] to our ,diction>y1 to see :i* w look be/2 & we *oose ,no x are y'1 :i*1 translat$ into concrete =m1 is ,no son ( m9e fails to be treat$ ) respect4 7#b7 ,all cats und]/& ,fr5*2 ,"s *ick5s are cats4 ,tak+ creatures z ,univ41 we write ^! z foll[s3-- ,all cats are creatures und]/&+ ,fr5*2 ,"s *ick5s are cats4 ,we c n[ con/ruct our ,diction>y1 viz4 m cats2 x und]/&+ ,fr5*2 y *ick5s4 ,! propos$ ,premisses1 translat$ into ab/ract =m1 are ,all m are x2 ,"s y are m4 ,9 ord] to repres5t ^! on a ,trilit]al ,diagram1 we break up ! fir/ into ! two ,propositions to :i* x is equival5t1 & ?us get ! ?ree ,propositions 7#a7 ,"s m are x2 7#b7 ,no m are x'2 7#c7 ,"s y are m4 ,! ,rule1 giv5 at p4 #ej1 w\ld make u take ^! 9 ! ord] #b1 #a1 #c4 ,?is1 h[ev]1 w\ld produce ! result ----------------- -------- 7,i77,i7 -------- 7,o7 7,o7 -------- ----------------- pg#jfb ,s x w\ld be bett] to take !m 9 ! ord] #b1 #c1 #a4 ,nos4 7#b7 & 7#c7 give u ! result "h %[n2 & n[ we ne$ n tr\ble ab\t ,no4 7#a71 z ! ,proposition ,"s m are x is already repres5t$ on ! ,diagram4 --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- ,transf]r+ our in=mation to a ,bilit]al ,diagram1 we get ------- 7,i7 ------ ------- ,?is result we c read ei!r z ,"s x are y or ,"s y are x4 ,aft] consult+ our ,diction>y1 we *oose ,"s y are x1 :i*1 translat$ into concrete =m1 is ,"s *ick5s und]/& ,fr5*4 7#c7 ,all dilig5t /ud5ts are successful2 ,all ignorant /ud5ts are unsuccessful4 ,let ,univ4 be /ud5ts2 m successful2 x dilig5t2 y ignorant4 ,^! ,premisses1 9 ab/ract =m1 are ,all x are m2 ,all y are m'4 ,^!1 brok5 up1 give u ! f\r ,propositions 7#a7 ,"s x are m2 7#b7 ,no x are m'2 7#c7 ,"s y are m'2 7#d7 ,no y are m4 :i* we w take 9 ! ord] #b1 #d1 #a1 #c4 ,repres5t+ ^! on a ,trilit]al ,diagram1 we get --------------- 7,o7 7,o7 ------ 7,o77,i7 ------------ 7,o7 ------ 7,i7 --------------- ,& ?is in=mation1 transf]r$ to a ,bilit]al ,diagram1 is ------- 7,o77,i7 ------ 7,i7 ------- ,"h we get two ,conclusions1 viz4 ,all x are y'2 ,all y are x'4 pg#jfc ,& ^!1 translat$ into concrete =m1 are ,all dilig5t /ud5ts are 7n-ignorant1 i4e47 le>n$2 ,all ignorant /ud5ts are 7n-dilig5t1 i4e47 idle4 7,see p4 #d47 7#d7 ,( ! prison]s :o 7 put on _! trial at ! la/ ,assizes1 all1 aga9/ :om ! v]dict 'guilty' 0 return$1 7 s5t5c$ to imprisonm5t2 ,"s1 :o 7 s5t5c$ to imprisonm5t1 7 also s5t5c$ to h>d lab\r4 ,let ,univ4 be ! prison]s :o 7 put on _! trial at ! la/ ,assizes2 m :o 7 s5t5c$ to imprisonm5t2 x aga9/ :om ! v]dict 'guilty' 0 return$2 y :o 7 s5t5c$ to h>d lab\r4 ,! ,premisses1 translat$ into ab/ract =m1 are ,all x are m2 ,"s m are y4 ,break+ up ! fir/1 we get ! ?ree 7#a7 ,"s x are m2 7#b7 ,no x are m'2 7#c7 ,"s m are y4 ,repres5t+ ^!1 9 ! ord] #b1 #a1 #c1 on a ,trilit]al ,diagram1 we get --------------- 7,o7 7,o7 ------ 7,i7 ---7,i7------ ------ --------------- ,"h we get no ,conclusion at all4 ,y w\ld v likely h guess$1 if y _h se5 only ! ,premisses1 t ! ,conclusion w\ld be ,"s1 aga9/ :om ! v]dict 'guilty' 0 return$1 7 s5t5c$ to h>d lab\r4 ,b ?is ,conclusion is n ev5 true1 ) reg>d to ! ,assizes ,i h "h inv5t$4 ,n true6 y exclaim4 ,!n :o 7 !y1 :o 7 s5t5c$ to imprisonm5t & 7 also s5t5c$ to h>d lab\r8 ,!y mu/ h _h ! v]dict 'guilty' return$ aga9/ !m1 or h[ c\ld !y be s5t5c$8 ,well1 x happ5$ l ?is1 y see4 ,!y 7 ?ree ruffians1 :o _h committ$ highway-robb]y4 ,:5 !y 7 put on _! trial1 !y plead$ 'guilty'4 ,s no v]dict 0 return$ at all2 & !y 7 s5t5c$ at once4 ,i w n[ "w out1 9 _! briefe/ =m1 z models = ! ,read] to imitate 9 work+ examples1 ! above f\r concrete ,problems4 pg#jfd 7#a7 see p4 #fj ,no son ( m9e is di%one/2 ,p always treat an hone/ man ) respect4 ,univ4 m52 m hone/2 x my sons2 y treat$ ) respect4 --------------- ------- ,no x are m'2 7,o7 7,o7 7,o7 ,all m are y4 ------ ------ 7,o7 ---7,i7------ ------- 7,o7 ------ 4'4 ,no x are y'4 --------------- i4e4 ,no son ( m9e ev] fails to be treat$ ) respect4 7#b7 see p4 #fa ,all cats und]/& ,fr5*2 ,"s *ick5s are cats4 ,univ4 creatures2 m cats2 x und]/&+ ,fr5*2 y *ick5s4 --------------- ------- ,all m are x2 7,i7 ,"s y are m4 ------ ------ 7,i7 ------------ ------- 7,o77,o7 ------ 4'4 ,"s y are x4 --------------- i4e4 ,"s *ick5s und]/& ,fr5*4 7#c7 see p4 #fb ,all dilig5t /ud5ts are successful2 ,all ignorant /ud5ts are unsuccessful4 ,univ4 /ud5ts2 m successful2 x dilig5t2 y ignorant4 --------------- ------- ,all x are m2 7,o7 7,o7 7,o77,i7 ,all y are m'4 ------ ------ 7,o77,i7 7,i7 ------------ ------- 7,o7 ------ 4'4 ,all x are y'2 7,i7 ,all y are x'4 --------------- i4e4 ,all dilig5t /ud5ts are le>n$2 & all ignorant /ud5ts are idle4 pg#jfe 7#d7 see p4 #fc ,( ! prison]s :o 7 put on _! trial at ! la/ ,assizes1 all1 aga9/ :om ! v]dict 'guilty' 0 return$1 7 s5t5c$ to imprisonm5t2 ,"s1 :o 7 s5t5c$ to imprisonm5t1 7 also s5t5c$ to h>d lab\r4 ,univ4 prison]s :o 7 put on _! trial at ! la/ ,assizes1 m s5t5c$ to imprisonm5t2 x aga9/ :om ! v]dict 'guilty' 0 return$2 y s5t5c$ to h>d lab\r4 --------------- ,all x are m2 7,o7 7,o7 ,"s m are y4 ------ 7,i7 ---7,i7------ ------ ,!re is no ,conclusion4 --------------- ,review ,tables ,,vii1 ,,viii 7pp4 #dh1 #di74 ,"w ,examples #a1 #ag-ba 7p4 #ig72 #d1 #a-f 7p4 #ajj72 #e1 #a-f 7p4 #aja74 pg#jff #c4 ,giv5 a ,trio ( ,propositions ( ,relation1 ( :i* e two conta9 a ,pair ( codivisional ,classes1 & :i* are propos$ z a ,syllogism2 to asc]ta9 :e!r ! propos$ ,conclusion is consequ5t f ! propos$ ,premisses1 &1 if s1 :e!r x is complete4 ,! ,rules1 = do+ ?is1 are z foll[s3-- 7#a7 ,take ! propos$ ,premisses1 & asc]ta91 by ! process describ$ at p4 #fj1 :at ,conclusion1 if any1 is consequ5t f !m4 7#b7 ,if !re be no ,conclusion1 say s4 7#c7 ,if !re be a ,conclusion1 comp>e x ) ! propos$ ,conclusion1 & pron\nce accord+ly4 ,i w n[ "w out1 9 _! briefe/ =m1 z models = ! ,read] to imitate 9 work+ examples1 six ,problems4 7#a7 ,all soldi]s are /rong2 ,all soldi]s are brave4 ,"s /rong m5 are brave4 ,univ4 m52 m soldi]s2 x /rong2 y brave4 pg#jfg --------------- ------- ,all m are x2 7,i7 ,all m are y4 ------ ------ ,"s x are y4 7,i77,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,"s x are y4 --------------- ,h5ce propos$ ,conclusion is "r4 7#b7 ,i admire ^! pictures2 ,:5 ,i admire any?+ ,i wi% to exam9e x ?or\ghly4 ,i wi% to exam9e "s ( ^! pictures ?or\ghly4 ,univ4 ?+s2 m admir$ by me2 x ^! pictures2 y ?+s :i* ,i wi% to exam9e ?or\ghly4 --------------- ------- ,all x are m2 7,o7 7,o7 7,i77,o7 ,all m are y4 ------ ------ ,"s x are y4 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,all x are y4 --------------- ,h5ce propos$ ,conclusion is incomplete1 ! complete "o be+ ,i wi% to exam9e all ^! pictures ?or\ghly4 7#c7 ,none b ! brave des]ve ! fair2 ,"s bragg>ts are c[>ds4 ,"s bragg>ts d n des]ve ! fair4 ,univ4 p]sons2 m brave2 x des]v+ ( ! fair2 y bragg>ts4 --------------- ------- ,no m' are x2 7,o7 7,o7 ,"s y are m'4 ------ ------ ,"s y are x'4 7,i7 ------------ ------- ------ 4'4 ,"s y are x'4 7,i7 --------------- ,h5ce propos$ ,conclusion is "r4 pg#jfh 7#d7 ,all soldi]s c m>*2 ,"s babies are n soldi]s4 ,"s babies _c m>*4 ,univ4 p]sons2 m soldi]s2 x able to m>*2 y babies4 --------------- ,all m are x2 ,"s y are m'4 ------ ,"s y are x'4 7,i7 7,i7--------- 7,o77,o7 ------ ,!re is no ,conclusion4 --------------- 7#e7 ,all selfi% m5 are unpopul>2 ,all oblig+ m5 are popul>4 ,all oblig+ m5 are unselfi%4 ,univ4 m52 m popul>2 x selfi%2 y oblig+4 --------------- ------- ,all x are m'2 7,o7 7,i7 7,o77,i7 ,all y are m4 ------ ------ ,all y are x'4 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 ,all x are y'2 7,o7 ,all y are x'4 --------------- ,h5ce propos$ ,conclusion is incomplete1 ! complete "o conta9+1 9 addition1 ,all selfi% m5 are disoblig+4 7#f7 ,no "o1 :o means to g by ! tra9 & _c get a conveyance1 & has n en\gh "t to walk to ! /ation1 c d )\t runn+2 ,?is p>ty ( t\ri/s mean to g by ! tra9 & _c get a conveyance1 b !y h pl5ty ( "t to walk to ! /ation4 ,?is p>ty ( t\ri/s ne$ n run4 ,univ4 p]sons mean+ to g by ! tra91 & unable to get a conveyance2 m hav+ en\gh "t to walk to ! /ation2 x ne$+ to run2 y ^! t\ri/s4 pg#jfi --------------- ,no m' are x'2 7,o7 ,all y are m4 ------ ,all y are x'4 ---7,i7------ ------ ,!re is no 7,o7 7,o7 ,conclusion4 --------------- ,"h is ano!r opportunity1 g5tle ,read]1 = play+ a trick on y\r innoc5t fri5d4 ,put ! propos$ ,syllogism be=e him1 & ask him :at he ?9ks ( ! ,conclusion4 ,he w reply ,:y1 x's p]fectly correct1 ( c\rse6 ,& if y\r preci\s ,logic-book tells y x isn't1 don't believe x6 ,y don't mean to tell me ^? t\ri/s ne$ to run8 ,if ,i 7 "o ( !m1 & knew ! ,premisses to be true1 ,i %\ld be q cle> t ,i ne$n't run--& ,i %\ld walk6 ,& y w reply ,b suppose !re 0 a mad bull beh9d y8 ,& !n y\r innoc5t fri5d w say ,hum6 ,ha6 ,i mu/ ?9k t ov] a bit6 ,y may !n expla9 to him1 z a conv5i5t te/ ( ! s\ndness ( a ,syllogism1 t1 if circum/ances c be inv5t$ :i*1 )\t int]f]+ ) ! tru? ( ! ,premisses1 w\ld make ! ,conclusion false1 ! ,syllogism mu/ be uns\nd4 ,review ,tables ,v-,,viii 7pp4 #df-di74 ,"w ,examples #d1 #g-ab 7p4 #ajj72 #e1 #g-ab 7p4 #aja72 #f1 #a-aj 7p4 #ajf72 #g1 #a-f 7pp4 #ajg1 #ajh74 pg#jgj ,,book ,,vi4 ,,! ,,me?od ,,( ,,subscripts4 ,,*apt] ,i4 ,,introductory4 ,let u agree t x#a %all mean ,"s exi/+ ,?+s h ! ,attribute x1 i4e4 7m briefly7 ,"s x exi/2 also t xy#a %all mean ,"s xy exi/1 & s on4 ,su* a ,proposition may be call$ an ',entity4' ,note t1 :5 !re are two lett]s 9 ! expression1 x does n 9 ! lea/ matt] :i* /&s fir/3 xy#a & yx#a mean exactly ! same4 ,also t x#j %all mean ,no exi/+ ,?+s h ! ,attribute x1 i4e4 7m briefly7 ,no x exi/2 also t xy#j %all mean ,no xy exi/1 & s on4 ,su* a ,proposition may be call$ a ',nullity'4 ,also t %all mean &4 ,?us ab#a cd#j means ,"s ab exi/ & no cd exi/4 ,also t %all mean w\ld1 if true1 prove4 ,?us1 x#j xy#j means ,! ,proposition ',no x exi/' w\ld1 if true1 prove ! ,proposition ',no xy exi/'4 ,:5 two ,lett]s are bo? ( !m acc5t$1 or bo? n acc5t$1 !y are said to h ',l ,signs'1 or to be ',l'3 :5 "o is acc5t$1 & ! o!r n1 !y are said to h ',unlike ,signs'1 or to be ',unlike'4 pg#jga ,,*apt] ,,ii4 ,,repres5tation ,,( ,,propositions ,,( ,,relation4 ,let u take1 fir/1 ! ,proposition ,"s x are y4 ,?is1 we "k1 is equival5t to ! ,proposition ( ,exi/5ce ,"s xy exi/4 7,see p4 #ca47 ,h5ce x may be repres5t$ by ! expression xy#a4 ,! ,conv]se ,proposition ,"s y are x may ( c\rse be repres5t$ by ! same expression1 viz4 xy#a4 ,simil>ly we may repres5t ! ?ree simil> ,pairs ( ,conv]se ,propositions1 viz4-- ,"s x are y' ,"s y' are x1 ,"s x' are y ,"s y are x'1 ,"s x' are y' ,"s y' are x'4 ,let u take1 next1 ! ,proposition ,no x are y4 ,?is1 we "k1 is equival5t to ! ,proposition ( ,exi/5ce ,no xy exi/4 7,see p4 #cc47 ,h5ce x may be repres5t$ by ! expression xy#j4 ,! ,conv]se ,proposition ,no y are x may ( c\rse be repres5t$ by ! same expression1 viz4 xy#j4 ,simil>ly we may repres5t ! ?ree simil> ,pairs ( ,conv]se ,propositions1 viz4-- ,no x are y' ,no y' are x1 ,no x' are y ,no y are x'1 ,no x' are y' ,no y' are x'4 pg#jgb ,let u take1 next1 ! ,proposition ,all x are y4 ,n[ x is evid5t t ! ,d\ble ,proposition ( ,exi/5ce ,"s x exi/ & no xy' exi/ tells u t "s x-,?+s exi/1 b t none ( !m h ! ,attribute y'3 t is1 x tells u t all ( !m h ! ,attribute y3 t is1 x tells u t ,all x are y4 ,also x is evid5t t ! expression x#a xy'#j repres5ts ?is ,d\ble ,proposition4 ,h5ce x also repres5ts ! ,proposition ,all x are y4 ,! ,read] w p]haps be puzzl$ by ! /atem5t t ! ,proposition ,all x are y is equival5t to ! ,d\ble ,proposition ,"s x exi/ & no xy' exi/1 rememb]+ t x 0 /at$1 at p4 #cc1 to be equival5t to ! ,d\ble ,proposition ,"s x are y & no x are y' 7i4e4 ,"s xy exi/ & no xy' exi/74 ,! explanation is t ! ,proposition ,"s xy exi/ conta9s sup]flu\s in=mation4 ,"s x exi/ is en\gh = our purpose4 ,?is expression may be writt5 9 a %ort] =m1 viz4 x#ay'#j1 s9ce ea* ,subscript takes effect back to ! beg9n+ ( ! expression4 ,simil>ly we may repres5t ! sev5 simil> ,propositions ,all x are y'1 ,all x' are y1 ,all x' are y'1 ,all y are x1 ,all y are x'1 ,all y' are x1 & ,all y' are x'4 ,! ,read] %\ld make out all ^! = himself4 ,x w be conv5i5t to rememb] t1 9 translat+ a ,proposition1 beg9n+ ) ,all1 f ab/ract =m into subscript =m1 or vice v]s1 ! ,pr$icate *anges sign 7t is1 *anges f positive to negative1 or else f negative to positive74 ,?us1 ! ,proposition ,all y are x' becomes y#ax#j1 :]e ! ,pr$icate *anges f x' to x4 ,aga91 ! expression x'#ay'#j becomes ,all x' are y1 :]e ! ,pr$icate *anges = y' to y4 pg#jgc ,,*apt] ,,iii4 ,,syllogisms4 #a4 ,repres5tation ( ,syllogisms4 ,we already "k h[ to repres5t ea* ( ! ?ree ,propositions ( a ,syllogism 9 subscript =m4 ,:5 t is done1 all we ne$1 besides1 is to write ! ?ree expressions 9 a r[1 ) betwe5 ! ,premisses1 & be=e ! ,conclusion4 ,?us ! ,syllogism ,no x are m'2 ,all m are y4 4'4 ,no x are y'4 may be repres5t$ ?us3-- xm'#j m#ay'#j xy'#j ,:5 a ,proposition has to be translat$ f concrete =m into subscript =m1 ! ,read] w f9d x conv5i5t1 j at fir/1 to translate x into ab/ract =m1 & !nce into subscript =m4 ,b1 aft] a little practice1 he w f9d x q easy to g /raight f concrete =m to subscript =m4 pg#jgd #b4 ,=mul = solv+ ,problems 9 ,syllogisms4 ,:5 once we h f\nd1 by ,diagrams1 ! ,conclusion to a giv5 ,pair ( ,premisses1 & h repres5t$ ! ,syllogism 9 subscript =m1 we h a ,=mula1 by :i* we c at once f9d1 )\t hav+ to use ,diagrams aga91 ! ,conclusion to any o!r ,pair ( ,premisses hav+ ! same subscript =ms4 ,?us1 ! expression xm#j ym'#j xy#j is a ,=mula1 by :i* we c f9d ! ,conclusion to any ,pair ( ,premisses ^: subscript =ms are xm#j ym'#j ,= example1 suppose we _h ! ,pair ( ,propositions ,no gluttons are heal?y2 ,no unheal?y m5 are /rong4 propos$ z ,premisses4 ,tak+ m5 z our ',univ]se'1 & mak+ m heal?y2 x gluttons2 y /rong2 we might translate ! ,pair into ab/ract =m1 ?us3-- ,no x are m2 ,no m' are y4 ,^!1 9 subscript =m1 w\ld be xm#j m'y#j :i* are id5tical ) ^? 9 our ,=mula4 ,h5ce we at once "k ! ,conclusion to be xy#j t is1 9 ab/ract =m1 ,no x are y2 t is1 9 concrete =m1 ,no gluttons are /rong4 ,i %all n[ take ?ree diff]5t =ms ( ,pairs ( ,premisses1 & "w out _! ,conclusions1 once = all1 by ,diagrams2 & ?us obta9 "s useful ,=mul4 ,i %all call !m ,fig4 ,i1 ,fig4 ,,ii1 & ,fig4 ,,iii4 pg#jge ,fig4 ,i4 ,?is includes any ,pair ( ,premisses :i* are bo? ( !m ,nullities1 & :i* conta9 ,unlike ,elim9&s4 ,! simple/ case is --------------- ------- xm#j ym'#j 7,o7 7,o7 ------ ------ 7,o77,o7 ------------ ------- ------ 4'4 xy#j 7,o7 --------------- ,9 ?is case we see t ! ,conclusion is a ,nullity1 & t ! ,ret95ds h kept _! ,signs4 ,& we %\ld f9d ?is ,rule to hold good ) any ,pair ( ,premisses :i* fulfil ! giv5 conditions4 ,! ,read] _h bett] satisfy himself ( ?is1 by work+ out1 on ,diagrams1 sev]al v>ieties1 su* z m#ax#j ym'#j 7:i* xy#j7 xm'#j m#ay#j 7:i* xy#j7 x'm#j ym'#j 7:i* x'y#j7 m'#ax'#j m#ay'#j 7:i* x'y'#j74 ,if ei!r ,ret95d is ass]t$ 9 ! ,premisses to exi/1 ( c\rse x may be s ass]t$ 9 ! ,conclusion4 ,h5ce we get two ,v>iants ( ,fig4 ,i1 viz4 7a7 :]e "o ,ret95d is s ass]t$2 7b7 :]e bo? are s ass]t$4 ,! ,read] _h bett] "w out1 on ,diagrams1 examples ( ^! two ,v>iants1 su* z m#ax#j y#am'#j 7:i* proves y#ax#j7 x#am'#j m#ay#j 7:i* proves x#ay#j7 x'#am#j y#am'#j 7:i* proves x'#ay#j y#ax'#j74 ,! ,=mula1 to be rememb]$1 is xm#j ym'#j xy#j ) ! foll[+ two ,rules3-- 7#a7 ,two ,nullities1 ) ,unlike ,elim9&s1 yield a ,nullity1 9 :i* bo? ,ret95ds keep _! ,signs4 pg#jgf 7#b7 ,a ,ret95d1 ass]t$ 9 ! ,premisses to exi/1 may be s ass]t$ 9 ! ,conclusion4 ,note t ,rule 7#a7 is m]ely ! ,=mula express$ 9 words4 ,fig4 ,,ii4 ,?is includes any ,pair ( ,premisses1 ( :i* "o is a ,nullity & ! o!r an ,entity1 & :i* conta9 ,l ,elim9&s4 ,! simple/ case is xm#j ym#a --------------- ------- ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 x'y#a --------------- ,9 ?is case we see t ! ,conclusion is an ,entity1 & t ! ,nullity-,ret95d has *ang$ its ,sign4 ,& we %\ld f9d ?is ,rule to hold good ) any ,pair ( ,premisses :i* fulfil ! giv5 conditions4 ,! ,read] _h bett] satisfy himself ( ?is1 by work+ out1 on ,diagrams1 sev]al v>ieties1 su* z x'm#j ym#a 7:i* xy#a7 x#am'#j y'm'#a 7:i* x'y'#a7 m#ax#j y'm#a 7:i* x'y'#a74 ,! ,=mula1 to be rememb]$1 is1 xm#j ym#a x'y#a ) ! foll[+ ,rule3-- ,a ,nullity & an ,entity1 ) ,l ,elim9&s1 yield an ,entity1 9 :i* ! ,nullity-,ret95d *anges its ,sign4 ,note t ?is ,rule is m]ely ! ,=mula express$ 9 words4 pg#jgg ,fig4 ,,iii4 ,?is includes any ,pair ( ,premisses :i* are bo? ( !m ,nullities1 & :i* conta9 ,l ,elim9&s ass]t$ to exi/4 ,! simple/ case is xm#j ym#j m#a ,note t m#a is "h /at$ sep>ately1 because x does n matt] 9 :i* ( ! two ,premisses x occurs3 s t ?is includes ! ?ree =ms m#ax#j ym#j1 xm#j m#ay#j1 & m#ax#j m#ay#j4 --------------- ------- ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,o77,i7 ------ 4'4 x'y'#a --------------- ,9 ?is case we see t ! ,conclusion is an ,entity1 & t bo? ,ret95ds h *ang$ _! ,signs4 ,& we %\ld f9d ?is ,rule to hold good ) any ,pair ( ,premisses :i* fulfil ! giv5 conditions4 ,! ,read] _h bett] satisfy himself ( ?is1 by work+ out1 on ,diagrams1 sev]al v>ieties1 su* z x'm#j m#ay#j 7:i* xy'#a7 m'#ax#j m'y'#j 7:i* x'y#a7 m#ax'#j m#ay'#j 7:i* xy#a74 ,! ,=mula1 to be rememb]$1 is xm#j ym#j m#a x'y'#a ) ! foll[+ ,rule 7:i* is m]ely ! ,=mula express$ 9 words73-- ,two ,nullities1 ) ,l ,elim9&s ass]t$ to exi/1 yield an ,entity1 9 :i* bo? ,ret95ds *ange _! ,signs4 99 99 99 99 99 ,9 ord] to help ! ,read] to rememb] ! peculi>ities & ,=mul ( ^! ?ree ,figures1 ,i w put !m all toge!r 9 "o ,table4 pg#jgh ,,table ,,ix4 ,fig4 ,i4 xm#j ym'#j xy#j ,two ,nullities1 ) ,unlike ,elim9&s1 yield a ,nullity1 9 :i* bo? ,ret95ds keep _! ,signs4 ,a ,ret95d1 ass]t$ 9 ! ,premisses to exi/1 may be s ass]t$ 9 ! ,conclusion4 ,fig4 ,,ii4 xm#j ym#a x'y#a ,a ,nullity & an ,entity1 ) ,l ,elim9&s1 yield an ,entity1 9 :i* ! ,nullity-,ret95d *anges its ,sign4 ,fig4 ,,iii4 xm#j ym#j m#a x'y'#a ,two ,nullities1 ) ,l ,elim9&s ass]t$ to exi/1 yield an ,entity1 9 :i* bo? ,ret95ds *ange _! ,signs4 ,i w n[ "w out1 by ^! ,=mul1 z models = ! ,read] to imitate1 "s ,problems 9 ,syllogisms :i* h be5 already work$1 by ,diagrams1 9 ,book ,v41 ,*ap4 ,,ii4 7#a7 see p4 #fd ,no son ( m9e is di%one/2 ,p always treat an hone/ man ) respect4 ,univ4 m52 m hone/2 x my sons2 y treat$ ) respect4 xm'#j m#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no son ( m9e ev] fails to be treat$ ) respect4 pg#jgi 7#b7 see p4 #fd ,all cats und]/& ,fr5*2 ,"s *ick5s are cats4 ,univ4 creatures2 m cats2 x und]/&+ ,fr5*2 y *ick5s4 m#ax'#j ym#a xy#a ,fig4 ,,ii4 i4e4 ,"s *ick5s und]/& ,fr5*4 7#c7 see p4 #fd ,all dilig5t /ud5ts are successful2 ,all ignorant /ud5ts are unsuccessful4 ,univ4 /ud5ts2 m successful2 x dilig5t2 y ignorant4 x#am'#j y#am#j x#ay#j y#ax#j ,fig4 ,i 7b74 i4e4 ,all dilig5t /ud5ts are le>n$2 & all ignorant /ud5ts are idle4 7#d7 see p4 #ff ,all soldi]s are /rong2 ,all soldi]s are brave4 ,"s /rong m5 are brave4 ,univ4 m52 m soldi]s2 x /rong2 y brave4 m#ax'#j m#ay'#j xy#a ,fig4 ,,iii4 ,h5ce propos$ ,conclusion is "r4 7#e7 see p4 #fg ,i admire ^! pictures2 ,:5 ,i admire any?+1 ,i wi% to exam9e x ?or\ghly4 ,i wi% to exam9e "s ( ^! pictures ?or\ghly4 ,univ4 ?+s2 m admir$ by me2 x ^!2 y ?+s :i* ,i wi% to exam9e ?or\ghly4 x#am'#j m#ay'#j x#ay'#j ,fig4 ,i 7a74 ,h5ce propos$ ,conclusion1 xy#a1 is incomplete1 ! complete "o be+ ,i wi% to exam9e all ^! pictures ?or\ghly4 pg#jhj 7#f7 see p4 #fg ,none b ! brave des]ve ! fair2 ,"s bragg>ts are c[>ds4 ,"s bragg>ts d n des]ve ! fair4 ,univ4 p]sons2 m brave2 x des]v+ ( ! fair2 y bragg>ts4 m'x#j ym'#a x'y#a ,fig4 ,,ii4 ,h5ce propos$ ,conclusion is "r4 7#g7 see p4 #fi ,no "o1 :o means to g by ! tra9 & _c get a conveyance1 & has n en\gh "t to walk to ! /ation1 c d )\t runn+2 ,?is p>ty ( t\ri/s mean to g by ! tra9 & _c get a conveyance1 b !y h pl5ty ( "t to walk to ! /ation4 ,?is p>ty ( t\ri/s ne$ n run4 ,univ4 p]sons mean+ to g by ! tra91 & unable to get a conveyance2 m hav+ en\gh "t to walk to ! /ation2 x ne$+ to run2 y ^! t\ri/s4 m'x'#j y#am'#j d n come "u any ( ! ?ree ,figures4 ,h5ce x is necess>y to return to ! ,me?od ( ,diagrams1 z %[n at p4 #fi4 ,h5ce !re is no ,conclusion4 ,"w ,examples #d1 #ab-bj 7p4 #ajj72 #e1 #ac-bd 7pp4 #aja1 #ajb72 #f1 #a-f 7p4 #ajf72 #g1 #a-c 7pp4 #ajg1 #ajh74 ,also read ,note 7,a71 at p4 #afd4 pg#jha #c4 ,fallacies4 ,any argum5t :i* deceives u1 by seem+ to prove :at x does n really prove1 may be call$ a ',fallacy' 7d]iv$ f ! ,lat9 v]b fallo ,i deceive73 b ! p>ticul> k9d1 to be n[ discuss$1 consi/s ( a ,pair ( ,propositions1 :i* are propos$ z ! ,premisses ( a ,syllogism1 b yield no ,conclusion4 ,:5 ea* ( ! propos$ ,premisses is a ,proposition 9 ,i1 or ,e1 or ,a1 7! only k9ds ) :i* we are n[ conc]n$17 ! ,fallacy may be detect$ by ! ',me?od ( ,diagrams1' by simply sett+ !m out on a ,trilit]al ,diagram1 & obs]v+ t !y yield no in=mation :i* c be transf]r$ to ! ,bilit]al ,diagram4 ,b suppose we 7 work+ by ! ',me?od ( ,subscripts1' & _h to deal ) a ,pair ( propos$ ,premisses1 :i* happ5$ to be a ',fallacy1' h[ c\ld we be c]ta9 t !y w\ld n yield any ,conclusion8 ,our be/ plan is1 ,i ?9k1 to deal ) ,fallacies 9 ! same 0 z we h already dealt ) ,syllogisms3 t is1 to take c]ta9 =ms ( ,pairs ( ,propositions1 & to "w !m out1 once = all1 on ! ,trilit]al ,diagram1 & asc]ta9 t !y yield no ,conclusion2 & !n to record !m1 = future use1 z ,=mul = ,fallacies1 j z we h already record$ our ?ree ,=mul = ,syllogisms4 pg#jhb ,n[1 if we 7 to record ! two ,sets ( ,=mul 9 ! same %ape1 viz4 by ! ,me?od ( ,subscripts1 !re w\ld be consid]able risk ( confus+ ! two k9ds4 ,h5ce1 9 ord] to keep !m di/9ct1 ,i propose to record ! ,=mul = ,fallacies 9 words1 & to call !m ,=ms in/ead ( ,=mul4 ,let u n[ proce$ to f9d1 by ! ,me?od ( ,diagrams1 ?ree ,=ms ( ,fallacies1 :i* we w !n put on record = future use4 ,!y are z foll[s3-- 7#a7 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 7#b7 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 7#c7 ,fallacy ( two ,entity-,premisses4 ,^! %all be discuss$ sep>ately1 & x w be se5 t ea* fails to yield a ,conclusion4 7#a7 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 ,x is evid5t t nei!r ( ! giv5 ,propositions c be an ,entity1 s9ce t k9d ass]ts ! exi/5ce ( bo? ( its ,t]ms 7see p4 #bj74 ,h5ce !y mu/ bo? be ,nullities4 ,h5ce ! giv5 ,pair may be repres5t$ by 7xm#j ym#j71 ) or )\t x#a1 y#a4 ,^!1 set out on ,trilit]al ,diagrams1 are xm#j ym#j x#am#j ym#j --------------- --------------- 7,i7 ------ ------ 7,o77,o7 7,o77,o7 ------------ ------------ 7,o7 7,o7 ------ ------ --------------- --------------- xm#j y#am#j x#am#j y#am#j --------------- --------------- 7,i7 ------ ------ 7,o77,o7 7,o77,o7 7,i7--------- 7,i7--------- 7,o7 7,o7 ------ ------ --------------- --------------- pg#jhc 7#b7 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 ,"h ! giv5 ,pair may be repres5t$ by 7xm#j ym'#a7 ) or )\t x#a or m#a4 ,^!1 set out on ,trilit]al ,diagrams1 are xm#j ym'#a x#am#j ym'#a m#ax#j ym'#a --------------- --------------- --------------- 7,i7 ------ ------ ------ 7,o77,o7 7,o77,o7 7,o77,o7 7,i7--------- 7,i7--------- 7,i7--------- 7,i7 ------ ------ ------ --------------- --------------- --------------- 7#c7 ,fallacy ( two ,entity-,premisses4 ,"h ! giv5 ,pair may be repres5t$ by ei!r 7xm#a ym#a7 or 7xm#a ym'#a74 ,^!1 set out on ,trilit]al ,diagrams1 are xm#a ym#a xm#a ym'#a --------------- --------------- ------ ------ 7,i7 7,i7 ---7,i7------ 7,i7--------- ------ ------ --------------- --------------- pg#jhd #d4 ,me?od ( proce$+ ) a giv5 ,pair ( ,propositions4 ,let u suppose t we h be=e u a ,pair ( ,propositions ( ,relation1 :i* conta9 betwe5 !m a ,pair ( codivisional ,classes1 & t we wi% to asc]ta9 :at ,conclusion1 if any1 is consequ5t f !m4 ,we translate !m1 if necess>y1 into subscript-=m1 & !n proce$ z foll[s3-- 7#a7 ,we exam9e _! ,subscripts1 9 ord] to see :e!r !y are 7a7 a ,pair ( ,nullities2 or 7b7 a ,nullity & an ,entity2 or 7c7 a ,pair ( ,entities4 7#b7 ,if !y are a ,pair ( ,nullities1 we exam9e _! ,elim9&s1 9 ord] to see :e!r !y are ,unlike or ,l4 ,if _! ,elim9&s are ,unlike1 x is a case ( ,fig4 ,i4 ,we !n exam9e _! ,ret95ds1 to see :e!r "o or bo? ( !m are ass]t$ to exi/4 ,if "o ,ret95d is s ass]t$1 x is a case ( ,fig4 ,i 7a72 if bo?1 x is a case ( ,fig4 ,i 7b74 ,if _! ,elim9&s are ,l1 we exam9e !m1 9 ord] to see :e!r ei!r ( !m is ass]t$ to exi/4 ,if s1 x is a case ( ,fig4 ,,iii42 if n1 x is a case ( ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 7#c7 ,if !y are a ,nullity & an ,entity1 we exam9e _! ,elim9&s1 9 ord] to see :e!r !y are ,l or ,unlike4 ,if _! ,elim9&s are ,l1 x is a case ( ,fig4 ,,ii42 if ,unlike1 x is a case ( ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 7#d7 ,if !y are a ,pair ( ,entities1 x is a case ( ,fallacy ( two ,entity-,premisses4 ,"w ,examples #d1 #a-aa 7p4 #ajj72 #e1 #a-ab 7p4 #aja72 #f1 #g-ab 7p4 #ajf72 #g1 #g-ab 7p4 #ajh74 pg#jhe ,,book ,,vii4 ,,soriteses4 ,,*apt] ,i4 ,,introductory4 ,:5 a ,set ( ?ree or m ,bilit]al ,propositions are su* t all _! ,t]ms are ,species ( ! same ,g5us1 & are also s relat$ t two ( !m1 tak5 toge!r1 yield a ,conclusion1 :i*1 tak5 ) ano!r ( !m1 yields ano!r ,conclusion1 & s on1 until all h be5 tak51 x is evid5t t1 if ! orig9al ,set 7 true1 ! la/ ,conclusion w\ld also be true4 ,su* a ,set1 ) ! la/ ,conclusion tack$ on1 is call$ a ',sorites'2 ! orig9al ,set ( ,propositions is call$ its ',premisses'2 ea* ( ! int]m$iate ,conclusions is call$ a ',p>tial ,conclusion' ( ! ,sorites2 ! la/ ,conclusion is call$ its ',complete ,conclusion1' or1 m briefly1 its ',conclusion'2 ! ,g5us1 ( :i* all ! ,t]ms are ,species1 is call$ its ',univ]se ( ,disc\rse'1 or1 m briefly1 its ',univ4'2 ! ,t]ms1 us$ z ,elim9&s 9 ! ,syllogisms1 are call$ its ',elim9&s'2 & ! two ,t]ms1 :i* are reta9$1 & !re=e appe> 9 ! ,conclusion1 are call$ its ',ret95ds'4 ,note t ea* ,p>tial ,conclusion conta9s "o or two ,elim9&s2 b t ! ,complete ,conclusion conta9s ,ret95ds only4 ,! ,conclusion is said to be 'consequ5t' f ! ,premisses2 = :i* reason x is usual to prefix to x ! ^w ,!re=e 7or ! symbol 4'474 ,note t ! "q1 :e!r ! ,conclusion is or is n consequ5t f ! ,premisses1 is n affect$ by ! actual tru? or falsity ( any "o ( ! ,propositions :i* make up ! ,sorites1 by dep5ds entirely on _! relation%ip to "o ano!r4 pg#jhf ,z a specim5-,sorites1 let u take ! foll[+ ,set ( #e ,propositions3-- 7#a7 ,no a are b'2 7#b7 ,all b are c2 7#c7 ,all c are d2 7#d7 ,no e' are a'2 7#e7 ,all h are e'4 ,"h ! fir/ & second1 tak5 toge!r1 yield ,no a are c'4 ,?is1 tak5 along ) ! ?ird1 yields ,no a are d'4 ,?is1 tak5 along ) ! f\r?1 yields ,no d' are e'4 ,& ?is1 tak5 along ) ! fif?1 yields ,all h are d4 ,h5ce1 if ! orig9al ,set 7 true1 ?is w\ld also be true4 ,h5ce ! orig9al ,set1 ) ?is tack$ on1 is a ,sorites2 ! orig9al ,set is its ,premisses2 ! ,proposition ,all h are d is its ,conclusion2 ! ,t]ms a1 b1 c1 e are its ,elim9&s2 & ! ,t]ms d & h are its ,ret95ds4 ,h5ce we may write ! :ole ,sorites ?us3-- ,no a are b'2 ,all b are c2 ,all c are d2 ,no e' are a'2 ,all h are e'4 4'4 ,all h are d4 ,9 ! above ,sorites1 ! #c ,p>tial ,conclusions are ! ,positions ,no a are e'1 ,no a are d'1 ,no d' are e'2 b1 if ! ,premisses 7 arrang$ 9 o!r ways1 o!r ,p>tial ,conclusions might be obta9$4 ,?us1 ! ord] #daebc yields ! ,p>tial ,conclusions ,no c' are b'1 ,all h are b1 ,all h are c4 ,!re are altoge!r n9e ,p>tial ,conclusions to ?is ,sorites1 :i* ! ,read] w f9d x an int]e/+ task to make out = himself4 pg#jhg ,,*apt] ,,ii4 ,,problems ,,9 ,,soriteses4 #a4 ,introductory4 ,! ,problems we %all h to solve are ( ! foll[+ =m3-- ,giv5 ?ree or m ,propositions ( ,relation1 :i* are propos$ z ,premisses3 to asc]ta9 :at ,conclusion1 if any1 is consequ5t f !m4 ,we w limit ourselves1 at pres5t1 to ,problems :i* c be work$ by ! ,=mul ( ,fig4 ,i4 7,see p4 #ge47 ,^?1 t require o!r ,=mul1 are r too h>d = beg9n]s4 ,su* ,problems may be solv$ by ei!r ( two ,me?ods1 viz4 7#a7 ,! ,me?od ( ,sep>ate ,syllogisms2 7#b7 ,! ,me?od ( ,und]scor+4 ,^! %all be discuss$ sep>ately4 pg#jhh #b4 ,solution by ,me?od ( ,sep>ate ,syllogisms4 ,! ,rules1 = do+ ?is1 are z foll[s3-- 7#a7 ,"n ! ',univ]se ( ,disc\rse'4 7#b7 ,con/ruct a ,diction>y1 mak+ a1 b1 c1 c4 repres5t ! ,t]ms4 7#c7 ,put ! ,propos$ ,premisses into subscript =m4 7#d7 ,select two :i*1 conta9+ betwe5 !m a pair ( codivisional ,classes1 c be us$ z ! ,premisses ( a ,syllogism4 7#e7 ,f9d _! ,conclusion by ,=mula4 7#f7 ,f9d a ?ird ,premiss :i*1 along ) ?is ,conclusion1 c be us$ z ! ,premisses ( a second ,syllogism4 7#g7 ,f9d a second ,conclusion by ,=mula4 7#h7 ,proce$ ?us1 until all ! propos$ ,premisses h be5 us$4 7#i7 ,put ! la/ ,conclusion1 :i* is ! ,complete ,conclusion ( ! ,sorites1 into concrete =m4 ,z an example ( ?is process1 let u take1 z ! propos$ ,set ( ,premisses1 7#a7 ,all ! policem5 on ?is beat sup ) our cook2 7#b7 ,no man ) long hair c fail to be a poet2 7#c7 ,amos ,judd has nev] be5 9 prison2 7#d7 ,our cook's 'c\s9s' all love cold mutton2 7#e7 ,none b policem5 on ?is beat are poets2 7#f7 ,none b h] 'c\s9s' ev] sup ) our cook2 7#g7 ,m5 ) %ort hair h all be5 9 prison4 ,univ4 m52 a ,amos ,judd2 b c\s9s ( our cook2 c hav+ be5 9 prison2 d long-hair$2 e lov+ cold mutton2 h poets2 k policem5 on ?is beat2 l supp+ ) our cook pg#jhi ,we n[ h to put ! propos$ ,premisses into subscript =m4 ,let u beg9 by putt+ !m into ab/ract =m4 ,! result is 7#a7 ,all k are l2 7#b7 ,no d are h'2 7#c7 ,all a are c'2 7#d7 ,all b are e2 7#e7 ,no k' are h2 7#f7 ,no b' are l2 7#g7 ,all d' are c4 ,& x is n[ easy to put !m into subscript =m1 z foll[s3-- 7#a7 k#al'#j 7#b7 dh'#j 7#c7 a#a;c#j 7#d7 b#a;e'#j 7#e7 k'h#j 7#f7 b'l#j 7#g7 d'#a;c'#j ,we n[ h to f9d a pair ( ,premisses :i* w yield a ,conclusion4 ,let u beg9 ) ,no4 7#a71 & look d[n ! li/1 till we come to "o :i* we c take along ) x1 s z to =m ,premisses belong+ to ,fig4 ,i4 ,we f9d t ,no4 7#e7 w d1 s9ce we c take k z our ,elim9&4 ,s our fir/ syllogism is 7#a7 k#al'#j 7#e7 k'h#j 4'4 l'h#j 444 7#h7 ,we mu/ n[ beg9 aga9 ) l'h#j & f9d a ,premiss to g along ) x4 ,we f9d t ,no4 7#b7 w d1 h be+ our ,elim9&4 ,s our next ,syllogism is 7#h7 l'h#j 7#b7 dh'#j 4'4 l'd#j 444 7#i7 ,we h n[ us$ up ,nos4 7#a71 7#e71 & 7#b71 & mu/ se>* among ! o!rs = a p>tn] = l'd#j4 ,we f9d t ,no4 7#f7 w d4 ,s we write 7#i7 l'd#j 7#f7 b'l#j 4'4 db'#j 444 7#aj7 ,n[ :at c we take along ) db'#j8 ,no4 7#d7 w d4 7#aj7 db'#j 7#d7 b#a;e'#j 4'4 de'#j 444 7#aa7 pg#jij ,along ) ?is we may take ,no4 7#g74 7#aa7 de'#j 7#g7 d'#a;c'#j 4'4 c'e'#j 444 7#ab7 ,& along ) ?is we may take ,no4 7#c74 7#ab7 c'e'#j 7#c7 a#a;c#j 4'4 a#a;e'#j ,?is ,complete ,conclusion1 translat$ into ab/ract =m1 is ,all a are e2 & ?is1 translat$ into concrete =m1 is ,amos ,judd loves cold mutton4 ,9 actually work+ ?is ,problem1 ! above explanations w\ld1 ( c\rse1 be omitt$1 & all1 t w\ld appe> on pap]1 w\ld be z foll[s3-- 7#a7 k#al'#j 7#b7 dh'#j 7#c7 a#a;c#j 7#d7 b#a;e'#j 7#e7 k'h#j 7#f7 b'l#j 7#g7 d'#a;c'#j 7#a7 k#al'#j 7#e7 k'h#j 4'4 l'h#j 444 7#h7 7#h7 l'h#j 7#b7 dh'#j 4'4 l'd#j 444 7#i7 7#i7 l'd#j 7#f7 b'l#j 4'4 db'#j 444 7#aj7 7#aj7 db'#j 7#d7 b#a;e'#j 4'4 de'#j 444 7#aa7 7#aa7 de'#j 7#g7 d'#a;c'#j 4'4 c'e'#j 444 7#ab7 7#ab7 c'e'#j 7#c7 a#a;c#j 4'4 a#a;e'#j ,note t1 9 work+ a ,sorites by ?is ,process1 we may beg9 ) any ,premiss we *oose4 pg#jia #c4 ,solution by ,me?od ( ,und]scor+4 ,consid] ! ,pair ( ,premisses xm#j ym'#j :i* yield ! ,conclusion xy#j ,we see t1 9 ord] to get ?is ,conclusion1 we mu/ elim9ate m & m'1 & write x & y toge!r 9 "o expression4 ,n[1 if we agree to m>k m & m' z elim9at$1 & to read ! two expressions toge!r1 z if !y 7 writt5 9 "o1 ! two ,premisses w !n exactly repres5t ! ,conclusion1 & we ne$ n write x out sep>ately4 ,let u agree to m>k ! elim9at$ lett]s by und]scor+ !m1 putt+ a s+le score "u ! fir/1 & a d\ble "o "u ! second4 ,! two ,premisses n[ become xm#j ym'#j - :i* we read z xy#j4 ,9 copy+ out ! ,premisses = und]scor+1 x w be conv5i5t to omit all subscripts4 ,z to ! #j's we may always suppose !m writt51 &1 z to ! #a's1 we are n conc]n$ to "k :i* ,t]ms are ass]t$ to exi/1 except ^? :i* appe> 9 ! ,complete ,conclusion2 & = !m x w be easy en\gh to ref] to ! orig9al li/4 pg#jib ,i w n[ g ?r\gh ! process ( solv+1 by ?is me?od1 ! example work$ 9 #b4 ,! ,data are #a #b #c #d k#al'#j dh'#j a#a;c#j b#a;e'#j #e #f #g k'h#j b'l#j d'#a;c'#j ,! ,read] %\ld take a piece ( pap]1 & write out ?is solution = himself4 ,! fir/ l9e w consi/ ( ! above ,data2 ! second mu/ be compos$1 bit by bit1 accord+ to ! foll[+ directions4 ,we beg9 by writ+ d[n ! fir/ ,premiss1 ) its num]al ov] x1 b omitt+ ! subscripts4 ,we h n[ to f9d a ,premiss :i* c be comb9$ ) ?is1 i4e41 a ,premiss conta9+ ei!r k' or l4 ,! fir/ we f9d is ,no4 #e2 & ?is we tack on1 ) a 4 ,to get ! ,conclusion f ^!1 k & k' mu/ be elim9at$1 & :at rema9s mu/ be tak5 z "o expression4 ,s we und]score !m1 putt+ a s+le score "u k1 & a d\ble "o "u k'4 ,! result we read z l'h4 ,we mu/ n[ f9d a ,premiss conta9+ ei!r l or h'4 ,look+ along ! r[1 we fix on ,no4 #b1 & tack x on4 ,n[ ^! #c ,nullities are really equival5t to 7l'h dh'71 9 :i* h & h' mu/ be elim9at$1 & :at rema9s tak5 z "o expression4 ,s we und]score !m4 ,! result reads z l'd4 ,we n[ want a ,premiss conta9+ l or d'4 ,no4 #f w d4 ,^! #d ,nullities are really equival5t to 7l'd b'l74 ,s we und]score l' & l4 ,! result reads z db'4 ,we n[ want a ,premiss conta9+ d' or b4 ,no4 #d w d4 ,"h we und]score b' & b4 ,! result reads z de'4 ,we n[ want a ,premiss conta9+ d' or e4 ,no4 #g w d4 ,"h we und]score d & d'4 ,! result reads z c'e'4 ,we n[ want a ,premiss conta9+ c or e4 ,no4 #c w d--9 fact mu/ d1 z x is ! only "o left4 ,"h we und]score c' & c2 &1 z ! :ole ?+ n[ reads z e'a1 we tack on e'a#j z ! ,conclusion1 ) a 4 ,we n[ look along ! r[ ( ,data1 to see :e!r e' or a has be5 giv5 z exi/5t4 ,we f9d t a has be5 s giv5 9 ,no4 #c4 ,s we add ?is fact to ! ,conclusion1 :i* n[ /&s z e'a#j a#a1 i4e4 a#a;e'#j2 i4e4 ,all a are e4 ,if ! ,read] has fai?fully obey$ ! above directions1 8 writt5 solution w n[ /& z foll[s3-- #a #b #c #d k#al'#j dh'#j a#a;c#j b#a;e'#j #e #f #g k'h#j b'l#j d'#a;c'#j #a #e #b #f #d #g #c kl' k'h dh' b'l be' d'c' ac -- - - - - e'a#j a#a i4e4 a#a;e'#j2 i4e4 ,all a are e4 pg#jic ,! ,read] %\ld n[ take a second piece ( pap]1 & copy ! ,data only1 & try to "w out ! solution = himself1 beg9n+ ) "s o!r ,premiss4 ,if he fails to br+ out ! ,conclusion a#a;e'#j1 ,i w\ld advise him to take a ?ird piece ( pap]1 & beg9 aga96 ,i w n[ "w out1 9 its briefe/ =m1 a ,sorites ( #e ,premisses1 to s]ve z a model = ! ,read] to imitate 9 work+ examples4 7#a7 ,i greatly value ev]y?+ t ,john gives me2 7#b7 ,no?+ b ?is bone w satisfy my dog2 7#c7 ,i take p>ticul> c>e ( ev]y?+ t ,i greatly value2 7#d7 ,?is bone 0 a pres5t f ,john2 7#e7 ,! ?+s1 ( :i* ,i take p>ticul> c>e1 are ?+s ,i d n give to my dog4 ,univ4 ?+s2 a giv5 by ,john to me2 b giv5 by me to my dog2 c greatly valu$ by me2 d satisfactory to my dog2 e tak5 p>ticul> c>e ( by me2 h ?is bone4 #a #b #c #d #e a#a;c'#j h'd#j c#a;e'#j h#a;a'#j e#a;b#j #a #c #d #b #e ac' ce' ha' h'd eb db#j -- - - i4e4 ,no?+1 t ,i give my dog1 satisfies him1 or1 ,my dog is n satisfi$ ) any?+ t ,i give him6 ,note t1 9 work+ a ,sorites by ?is process1 we may beg9 ) any ,premiss we *oose4 ,= in/ance1 we might beg9 ) ,no4 #e1 & ! result w\ld !n be #e #c #a #d #b eb ce' ac' ha' h'd bd#j - - - - ,"w ,examples #d1 #be-cj 7p4 #ajj72 #e1 #be-cj 7p4 #ajb72 #f1 #ac-ae 7p4 #ajf72 #g1 #ac-ae 7p4 #ajh72 #h1 #a-d1 #ac1 #ad1 #ai1 #bd 7pp4 #aaj1 #aaa72 #i1 #a-d1 #bf1 #bg1 #dj1 #dh 7pp4 #aab1 #aaf1 #aai1 #aba74 pg#jid ,! ,read]1 :o has successfully grappl$ ) all ! ,examples hi!rto set1 & :o ?ir/s1 l ,alex&] ! ,great1 = m worlds to conqu]1 may employ 8 sp>e en]gies on ! foll[+ #ag ,exam9ation-,pap]s4 ,he is recomm5d$ n to attempt m ?an "o ,pap] on any "o day4 ,! answ]s to ! que/ions ab\t words & phrases may be f\nd by ref]r+ to ! ,index at p4 #aig4 ,i4 #d1 #ca 7p4 #ajj72 #e1 #ca-cd 7p4 #ajb72 #f1 #af1 #ag 7p4 #ajf72 #g1 #af 7p4 #ajh72 #h1 #e1 #f 7p4 #aaj72 #i1 #e1 #bb1 #db 7pp4 #aab1 #aae1 #aai74 ,:at is ',classification'8 ,& :at is a ',class'8 ,,ii4 #d1 #cb 7p4 #ajj72 #e1 #ce-ch 7pp4 #ajb1 #ajc72 #f1 #ah 7p4 #ajg72 #g1 #ag1 #ah 7p4 #ajh72 #h1 #g1 #h 7p4 #aaj72 #i1 #f1 #bc1 #dc 7pp4 #aab1 #aae1 #aai74 ,:at are ',g5us'1 ',species'1 & ',diff]5tia'8 ,,iii4 #d1 #cc 7p4 #ajj72 #e1 #ci-db 7p4 #ajc72 #f1 #ai1 #bj 7p4 #ajg72 #g1 #ai 7p4 #aji72 #h1 #i1 #aj 7p4 #aaa72 #i1 #g1 #bd1 #dd 7pp4 #aac1 #aaf1 #abj74 ,:at are ',real' & ',imag9>y' ,classes8 ,,iv4 #d1 #cd 7p4 #ajj72 #e1 #dc-df 7p4 #ajc72 #f1 #ba 7p4 #ajg72 #g1 #bj1 #ba 7p4 #aji72 #h1 #aa1 #ab 7p4 #aaa72 #i1 #h1 #be1 #de 7pp4 #aac1 #aaf1 #abj74 ,:at is ',division'8 ,:5 are ,classes said to be ',codivisional'8 ,v4 #d1 #ce 7p4 #ajj72 #e1 #dg-ej 7p4 #ajc72 #f1 #bb1 #bc 7p4 #ajg72 #g1 #bb 7p4 #aji72 #h1 #ae1 #af 7p4 #aaa72 #i1 #i1 #bh1 #df 7pp4 #aac1 #aaf1 #abj74 ,:at is ',di*otomy'8 ,:at arbitr>y rule does x sometimes require8 pg#jie ,,vi4 #d1 #cf 7p4 #ajj72 #e1 #ea-ed 7p4 #ajc72 #f1 #bd 7p4 #ajg72 #g1 #bc1 #bd 7p4 #aji72 #h1 #ag 7p4 #aaa72 #i1 #aj1 #bi1 #dg 7pp4 #aac1 #aag1 #abj74 ,:at is a ',def9ition'8 ,,vii4 #d1 #cg 7p4 #ajj72 #e1 #ee-eh 7pp4 #ajc1 #ajd72 #f1 #be1 #bf 7p4 #ajg72 #g1 #be 7p4 #aji72 #h1 #ah 7p4 #aaa72 #i1 #aa1 #cj1 #di 7pp4 #aac1 #aag1 #aba74 ,:at are ! ',subject' & ! ',pr$icate' ( a ,proposition8 ,:at is its ',normal' =m8 ,,viii4 #d1 #ch 7p4 #ajj72 #e1 #ei-fb 7p4 #ajd72 #f1 #bg 7p4 #ajg72 #g1 #bf1 #bg 7p4 #aji72 #h1 #bj 7p4 #aaa72 #i1 #ab1 #ca1 #ej 7pp4 #aac1 #aag1 #aba74 ,:at is a ,proposition '9 ,i'8 ',9 ,e'8 ,& '9 ,a'8 ,,ix4 #d1 #ci 7p4 #ajj72 #e1 #fc-ff 7p4 #ajd72 #f1 #bh1 #bi 7p4 #ajg72 #g1 #bh 7p4 #aji72 #h1 #ba 7p4 #aaa72 #i1 #ac1 #cb1 #ea 7pp4 #aad1 #aag1 #aba74 ,:at is ! ',normal' =m ( a ,proposition ( ,exi/5ce8 ,x4 #d1 #dj 7p4 #ajj72 #e1 #fg-gj 7p4 #ajd72 #f1 #cj 7p4 #ajg72 #g1 #bi1 #cj 7p4 #aji72 #h1 #bb 7p4 #aaa72 #i1 #ad1 #cc1 #eb 7pp4 #aad1 #aag1 #abb74 ,:at is ! ',univ]se ( ,disc\rse'8 ,,xi4 #d1 #da 7p4 #ajj72 #e1 #ga-gd 7p4 #ajd72 #f1 #ca1 #cb 7p4 #ajg72 #g1 #ca 7p4 #aji72 #h1 #bc 7p4 #aaa72 #i1 #ae1 #cd1 #ec 7pp4 #aad1 #aah1 #abb74 ,:at is impli$1 9 a ,proposition ( ,relation1 z to ! ,reality ( its ,t]ms8 ,,xii4 #d1 #db 7p4 #ajj72 #e1 #ge-gh 7p4 #aje72 #f1 #cc 7p4 #ajg72 #g1 #cb1 #cc 7pp4 #aji1 #aaj72 #h1 #be 7p4 #aaa72 #i1 #af1 #ce1 #ed 7pp4 #aad1 #aah1 #abb74 ,expla9 ! phrase sitt+ on ! f5ce4 ,,xiii4 #e1 #gi-hc 7p4 #aje72 #f1 #cd1 #ce 7p4 #ajg72 #g1 #cd 7p4 #aaj72 #h1 #bf 7p4 #aaa72 #i1 #ag1 #cf1 #ee 7pp4 #aad1 #aah1 #abb74 ,:at are ',conv]se' ,propositions8 ,,xiv4 #e1 #hd-hh 7p4 #aje72 #f1 #cf 7p4 #ajg72 #g1 #ce1 #cf 7p4 #aaj72 #h1 #bg 7p4 #aaa72 #i1 #ah1 #cg1 #ef 7pp4 #aad1 #aah1 #abc74 ,:at are ',concrete' & ',ab/ract' ,propositions8 pg#jif ,,xv4 #e1 #hi-ic 7p4 #aje72 #f1 #cg1 #ch 7p4 #ajg72 #g1 #cg 7p4 #aaj72 #h1 #bh 7p4 #aaa72 #i1 #ai1 #ch1 #eg 7pp4 #aae1 #aah1 #abc74 ,:at is a ',syllogism'8 ,& :at are its ',premisses' & its ',conclusion'8 ,,xvi4 #e1 #id-ig 7p4 #ajf72 #f1 #ci 7p4 #ajg72 #g1 #ch1 #ci 7p4 #aaj72 #h1 #bi 7p4 #aaa72 #i1 #bj1 #ci1 #eh 7pp4 #aae1 #aai1 #abc74 ,:at is a ',sorites'8 ,& :at are its ',premisses'1 its ',p>tial ,conclusions'1 & its ',complete ,conclusion'8 ,,xvii4 #e1 #ih-aja 7p4 #ajf72 #f1 #dj 7p4 #ajg72 #g1 #dj 7p4 #aaj72 #h1 #cj 7p4 #aaa72 #i1 #ba1 #da1 #ei1 #fj 7pp4 #aae1 #aai1 #abd74 ,:at are ! ',univ]se ( ,disc\rse'1 ! ',elim9&s'1 & ! ',ret95ds'1 ( a ,syllogism8 ,& ( a ,sorites8 pg#jig ,,book ,,viii4 ,,examples1 ,,answ]s1 ,,& ,,solutions4 ,n4,b4 ,ref]5ce tags = ,examples1 ,answ]s ,solutions w be f\nd 9 ! "r m>g94 ,,*apt] ,i4 ,,examples4 #a4 ,,ex#a ,propositions ( ,relation1 to be r$uc$ to normal =m4 #a4 ,i h be5 out = a walk4 #b4 ,i am feel+ bett]4 #c4 ,no "o has read ! lett] b ,john4 #d4 ,nei!r y nor ,i are old4 #e4 ,no fat creatures run well4 #f4 ,none b ! brave des]ve ! fair4 #g4 ,no "o looks poetical unless he is pale4 #h4 ,"s judges lose _! temp]s4 #i4 ,i nev] neglect important bus9ess4 #aj4 ,:at is difficult ne$s att5tion4 #aa4 ,:at is un:olesome %\ld be avoid$4 #ab4 ,all ! laws pass$ la/ week relate to excise4 #ac4 ,logic puzzles me4 #ad4 ,!re are no ,jews 9 ! h\se4 #ae4 ,"s di%es are un:olesome if n well-cook$4 #af4 ,unexcit+ books make "o dr[sy4 #ag4 ,:5 a man kn[s :at he's ab\t1 he c detect a %>p]4 #ah4 ,y & ,i "k :at we're ab\t4 #ai4 ,"s bald p we> wigs4 #bj4 ,^? :o are fully occupi$ nev] talk ab\t _! grievances4 #ba4 ,no riddles int]e/ me if !y c be solv$4 pg#jih #b4 ,,ex#b ,pairs ( ,ab/ract ,propositions1 "o 9 t]ms ( x & m1 & ! o!r 9 t]ms ( y & m1 to be repres5t$ on ! same ,trilit]al ,diagram4 #a4 ,no x are m2 ,no m' are y4 #b4 ,no x' are m'2 ,all m' are y4 #c4 ,"s x' are m2 ,no m are y4 #d4 ,all m are x2 ,all m' are y'4 #e4 ,all m' are x2 ,all m' are y'4 #f4 ,all x' are m'2 ,no y' are m4 #g4 ,all x are m2 ,all y' are m'4 #h4 ,"s m' are x'2 ,no m are y4 #i4 ,all m are x'2 ,no m are y4 #aj4 ,no m are x'2 ,no y are m'4 #aa4 ,no x' are m'2 ,no m are y4 #ab4 ,"s x are m2 ,all y' are m4 #ac4 ,all x' are m2 ,no m are y4 #ad4 ,"s x are m'2 ,all m are y4 #ae4 ,no m' are x'2 ,all y are m4 #af4 ,all x are m'2 ,no y are m4 #ag4 ,"s m' are x2 ,no m' are y'4 #ah4 ,all x are m'2 ,"s m' are y'4 #ai4 ,all m are x2 ,"s m are y'4 #bj4 ,no x' are m2 ,"s y are m4 #ba4 ,"s x' are m'2 ,all y' are m4 #bb4 ,no m are x2 ,"s m are y4 #bc4 ,no m' are x2 ,all y are m'4 #bd4 ,all m are x2 ,no y' are m'4 #be4 ,"s m are x2 ,no y' are m4 #bf4 ,all m' are x'2 ,"s y are m'4 #bg4 ,"s m are x'2 ,no y' are m'4 #bh4 ,no x are m'2 ,all m are y'4 #bi4 ,no x' are m2 ,no m are y'4 #cj4 ,no x are m2 ,"s y' are m'4 #ca4 ,"s m' are x2 ,all y' are m2 #cb4 ,all x are m'2 ,all y are m4 pg#jii #c4 ,,ex#c ,m>k$ ,trilit]al ,diagrams1 to be int]pret$ 9 t]ms ( x & y4 #a --------------- 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ 7,o7 --------------- #b --------------- 7,o7 ------ 7,o7 ---------7,i7 7,o7 ------ 7,o7 --------------- #c --------------- 7,o7 ------ 7,o77,o7 ------------ 7,i7 ------ 7,o7 --------------- #d --------------- 7,o7 7,o7 ------ 7,o7 ------7,i7--- 7,o7 ------ --------------- #e --------------- 7,i7 ------ 7,o7 ------------ 7,o7 ------ 7,o7 7,o7 --------------- #f --------------- 7,o7 7,o7 ------ ------------ 7,o7 ------ 7,i7 7,o7 --------------- #g --------------- 7,o7 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ --------------- #h --------------- 7,i7 ------ 7,o7 ------------ 7,o77,i7 ------ 7,o7 --------------- #i --------------- ------ 7,o7 ------------ 7,o77,i7 ------ 7,o7 7,o7 --------------- #aj --------------- 7,o7 7,o7 ------ 7,o77,i7 ------------ 7,o7 ------ --------------- #aa --------------- 7,o7 7,o7 ------ 7,i7 ------------ 7,o7 ------ 7,o7 --------------- #ab --------------- 7,o7 ------ ---7,i7------ ------ 7,o7 7,i7 --------------- #ac --------------- 7,o7 7,i7 ------ 7,o7 ------------ 7,o7 ------ 7,o7 --------------- #ad --------------- 7,o7 7,o7 ------ 7,o7 ------------ 7,o7 ------ 7,i7 --------------- #ae --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- #af --------------- 7,i7 ------ ------------ 7,o7 ------ 7,o7 7,o7 --------------- #ag --------------- 7,o7 ------ 7,i7 ------------ 7,o77,o7 ------ 7,i7 7,o7 --------------- #ah --------------- 7,o7 7,o7 ------ 7,o77,i7 ------------ 7,o7 ------ 7,i7 --------------- #ai --------------- 7,o7 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ 7,i7 --------------- #bj --------------- 7,o7 ------ 7,o77,o7 ------------ 7,i7 ------ 7,o7 --------------- pg#ajj #d4 ,,ex#d ,pairs ( ,ab/ract ,propositions1 propos$ z ,premisses3 ,conclusions to be f\nd4 #a4 ,no m are x'2 ,all m' are y4 #b4 ,no m' are x2 ,"s m' are y'4 #c4 ,all m' are x2 ,all m' are y'4 #d4 ,no x' are m'2 ,all y' are m4 #e4 ,"s m are x'2 ,no y are m4 #f4 ,no x' are m2 ,no m are y4 #g4 ,no m are x'2 ,"s y' are m4 #h4 ,all m' are x'2 ,no m' are y4 #i4 ,"s x' are m'2 ,no m are y'4 #aj4 ,all x are m2 ,all y' are m'4 #aa4 ,no m are x2 ,all y' are m'4 #ab4 ,no x are m2 ,all y are m4 #ac4 ,all m' are x2 ,no y are m4 #ad4 ,all m are x2 ,all m' are y4 #ae4 ,no x are m2 ,no m' are y4 #af4 ,all x are m'2 ,all y are m4 #ag4 ,no x are m2 ,all m' are y4 #ah4 ,no x are m'2 ,no m are y4 #ai4 ,all m are x2 ,all m are y'4 #bj4 ,no m are x2 ,all m' are y4 #ba4 ,all x are m2 ,"s m' are y4 #bb4 ,"s x are m2 ,all y are m4 #bc4 ,all m are x2 ,"s y are m4 #bd4 ,no x are m2 ,all y are m4 #be4 ,"s m are x'2 ,all y' are m'4 #bf4 ,no m are x'2 ,all y are m4 #bg4 ,all x are m'2 ,all y' are m4 #bh4 ,all m are x'2 ,"s m are y4 #bi4 ,no m are x2 ,all y are m'4 #cj4 ,all x are m'2 ,"s y are m4 #ca4 ,all x are m2 ,all y are m4 #cb4 ,no x are m'2 ,all m are y4 #cc4 ,no m are x2 ,no m are y4 #cd4 ,no m are x'2 ,"s y are m4 #ce4 ,no m are x2 ,all y are m4 #cf4 ,all m are x'2 ,"s y are m4 #cg4 ,all m are x2 ,no y are m4 #ch4 ,no m are x2 ,no m' are y4 #ci4 ,"s m are x'2 ,no m are y4 #dj4 ,no x' are m2 ,all y' are m4 #da4 ,all x are m'2 ,no y are m'4 #db4 ,no m' are x2 ,no y are m4 pg#aja #e4 ,,ex#e ,pairs ( ,concrete ,propositions1 propos$ z ,premisses3 ,conclusions to be f\nd4 #a4 ,i h be5 out = a walk2 ,i am feel+ bett]4 #b4 ,no "o has read ! lett] b ,john2 ,no "o1 :o has n read x1 kn[s :at x is ab\t4 #c4 ,^? :o are n old l walk+2 ,y & ,i are "y4 #d4 ,y\r c\rse is always hone/2 ,y\r c\rse is always ! be/ policy4 #e4 ,no fat creatures run well2 ,"s greyh\nds run well4 #f4 ,"s1 :o des]ve ! fair1 get _! des]ts2 ,none b ! brave des]ve ! fair4 #g4 ,"s ,jews are ri*2 ,all ,esquimaux are ,g5tiles4 #h4 ,sug>-plums are sweet2 ,"s sweet ?+s are lik$ by *ildr54 #i4 ,john is 9 ! h\se2 ,ev]ybody 9 ! h\se is ill4 #aj4 ,umbrellas are useful on a j\rney2 ,:at is useless on a j\rney %\ld be left beh9d4 #aa4 ,audible music causes vibration 9 ! air2 ,inaudible music is n wor? pay+ =4 #ab4 ,"s holidays are ra9y2 ,ra9y days are tiresome4 #ac4 ,no ,fr5*m5 l plumpudd+2 ,all ,engli%m5 l plumpudd+4 #ad4 ,no portrait ( a lady1 t makes h] simp] or sc[l1 is satisfactory2 ,no photograph ( a lady ev] fails to make h] simp] or sc[l4 #ae4 ,all pale p are phlegmatic2 ,no "o looks poetical unless he is pale4 #af4 ,no old mis]s are *e]ful2 ,"s old mis]s are ?94 #ag4 ,no "o1 :o ex]cises self-control1 fails to keep 8 temp]2 ,"s judges lose _! temp]s4 pg#ajb #ah4 ,all pigs are fat2 ,no?+ t is f$ on b>ley-wat] is fat4 #ai4 ,all rabbits1 t are n gre$y1 are black2 ,no old rabbits are free f gre$9ess4 #bj4 ,"s pictures are n fir/ attempts2 ,no fir/ attempts are really good4 #ba4 ,i nev] neglect important bus9ess2 ,y\r bus9ess is unimportant4 #bb4 ,"s lessons are difficult2 ,:at is difficult ne$s att5tion4 #bc4 ,all clev] p are popul>2 ,all oblig+ p are popul>4 #bd4 ,?\ghtless p d mis*ief2 ,no ?\ghtful p]son =gets a promise4 #be4 ,pigs _c fly2 ,pigs are gre$y4 #bf4 ,all soldi]s m>* well2 ,"s babies are n soldi]s4 #bg4 ,no bride-cakes are :olesome2 ,:at is un:olesome %\ld be avoid$4 #bh4 ,john is indu/ri\s2 ,no indu/ri\s p are unhappy4 #bi4 ,no philosoph]s are conceit$2 ,"s conceit$ p]sons are n gambl]s4 #cj4 ,"s excise laws are unju/2 ,all ! laws pass$ la/ week relate to excise4 #ca4 ,no milit>y m5 write poetry2 ,none ( my lodg]s are civilians4 #cb4 ,no m$ic9e is nice2 ,s5na is a m$ic9e4 #cc4 ,"s circul>s are n read ) pleasure2 ,no begg+-lett]s are read ) pleasure4 #cd4 ,all ,britons are brave2 ,no sailors are c[>ds4 #ce4 ,no?+ intelligible ev] puzzles me2 ,logic puzzles me4 #cf4 ,"s pigs are wild2 ,all pigs are fat4 pg#ajc #cg4 ,all wasps are unfri5dly2 ,all unfri5dly creatures are unwelcome4 #ch4 ,no old rabbits are gre$y2 ,all black rabbits are gre$y4 #ci4 ,"s eggs are h>d-boil$2 ,no eggs are uncrackable4 #dj4 ,no antelope is ungraceful2 ,graceful creatures delight ! eye4 #da4 ,all well-f$ can>ies s+ l\d2 ,no can>y is melan*oly if x s+s l\d4 #db4 ,"s poetry is orig9al2 ,no orig9al "w is producible at w4 #dc4 ,no c\ntry1 t has be5 explor$1 is infe/$ by dragons2 ,unexplor$ c\ntries are fasc9at+4 #dd4 ,no coals are :ite2 ,no nigg]s are :ite4 #de4 ,no bridges are made ( sug>2 ,"s bridges are picturesque4 #df4 ,no *ildr5 are pati5t2 ,no impati5t p]son c sit /ill4 #dg4 ,no quadrup$s c :i/le2 ,"s cats are quadrup$s4 #dh4 ,bores are t]rible2 ,y are a bore4 #di4 ,"s oy/]s are sil5t2 ,no sil5t creatures are amus+4 #ej4 ,!re are no ,jews 9 ! h\se2 ,no ,g5tiles h be>ds a y>d long4 #ea4 ,can>ies1 t d n s+ l\d1 are unhappy2 ,no well-f$ can>ies fail to s+ l\d4 #eb4 ,all my si/]s h colds2 ,no "o c s+ :o has a cold4 #ec4 ,all t is made ( gold is preci\s2 ,"s caskets are preci\s4 #ed4 ,"s buns are ri*2 ,all buns are nice4 #ee4 ,all my c\s9s are unju/2 ,all judges are j4 pg#ajd #ef4 ,pa9 is we>isome2 ,no pa9 is eag]ly wi%$ =4 #eg4 ,all m$ic9e is na/y2 ,s5na is a m$ic9e4 #eh4 ,"s unk9d rem>ks are annoy+2 ,no critical rem>ks are k9d4 #ei4 ,no tall m5 h woolly hair2 ,nigg]s h woolly hair4 #fj4 ,all philosoph]s are logical2 ,an illogical man is always ob/9ate4 #fa4 ,john is indu/ri\s2 ,all indu/ri\s p are happy4 #fb4 ,^! di%es are all well-cook$2 ,"s di%es are un:olesome if n well-cook$4 #fc4 ,no excit+ books suit fev]i% pati5ts2 ,unexcit+ books make "o dr[sy4 #fd4 ,no pigs c fly2 ,all pigs are gre$y4 #fe4 ,:5 a man kn[s :at he's ab\t1 he c detect a %>p]2 ,y & ,i "k :at we're ab\t4 #ff4 ,"s dreams are t]rible2 ,no lambs are t]rible4 #fg4 ,no bald creature ne$s a hairbru%2 ,no liz>ds h hair4 #fh4 ,all battles are noisy2 ,:at makes no noise may escape notice4 #fi4 ,all my c\s9s are unju/2 ,no judges are unju/4 #gj4 ,all eggs c be crack$2 ,"s eggs are h>d-boil$4 #ga4 ,prejudic$ p]sons are untru/wor?y2 ,"s unprejudic$ p]sons are dislik$4 #gb4 ,no dictatorial p]son is popul>2 ,%e is dictatorial4 #gc4 ,"s bald p we> wigs2 ,all y\r *ildr5 h hair4 #gd4 ,no lob/]s are unreasonable2 ,no reasonable creatures expect impossibilities4 pg#aje #ge4 ,no nightm>e is pleasant2 ,unpleasant exp]i5ces are n eag]ly desir$4 #gf4 ,no plumcakes are :olesome2 ,"s :olesome ?+s are nice4 #gg4 ,no?+ t is nice ne$ be %unn$2 ,"s k9ds ( jam are nice4 #gh4 ,all ducks waddle2 ,no?+ t waddles is graceful4 #gi4 ,s&wi*es are satisfy+2 ,no?+ 9 ?is di% is unsatisfy+4 #hj4 ,no ri* man begs 9 ! /reet2 ,^? :o are n ri* %\ld keep acc\nts4 #ha4 ,spid]s sp9 webs2 ,"s creatures1 t d n sp9 webs1 are savage4 #hb4 ,"s ( ^! %ops are n cr[d$2 ,no cr[d$ %ops are com=table4 #hc4 ,prud5t travel]s c>ry pl5ty ( small *ange2 ,imprud5t travel]s lose _! luggage4 #hd4 ,"s g]aniums are r$2 ,all ^! fl[]s are r$4 #he4 ,none ( my c\s9s are j2 ,all judges are j4 #hf4 ,no ,jews are mad2 ,all my lodg]s are ,jews4 #hg4 ,busy folk are n always talk+ ab\t _! grievances2 ,discont5t$ folk are always talk+ ab\t _! grievances4 #hh4 ,none ( my c\s9s are j2 ,no judges are unju/4 #hi4 ,all teetotal]s l sug>2 ,no night+ale dr9ks w9e4 #ij4 ,no riddles int]e/ me if !y c be solv$2 ,all ^! riddles are insoluble4 #ia4 ,all cle> explanations are satisfactory2 ,"s excuses are unsatisfactory4 #ib4 ,all eld]ly ladies are talkative2 ,all good-temp]$ ladies are talkative4 #ic4 ,no k9d de$ is unlawful2 ,:at is lawful may be done )\t scruple4 pg#ajf #id4 ,no babies are /udi\s2 ,no babies are good viol9i/s4 #ie4 ,all %ill+s are r\nd2 ,all ^! co9s are r\nd4 #if4 ,no hone/ m5 *eat2 ,no di%one/ m5 are tru/wor?y4 #ig4 ,none ( my boys are clev]2 ,none ( my girls are gre$y4 #ih4 ,all jokes are meant to amuse2 ,no ,act ( ,p>liam5t is a joke4 #ii4 ,no ev5tful t\r is ev] =gott52 ,unev5tful t\rs are n wor? writ+ a book ab\t4 #ajj4 ,all my boys are disob$i5t2 ,all my girls are discont5t$4 #aja4 ,no unexpect$ pleasure annoys me2 ,y\r visit is an unexpect$ pleasure4 #f4 ,,ex#f ,trios ( ,ab/ract ,propositions1 propos$ z ,syllogisms3 to be exam9$4 #a4 ,"s x are m2 ,no m are y'4 ,"s x are y4 #b4 ,all x are m2 ,no y are m'4 ,no y are x'4 #c4 ,"s x are m'2 ,all y' are m4 ,"s x are y4 #d4 ,all x are m2 ,no y are m4 ,all x are y'4 #e4 ,"s m' are x'2 ,no m' are y4 ,"s x' are y'4 #f4 ,no x' are m2 ,all y are m'4 ,all y are x'4 #g4 ,"s m' are x'2 ,all y' are m'4 ,"s x' are y'4 #h4 ,no m' are x'2 ,all y' are m'4 ,all y' are x4 #i4 ,"s m are x'2 ,no m are y4 ,"s x' are y'4 #aj4 ,all m' are x'2 ,all m' are y4 ,"s y are x'4 #aa4 ,all x are m'2 ,"s y are m4 ,"s y are x'4 #ab4 ,no x are m2 ,no m' are y'4 ,no x are y'4 #ac4 ,no x are m2 ,all y' are m4 ,all y' are x'4 #ad4 ,all m' are x'2 ,all m' are y4 ,"s y are x'4 #ae4 ,"s m are x'2 ,all y are m'4 ,"s x' are y'4 #af4 ,no x' are m2 ,all y' are m'4 ,"s y' are x4 #ag4 ,no m' are x2 ,all m' are y'4 ,"s x' are y'4 pg#ajg #ah4 ,no x' are m2 ,"s m are y4 ,"s x are y4 #ai4 ,"s m are x2 ,all m are y4 ,"s y are x'4 #bj4 ,no x' are m'2 ,"s m' are y'4 ,"s x are y'4 #ba4 ,no m are x2 ,all m are y'4 ,"s x' are y'4 #bb4 ,all x' are m2 ,"s y are m'4 ,all x' are y'4 #bc4 ,all m are x2 ,no m' are y'4 ,no x' are y'4 #bd4 ,all x are m'2 ,all m' are y4 ,all x are y4 #be4 ,no x are m'2 ,all m are y4 ,no x are y'4 #bf4 ,all m are x'2 ,all y are m4 ,all y are x'4 #bg4 ,all x are m2 ,no m are y'4 ,all x are y4 #bh4 ,all x are m2 ,no y' are m'4 ,all x are y4 #bi4 ,no x' are m2 ,no m' are y'4 ,no x' are y'4 #cj4 ,all x are m2 ,all m are y'4 ,all x are y'4 #ca4 ,all x' are m'2 ,no y' are m'4 ,all x' are y4 #cb4 ,no x are m2 ,no y' are m'4 ,no x are y'4 #cc4 ,all m are x'2 ,all y' are m4 ,all y' are x'4 #cd4 ,all x are m'2 ,"s y are m'4 ,"s y are x4 #ce4 ,"s x are m2 ,all m are y4 ,"s x are y4 #cf4 ,all m are x'2 ,all y are m4 ,all y are x'4 #cg4 ,no m are x'2 ,all m are y'4 ,"s x are y'4 #ch4 ,no x are m2 ,no m are y'4 ,no x are y'4 #ci4 ,no m are x2 ,"s m are y'4 ,"s x' are y'4 #dj4 ,no m are x'2 ,"s y are m4 ,"s x are y4 #g4 ,,ex#g ,trios ( ,concrete ,propositions1 propos$ z ,syllogisms3 to be exam9$4 #a4 ,no doctors are en?usia/ic2 ,y are en?usia/ic4 ,y are n a doctor4 #b4 ,diction>ies are useful2 ,useful books are valuable4 ,diction>ies are valuable4 #c4 ,no mis]s are unselfi%2 ,none b mis]s save egg-%ells4 ,no unselfi% p save egg-%ells4 #d4 ,"s epicures are ung5]\s2 ,all my uncles are g5]\s4 ,my uncles are n epicures4 pg#ajh #e4 ,gold is heavy2 ,no?+ b gold w sil5ce him4 ,no?+ light w sil5ce him4 #f4 ,"s heal?y p are fat2 ,no unheal?y p are /rong4 ,"s fat p are n /rong4 #g4 ,i saw x 9 a newspap]4 ,all newspap]s tell lies4 ,x 0 a lie4 #h4 ,"s cravats are n arti/ic2 ,i admire any?+ arti/ic4 ,!re are "s cravats t ,i d n admire4 #i4 ,8 songs nev] la/ an h\r2 ,a song1 t la/s an h\r1 is t$i\s4 ,8 songs are nev] t$i\s4 #aj4 ,"s c&les give v little light2 ,c&les are meant to give light4 ,"s ?+s1 t are meant to give light1 give v little4 #aa4 ,all1 :o are anxi\s to le>n1 "w h>d2 ,"s ( ^! boys "w h>d4 ,"s ( ^! boys are anxi\s to le>n4 #ab4 ,all lions are fi]ce2 ,"s lions d n dr9k c(fee4 ,"s creatures t dr9k c(fee are n fi]ce4 #ac4 ,no mis]s are g5]\s2 ,"s old m5 are ung5]\s4 ,"s old m5 are mis]s4 #ad4 ,no fossil c be cross$ 9 love2 ,an oy/] may be cross$ 9 love4 ,oy/]s are n fossils4 #ae4 ,all un$ucat$ p are %all[2 ,/ud5ts are all educat$4 ,no /ud5ts are %all[4 #af4 ,all "y lambs jump2 ,no "y animals are heal?y1 unless !y jump4 ,all "y lambs are heal?y4 #ag4 ,ill-manag$ bus9ess is unpr(itable2 ,railways are nev] ill-manag$4 ,all railways are pr(itable4 #ah4 ,no ,pr(essors are ignorant2 ,all ignorant p are va94 ,no pr(essors are va94 pg#aji #ai4 ,a prud5t man %uns hynas2 ,no bank] is imprud5t4 ,no bank] fails to %un hynas4 #bj4 ,all wasps are unfri5dly2 ,no puppies are unfri5dly4 ,puppies are n wasps4 #ba4 ,no ,jews are hone/2 ,"s ,g5tiles are ri*4 ,"s ri* p are di%one/4 #bb4 ,no idl]s w9 fame2 ,"s pa9t]s are n idle4 ,"s pa9t]s w9 fame4 #bc4 ,no monkeys are soldi]s2 ,all monkeys are mis*iev\s4 ,"s mis*iev\s creatures are n soldi]s4 #bd4 ,all ^! bonbons are *ocolate-creams2 ,all ^! bonbons are delici\s4 ,*ocolate-creams are delici\s4 #be4 ,no muff9s are :olesome2 ,all buns are un:olesome4 ,buns are n muff9s4 #bf4 ,"s unau?oris$ reports are false2 ,all au?oris$ reports are tru/wor?y4 ,"s false reports are n tru/wor?y4 #bg4 ,"s pill[s are s(t2 ,no pok]s are s(t4 ,"s pok]s are n pill[s4 #bh4 ,improbable /ories are n easily believ$2 ,none ( 8 /ories are probable4 ,none ( 8 /ories are easily believ$4 #bi4 ,no ?ieves are hone/2 ,"s di%one/ p are f\nd out4 ,"s ?ieves are f\nd out4 #cj4 ,no muff9s are :olesome2 ,all puffy food is un:olesome4 ,all muff9s are puffy4 #ca4 ,no birds1 except peacocks1 are pr\d ( _! tails2 ,"s birds1 t are pr\d ( _! tails1 _c s+4 ,"s peacocks _c s+4 #cb4 ,w>m? relieves pa92 ,no?+1 t does n relieve pa91 is useful 9 too?a*e4 ,w>m? is useful 9 too?a*e4 pg#aaj #cc4 ,no bankrupts are ri*2 ,"s m]*ants are n bankrupts4 ,"s m]*ants are ri*4 #cd4 ,bores are dread$2 ,no bore is ev] begg$ to prolong 8 visit4 ,no "o1 :o is dread$1 is ev] begg$ to prolong 8 visit4 #ce4 ,all wise m5 walk on _! feet2 ,all unwise m5 walk on _! h&s4 ,no man walks on bo?4 #cf4 ,no :eelb>r[s are com=table2 ,no uncom=table vehicles are popul>4 ,no :eelb>r[s are popul>4 #cg4 ,no frogs are poetical2 ,"s ducks are unpoetical4 ,"s ducks are n frogs4 #ch4 ,no emp]ors are d5ti/s2 ,all d5ti/s are dread$ by *ildr54 ,no emp]ors are dread$ by *ildr54 #ci4 ,sug> is sweet2 ,salt is n sweet4 ,salt is n sug>4 #dj4 ,e eagle c fly2 ,"s pigs _c fly4 ,"s pigs are n eagles4 #h4 ,,ex#h ,sets ( ,ab/ract ,propositions1 propos$ z ,premisses = ,soriteses3 ,conclusions to be f\nd4 ,n4,b4 ,at ! end ( ?is ,section in/ructions are giv5 = v>y+ ^! ,examples4 #a4 #a4 ,no c are d2 #b4 ,all a are d2 #c4 ,all b are c4 #b4 #a4 ,all d are b2 #b4 ,no a are c'2 #c4 ,no b are c4 #c4 #a4 ,no b are a2 #b4 ,no c are d'2 #c4 ,all d are b4 #d4 #a4 ,no b are c2 #b4 ,all a are b2 #c4 ,no c' are d4 #e4 #a4 ,all b' are a'2 #b4 ,no b are c2 #c4 ,no a' are d4 #f4 #a4 ,all a are b'2 #b4 ,no b' are c2 #c4 ,all d are a4 #g4 #a4 ,no d are b'2 #b4 ,all b are a2 #c4 ,no c are d'4 #h4 #a4 ,no b' are d2 #b4 ,no a' are b2 #c4 ,all c are d4 pg#aaa #i4 #a4 ,all b' are a2 #b4 ,no a are d2 #c4 ,all b are c4 #aj4 #a4 ,no c are d2 #b4 ,all b are c2 #c4 ,no a are d'4 #aa4 #a4 ,no b are c2 #b4 ,all d are a2 #c4 ,all c' are a'4 #ab4 #a4 ,no c are b'2 #b4 ,all c' are d'2 #c4 ,all b are a4 #ac4 #a4 ,all d are e2 #b4 ,all c are a2 #c4 ,no b are d'2 #d4 ,all e are a'4 #ad4 #a4 ,all e are b2 #b4 ,all a are e2 #c4 ,all d are b'2 #d4 ,all a' are c2 #ae4 #a4 ,no b' are d2 #b4 ,all e are c2 #c4 ,all b are a2 #d4 ,all d' are c'4 #af4 #a4 ,no a' are e2 #b4 ,all d are c'2 #c4 ,all a are b2 #d4 ,all e' are d4 #ag4 #a4 ,all d are c2 #b4 ,all a are e2 #c4 ,no b are d'2 #d4 ,all c are e'4 #ah4 #a4 ,all a are b2 #b4 ,all d are e2 #c4 ,all a' are c'2 #d4 ,no b are e4 #ai4 #a4 ,no b are c2 #b4 ,all e are h2 #c4 ,all a are b2 #d4 ,no d are h2 #e4 ,all e' are c4 #bj4 #a4 ,no d are h'2 #b4 ,no c are e2 #c4 ,all h are b2 #d4 ,no a are d'2 #e4 ,no b are e'4 #ba4 #a4 ,all b are a2 #b4 ,no d are h2 #c4 ,no c are e2 #d4 ,no a are h'2 #e4 ,all c' are b4 #bb4 #a4 ,all e are d'2 #b4 ,no b' are h'2 #c4 ,all c' are d2 #d4 ,all a are e2 #e4 ,no c are h4 #bc4 #a4 ,all b' are a'2 #b4 ,no d are e'2 #c4 ,all h are b'2 #d4 ,no c are e2 #e4 ,all d' are a4 #bd4 #a4 ,all h' are k'2 #b4 ,no b' are a2 #c4 ,all c are d2 #d4 ,all e are h'2 #e4 ,no d are k'2 #f4 ,no b are c'4 #be4 #a4 ,all a are d2 #b4 ,all k are b2 #c4 ,all e are h2 #d4 ,no a' are b2 #e4 ,all d are c2 #f4 ,all h are k4 #bf4 #a4 ,all a' are h2 #b4 ,no d' are k'2 #c4 ,all e are b'2 #d4 ,no h are k2 #e4 ,all a are e2 #f4 ,no b' are d4 #bg4 #a4 ,all c are d'2 #b4 ,no h are b2 #c4 ,all a' are k2 #d4 ,no c are e'2 #e4 ,all b' are d2 #f4 ,no a are c'4 #bh4 #a4 ,no a' are k2 #b4 ,all e are b2 #c4 ,no h are k'2 #d4 ,no d' are c2 #e4 ,no a are b2 #f4 ,all c' are h4 #bi4 #a4 ,no e are k2 #b4 ,no b' are m2 #c4 ,no a are c'2 #d4 ,all h' are e2 #e4 ,all d are k2 #f4 ,no c are b2 #g4 ,all d' are l2 #h4 ,no h are m'4 #cj4 #a4 ,all n are m2 #b4 ,all a' are e2 #c4 ,no c' are l2 #d4 ,all k are r'2 #e4 ,no a are h'2 #f4 ,no d are l'2 #g4 ,no c are n'2 #h4 ,all e are b2 #i4 ,all m are r2 #aj4 ,all h are d4 ,n4,b4 ,9 ea* ,example1 9 ,sections #h & #i1 x is possible to beg9 ) any ,premiss1 at pleasure1 & ?us to get z _m diff]5t ,solutions 7all ( c\rse yield+ ! same ,complete ,conclusion7 z !re are ,premisses 9 ! ,example4 ,h5ce #h really conta9s #abi diff]5t ,examples1 & #i conta9s #bgc4 pg#aab #i4 ,,ex#i ,sets ( ,concrete ,propositions1 propos$ z ,premisses = ,soriteses3 ,conclusions to be f\nd4 #a4 7#a7 ,babies are illogical2 7#b7 ,nobody is despis$ :o c manage a crocodile2 7#c7 ,illogical p]sons are despis$4 ,univ4 p]sons2 a able to manage a crocodile2 b babies2 c despis$2 d logical4 #b4 7#a7 ,my saucepans are ! only ?+s ,i h t are made ( t92 7#b7 ,i f9d all y\r pres5ts v useful2 7#c7 ,none ( my saucepans are ( ! slighte/ use4 ,univ4 ?+s ( m9e2 a made ( t92 b my saucepans2 c useful2 d y\r pres5ts4 #c4 7#a7 ,no potatoes ( m9e1 t are new1 h be5 boil$2 7#b7 ,all my potatoes 9 ?is di% are fit to eat2 7#c7 ,no unboil$ potatoes ( m9e are fit to eat4 ,univ4 my potatoes2 a boil$2 b eatable2 c 9 ?is di%2 d new4 #d4 7#a7 ,!re are no ,jews 9 ! kit*52 7#b7 ,no ,g5tiles say %poonj2 7#c7 ,my s]vants are all 9 ! kit*54 ,univ4 p]sons2 a 9 ! kit*52 b ,jews2 c my s]vants2 d say+ %poonj4 #e4 7#a7 ,no ducks waltz2 7#b7 ,no (fic]s ev] decl9e to waltz2 7#c7 ,all my p\ltry are ducks4 ,univ4 creatures2 a ducks2 b my p\ltry2 c (fic]s2 d will+ to waltz4 #f4 7#a7 ,e "o :o is sane c d ,logic2 7#b7 ,no lunatics are fit to s]ve on a jury2 7#c7 ,none ( y\r sons c d ,logic4 ,univ4 p]sons2 a able to d ,logic2 b fit to s]ve on a jury2 c sane2 d y\r sons4 pg#aac #g4 7#a7 ,!re are no p5cils ( m9e 9 ?is box2 7#b7 ,no sug>-plums ( m9e are cig>s2 7#c7 ,! :ole ( my prop]ty1 t is n 9 ?is box1 consi/s ( cig>s4 ,univ4 ?+s ( m9e2 a cig>s2 b 9 ?is box2 c p5cils2 d sug>-plums4 #h4 7#a7 ,no exp]i5c$ p]son is incompet5t2 7#b7 ,j5k9s is always blund]+2 7#c7 ,no compet5t p]son is always blund]+4 ,univ4 p]sons2 a always blund]+2 b compet5t2 c exp]i5c$2 d ,j5k9s4 #i4 7#a7 ,no t]ri]s w&] among ! signs ( ! zodiac2 7#b7 ,no?+1 t does n w&] among ! signs ( ! zodiac1 is a comet2 7#c7 ,no?+ b a t]ri] has a curly tail4 ,univ4 ?+s2 a comets2 b curly-tail$2 c t]ri]s2 d w&]+ among ! signs ( ! zodiac4 #aj4 7#a7 ,no "o takes 9 ! ,times1 unless he is well-educat$2 7#b7 ,no h$ge-hogs c read2 7#c7 ,^? :o _c read are n well-educat$4 ,univ4 creatures2 a able to read2 b h$ge-hogs2 c tak+ 9 ! ,times2 d well-educat$4 #aa4 7#a7 ,all pudd+s are nice2 7#b7 ,?is di% is a pudd+2 7#c7 ,no nice ?+s are :olesome4 ,univ4 ?+s2 a nice2 b pudd+s2 c ?is di%2 d :olesome4 #ab4 7#a7 ,my g>d5] is well wor? li/5+ to on milit>y subjects2 7#b7 ,no "o c rememb] ! battle ( ,wat]loo1 unless he is v old2 7#c7 ,nobody is really wor? li/5+ to on milit>y subjects1 unless he c rememb] ! battle ( ,wat]loo4 ,univ4 p]sons2 a able to rememb] ! battle ( ,wat]loo2 b my g>d5]2 c well wor? li/5+ to on milit>y subjects2 d v old4 pg#aad #ac4 7#a7 ,all humm+-birds are ri*ly col\r$2 7#b7 ,no l>ge birds live on honey2 7#c7 ,birds t d n live on honey are dull 9 col\r4 ,univ4 birds2 a humm+-birds2 b l>ge2 c liv+ on honey2 d ri*ly col\r$4 #ad4 7#a7 ,no ,g5tiles h hook$ noses2 7#b7 ,a man :o is a good h& at a b>ga9 always makes money2 7#c7 ,no ,jew is ev] a bad h& at a b>ga94 ,univ4 p]sons2 a good h&s at a b>ga92 b hook-nos$2 c ,jews2 d mak+ money4 #ae4 7#a7 ,all ducks 9 ?is village1 t are br&$ ',b1' belong to ,mrs4 ,bond2 7#b7 ,ducks 9 ?is village nev] we> lace coll>s1 unless !y are br&$ ',b'2 7#c7 ,mrs4 ,bond has no gray ducks 9 ?is village4 ,univ4 ducks 9 ?is village2 a belong+ to ,mrs4 ,bond2 b br&$ ',b'2 c gray2 d we>+ lace-coll>s4 #af4 7#a7 ,all ! old articles 9 ?is cupbo>d are crack$2 7#b7 ,no jug 9 ?is cupbo>d is new2 7#c7 ,no?+ 9 ?is cupbo>d1 t is crack$1 w hold wat]4 ,univ4 ?+s 9 ?is cupbo>d2 a able to hold wat]2 b crack$2 c jugs2 d old4 #ag4 7#a7 ,all unripe fruit is un:olesome2 7#b7 ,all ^! apples are :olesome2 7#c7 ,no fruit1 gr[n 9 ! %ade1 is ripe4 ,univ4 fruit2 a gr[n 9 ! %ade2 b ripe2 c ^! apples2 d :olesome4 #ah4 7#a7 ,puppies1 t w n lie /ill1 are always grateful = ! loan ( a skipp+-rope2 7#b7 ,a lame puppy w\ld n say ?ank y if y (f]$ to l5d x a skipp+-rope4 7#c7 ,none b lame puppies ev] c>e to d wor/$-"w4 ,univ4 puppies2 a c>+ to d wor/$-"w2 b grateful = ! loan ( a skipp+-rope2 c lame2 d will+ to lie /ill4 pg#aae #ai4 7#a7 ,no "n 9 ?is li/ is unsuitable = ! h]o ( a romance2 7#b7 ,names beg9n+ ) a v[el are always melodi\s2 7#c7 ,no "n is suitable = ! h]o ( a romance1 if x beg9s ) a consonant4 ,univ4 names2 a beg9n+ ) a v[el2 b 9 ?is li/2 c melodi\s2 d suitable = ! h]o ( a romance4 #bj4 7#a7 ,all memb]s ( ! ,h\se ( ,commons h p]fect self-comm&2 7#b7 ,no ,m4,p41 :o we>s a coronet1 %\ld ride 9 a donkey-race2 7#c7 ,all memb]s ( ! ,h\se ( ,lords we> coronets4 ,univ4 ,m4,p4's2 a belong+ to ! ,h\se ( ,commons2 b hav+ p]fect self-comm&2 c "o :o may ride 9 a donkey-race2 d we>+ a coronet4 #ba4 7#a7 ,no goods 9 ?is %op1 t h be5 b\ght & paid =1 are /ill on sale2 7#b7 ,none ( ! goods may be c>ri$ away1 unless label$ sold2 7#c7 ,none ( ! goods are label$ sold1 unless !y h be5 b\ght & paid =4 ,univ4 goods 9 ?is %op2 a all[$ to be c>ri$ away2 b b\ght & paid =2 c label$ sold2 d on sale4 #bb4 7#a7 ,no acrobatic feats1 t are n ann\nc$ 9 ! bills ( a circus1 are ev] attempt$ !re2 7#b7 ,no acrobatic feat is possible1 if x involves turn+ a quadruple som]sault2 7#c7 ,no impossible acrobatic feat is ev] ann\nc$ 9 a circus bill4 ,univ4 acrobatic feats2 a ann\nc$ 9 ! bills ( a circus2 b attempt$ 9 a circus2 c involv+ ! turn+ ( a quadruple som]sault2 d possible4 #bc4 7#a7 ,nobody1 :o really appreciates ,bee?ov51 fails to keep sil5ce :ile ! ,moonlight-,sonata is be+ play$2 7#b7 ,gu9ea-pigs are hopelessly ignorant ( music2 7#c7 ,no "o1 :o is hopelessly ignorant ( music1 ev] keeps sil5ce :ile ! ,moonlight-,sonata is be+ play$4 ,univ4 creatures2 a gu9ea-pigs2 b hopelessly ignorant ( music2 c keep+ sil5ce :ile ! ,moonlight-,sonata is be+ play$2 d really appreciat+ ,bee?ov54 pg#aaf #bd4 7#a7 ,col\r$ fl[]s are always sc5t$2 7#b7 ,i dislike fl[]s t are n gr[n 9 ! op5 air2 7#c7 ,no fl[]s gr[n 9 ! op5 air are col\rless4 ,univ4 fl[]s2 a col\r$2 b gr[n 9 ! op5 air2 c lik$ by me2 d sc5t$4 #be4 7#a7 ,%[y talk]s ?9k too mu* ( !mselves2 7#b7 ,no really well-in=m$ p are bad company2 7#c7 ,p :o ?9k too mu* ( !mselves are n good company4 ,univ4 p]sons2 a good company2 b really well-in=m$2 c %[y talk]s2 d ?9k+ too mu* ( "o's self4 #bf4 7#a7 ,no boys "u #ab are admitt$ to ?is s*ool z bo>d]s2 7#b7 ,all ! indu/ri\s boys h r$ hair2 7#c7 ,none ( ! day-boys le>n ,greek2 7#d7 ,none b ^? "u #ab are idle4 ,univ4 boys 9 ?is s*ool2 a bo>d]s2 b indu/ri\s2 c le>n+ ,greek2 d r$-hair$2 e "u #ab4 #bg4 7#a7 ,! only articles ( food1 t my doctor all[s me1 are su* z are n v ri*2 7#b7 ,no?+ t agrees ) me is unsuitable = supp]2 7#c7 ,w$d+-cake is always v ri*2 7#d7 ,my doctor all[s me all articles ( food t are suitable = supp]4 ,univ4 articles ( food2 a agree+ ) me2 b all[$ by my doctor2 c suitable = supp]2 d v ri*2 e w$d+-cake4 #bh4 7#a7 ,no discussions 9 our ,debat+-,club are likely to r\se ! ,briti% ,lion1 s long z !y are *eck$ :5 !y become too noisy2 7#b7 ,discussions1 unwisely conduct$1 endang] ! peacefulness ( our ,debat+-,club2 7#c7 ,discussions1 t g on :ile ,tomk9s is 9 ! ,*air1 are likely to r\se ! ,briti% ,lion2 7#d7 ,discussions 9 our ,debat+-,club1 :5 wisely conduct$1 are always *eck$ :5 !y become too noisy4 ,univ4 discussions 9 our ,debat+-,club2 a *eck$ :5 too noisy2 b dang]\s to ! peacefulness ( our ,debat+-,club2 c go+ on :ile ,tomk9s is 9 ! *air2 d likely to r\se ! ,briti% ,lion2 e wisely conduct$4 pg#aag #bi4 7#a7 ,all my sons are slim2 7#b7 ,no *ild ( m9e is heal?y :o takes no ex]cise2 7#c7 ,all gluttons1 :o are *ildr5 ( m9e1 are fat2 7#d7 ,no daught] ( m9e takes any ex]cise4 ,univ4 my *ildr52 a fat2 b gluttons2 c heal?y2 d sons2 e tak+ ex]cise4 #cj4 7#a7 ,?+s sold 9 ! /reet are ( no great value2 7#b7 ,no?+ b rubbi% c be _h = a song2 7#c7 ,eggs ( ! ,great ,auk are v valuable2 7#d7 ,x is only :at is sold 9 ! /reet t is really rubbi%4 ,univ4 ?+s2 a able to be _h = a song2 b eggs ( ! ,great ,auk2 c rubbi%2 d sold 9 ! /reet2 e v valuable4 #ca4 7#a7 ,no books sold "h h gilt edges1 except :at are 9 ! front %op2 7#b7 ,all ! au?oris$ editions h r$ labels2 7#c7 ,all ! books ) r$ labels are pric$ at #es4 & upw>ds2 7#d7 ,none b au?oris$ editions are ev] plac$ 9 ! front %op4 ,univ4 books sold "h2 a au?oris$ editions2 b gilt-edg$2 c hav+ r$ labels2 d 9 ! front %op2 e pric$ at #es4 & upw>ds4 #cb4 7#a7 ,rem$ies = ble$+1 :i* fail to *eck x1 are a mock]y2 7#b7 ,t9cture ( ,cal5dula is n to be despis$2 7#c7 ,rem$ies1 :i* w *eck ! ble$+ :5 y cut y\r f+]1 are useful2 7#d7 ,all mock rem$ies = ble$+ are despicable4 ,univ4 rem$ies = ble$+2 a able to *eck ble$+2 b despicable2 c mock]ies2 d ,t9cture ( ,cal5dula2 e useful :5 y cut y\r f+]4 #cc4 7#a7 ,none ( ! unnotic$ ?+s1 met ) at sea1 are m]maids2 7#b7 ,?+s ent]$ 9 ! log1 z met ) at sea1 are sure to be wor? rememb]+2 7#c7 ,i h nev] met ) any?+ wor? rememb]+1 :5 on a voyage2 7#d7 ,?+s met ) at sea1 t are notic$1 are sure to be record$ 9 ! log2 ,univ4 ?+s met ) at sea2 a ent]$ 9 log2 b m]maids2 c met ) by me2 d notic$2 e wor? rememb]+4 pg#aah #cd4 7#a7 ,! only books 9 ?is libr>y1 t ,i d n recomm5d = read+1 are unheal?y 9 tone2 7#b7 ,! b\nd books are all well-writt52 7#c7 ,all ! romances are heal?y 9 tone2 7#d7 ,i d n recomm5d y to read any ( ! unb\nd books4 ,univ4 books 9 ?is libr>y2 a b\nd2 b heal?y 9 tone2 c recomm5d$ by me2 d romances2 e well-writt54 #ce4 7#a7 ,no birds1 except o/ri*es1 are #i feet high2 7#b7 ,!re are no birds 9 ?is avi>y t belong to any "o b me2 7#c7 ,no o/ri* lives on m9ce-pies2 7#d7 ,i h no birds less ?an #i feet high4 ,univ4 birds2 a 9 ?is avi>y2 b liv+ on m9ce-pies2 c my2 d #i feet high2 e o/ri*es4 #cf4 7#a7 ,a plum-pudd+1 t is n really solid1 is m]e porridge2 7#b7 ,e plum-pudd+1 s]v$ at my table1 has be5 boil$ 9 a clo?2 7#c7 ,a plum-pudd+ t is m]e porridge is indi/+ui%able f s\p2 7#d7 ,no plum-pudd+s are really solid1 except :at are s]v$ at my table4 ,univ4 plum-pudd+s2 a boil$ 9 a clo?2 b di/+ui%able f s\p2 c m]e porridge2 d really solid2 e s]v$ at my table4 #cg4 7#a7 ,no int]e/+ poems are unpopul> among p ( real ta/e2 7#b7 ,no mod]n poetry is free f affectation2 7#c7 ,all y\r poems are on ! subject ( soap-bubbles2 7#d7 ,no affect$ poetry is popul> among p ( real ta/e2 7#e7 ,no anci5t poem is on ! subject ( soap-bubbles4 ,univ4 poems2 a affect$2 b anci5t2 c int]e/+2 d on ! subject ( soap-bubbles2 e popul> among p ( real ta/e2 h writt5 by y4 #ch4 7#a7 ,all ! fruit at ?is ,%[1 t fails to get a prize1 is ! prop]ty ( ! ,committee2 7#b7 ,none ( my pea*es h got prizes2 7#c7 ,none ( ! fruit1 sold (f 9 ! ev5+1 is unripe2 7#d7 ,none ( ! ripe fruit has be5 gr[n 9 a hot-h\se2 7#e7 ,all fruit1 t belongs to ! ,committee1 is sold (f 9 ! ev5+4 ,univ4 fruit at ?is ,%[2 a belong+ to ! ,committee2 b gett+ prizes2 c gr[n 9 a hot-h\se2 d my pea*es2 e ripe2 h sold (f 9 ! ev5+4 pg#aai #ci4 7#a7 ,promise-break]s are untru/wor?y2 7#b7 ,w9e-dr9k]s are v communicative2 7#c7 ,a man :o keeps 8 promises is hone/2 7#d7 ,no teetotal]s are pawnbrok]s2 7#e7 ,"o c always tru/ a v communicative p]son4 ,univ4 p]sons2 a hone/2 b pawnbrok]s2 c promise-break]s2 d tru/wor?y2 e v communicative2 h w9e-dr9k]s4 #dj4 7#a7 ,no kitt51 t loves fi%1 is untea*able2 7#b7 ,no kitt5 )\t a tail w play ) a gorilla2 7#c7 ,kitt5s ) :isk]s always love fi%2 7#d7 ,no tea*able kitt5 has gre5 eyes2 7#e7 ,no kitt5s h tails unless !y h :isk]s4 ,univ4 kitt5s2 a gre5-ey$2 b lov+ fi%2 c tail$2 d tea*able2 e :isk]$2 h will+ to play ) a gorilla4 #da4 7#a7 ,all ! ,eton m5 9 ?is ,college play cricket2 7#b7 ,none b ! ,s*ol>s d9e at ! high] table2 7#c7 ,none ( ! cricket]s r[2 7#d7 ,my fri5ds 9 ?is ,college all come f ,eton2 7#e7 ,all ! ,s*ol>s are r[+-m54 ,univ4 m5 9 ?is ,college2 a cricket]s2 b d9+ at ! high] table2 c ,etonians2 d my fri5ds2 e r[+-m52 h ,s*ol>s4 #db4 7#a7 ,!re is no box ( m9e "h t ,i d>e op52 7#b7 ,my writ+-desk is made ( rose-wood2 7#c7 ,all my boxes are pa9t$1 except :at are "h2 7#d7 ,!re is no box ( m9e t ,i d>e n op51 unless x is full ( live scorpions2 7#e7 ,all my rose-wood boxes are unpa9t$4 ,univ4 my boxes2 a boxes t ,i d>e op52 b full ( live scorpions2 c "h2 d made ( rose-wood2 e pa9t$2 h writ+-desks4 #dc4 7#a7 ,g5tiles h no objection to pork2 7#b7 ,nobody :o admires pig/ies ev] reads ,hogg's poems2 7#c7 ,no ,m&>9 kn[s ,hebrew2 7#d7 ,e "o1 :o does n object to pork1 admires pig/ies2 7#e7 ,no ,jew is ignorant ( ,hebrew4 ,univ4 p]sons2 a admir+ pig/ies2 b ,jews2 c kn[+ ,hebrew2 d ,m&>9s2 e object+ to pork2 h read+ ,hogg's poems4 pg#abj #dd4 7#a7 ,all writ]s1 :o und]/& human nature1 are clev]2 7#b7 ,no "o is a true poet unless he c /ir ! he>ts ( m52 7#c7 ,%akespe>e wrote ,hamlet2 7#d7 ,no writ]1 :o does n und]/& human nature1 c /ir ! he>ts ( m52 7#e7 ,none b a true poet c\ld h writt5 ,hamlet42 ,univ4 writ]s2 a able to /ir ! he>ts ( m52 b clev]2 c ,%akespe>e2 d true poets2 e und]/&+ human nature2 h writ] ( ',hamlet4' #de4 7#a7 ,i despise any?+ t _c be us$ z a bridge2 7#b7 ,ev]y?+1 t is wor? writ+ an ode to1 w\ld be a welcome gift to me2 7#c7 ,a ra9b[ w n be> ! weight ( a :eel-b>r[2 7#d7 ,:atev] c be us$ z a bridge w be> ! weight ( a :eel-b>r[2 7#e7 ,i w\ld n take1 z a gift1 a ?+ t ,i despise4 ,univ4 ?+s2 a able to be> ! weight ( a :eel-b>r[2 b acceptable to me2 c despis$ by me2 d ra9b[s2 e useful z a bridge2 h wor? writ+ an ode to4 #df4 7#a7 ,:5 ,i "w a ,logic-example )\t grumbl+1 y may be sure x is "o t ,i c und]/&2 7#b7 ,^! ,soriteses are n arrang$ 9 regul> ord]1 l ! examples ,i am us$ to2 7#c7 ,no easy example ev] make my head a*e2 7#d7 ,i ca'n't und]/& examples t are n arrang$ 9 regul> ord]1 l ^? ,i am us$ to2 7#e7 ,i nev] grumble at an example1 unless x gives me a heada*e4 ,univ4 ,logic-examples work$ by me2 a arrang$ 9 regul> ord]1 l ! examples ,i am us$ to2 b easy2 c grumbl$ at by me2 d mak+ my head a*e2 e ^! ,soriteses2 h und]/ood by me4 #dg4 7#a7 ,e idea ( m9e1 t _c be express$ z a ,syllogism1 is really ridicul\s2 7#b7 ,none ( my ideas ab\t ,ba?-buns are wor? writ+ d[n2 7#c7 ,no idea ( m9e1 t fails to come true1 c be express$ z a ,syllogism2 7#d7 ,i nev] h any really ridicul\s idea1 t ,i d n at once ref] to my solicitor2 7#e7 ,my dreams are all ab\t ,ba?-buns2 7#f7 ,i nev] ref] any idea ( m9e to my solicitor1 unless x is wor? writ+ d[n4 ,univ4 my ideas2 a able to be express$ z a ,syllogism2 b ab\t ,ba?-buns2 c com+ true2 d dreams2 e really ridicul\s h ref]r$ to my solicitor2 k wor? writ+ d[n4 pg#aba #dh4 7#a7 ,none ( ! pictures "h1 except ! battle-pieces1 are valuable2 7#b7 ,none ( ! unfram$ ones are v>ni%$2 7#c7 ,all ! battle-pieces are pa9t$ 9 oils2 7#d7 ,all ^? t h be5 sold are valuable2 7#e7 ,all ! ,engli% ones are v>ni%$2 7#f7 ,all ^? 9 frames h be5 sold4 ,univ4 ! pictures "h2 a battle-pieces2 b ,engli%2 c fram$2 d oil-pa9t+s2 e sold2 h valuable2 k v>ni%$4 #di4 7#a7 ,animals1 t d n kick1 are always unexcitable2 7#b7 ,donkeys h no horns2 7#c7 ,a buffalo c always toss "o ov] a gate2 7#d7 ,no animals t kick are easy to swall[2 7#e7 ,no hornless animal c toss "o ov] a gate2 7#f7 ,all animals are excitable1 except buffaloes4 ,univ4 animals2 a able to toss "o ov] a gate2 b buffaloes2 c donkeys2 d easy to swall[2 e excitable2 h horn$2 k kick+4 #ej4 7#a7 ,no "o1 :o is go+ to a p>ty1 ev] fails to bru% 8 hair2 7#b7 ,no "o looks fasc9at+1 if he is untidy2 7#c7 ,opium-eat]s h no self-comm&2 7#d7 ,e "o1 :o has bru%$ 8 hair1 looks fasc9at+2 7#e7 ,no "o we>s :ite kid gloves1 unless he is go+ to a p>ty2 7#f7 ,a man is always untidy1 if he has no self-comm&4 ,univ4 p]sons2 a go+ to a p>ty2 b hav+ bru%$ "o's hair2 c hav+ self-comm&2 d look+ fasc9at+2 e opium-eat]s2 h tidy2 k we>+ :ite kid gloves4 #ea4 7#a7 ,no husb&1 :o is always giv+ 8 wife new dresses1 c be a cross-gra9$ man2 7#b7 ,a me?odical husb& always comes home = 8 tea2 7#c7 ,no "o1 :o hangs up 8 hat on ! gas-jet1 c be a man t is kept 9 prop] ord] by 8 wife2 7#d7 ,a good husb& is always giv+ 8 wife new dresses2 7#e7 ,no husb& c fail to be cross-gra9$1 if 8 wife does n keep him 9 prop] ord]2 7#f7 ,an unme?odical husb& always hangs up 8 hat on ! gas-jet4 ,univ4 husb&s2 a always com+ home = 8 tea2 b always giv+ 8 wife new dresses2 c cross-gra9$2 d good2 e hang+ up 8 hat on ! gas-jet2 h kept 9 prop] ord]2 k me?odical4 pg#abb #eb4 7#a7 ,ev]y?+1 n absolutely ugly1 may be kept 9 a draw+-room2 7#b7 ,no?+1 t is encru/$ ) salt1 is ev] q dry2 7#c7 ,no?+ %\ld be kept 9 a draw+-room1 unless x is free f damp2 7#d7 ,ba?+-ma*9es are always kept ne> ! sea2 7#e7 ,no?+1 t is made ( "m-(-pe>l1 c be absolutely ugly2 7#f7 ,:atev] is kept ne> ! sea gets encru/$ ) salt4 ,univ4 ?+s2 a absolutely ugly2 b ba?+-ma*9es2 c encru/$ ) salt2 d kept ne> ! sea2 e made ( "m-(-pe>l2 h q dry2 k ?+s t may be kept 9 a draw+-room4 #ec4 7#a7 ,i call no day unlucky1 :5 ,rob9son is civil to me2 7#b7 ,w$nesdays are always cl\dy2 7#c7 ,:5 p take umbrellas1 ! day nev] turns out f9e2 7#d7 ,! only days :5 ,rob9son is uncivil to me are ,w$nesdays2 7#e7 ,ev]ybody takes 8 umbrella ) him :5 x is ra9+2 7#f7 ,my lucky days always turn out f9e4 ,univ4 days2 a call$ by me 'lucky'2 b cl\dy2 c days :5 p take umbrellas2 d days :5 ,rob9son is civil to me2 e ra9y2 h turn+ out f9e2 k ,w$nesdays4 #ed4 7#a7 ,no %>k ev] d\bts t x is well fitt$ out2 7#b7 ,a fi%1 t _c dance a m9uet1 is contemptible2 7#c7 ,no fi% is q c]ta9 t x is well fitt$ out1 unless x has ?ree r[s ( tee?2 7#d7 ,all fi%es1 except %>ks1 are k9d to *ildr52 7#e7 ,no heavy fi% c dance a m9uet2 7#f7 ,a fi% ) ?ree r[s ( tee? is n to be despis$4 ,univ4 fi%es2 a able to dance a m9uet2 b c]ta9 t he is well fitt$ out2 c contemptible2 d hav+ #c r[s ( tee?2 e heavy2 h k9d to *ildr52 k %>ks4 #ee4 7#a7 ,all ! human race1 except my footm51 h a c]ta9 am\nt ( common-s5se2 7#b7 ,no "o1 :o lives on b>ley-sug>1 c be any?+ b a m]e baby2 7#c7 ,none b a hop-scot* play] kn[s :at real happ9ess is2 7#d7 ,no m]e baby has a gra9 ( common s5se2 7#e7 ,no eng9e-driv] ev] plays hop-scot*2 7#f7 ,no footman ( m9e is ignorant ( :at true happ9ess is4 ,univ4 human be+s2 a eng9e-driv]s2 b hav+ common s5se2 c hop-scot* play]s2 d kn[+ :at real happ9ess is2 e liv+ on b>ley-sug>2 h m]e babies2 k my footm54 pg#abc #ef4 7#a7 ,i tru/ e animal t belongs to me2 7#b7 ,dogs gnaw bones2 7#c7 ,i admit no animals into my /udy1 unless !y w beg :5 told to d s2 7#d7 ,all ! animals 9 ! y>d are m9e2 7#e7 ,i admit e animal1 t ,i tru/1 into my /udy2 7#f7 ,! only animals1 t are really will+ to beg :5 told to d s1 are dogs4 ,univ4 animals2 a admitt$ to my /udy2 b animals t ,i tru/2 c dogs2 d gnaw+ bones2 e 9 ! y>d2 h my2 k will+ to beg :5 told4 #eg4 7#a7 ,animals are always mortally (f5d$ if ,i fail to notice !m2 7#b7 ,! only animals t belong to me are 9 t field2 7#c7 ,no animal c guess a conundrum1 unless x has be5 prop]ly tra9$ 9 a ,bo>d-,s*ool2 7#d7 ,none ( ! animals 9 t field are badg]s2 7#e7 ,:5 an animal is mortally (f5d$1 x always ru%es ab\t wildly & h[ls2 7#f7 ,i nev] notice any animal1 unless x belongs to me2 7#g7 ,no animal1 t has be5 prop]ly tra9$ 9 a ,bo>d-,s*ool1 ev] ru%es ab\t wildly & h[ls4 ,univ4 animals2 a able to guess a conundrum2 b badg]s2 c 9 t field2 d mortally (f5d$2 e my2 h notic$ by me2 k prop]ly tra9$ 9 a ,bo>d-,s*ool2 l ru%+ ab\t wildly & h[l+4 #eh4 7#a7 ,i nev] put a *eque1 receiv$ by me1 on t file1 unless ,i am anxi\s ab\t x2 7#b7 ,all ! *eques receiv$ by me1 t are n m>k$ ) a cross1 are payable to be>]2 7#c7 ,none ( !m are ev] br\ght back to me1 unless !y h be5 di%on\r$ at ! ,bank2 7#d7 ,all ( !m1 t are m>k$ ) a cross1 are = am\nts ( ov] #ajj2 7#e7 ,all ( !m1 t are n on t file1 are m>k$ n negotiable2 7#f7 ,no *eque ( y\rs1 receiv$ by me1 has ev] be5 di%on\r$2 7#g7 ,i am nev] anxi\s ab\t a *eque1 receiv$ by me1 unless x %\ld happ5 to be br\ght back to me2 7#h7 ,none ( ! *eques receiv$ by me1 t are m>k$ n negotiable1 are = am\nts ( ov] #ajj4 ,univ4 *eques receiv$ by me2 a br\ght back to me2 b *eques t ,i am anxi\s ab\t2 c hon\r$2 d m>k$ ) a cross2 e m>k$ 'n negotiable'2 h on t file2 k ov] #ajj2 l payable to be>]2 m y\r4 pg#abd #ei4 7#a7 ,all ! dat$ lett]s 9 ?is room are writt5 on blue pap]2 7#b7 ,none ( !m are 9 black ink1 except ^? t are writt5 9 ! ?ird p]son2 7#c7 ,i h n fil$ any ( !m t ,i c read2 7#d7 ,none ( !m1 t are writt5 on "o %eet1 are undat$2 7#e7 ,all ( !m1 t are n cross$1 are 9 black ink2 7#f7 ,all ( !m1 writt5 by ,br[n1 beg9 ) ,de> ,sir2 7#g7 ,all ( !m1 writt5 on blue pap]1 are fil$2 7#h7 ,none ( !m1 writt5 on m ?an "o %eet1 are cross$2 7#i7 ,none ( !m1 t beg9 ) ,de> ,sir1 are writt5 9 ! ?ird p]son4 ,univ4 lett]s 9 ?is room2 a beg9n+ ) ,de> ,sir2 b cross$2 c dat$2 d fil$2 e 9 black ink2 h 9 ?ird p]son2 k lett]s t ,i c read2 l on blue pap]2 m on "o %eet2 n writt5 by ,br[n4 #fj4 7#a7 ,! only animals 9 ?is h\se are cats2 7#b7 ,e animal is suitable = a pet1 t loves to gaze at ! moon2 7#c7 ,:5 ,i dete/ an animal1 ,i avoid x2 7#d7 ,no animals are c>nivor\s1 unless !y pr[l at night2 7#e7 ,no cats fails to kill mice2 7#f7 ,no animals ev] take to me1 except :at are 9 ?is h\se2 7#g7 ,kang>oos are n suitable = pets2 7#h7 ,none b c>nivora kill mice2 7#i7 ,i dete/ animals t d n take to me2 7#aj7 ,animals1 t pr[l at night1 always love to gaze at ! moon4 ,univ4 animals2 a avoid$ by me2 b c>nivora2 c cats2 d dete/$ by me2 e 9 ?is h\se2 h kang>oos2 k kill+ mice2 l lov+ to gaze at ! moon2 m pr[l+ at night2 n suitable = pets2 r tak+ to me4 pg#abe ,,*apt] ,,ii4 ,,answ]s4 ,answ]s to #a4 ,,an#a #a4 ,all ,sign ( ,quantity4 p]sons repres5t$ by ! ,"n ',i' 7or ,i's7 ,subject4 are ,copula4 p]sons :o h be5 out = a walk ,pr$icate4 or1 m briefly1 ,all ',i's are p]sons :o h be5 out = a walk4 #b4 ,all ',i's are p]sons :o feel bett]4 #c4 ,no p]sons :o are n ',john' are p]sons :o h read ! lett]4 #d4 ,no ,memb]s ( ! ,class 'y & ,i' are old p]sons4 #e4 ,no fat creatures are creatures t run well4 #f4 ,no n-brave p]sons are p]sons des]v+ ( ! fair4 #g4 ,no n-pale p]sons are p]sons :o look poetical4 #h4 ,"s judges are p]sons :o lose _! temp]s4 #i4 ,all ',i's are p]sons :o d n neglect important bus9ess4 #aj4 ,all difficult ?+s are ?+s t ne$ att5tion4 #aa4 ,all un:olesome ?+s are ?+s t %\ld be avoid$4 #ab4 ,all laws pass$ la/ week are laws relat+ to excise4 #ac4 ,all logical /udies are ?+s t puzzle me4 #ad4 ,no p]sons 9 ! h\se are ,jews4 #ae4 ,"s n well-cook$ di%es are un:olesome di%es4 #af4 ,all unexcit+ books are books t make "o dr[sy4 #ag4 ,all m5 :o "k :at !y're ab\t are m5 :o c detect a %>p]4 #ah4 ,all ,memb]s ( ! ,class 'y & ,i' are p]sons :o "k :at !y're ab\t4 #ai4 ,"s bald p]sons are p]sons accu/om$ to we> wigs4 #bj4 ,all fully occupi$ p]sons are p]sons :o d n talk ab\t _! grievances4 #ba4 ,no riddles t c be solv$ are riddles t int]e/ me4 pg#abf ,answ]s to #b4 ,,an#b #a --------------- 7,o7 ------ 7,o77,o7 ------------ ------ 7,o7 --------------- #b --------------- 7,i7 7,o7 ------ ------------ ------ 7,o7 7,o7 --------------- #c --------------- ------ 7,o7 ------------ 7,o77,i7 ------ --------------- #d --------------- 7,o7 ------ 7,i7 ---------7,i7 7,o77,o7 ------ 7,o7 --------------- #e --------------- 7,o7 7,i7 ------ ------------ ------ 7,o7 7,o7 --------------- #f --------------- ------ 7,o7 ------------ 7,o77,o7 ------ 7,i7 --------------- #g --------------- 7,o7 7,o7 ------ 7,i77,o7 ------------ 7,o7 ------ 7,i7 --------------- #h --------------- ------ 7,o7 ------------ 7,o7 ------ 7,i7 --------------- #i --------------- ------ 7,o77,o7 ------------ 7,o77,i7 ------ --------------- #aj --------------- 7,o7 ------ ------------ 7,o77,o7 ------ 7,o7 --------------- #aa --------------- ------ 7,o7 ------------ 7,o7 ------ 7,o7 7,o7 --------------- #ab --------------- 7,o7 ------ 7,i7 ------7,i7--- ------ 7,o7 --------------- #ac --------------- ------ 7,o7 ------------ 7,i77,o7 ------ 7,o7 7,o7 --------------- #ad --------------- 7,i7 ------ 7,o7 ---7,i7------ 7,o7 ------ --------------- #ae --------------- 7,o7 ------ ---7,i7------ ------ 7,o7 7,o7 --------------- #af --------------- 7,i7 ------ 7,o77,o7 ------------ 7,o7 ------ --------------- #ag --------------- 7,i7 7,o7 ------ ------------ ------ 7,o7 --------------- #ah --------------- 7,i7 ------ 7,o77,o7 ---------7,i7 ------ --------------- #ai --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- #bj --------------- ------ 7,i7 ------------ 7,o77,o7 ------ --------------- #ba --------------- 7,o7 ------ ------7,i7--- ------ 7,i7 7,o7 --------------- #bb --------------- ------ 7,o77,o7 ------------ 7,i7 ------ --------------- #bc --------------- 7,o7 7,o7 ------ 7,o7 ------------ 7,o7 ------ 7,i7 --------------- #bd --------------- 7,o7 ------ 7,i7 ------------ 7,o77,o7 ------ 7,o7 --------------- pg#abg #be --------------- ------ 7,i77,o7 ------------ 7,o7 ------ --------------- #bf --------------- 7,o7 7,o7 ------ ------------ ------ 7,i7 --------------- #bg --------------- 7,o7 ------ ------------ 7,i7 ------ 7,o7 --------------- #bh --------------- 7,o7 7,o7 ------ 7,o7 ------7,i7--- 7,o7 ------ --------------- #bi --------------- ------ 7,o7 ------------ 7,o77,o7 ------ --------------- #cj --------------- ------ 7,o77,o7 ---------7,i7 ------ --------------- #ca --------------- 7,i7 7,o7 ------ ------7,i7--- ------ 7,o7 --------------- #cb --------------- 7,o7 7,i7 ------ 7,o77,o7 ------------ 7,i7 ------ 7,o7 --------------- ,answ]s to #c4 ,,an#c #a4 ,"s xy exi/1 or "s x are y1 or "s y are x4 #b4 ,no in=mation4 #c4 ,all y' are x'4 #d4 ,no xy exi/1 c4 #e4 ,all y' are x4 #f4 ,all x' are y4 #g4 ,all x are y4 #h4 ,all x' are y'1 & all y are x4 #i4 ,all x' are y'4 #aj4 ,all x are y'4 #aa4 ,no in=mation4 #ab4 ,"s x'y' exi/1 c4 #ac4 ,"s xy' exi/1 c4 #ad4 ,no xy' exi/1 c4 #ae4 ,"s xy exi/1 c4 #af4 ,all y are x4 #ag4 ,all x' are y1 & all y' are x4 #ah4 ,all x are y'1 & all y are x'4 #ai4 ,all x are y1 & all y' are x'4 #bj4 ,all y are x'4 ,answ]s to #d4 ,,an#d #a4 ,no x' are y'4 #b4 ,"s x' are y'4 #c4 ,"s x are y'4 #d4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #e4 ,"s x' are y'4 #f4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #g4 ,"s x are y'4 #h4 ,"s x' are y'4 #i4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #aj4 ,all x are y1 & all y' are x'4 #aa4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ab4 ,all y are x'4 #ac4 ,no x' are y4 #ad4 ,no x' are y'4 #ae4 ,no x are y4 #af4 ,all x are y'1 & all y are x'4 pg#abh #ag4 ,no x are y'4 #ah4 ,no x are y4 #ai4 ,"s x are y'4 #bj4 ,no x are y'4 #ba4 ,"s y are x'4 #bb4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bc4 ,"s x are y4 #bd4 ,all y are x'4 #be4 ,"s y are x'4 #bf4 ,all y are x4 #bg4 ,all x are y1 & all y' are x'4 #bh4 ,"s y are x'4 #bi4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cj4 ,"s y are x'4 #ca4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cb4 ,no x are y'4 #cc4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cd4 ,"s x are y4 #ce4 ,all y are x'4 #cf4 ,"s y are x'4 #cg4 ,"s x are y'4 #ch4 ,no x are y4 #ci4 ,"s x' are y'4 #dj4 ,all y' are x4 #da4 ,all x are y'4 #db4 ,no x are y4 ,answ]s to #e4 ,,an#e #a4 ,somebody :o has be5 out = a walk is feel+ bett]4 #b4 ,no "o b ,john kn[s :at ! lett] is ab\t4 #c4 ,y & ,i l walk+4 #d4 ,hone/y is sometimes ! be/ policy4 #e4 ,"s greyh\nds are n fat4 #f4 ,"s brave p]sons get _! des]ts4 #g4 ,"s ri* p]sons are n ,esquimaux4 #h4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #i4 ,john is ill4 #aj4 ,"s ?+s1 t are n umbrellas1 %\ld be left beh9d on a j\rney4 #aa4 ,no music is wor? pay+ =1 unless x causes vibration 9 ! air4 #ab4 ,"s holidays are tiresome4 #ac4 ,engli%m5 are n ,fr5*m54 #ad4 ,no photograph ( a lady is satisfactory4 #ae4 ,no "o looks poetical unless he is phlegmatic4 #af4 ,"s ?9 p]sons are n *e]ful4 #ag4 ,"s judges d n ex]cise self-control4 #ah4 ,pigs are n f$ on b>ley-wat]4 #ai4 ,"s black rabbits are n old4 pg#abi #bj4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ba4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bb4 ,"s lessons ne$ att5tion4 #bc4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bd4 ,no "o1 :o =gets a promise1 fails to d mis*ief4 #be4 ,"s gre$y creatures _c fly4 #bf4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bg4 ,no bride-cakes are ?+s t ne$ n be avoid$4 #bh4 ,john is happy4 #bi4 ,"s p1 :o are n gambl]s1 are n philosoph]s4 #cj4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ca4 ,none ( my lodg]s write poetry4 #cb4 ,s5na is n nice4 #cc4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #cd4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ce4 ,logic is un9telligible4 #cf4 ,"s wild creatures are fat4 #cg4 ,all wasps are unwelcome4 #ch4 ,all black rabbits are "y4 #ci4 ,"s h>d-boil$ ?+s c be crack$4 #dj4 ,no antelopes fail to delight ! eye4 #da4 ,all well-f$ can>ies are *e]ful4 #db4 ,"s poetry is n producible at w4 #dc4 ,no c\ntry infe/$ by dragons fails to be fasc9at+4 #dd4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #de4 ,"s picturesque ?+s are n made ( sug>4 #df4 ,no *ildr5 c sit /ill4 #dg4 ,"s cats _c :i/le4 #dh4 ,y are t]rible4 #di4 ,"s oy/]s are n amus+4 #ej4 ,nobody 9 ! h\se has a be>d a y>d long4 #ea4 ,"s ill-f$ can>ies are unhappy4 #eb4 ,my si/]s _c s+4 #ec4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ed4 ,"s ri* ?+s are nice4 #ee4 ,my c\s9s are none ( !m judges1 & judges are none ( !m c\s9s ( m9e4 #ef4 ,some?+ we>isome is n eag]ly wi%$ =4 #eg4 ,s5na is na/y4 #eh4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ei4 ,nigg]s are n any ( !m tall4 #fj4 ,"s ob/9ate p]sons are n philosoph]s4 #fa4 ,john is happy4 #fb4 ,"s un:olesome di%es are n pres5t "h 7i4e4 _c be spok5 ( z ^!74 #fc4 ,no books suit fev]i% pati5ts unless !y make "o dr[sy4 #fd4 ,"s gre$y creatures _c fly4 #fe4 ,y & ,i c detect a %>p]4 #ff4 ,"s dreams are n lambs4 pg#acj #fg4 ,no liz>d ne$s a hairbru%4 #fh4 ,"s ?+s1 t may escape notice1 are n battles4 #fi4 ,my c\s9s are n any ( !m judges4 #gj4 ,"s h>d-boil$ ?+s c be crack$4 #ga4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #gb4 ,%e is unpopul>4 #gc4 ,"s p1 :o we> wigs1 are n *ildr5 ( y\rs4 #gd4 ,no lob/]s expect impossibilities4 #ge4 ,no nightm>e is eag]ly desir$4 #gf4 ,"s nice ?+s are n plumcakes4 #gg4 ,"s k9ds ( jam ne$ n be %unn$4 #gh4 ,all ducks are ungraceful4 #gi4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #hj4 ,no man1 :o begs 9 ! /reet1 %\ld fail to keep acc\nts4 #ha4 ,"s savage creatures are n spid]s4 #hb4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #hc4 ,no travel]s1 :o d n c>ry pl5ty ( small *ange1 fail to lose _! luggage4 #hd4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #he4 ,judges are none ( !m c\s9s ( m9e4 #hf4 ,all my lodg]s are sane4 #hg4 ,^? :o are busy are cont5t$1 & discont5t$ p are n busy4 #hh4 ,none ( my c\s9s are judges4 #hi4 ,no night+ale dislikes sug>4 #ij4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ia4 ,"s excuses are n cle> explanations4 #ib4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ic4 ,no k9d de$ ne$ cause scruple4 #id4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ie4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #if4 ,no *eats are tru/wor?y4 #ig4 ,no clev] *ild ( m9e is gre$y4 #ih4 ,"s ?+s1 t are meant to amuse1 are n ,acts ( ,p>liam5t4 #ii4 ,no t\r1 t is ev] =gott51 is wor? writ+ a book ab\t4 #ajj4 ,no ob$i5t *ild ( m9e is cont5t$4 #aja4 ,y\r visit does n annoy me4 ,answ]s to #f4 ,,an#f #a4 ,conclusion "r4 #b4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #c4 ,concl4 "r4 #d4 ,concl4 "r4 #e4 ,concl4 "r4 #f4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #g4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #h4 ,concl4 "r4 #i4 ,concl4 "r4 #aj4 ,concl4 "r4 #aa4 ,concl4 "r4 #ab4 ,concl4 "r4 #ac4 ,concl4 "r4 #ad4 ,concl4 "r4 #ae4 ,concl4 "r4 pg#aca #af4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ag4 ,concl4 "r4 #ah4 ,concl4 "r4 #ai4 ,concl4 "r4 #bj4 ,concl4 "r4 #ba4 ,concl4 "r4 #bb4 ,concl4 wrong3 ! "r "o is ,"s x are y4 #bc4 ,concl4 "r4 #bd4 ,concl4 "r4 #be4 ,concl4 "r4 #bf4 ,concl4 "r4 #bg4 ,concl4 "r4 #bh4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bi4 ,concl4 "r4 #cj4 ,concl4 "r4 #ca4 ,concl4 "r4 #cb4 ,concl4 "r4 #cc4 ,concl4 "r4 #cd4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ce4 ,concl4 "r4 #cf4 ,concl4 "r4 #cg4 ,concl4 "r4 #ch4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ci4 ,concl4 "r4 #dj4 ,concl4 "r4 ,answ]s to #g4 ,,an#g #a4 ,concl4 "r4 #b4 ,concl4 "r4 #c4 ,concl4 "r4 #d4 ,concl4 wrong3 "r "o is ,"s epicures are n uncles ( m9e4 #e4 ,concl4 "r4 #f4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #g4 ,concl4 wrong3 "r "o is ,! publication1 9 :i* ,i saw x1 tells lies4 #h4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #i4 ,concl4 wrong3 "r "o is ,"s t$i\s songs are n 84 #aj4 ,concl4 "r4 #aa4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ab4 ,concl4 wrong3 "r "o is ,"s fi]ce creatures d n dr9k c(fee4 #ac4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ad4 ,concl4 "r4 #ae4 ,concl4 wrong3 "r "o is ,"s %all[ p]sons are n /ud5ts4 #af4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ag4 ,concl4 wrong3 "r "o is ,"s bus9ess1 o!r ?an railways1 is unpr(itable4 #ah4 ,concl4 wrong3 "r "o is ,"s va9 p]sons are n ,pr(essors4 #ai4 ,concl4 "r4 #bj4 ,concl4 wrong3 "r "o is ,wasps are n puppies4 #ba4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bb4 ,no ,concl4 ,same ,fallacy4 #bc4 ,concl4 "r4 #bd4 ,concl4 wrong3 "r "o is ,"s *ocolate-creams are delici\s4 #be4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bf4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bg4 ,concl4 wrong3 "r "o is ,"s pill[s are n pok]s4 #bh4 ,concl4 "r4 #bi4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #cj4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ca4 ,concl4 "r4 #cb4 ,no ,concl4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cc4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 pg#acb #cd4 ,concl4 wrong3 "r "o is ,"s dread$ p]sons are n begg$ to prolong _! visits4 #ce4 ,concl4 wrong3 "r "o is ,no man walks on nei!r4 #cf4 ,concl4 "r4 #cg4 ,no ,concl4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ch4 ,concl4 wrong3 "r "o is ,"s p]sons1 dread$ by *ildr51 are n emp]ors4 #ci4 ,concl4 incomplete3 ! omitt$ portion is ,sug> is n salt4 #dj4 ,concl4 "r4 ,answ]s to #h4 ,,an#h #a4 a#a;b#j b#a;a#j4 #b4 d#a;a#j4 #c4 ac#j4 #d4 a#a;d#j4 #e4 cd#j4 #f4 d#a;c#j4 #g4 a'c#j4 #h4 c#a;a'#j4 #i4 c'd#j4 #aj4 b#a;a#j4 #aa4 d#a;b#j4 #ab4 a'd#j4 #ac4 e#a;b#j4 #ad4 d#a;e'#j4 #ae4 e#a;a'#j4 #af4 b'c#j4 #ag4 a#a;b#j4 #ah4 d#a;c#j4 #ai4 a#a;d#j4 #bj4 ac#j4 #ba4 de#j4 #bb4 a#a;b'#j4 #bc4 h#a;c#j4 #bd4 e#a;a#j4 #be4 e#a;c'#j4 #bf4 e#a;c'#j4 #bg4 hk'#j4 #bh4 e#a;d'#j4 #bi4 l'a#j4 #cj4 k#a;b'#j4 ,answ]s to #i4 ,,an#i #a4 ,babies _c manage crocodiles4 #b4 ,y\r pres5ts to me are n made ( t94 #c4 ,all my potatoes 9 ?is di% are old ones4 #d4 ,my s]vants nev] say %poonj4 #e4 ,my p\ltry are n (fic]s4 #f4 ,none ( y\r sons are fit to s]ve on a jury4 #g4 ,no p5cils ( m9e are sug>-plums4 #h4 ,j5k9s is inexp]i5c$4 #i4 ,no comet has a curly tail4 #aj4 ,no h$ge-hog takes 9 ! ,times4 #aa4 ,?is di% is un:olesome4 #ab4 ,my g>d5] is v old4 #ac4 ,all humm+-birds are small4 #ad4 ,no "o ) a hook$ nose ev] fails to make money4 #ae4 ,no gray ducks 9 ?is village we> lace coll>s4 #af4 ,no jug 9 ?is cupbo>d w hold wat]4 #ag4 ,^! apples 7 gr[n 9 ! sun4 #ah4 ,puppies1 t w n lie /ill1 nev] c>e to d wor/$ "w4 #ai4 ,no "n 9 ?is li/ is unmelodi\s4 #bj4 ,no ,m4,p4 %\ld ride 9 a donkey-race1 unless he has p]fect self-comm&4 #ba4 ,no goods 9 ?is %op1 t are /ill on sale1 may be c>ri$ away4 pg#acc #bb4 ,no acrobatic feat1 :i* involves turn+ a quadruple som]sault1 is ev] attempt$ 9 a circus4 #bc4 ,gu9ea-pigs nev] really appreciate ,bee?ov54 #bd4 ,no sc5tless fl[]s please me4 #be4 ,%[y talk]s are n really well-in=m$4 #bf4 ,none b r$-hair$ boys le>n ,greek 9 ?is s*ool4 #bg4 ,w$d+-cake always disagrees ) me4 #bh4 ,discussions1 t g on :ile ,tomk9s is 9 ! *air1 endang] ! peacefulness ( our ,debat+-,club4 #bi4 ,all gluttons1 :o are *ildr5 ( m9e1 are unheal?y4 #cj4 ,an egg ( ! ,great ,auk is n to be _h = a song4 #ca4 ,no books sold "h h gilt edges1 unless !y are pric$ at #es4 & upw>ds4 #cb4 ,:5 y cut y\r f+]1 y w f9d ,t9cture ( ,cal5dula useful4 #cc4 ,i h nev] come across a m]maid at sea4 #cd4 ,all ! romances 9 ?is libr>y are well-writt54 #ce4 ,no bird 9 ?is avi>y lives on m9ce-pies4 #cf4 ,no plum-pudd+1 t has n be5 boil$ 9 a clo?1 c be di/+ui%$ f s\p4 #cg4 ,all y\r poems are un9t]e/+4 #ch4 ,none ( my pea*es h be5 gr[n 9 a hot-h\se4 #ci4 ,no pawnbrok] is di%one/4 #dj4 ,no kitt5 ) gre5 eyes w play ) a gorilla4 #da4 ,all my fri5ds d9e at ! l[] table4 #db4 ,my writ+-desk is full ( live scorpions4 #dc4 ,no ,m&>9 ev] reads ,hogg's poems4 #dd4 ,%akespe>e 0 clev]4 #de4 ,ra9b[s are n wor? writ+ odes to4 #df4 ,^! ,sorites-examples are difficult4 #dg4 ,all my dreams come true4 #dh4 ,all ! ,engli% pictures "h are pa9t$ 9 oils4 #di4 ,donkeys are n easy to swall[4 #ej4 ,opium-eat]s nev] we> :ite kid gloves4 #ea4 ,a good husb& always comes home = 8 tea4 #eb4 ,ba?+-ma*9es are nev] made ( "m-(-pe>l4 #ec4 ,ra9y days are always cl\dy4 #ed4 ,no heavy fi% is unk9d to *ildr54 #ee4 ,no eng9e-driv] lives on b>ley-sug>4 #ef4 ,all ! animals 9 ! y>d gnaw bones4 #eg4 ,no badg] c guess a conundrum4 #eh4 ,no *eque ( y\rs1 receiv$ by me1 is payable to ord]4 #ei4 ,i _c read any ( ,br[n's lett]s4 #fj4 ,i always avoid a kang>oo4 pg#acd ,,*apt] ,,iii4 ,,solutions4 #a4 ,propositions ( ,relation r$uc$ to normal =m4 ,solutions = #a4 ,,sl#a #a4 ,! ,univ4 is p]sons4 ,! ,individual ,i may be reg>d$ z a ,class1 ( p]sons1 ^: peculi> ,attribute is repres5t$ by ! ,"n ',i'1 & may be call$ ! ,class ( ,i's4 ,x is evid5t t ?is ,class _c possibly conta9 m ?an "o ,memb]3 h5ce ! ,sign ( ,quantity is all4 ,! v]b h be5 may be replac$ by ! phrase are p]sons :o h be54 ,! ,proposition may be writt5 ?us3-- ,all ,sign ( ,quantity4 ,i's ,subject4 are ,copula4 p]sons :o h be5 out = a walk ,pr$icate4 or1 m briefly1 ,all ,i's are p]sons :o h be5 out = a walk4 #b4 ,! ,univ4 & ! ,subject are ! same z 9 ,ex4 #a4 ,! ,proposition may be writt5 ,all ,i's are p]sons :o feel bett]4 #c4 ,univ4 is p]sons4 ,! ,subject is evid5tly ! ,class ( p]sons f :i* ,john is exclud$2 i4e4 x is ! ,class conta9+ all p]sons :o are n ,john4 ,! ,sign ( ,quantity is no4 ,! v]b has read may be replac$ by ! phrase are p]sons :o h read4 ,! ,proposition may be writt5 ,no p]sons :o are n ',john' are p]sons :o h read ! lett]4 #d4 ,univ4 is p]sons4 ,! ,subject is evid5tly ! ,class ( p]sons ^: only two ,memb]s are y & ,i4 ,h5ce ! ,sign ( ,quantity is no4 ,! ,proposition may be writt5 ,no ,memb]s ( ! ,class 'y & ,i' are old p]sons4 pg#ace #e4 ,univ4 is creatures4 ,! v]b run well may be replac$ by ! phrase are creatures t run well4 ,! ,proposition may be writt5 ,no fat creatures are creatures t run well4 #f4 ,univ4 is p]sons4 ,! ,subject is evid5tly ! ,class ( p]sons :o are n brave4 ,! v]b des]ve may be replac$ by ! phrase are des]v+ (4 ,! ,proposition may be writt5 ,no n-brave p]sons are p]sons des]v+ ( ! fair4 #g4 ,univ4 is p]sons4 ,! phrase looks poetical evid5tly belongs to ! ,pr$icate2 & ! ,subject is ! ,class1 ( p]sons1 ^: peculi> ,attribute is n-pale4 ,! ,proposition may be writt5 ,no n-pale p]sons are p]sons :o look poetical4 #h4 ,univ4 is p]sons4 ,! ,proposition may be writt5 ,"s judges are p]sons :o lose _! temp]s4 #i4 ,univ4 is p]sons4 ,! phrase nev] neglect is m]ely a /rong] =m ( ! phrase am a p]son :o does n neglect4 ,! ,proposition may be writt5 ,all ',i's' are p]sons :o d n neglect important bus9ess4 #aj4 ,univ4 is ?+s4 ,! phrase :at is difficult 7i4e4 t :i* is difficult7 is equival5t to ! phrase all difficult ?+s4 ,! ,proposition may be writt5 ,all difficult ?+s are ?+s t ne$ att5tion4 #aa4 ,univ4 is ?+s4 ,! phrase :at is un:olesome may be int]pret$ z 9 ,ex4 #aj4 ,! ,proposition may be writt5 ,all un:olesome ?+s are ?+s t %\ld be avoid$4 #ab4 ,univ4 is laws4 ,! ,pr$icate is evid5tly a ,class ^: peculi> ,attribute is relat+ to excise4 ,! ,proposition may be writt5 ,all laws pass$ la/ week are laws relat+ to excise4 #ac4 ,univ4 is ?+s4 ,! ,subject is evid5tly ! ,class1 ( /udies1 ^: peculi> ,attribute is logical2 h5ce ! ,sign ( ,quantity is all4 ,! ,proposition may be writt5 ,all logical /udies are ?+s t puzzle me4 #ad4 ,univ4 is p]sons4 ,! ,subject is evid5tly p]sons 9 ! h\se4 ,! ,proposition may be writt5 ,no p]sons 9 ! h\se are ,jews4 #ae4 ,univ4 is di%es4 ,! phrase if n well-cook$ is equival5t to ! ,attribute n well-cook$4 ,! ,proposition may be writt5 ,"s n well-cook$ di%es are un:olesome di%es4 pg#acf #af4 ,univ4 is books4 ,! phrase make "o dr[sy may be replac$ by ! phrase are books t make "o dr[sy4 ,! ,sign ( ,quantity is evid5tly all4 ,! ,proposition may be writt5 ,all unexcit+ books are books t make "o dr[sy4 #ag4 ,univ4 is m54 ,! ,subject is evid5tly a man :o kn[s :at he's ab\t2 & ! ^w :5 %[s t ! ,proposition is ass]t$ ( e su* man1 i4e4 ( all su* m54 ,! v]b c may be replac$ by are m5 :o c4 ,! ,proposition may be writt5 ,all m5 :o "k :at !y're ab\t are m5 :o c detect a %>p]4 #ah4 ,! ,univ4 & ! ,subject are ! same z 9 ,ex4 #d4 ,! ,proposition may be writt5 ,all ,memb]s ( ! ,class 'y & ,i' are p]sons :o "k :at !y're ab\t4 #ai4 ,univ4 is p]sons4 ,! v]b we> may be replac$ by ! phrase are accu/om$ to we>4 ,! ,proposition may be writt5 ,"s bald p]sons are p]sons accu/om$ to we> wigs4 #bj4 ,univ4 is p]sons4 ,! phrase nev] talk is m]ely a /rong] =m ( are p]sons :o d n talk4 ,! ,proposition may be writt5 ,all fully occupi$ p]sons are p]sons :o d n talk ab\t _! grievances4 #ba4 ,univ4 is riddles4 ,! phrase if !y c be solv$ is equival5t to ! ,attribute t c be solv$4 ,! ,proposition may be writt5 ,no riddles t c be solv$ are riddles t int]e/ me4 #b4 ,me?od ( ,diagrams4 ,solutions = #d1 ,nos4 #a-ab4 ,,sl#d-;,a --------------- ------- #a4 ,no m are x'2 7,o7 ,all m' are y4 ------ ------ 7,o7 7,i7--------- ------- 7,o77,o7 ------ 4'4 ,no x' are y'4 7,o7 --------------- pg#acg --------------- ------- #b4 ,no m' are x2 7,o7 7,o7 ,"s m' are y'4 ------ ------ 7,i7 ------------ ------- ------ 4'4 ,"s x are y'4 7,i7 --------------- --------------- ------- #c4 ,all m' are x2 7,o7 7,i7 7,i7 ,all m' are y'4 ------ ------ ------------ ------- ------ 4'4 ,"s x are y'4 7,o7 7,o7 --------------- --------------- #d4 ,no x' are m'2 7,o7 ,all y' are m4 ------ ------7,i7--- ,!re is no ,conclusion4 ------ 7,o7 7,o7 --------------- --------------- ------- #e4 ,"s m are x'2 ,no y are m4 ------ ------ 7,o7 7,i7 ------------ ------- 7,o77,i7 ------ 4'4 ,"s x' are y'4 --------------- --------------- #f4 ,no x' are m2 ,no m are y4 ------ 7,o7 ------------ ,!re is no ,conclusion4 7,o77,o7 ------ --------------- --------------- ------- #g4 ,no m are x'2 7,i7 ,"s y' are m4 ------ ------ 7,i7 ------------ ------- 7,o77,o7 ------ 4'4 ,"s x are y'4 --------------- --------------- ------- #h4 ,all m' are x'2 7,o7 7,o7 ,no m' are y4 ------ ------ 7,i7 ------------ ------- ------ 4'4 ,"s x' are y'4 7,o7 7,i7 --------------- pg#ach --------------- #i4 ,"s x' are m'2 ,no m are y'4 ------ 7,o7 ------------ ,!re is no ,conclusion4 7,o7 ------ 7,i7 --------------- --------------- ------- #aj4 ,all x are m2 7,o7 7,o7 7,i77,o7 ,all y' are m'4 ------ ------ 7,i77,o7 7,i7 ------------ ------- 7,o7 ------ 4'4 ,all x are y2 7,i7 ,all y' are x'4 --------------- --------------- #aa4 ,no m are x2 ,all y' are m'4 ------ 7,o77,o7 ---------7,i7 ,!re is no ,conclusion4 7,o7 ------ --------------- --------------- ------- #ab4 ,no x are m2 7,o7 7,o7 ,all y are m4 ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 ,all y are x'4 7,o7 --------------- ,solutions = #e1 ,nos4 #a-ab4 ,,sl#e-;,a #a4 ,i h be5 out = a walk2 ,i am feel+ bett]4 ,univ4 is p]sons2 m ! ,class ( ,i's2 x p]sons :o h be5 out = a walk2 y p]sons :o are feel+ bett]4 --------------- ------- ,all m are x2 7,i7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,"s x are y4 --------------- i4e4 ,somebody1 :o has be5 out = a walk1 is feel+ bett]4 pg#aci #b4 ,no "o has read ! lett] b ,john2 ,no "o1 :o has n read x1 kn[s :at x is ab\t4 ,univ4 is p]sons2 m p]sons :o h read ! lett]2 x ! ,class ( ,johns2 y p]sons :o "k :at ! lett] is ab\t4 --------------- ------- ,no x' are m2 7,o7 ,no m' are y4 ------ ------ 7,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- i4e4 ,no "o1 b ,john1 kn[s :at ! lett] is ab\t4 #c4 ,^? :o are n old l walk+2 ,y & ,i are "y4 ,univ4 is p]sons2 m old2 x p]sons :o l walk+2 y y & ,i4 --------------- ------- ,all m' are x2 7,i7 7,i7 ,all y are m'4 ------ ------ 7,o7 7,o7 ------------ ------- 7,o7 ------ 4'4 ,all y are x4 7,o7 7,o7 --------------- i4e4 ,y & ,i l walk+4 #d4 ,y\r c\rse is always hone/2 ,y\r c\rse is always ! be/ policy4 ,univ4 is c\rses2 m y\r2 x hone/2 y c\rses :i* are ! be/ policy4 --------------- ------- ,all m are x2 7,i7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o77,o7 ------ 4'4 ,"s x are y4 --------------- i4e4 ,hone/y is sometimes ! be/ policy4 #e4 ,no fat creatures run well2 ,"s greyh\nds run well4 ,univ4 is creatures2 m creatures t run well2 x fat2 y greyh\nds4 --------------- ------- ,no x are m2 ,"s y are m4 ------ ------ 7,o77,o7 7,i7 ------------ ------- 7,i7 ------ 4'4 ,"s y are x'4 --------------- i4e4 ,"s greyh\nds are n fat4 pg#adj #f4 ,"s1 :o des]ve ! fair1 get _! des]ts2 ,none b ! brave des]ve ! fair4 ,univ4 is p]sons2 m p]sons :o des]ve ! fair2 x p]sons :o get _! des]ts2 y brave4 --------------- ------- ,"s m are x2 7,i7 ,no y' are m4 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,"s y are x4 --------------- i4e4 ,"s brave p]sons get _! des]ts4 #g4 ,"s ,jews are ri*2 ,all ,esquimaux are ,g5tiles4 ,univ4 is p]sons2 m ,jews2 x ri*2 y ,esquimaux4 --------------- ------- ,"s m are x2 7,i7 ,all y are m'4 ------ ------ 7,o77,i7 7,i7--------- ------- 7,o7 ------ 4'4 ,"s x are y'4 --------------- i4e4 ,"s ri* p]sons are n ,esquimaux4 #h4 ,sug>-plums are sweet2 ,"s sweet ?+s are lik$ by *ildr54 ,univ4 is ?+s2 m sweet2 x sug>-plums2 y ?+s t are lik$ by *ildr54 --------------- ,all x are m2 7,o7 7,o7 ,"s m are y4 ------ 7,i7 ---7,i7------ ------ --------------- ,!re is no ,conclusion4 #i4 ,john is 9 ! h\se2 ,ev]ybody 9 ! h\se is ill4 ,univ4 is p]sons2 m p]sons 9 ! h\se2 x ! ,class ( ,johns2 y ill4 --------------- ------- ,all x are m2 7,o7 7,o7 7,i77,o7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,all x are y4 --------------- i4e4 ,john is ill4 pg#ada #aj4 ,umbrellas are useful on a j\rney2 ,:at is useless on a j\rney %\ld be left beh9d4 ,univ4 is ?+s2 m useful on a j\rney2 x umbrellas2 y ?+s t %\ld be left beh9d4 --------------- ------- ,all x are m2 7,o7 7,o7 ,all m' are y4 ------ ------ 7,i7 7,i7 ------------ ------- ------ 4'4 ,"s x' are y4 7,i7 7,o7 --------------- i4e4 ,"s ?+s1 t are n umbrellas1 %\ld be left beh9d on a j\rney4 #aa4 ,audible music causes vibration 9 ! air2 ,inaudible music is n wor? pay+ =4 ,univ4 is music2 m audible2 x music t causes vibration 9 ! air2 y wor? pay+ =4 --------------- ------- ,all m are x2 7,o7 ,all m' are y'4 ------ ------ 7,i7 7,o7 ---------7,i7 ------- 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- i4e4 ,no music is wor? pay+ =1 unless x causes vibration 9 ! air4 #ab4 ,"s holidays are ra9y2 ,ra9y days are tiresome4 ,univ4 is days2 m ra9y2 x holidays2 y tiresome4 --------------- ------- ,"s x are m2 7,i7 ,all m are y4 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ 4'4 ,"s x are y4 --------------- i4e4 ,"s holidays are tiresome4 ,solutions = #f1 ,nos4 #a-aj4 ,,sl#f-;,a #a4 ,"s x are m2 ,no m are y'4 ,"s x are y4 --------------- ------- 7,i7 ------ ------ 7,i77,o7 ------------ ------- 7,o7 ------ ,h5ce propos$ ,conclusion is "r4 --------------- pg#adb #b4 ,all x are m2 ,no y are m'4 ,no y are x'4 --------------- 7,o7 7,o7 ------ 7,i7 ------------ ,!re is no ,conclusion4 ------ 7,o7 --------------- #c4 ,"s x are m'2 ,all y' are m4 ,"s x are y4 --------------- ------- 7,i7 7,o7 7,i7 ------ ------ ------7,i7--- ------- ------ ,h5ce propos$ ,conclusion is "r4 7,o7 --------------- #d4 ,all x are m2 ,no y are m4 ,all x are y'4 --------------- ------- 7,o7 7,o7 7,o77,i7 ------ ------ 7,o77,i7 ------------ ------- 7,o7 ------ ,h5ce propos$ ,conclusion is "r4 --------------- #e4 ,"s m' are x'2 ,no m' are y4 ,"s x' are y'4 --------------- ------- 7,o7 ------ ------ 7,i7 ------------ ------- ------ ,h5ce propos$ ,conclusion is "r4 7,o7 7,i7 --------------- #f4 ,no x' are m2 ,all y are m'4 ,all y are x4 --------------- ------ 7,o7 7,i7--------- ,!re is no ,conclusion4 7,o77,o7 ------ --------------- pg#adc #g4 ,"s m' are x'2 ,all y' are m'4 ,"s x' are y'4 --------------- ------ 7,o7 ---------7,i7 ,!re is no ,conclusion4 7,o7 ------ 7,i7 --------------- #h4 ,no m' are x'2 ,all y' are m'4 ,all y' are x4 --------------- ------- 7,i7 7,i7 ------ ------ 7,o7 7,o7 ------------ ------- 7,o7 ------ ,h5ce propos$ ,conclusion is "r4 7,o7 7,o7 --------------- #i4 ,"s m are x'2 ,no m are y4 ,"s x' are y'4 --------------- ------- ------ ------ 7,o7 7,i7 ------------ ------- 7,o77,i7 ------ ,h5ce propos$ ,conclusion is "r4 --------------- #aj4 ,all m' are x'2 ,all m are y4 ,"s y are x'4 --------------- ------- 7,o7 7,o7 ------ ------ 7,i7 ------------ ------- ------ ,h5ce propos$ ,conclusion is "r4 7,i7 7,o7 --------------- pg#add ,solutions = #g1 ,nos4 #a-f4 ,,sl#g-;,a #a4 ,no doctors are en?usia/ic2 ,y are en?usia/ic4 ,y are n a doctor4 ,univ4 p]sons2 m en?usia/ic2 x doctors2 y y4 --------------- ------- 7,o7 7,o7 ------ ------ ,no x are m2 7,o77,o7 7,i7 ,all y are m4 ------------ ------- ,all y are x'4 7,i7 ------ 4'4 ,all y are x'4 7,o7 --------------- ,h5ce propos$ ,conclusion is "r4 #b4 ,all diction>ies are useful2 ,useful books are valuable4 ,diction>ies are valuable4 ,univ4 books2 m useful2 x diction>ies2 y valuable4 --------------- ------- 7,o7 7,o7 7,i77,o7 ------ ------ ,all x are m2 7,i77,o7 ,all m are y4 ------------ ------- ,all x are y4 7,o7 ------ 4'4 ,all x are y4 --------------- ,h5ce propos$ ,conclusion is "r4 #c4 ,no mis]s are unselfi%2 ,none b mis]s save egg-%ells4 ,no unselfi% p save egg-%ells4 ,univ4 p2 m mis]s2 x selfi%2 y p :o save egg-%ells4 --------------- ------- 7,o7 ------ ------ ,no m are x'2 7,o7 ,no m' are y4 ------------ ------- ,no x' are y4 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- ,h5ce propos$ ,conclusion is "r4 pg#ade #d4 ,"s epicures are ung5]\s2 ,all my uncles are g5]\s4 ,my uncles are n epicures4 ,univ4 p]sons2 m g5]\s2 x epicures2 y my uncles4 --------------- ------- 7,o7 7,i7 7,i7 ------ ------ ,"s x are m'4 ,all y are m4 ---7,i7------ ------- ,all y are x'4 ------ 4'4 ,"s x are y'4 7,o7 --------------- ,h5ce propos$ ,conclusion is wrong1 ! "r "o be+ ,"s epicures are n uncles ( m9e4 #e4 ,gold is heavy2 ,no?+ b gold w sil5ce him4 ,no?+ light w sil5ce him4 ,univ4 ?+s2 m gold2 x heavy2 y able to sil5ce him4 --------------- ------- 7,o7 ------ ------ ,all m are x2 7,i7 7,o7 ,no m' are y4 ------------ ------- ,no x' are y4 7,o77,o7 ------ 4'4 ,no x' are y4 7,o7 --------------- ,h5ce propos$ ,conclusion is "r4 #f4 ,"s heal?y p are fat2 ,no unheal?y p are /rong4 ,"s fat p are n /rong4 ,univ4 p]sons2 m heal?y2 x fat2 y /rong4 --------------- 7,o7 ------ ,"s m are x2 7,i7 ,no m' are y4 ------------ ,!re is no ,conclusion4 ,"s x are y'4 ------ 7,o7 --------------- pg#adf #c4 ,me?od ( ,subscripts4 ,solutions = #d4 ,,sl#d-;,b #a4 mx'#j m'#ay'#j x'y'#j ,fig4 ,i4 i4e4 ,no x' are y'4 #b4 m'x#j m'y'#a x'y'#a ,fig4 ,,ii4 i4e4 ,"s x' are y'4 #c4 m'#ax'#j m'#ay#j xy'#a ,fig4 ,,iii4 i4e4 ,"s x are y'4 #d4 x'm'#j y'#am'#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #e4 mx'#a ym#j x'y'#a ,fig4 ,,ii4 i4e4 ,"s x' are y'4 #f4 x'm#j my#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #g4 mx'#j y'm#a xy'#a ,fig4 ,,ii4 i4e4 ,"s x are y'4 #h4 m'#ax#j m'y#j x'y'#a ,fig4 ,,iii4 i4e4 ,"s x' are y'4 #i4 x'm'#a my#j no?+4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #aj4 x#am'#j y'#am#j x#ay'#j y'#ax#j ,fig4 ,i 7b74 i4e4 ,all x are y1 & all y' are x'4 #aa4 mx#j y'#am#j no?+4#a ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ab4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,all y are x'4 #ac4 m'#ax'#j ym#j x'y#j ,fig4 ,i4 i4e4 ,no x' are y4 #ad4 m#ax'#j m'#ay'#j x'y'#j ,fig4 ,i4 i4e4 ,no x' are y'4 #ae4 xm#j m'y#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 #af4 x#am#j y#am'#j 7x#ay#j y#ax#j7 ,fig4 ,i 7b74 i4e4 ,all x are y' & all y are x'4 #ag4 xm#j m'#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no x are y'4 #ah4 xm'#j my#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 #ai4 m#ax'#j m#ay#j xy'#a ,fig4 ,,iii4 i4e4 ,"s x are y'4 #bj4 mx#j m'#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no x are y'4 #ba4 x#am'#j m'y#a x'y#a ,fig4 ,,ii4 i4e4 ,"s x' are y4 #bb4 xm#a y#am'#j no?+4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bc4 m#ax'#j ym#a xy#a ,fig4 ,,ii4 i4e4 ,"s x are y4 #bd4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,all y are x'4 #be4 mx'#a my'#j x'y#a ,fig4 ,,ii4 i4e4 ,"s x' are y4 #bf4 mx'#j y#am'#j y#ax'#j ,fig4 ,i 7a74 i4e4 ,all y are x4 #bg4 x#am#j y'#am'#j 7x#ay'#j y'#ax#j7 ,fig4 ,i 7b74 i4e4 ,all x are y1 & all y' are x'4 #bh4 m#ax#j my#a x'y#a ,fig4 ,,ii4 i4e4 ,"s x' are y4 #bi4 mx#j y#am#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cj4 x#am#j ym#a x'y#a ,fig4 ,,ii4 i4e4 ,"s y are x'4 #ca4 x#am'#j y#am'#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 pg#adg #cb4 xm'#j m#ay'#j xy'#j ,fig4 ,i4 i4e4 ,no x are y'4 #cc4 mx#j my#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cd4 mx'#j ym#a xy#a ,fig4 ,,ii4 i4e4 ,"s x are y4 #ce4 mx#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,all y are x'4 #cf4 m#ax#j ym#a x'y#a ,fig4 ,,ii4 i4e4 ,"s x' are y4 #cg4 m#ax'#j ym#j xy'#a ,fig4 ,,iii4 i4e4 ,"s x are y'4 #ch4 mx#j m'y#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 #ci4 mx'#a my#j x'y'#a ,fig4 ,,ii4 i4e4 ,"s x' are y'4 #dj4 x'm#j y'#am'#j y'#ax'#j ,fig4 ,i 7a74 i4e4 ,all y' are x4 #da4 x#am#j ym'#j x#ay#j ,fig4 ,i 7a74 i4e4 ,all x are y'4 #db4 m'x#j ym#j xy#j ,fig4 ,i4 i4e4 ,no x are y4 ,solutions = #e1 ,nos4 #ac-bd4 ,,sl#e-;,b #ac4 ,no ,fr5*m5 l plumpudd+2 ,all ,engli%m5 l plumpudd+4 ,univ4 m52 m lik+ plumpudd+2 x ,fr5*2 y ,engli%4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 i4e4 ,engli%m5 are n ,fr5*m54 #ad4 ,no portrait ( a lady1 t makes h] simp] or sc[l1 is satisfactory2 ,no photograph ( a lady ev] fails to make h] simp] or sc[l4 ,univ4 portraits ( ladies2 m mak+ ! subject simp] or sc[l2 x satisfactory2 y photographic4 mx#j ym'#j xy#j ,fig4 ,i4 i4e4 ,no photograph ( a lady is satisfactory4 #ae4 ,all pale p are phlegmatic2 ,no "o looks poetical unless he is pale4 ,univ4 p2 m pale2 x phlegmatic2 y look+ poetical4 m#ax'#j m'y#j x'y#j ,fig4 ,i4 i4e4 ,no "o looks poetical unless he is phlegmatic4 #af4 ,no old mis]s are *e]ful2 ,"s old mis]s are ?94 ,univ4 p]sons2 m old mis]s2 x *e]ful2 y ?94 mx#j my#a x'y#a ,fig4 ,,ii4 i4e4 ,"s ?9 p]sons are n *e]ful4 #ag4 ,no "o1 :o ex]cises self-control1 fails to keep 8 temp]2 ,"s judges lose _! temp]s4 ,univ4 p]sons2 m keep+ _! temp]s2 x ex]cis+ self-control2 y judges4 xm'#j ym'#a x'y#a ,fig4 ,,ii4 i4e4 ,"s judges d n ex]cise self-control4 pg#adh #ah4 ,all pigs are fat2 ,no?+ t is f$ on b>ley-wat] is fat4 ,univ4 is ?+s2 m fat2 x pigs2 y f$ on b>ley-wat]4 x#am'#j ym#j x#ay#j ,fig4 ,i 7a74 i4e4 ,pigs are n f$ on b>ley-wat]4 #ai4 ,all rabbits1 t are n gre$y1 are black2 ,no old rabbits are free f gre$9ess4 ,univ4 is rabbits2 m gre$y2 x black2 y old4 m'#ax'#j ym'#j xy'#a ,fig4 ,,iii4 i4e4 ,"s black rabbits are n old4 #bj4 ,"s pictures are n fir/ attempts2 ,no fir/ attempts are really good4 ,univ4 is ?+s2 m fir/ attempts2 x pictures2 y really good4 xm'#a my#j no?+4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ba4 ,i nev] neglect important bus9ess2 ,y\r bus9ess is unimportant4 ,univ4 is bus9ess2 m important2 x neglect$ by me2 y y\r4 mx#j y#am#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bb4 ,"s lessons are difficult2 ,:at is difficult ne$s att5tion4 ,univ4 is ?+s2 m difficult2 x lessons2 y ne$+ att5tion4 xm#a m#ay'#j xy#a ,fig4 ,,ii4 i4e4 ,"s lessons ne$ att5tion4 #bc4 ,all clev] p are popul>2 ,all oblig+ p are popul>4 ,univ4 is p2 m popul>2 x clev]2 y oblig+4 x#am'#j y#am'#j no?+4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bd4 ,?\ghtless p d mis*ief2 ,no ?\ghtful p]son =gets a promise4 ,univ4 is p]sons2 m ?\ghtful2 x mis*iev\s2 y =getful ( promises4 m'#ax'#j my#j x'y#j i4e4 ,no "o1 :o =gets a promise1 fails to d mis*ief4 ,solutions = #f4 ,,sl#f-;,b #a4 xm#a my'#j xy#a ,fig4 ,,ii4 ,concl4 "r4 #b4 x#am'#j ym'#j ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #c4 xm'#a y'#am'#j xy#a ,fig4 ,,ii4 ,concl4 "r4 pg#adi #d4 x#am'#j ym#j x#ay#j ,fig4 ,i 7a74 ,concl4 "r4 #e4 m'x'#a m'y#j x'y'#a ,fig4 ,,ii4 #f4 x'm#j y#am#j ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #g4 m'x'#a y'#am#j ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #h4 m'x'#j y'#am#j y'#ax'#j ,fig4 ,i 7a74 ,concl4 "r4 #i4 mx'#a my#j x'y'#a ,fig4 ,,ii4 #aj4 m'#ax#j m'#ay'#j x'y#a ,fig4 ,,iii4 #aa4 x#am#j ym#a x'y#a ,fig4 ,,ii4 #ab4 xm#j m'y'#j xy'#j ,fig4 ,i4 #ac4 xm#j y'#am'#j y'#ax#j ,fig4 ,i 7a74 #ad4 m'#ax#j m'#ay'#j x'y#a ,fig4 ,,iii4 #ae4 mx'#a y#am#j x'y'#a ,fig4 ,,ii4 #af4 x'm#j y'#am#j ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ag4 m'x#j m'#ay#j x'y'#a ,fig4 ,,iii4 ,concl4 "r4 #ah4 x'm#j my#a xy#a ,fig4 ,,ii4 #ai4 mx'#a m#ay'#j x'y#a #bj4 x'm'#j m'y'#a xy'#a #ba4 mx#j m#ay#j x'y'#a ,fig4 ,,iii4 #bb4 x'#am'#j ym'#a xy#a ,fig4 ,,ii4 ,concl4 wrong3 ! "r "o is ,"s x are y4 #bc4 m#ax'#j m'y'#j x'y'#j ,fig4 ,i4 ,concl4 "r4 #bd4 x#am#j m'#ay'#j x#ay'#j ,fig4 ,i 7a74 #be4 xm'#j m#ay'#j xy'#j ,fig4 ,i4 #bf4 m#ax#j y#am'#j y#ax#j ,fig4 ,i 7a74 #bg4 x#am'#j my'#j x#ay'#j #bh4 x#am'#j y'm'#j ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bi4 x'm#j m'y'#j x'y'#j ,fig4 ,i4 ,concl4 "r4 #cj4 x#am'#j m#ay#j x#ay#j ,fig4 ,i 7a74 #ca4 x'#am#j y'm'#j x'#ay'#j #cb4 xm#j y'm'#j xy'#j ,fig4 ,i4 #cc4 m#ax#j y'#am'#j y'#ax#j ,fig4 ,i 7a74 #cd4 x#am#j ym'#a ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ce4 xm#a m#ay'#j xy#a ,fig4 ,,ii4 ,concl4 "r4 #cf4 m#ax#j y#am'#j y#ax#j ,fig4 ,i 7a74 #cg4 mx'#j m#ay#j xy'#a ,fig4 ,,iii4 #ch4 xm#j my'#j ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ci4 mx#j my'#a x'y'#a ,fig4 ,,ii4 ,concl4 "r4 #dj4 mx'#j ym#a xy#a ,fig4 ,,ii4 pg#aej ,solutions = #g4 ,,sl#g-;,b #a4 ,no doctors are en?usia/ic2 ,y are en?usia/ic4 ,y are n a doctor4 ,univ4 p]sons2 m en?usia/ic2 x doctors2 y y4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 ,conclusion "r4 #b4 ,diction>ies are useful2 ,useful books are valuable4 ,diction>ies are valuable4 ,univ4 books2 m useful2 x diction>ies2 y valuable4 x#am'#j m#ay'#j x#ay'#j ,fig4 ,i 7a74 ,conclusion "r4 #c4 ,no mis]s are unselfi%2 ,none b mis]s save egg-%ells4 ,no unselfi% p save egg-%ells4 ,univ4 p2 m mis]s2 x selfi%2 y p :o save egg-%ells4 mx'#j m'y#j x'y#j ,fig4 ,i4 ,conclusion "r4 #d4 ,"s epicures are ung5]\s2 ,all my uncles are g5]\s4 ,my uncles are n epicures4 ,univ4 p]sons2 m g5]\s2 x epicures2 y my uncles4 xm'#a y#am'#j xy'#a ,fig4 ,,ii4 ,conclusion wrong3 "r "o is ,"s epicures are n uncles ( m9e4 #e4 ,gold is heavy2 ,no?+ b gold w sil5ce him4 ,no?+ light w sil5ce him4 ,univ4 ?+s2 m gold2 x heavy2 y able to sil5ce him4 m#ax'#j m'y#j x'y#j ,fig4 ,i4 ,conclusion "r4 #f4 ,"s heal?y p are fat2 ,no unheal?y p are /rong4 ,"s fat p are n /rong4 ,univ4 p2 m heal?y2 x fat2 y /rong4 mx#a m'y#j ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #g4 ,i saw x 9 a newspap]2 ,all newspap]s tell lies4 ,x 0 a lie4 ,univ4 publications2 m newspap]s2 x publications 9 :i* ,i saw x2 y tell+ lies4 x#am'#j m#ay'#j x#ay'#j ,fig4 ,i 7a74 ,conclusion wrong3 "r "o is ,! publication1 9 :i* ,i saw x1 tells lies4 pg#aea #h4 ,"s cravats are n arti/ic2 ,i admire any?+ arti/ic4 ,!re are "s cravats t ,i d n admire4 ,univ4 ?+s2 m arti/ic2 x cravats2 y ?+s t ,i admire4 xm#a m#ay#j ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #i4 ,8 songs nev] la/ an h\r4 ,a song1 t la/s an h\r1 is t$i\s4 ,8 songs are nev] t$i\s4 ,univ4 songs2 m la/+ an h\r2 x 82 y t$i\s4 x#am#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion wrong3 "r "o is ,"s t$i\s songs are n 84 #aj4 ,"s c&les give v little light2 ,c&les are meant to give light4 ,"s ?+s1 t are meant to give light1 give v little4 ,univ4 ?+s2 m c&les2 x giv+ c42 y meant c4 mx#a m#ay'#j xy#a ,fig4 ,,ii4 ,conclusion "r4 #aa4 ,all1 :o are anxi\s to le>n1 "w h>d4 ,"s ( ^! boys "w h>d4 ,"s ( ^! boys are anxi\s to le>n4 ,univ4 p]sons2 m h>d-work+2 x anxi\s to le>n2 y ^! boys4 x#am'#j ym#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ab4 ,all lions are fi]ce2 ,"s lions d n dr9k c(fee4 ,"s creatures t dr9k c(fee are n fi]ce4 ,univ4 creatures2 m lions2 x fi]ce2 y creatures t dr9k c(fee4 m#ax'#j my'#a xy'#a ,fig4 ,,ii4 ,conclusion wrong3 "r "o is ,"s fi]ce creatures d n dr9k c(fee4 #ac4 ,no mis]s are g5]\s2 ,"s old m5 are ung5]\s4 ,"s old m5 are mis]s4 ,univ4 p]sons2 m g5]\s2 x mis]s2 y old m54 xm#j ym'#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ad4 ,no fossil c be cross$ 9 love2 ,an oy/] may be cross$ 9 love4 ,oy/]s are n fossils4 ,univ4 ?+s2 m ?+s t c be cross$ 9 love2 x fossils2 y oy/]s4 xm#j y#am'#j y#ax#j ,fig4 ,i 7a74 ,conclusion "r4 pg#aeb #ae4 ,all un$ucat$ p are %all[2 ,/ud5ts are all educat$4 ,no /ud5ts are %all[4 ,univ4 p2 m educat$2 x %all[2 y /ud5ts4 m'#ax'#j y#am'#j xy'#a ,fig4 ,,iii4 ,conclusion wrong3 "r "o is ,"s %all[ p are n /ud5ts4 #af4 ,all "y lambs jump2 ,no "y animals are heal?y1 unless !y jump4 ,all "y lambs are heal?y4 ,univ4 "y animals2 m "y animals t jump2 x lambs2 y heal?y4 x#am'#j m'y#j ,no ,conclusion4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ag4 ,ill-manag$ bus9ess is unpr(itable2 ,railways are nev] ill-manag$4 ,all railways are pr(itable4 ,univ4 bus9ess2 m ill-manag$2 x pr(itable2 y railways4 m#ax#j y#am#j x'y'#a ,fig4 ,,iii4 ,conclusion wrong3 "r "o is ,"s bus9ess1 o!r ?an railways1 is pr(itable4 #ah4 ,no ,pr(essors are ignorant2 ,all ignorant p are va94 ,no ,pr(essors are va94 ,univ4 p2 m ignorant2 x ,pr(essors2 y va94 xm#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion wrong3 "r "o is ,"s va9 p]sons are n ,pr(essors4 #ai4 ,a prud5t man %uns hynas4 ,no bank] is imprud5t4 ,no bank] fails to %un hynas4 ,univ4 m52 m prud5t2 x %unn+ hynas2 y bank]s4 m#ax'#j ym'#j x'y#j ,fig4 ,i4 ,conclusion "r4 #bj4 ,all wasps are unfri5dly2 ,no puppies are unfri5dly4 ,no puppies are wasps4 ,univ4 creatures2 m fri5dly2 x wasps2 y puppies4 x#am#j ym'#j x#ay#j ,fig4 ,i 7a74 ,conclusion incomplete3 complete "o is ,wasps are n puppies4 #ba4 ,no ,jews are hone/2 ,"s ,g5tiles are ri*4 ,"s ri* p are di%one/4 ,univ4 p]sons2 m ,jews2 x hone/2 y ri*4 mx#j m'y#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 pg#aec #bb4 ,no idl]s w9 fame2 ,"s pa9t]s are n idle4 ,"s pa9t]s w9 fame4 ,univ4 p]sons2 m idl]s2 x p]sons :o w9 fame2 y pa9t]s4 mx#j ym'#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bc4 ,no monkeys are soldi]s2 ,all monkeys are mis*iev\s4 ,"s mis*iev\s creatures are n soldi]s4 ,univ4 creatures2 m monkeys2 x soldi]s2 y mis*iev\s4 mx#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion "r4 #bd4 ,all ^! bonbons are *ocolate-creams2 ,all ^! bonbons are delici\s4 ,*ocolate-creams are delici\s4 ,univ4 food2 m ^! bonbons2 x *ocolate-creams2 y delici\s4 m#ax'#j m#ay'#j xy#a ,fig4 ,,iii4 ,conclusion wrong1 be+ 9 excess ( ! "r "o1 :i* is ,"s *ocolate-creams are delici\s4 #be4 ,no muff9s are :olesome2 ,all buns are un:olesome4 ,buns are n muff9s4 ,univ4 food2 m :olesome2 x muff9s2 y buns4 xm#j y#am#j ,no ,conclusion4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #bf4 ,"s unau?oris$ reports are false2 ,all au?oris$ reports are tru/wor?y4 ,"s false reports are n tru/wor?y4 ,univ4 reports2 m au?oris$2 x true2 y tru/wor?y4 m'x'#a m#ay'#j ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #bg4 ,"s pill[s are s(t2 ,no pok]s are s(t4 ,"s pok]s are n pill[s4 ,univ4 ?+s2 m s(t2 x pill[s2 y pok]s4 xm#a ym#j xy'#a ,fig4 ,,ii4 ,conclusion wrong3 "r "o is ,"s pill[s are n pok]s4 #bh4 ,improbable /ories are n easily believ$2 ,none ( 8 /ories are probable4 ,none ( 8 /ories are easily believ$4 ,univ4 /ories2 m probable2 x easily believ$2 y 84 m'#ax#j ym#j xy#j ,fig4 ,i4 ,conclusion "r4 pg#aed #bi4 ,no ?ieves are hone/2 ,"s di%one/ p are f\nd out4 ,"s ?ieves are f\nd out4 ,univ4 p2 m hone/2 x ?ieves2 y f\nd out4 xm#j m'y#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #cj4 ,no muff9s are :olesome2 ,all puffy food is un:olesome4 ,all muff9s are puffy4 ,univ4 is food2 m :olesome2 x muff9s2 y puffy4 xm#j y#am#j ,no ,conclusion4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #ca4 ,no birds1 except peacocks1 are pr\d ( _! tails2 ,"s birds1 t are pr\d ( _! tails1 _c s+4 ,"s peacocks _c s+4 ,univ4 birds2 m pr\d ( _! tails2 x peacocks2 y birds t _c s+4 x'm#j my'#a xy'#a ,fig4 ,,ii4 ,conclusion "r4 #cb4 ,w>m? relieves pa92 ,no?+1 t does n relieve pa91 is useful 9 too?a*e4 ,w>m? is useful 9 too?a*e4 ,univ4 applications2 m reliev+ pa92 x w>m?2 y useful 9 too?a*e4 x#am'#j m'y#j ,no ,conclusion4 ,fallacy ( ,l ,elim9&s n ass]t$ to exi/4 #cc4 ,no bankrupts are ri*2 ,"s m]*ants are n bankrupts4 ,"s m]*ants are ri*4 ,univ4 p]sons2 m bankrupts2 x ri*2 y m]*ants4 mx#j ym'#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #cd4 ,bores are dread$2 ,no bore is ev] begg$ to prolong 8 visit4 ,no "o1 :o is dread$1 is ev] begg$ to prolong 8 visit4 ,univ4 p]sons2 m bores2 x dread$2 y begg$ to prolong _! visits4 m#ax'#j my#j xy'#a ,fig4 ,,iii4 ,conclusion wrong3 ! "r "o is ,"s dread$ p]sons are n begg$ to prolong _! visits4 #ce4 ,all wise m5 walk on _! feet2 ,all unwise m5 walk on _! h&s4 ,no man walks on bo?4 ,univ4 m52 m wise2 x walk+ on _! feet2 y walk+ on _! h&s4 m#ax'#j m'#ay'#j x'y'#j ,fig4 ,i4 ,conclusion wrong3 "r "o is ,no man walks on nei!r4 pg#aee #cf4 ,no :eelb>r[s are com=table2 ,no uncom=table vehicles are popul>4 ,no :eelb>r[s are popul>4 ,univ4 vehicles2 m com=table2 x :eelb>r[s2 y popul>4 xm#j m'x#j xy#j ,fig4 ,i4 ,conclusion "r4 #cg4 ,no frogs are poetical2 ,"s ducks are unpoetical4 ,"s ducks are n frogs4 ,univ4 creatures2 m poetical2 x frogs2 y ducks4 xm#j ym'#a ,no ,conclusion4 ,fallacy ( ,unlike ,elim9&s ) an ,entity-,premiss4 #ch4 ,no emp]ors are d5ti/s2 ,all d5ti/s are dread$ by *ildr54 ,no emp]ors are dread$ by *ildr54 ,univ4 p]sons2 m d5ti/s2 x emp]ors2 y dread$ by *ildr54 xm#j m#ay'#j x'y#a ,fig4 ,,iii4 ,conclusion wrong3 "r "o is ,"s p]sons1 dread$ by *ildr51 are n emp]ors4 #ci4 ,sug> is sweet2 ,salt is n sweet4 ,salt is n sug>4 ,univ4 ?+s2 m sweet2 x sug>2 y salt4 x#am'#j y#am#j 7x#ay#j y#ax#j7 ,fig4 ,i 7b74 ,conclusion incomplete3 omitt$ portion is ,sug> is n salt4 #dj4 ,e eagle c fly2 ,"s pigs _c fly4 ,"s pigs are n eagles4 ,univ4 creatures2 m creatures t c fly2 x eagles2 y pigs4 x#am'#j ym'#a x'y#a ,fig4 ,,ii4 ,conclusion "r4 ,solutions = #h4 ,,sl#h #a #b #c #a4 cd#j a#a;d'#j b#a;c'#j2 #a #b #c cd ad' bc' ab#j a#a b#a -- i4e4 a#a;b#j b#a;a#j #a #b #c #b4 d#a;b'#j ac'#j bc#j2 #a #c #b db' bc ac' da#j d#a i4e4 d#a;a#j - - #a #b #c #c4 ba#j cd'#j d#a;b'#j2 #a #c #b ba db' cd' ac#j - - #a #b #c #d4 bc#j a#a;b'#j c'd#j2 #a #b #c bc ab' c'd ad#j a#a i4e4 a#a;d#j -- pg#aef #a #b #c #a #b #c #e4 b'#a;a#j bc#j a'd#j2 b'a bc a'd cd#j - - #a #b #c #f4 a#a;b#j b'c#j d#a;a'#j2 #a #b #c ab b'c da' cd#j d#a i4e4 d#a;c#j -- #a #b #c #a #b #c #g4 db'#j b#a;a'#j cd'#j2 db' ba' cd' a'c#j -- #a #b #c #h4 b'd#j a'b#j c#a;d'#j2 #a #b #c b'd a'b cd' a'c#j c#a i4e4 c#a;a'#j - - #a #b #c #i4 b'#a;a'#j ad#j b#a;c'#j2 #a #b #c b'a' ad bc' dc'#j - - #a #b #c #aj4 cd#j b#a;c'#j ad'#j2 #a #b #c cd bc' ad' ba#j b#a i4e4 b#a;a#j -- #a #b #c #aa4 bc#j d#a;a'#j c'#a;a#j2 #a #c #b bc c'a da' bd#j d#a i4e4 d#a;b#j - - #a #b #c #ab4 cb'#j c'#a;d#j b#a;a'#j2 #a #b #c cb' c'd ba' da'#j -- #a #b #c #d #ac4 d#a;e'#j c#a;a'#j bd'#j e#a;a#j2 #a #c #d #b de' bd' ea ca' bc#j c#a i4e4 c#a;b#j -- - #a #b #c #d #ad4 c#a;b'#j a#a;e'#j d#a;b#j a'#a;c'#j2 #a #c #d #b cb' db a'c' ae' de'#j d#a i4e4 d#a;e'#j -- - #a #b #c #d #ae4 b'd#j e#a;c'#j b#a;a'#j d'#a;c#j2 #a #c #d #b b'd ba' d'c ec' a'e#j e#a i4e4 e#a;a'#j - - - #a #b #c #d #af4 a'e#j d#a;c#j a#a;b'#j e'#a;d'#j2 #a #c #d #b a'e ab' e'd' dc b'c#j - - - #a #b #c #d #ag4 d#a;c'#j a#a;e'#j bd'#j c#a;e#j2 #a #c #d #b dc' bd' ce ae' ba#j a#a i4e4 a#a;b#j -- - #a #b #c #d #ah4 a#a;b'#j d#a;e'#j a'#a;c#j be#j2 #a #c #d #b ab' a'c be de' cd#j d#a i4e4 d#a;c#j -- - #a #b #c #d #e #ai4 bc#j e#a;h'#j a#a;b'#j dh#j e'#a;c'#j2 #a #c #e #b #d bc ab' e'c' eh' dh ad#j a#a -- - - i4e4 a#a;d#j #a #b #c #d #e #bj4 dh'#j ce#j h#a;b'#j ad'#j be'#j2 #a #c #d #e #b dh' hb' ad' be' ce ac#j -- - - #a #b #c #d #e #ba4 b#a;a'#j dh#j ce#j ah'#j c'#a;b'#j2 #a #d #b #e #c ba' ah' dh c'b' ce de#j -- - - #a #b #c #d #e #bb4 e#a;d#j b'h'#j c'#a;d'#j a#a;e'#j *#j2 #a #c #d #e #b ed c'd' ae' * b'h' ab'#j a#a -- - - i4e4 a#a;b#j pg#aeg #a #b #c #d #e #bc4 b'#a;a#j de'#j h#a;b#j ce#j d'#a;a'#j2 #a #c #e #b #d b'a hb d'a' de' ce - - - - hc#j h#a i4e4 h#a;c#j #a #b #c #d #e #f #bd4 h'#ak#j b'a#j c#a;d'#j e#a;h#j dk'#j bc'#j2 #a #d #e #c #f #b h'k eh dk' cd' bc' b'a ea#j e#a - - - - - i4e4 e#a;a#j #a #b #c #d #be4 a#a;d'#j k#a;b'#j e#a;h'#j a'b#j #e #f d#a;c'#j h#ak'#j2 #a #d #b #e #f #c ad' a'b kb' dc' hk' eh' c'e#j e#a -- - - - i4e4 e#a;c'#j #a #b #c #d #e #bf4 a'#a;h'#j d'k'#j e#a;b#j hk#j a#a;c'#j #f b'd#j2 #a #d #b #e #f #c a'h' hk d'k' ac' b'd eb c'e#j e#a - - - - - i4e4 e#a;c'#j #a #b #c #d #e #bg4 e#a;d#j hb#j a'#ak'#j ce'#j b'#a;d'#j #f ac'#j2 #a #d #e #b #f #c ed ce' b'd' hb ac' a'k' hk'#j -- - - - #a #b #c #d #e #bh4 a'k#j e#a;b'#j hk'#j d'c#j ab#j #f c'#a;h'#j2 #a #c #e #b #f #d a'k hk' ab eb' c'h' d'c ed'#j e#a - - - - - i4e4 e#a;d'#j #a #b #c #d #e #bi4 ek#j b'm#j ac'#j h'#a;e'#j d#ak'#j #f #g #h cb#j d'#al'#j hm'#j2 #a #d #e #g #h #b #f #c ek h'e' dk' d'l' hm' b'm cb ac' -- - - - - - l'a#j #a #b #c #d #e #cj4 n#am'#j a'#a;e'#j c'l#j k#ar#j ah'#j #f #g #h #i #aj dl'#j cn'#j e#a;b'#j m#ar'#j h#a;d'#j2 #a #g #c #f #i #d #aj #e #b #h nm' cn' c'l dl' mr' kr hd' ah' a'e' eb' -- - - - - - - - kb'#j k#a i4e4 k#a;b'#j ,solutions = #i4 ,,sl#i #a4 #a #b #c b#a;d#j ac#j d'#a;c'#j2 #a #c #b bd d'c' ac ba#j b#a1 i4e4 b#a;a#j - - i4e4 ,babies _c manage crocodiles4 #b4 #a #b #c a#a;b'#j d#a;c'#j bc#j2 #a #c #b ab' bc dc' ad#j d#a1 i4e4 d#a;a#j - - i4e4 ,y\r pres5ts to me are n made ( t94 pg#aeh #c4 #a #b #c da#j c#a;b'#j a'b#j2 #a #c #b da a'b cb' dc#j c#a1 i4e4 c#a;d#j - - i4e4 ,all my potatoes 9 ?is di% are old ones4 #d4 #a #b #c ba#j b'd#j c#a;a'#j2 #a #b #c ba b'd ca' dc#j c#a1 i4e4 c#a;d#j -- i4e4 ,my s]vants nev] say %poonj4 #e4 #a #b #c ad#j cd'#j b#a;a'#j2 #a #b #c ad cd' ba' cb#j b#a1 i4e4 b#a;c#j -- i4e4 ,my p\ltry are n (fic]s4 #f4 #a #b #c #a #b #c c#a;a'#j c'b#j da#j2 ca' c'b da bd#j -- i4e4 ,none ( y\r sons are fit to s]ve on a jury4 #g4 #a #b #c #a #c #b cb#j da#j b'#a;a'#j2 cb b'a' da cd#j - - i4e4 ,no p5cils ( m9e are sug>plums4 #h4 #a #b #c cb'#j d#a;a'#j ba#j2 #a #c #b cb' ba da' cd#j d#a1 i4e4 d#a;c#j - - i4e4 ,j5k9s is inexp]i5c$4 #i4 #a #b #c #a #b #c cd#j d'a#j c'b#j2 cd d'a c'b ab#j -- i4e4 ,no comet has a curly tail4 #aj4 #a #b #c #a #c #b d'c#j ba#j a'#a;d#j2 d'c a'd ba cb#j - - i4e4 ,no h$gehog takes 9 ! ,times4 #aa4 #a #b #c b#a;a'#j c#a;b'#j ad#j2 #a #b #c ba' cb' ad cd#j c#a1 i4e4 c#a;d#j -- i4e4 ,?is di% is un:olesome4 #ab4 #a #b #c b#a;c'#j d'a#j a'c#j2 #a #c #b bc' a'c d'a bd'#j b#a1 i4e4 b#a;d'#j - - i4e4 ,my g>d5] is v old4 #ac4 #a #b #c a#a;d'#j bc#j c'#a;d#j2 #a #c #b ad' c'd bc ab#j a#a1 i4e4 a#a;b#j - - i4e4 ,all humm+-birds are small4 pg#aei #ad4 #a #b #c #a #c #b c'b#j a#a;d'#j ca'#j2 c'b ca' ad' bd'#j - - i4e4 ,no "o ) a hook$ nose ev] fails to make money4 #ae4 #a #b #c #a #b #c b#a;a'#j b'#a;d#j ca#j2 ba' b'd ca dc#j -- i4e4 ,no gray ducks 9 ?is village we> lace coll>s4 #af4 #a #b #c #a #b #c d#a;b'#j cd'#j ba#j2 db' cd' ba ca#j -- i4e4 ,no jug 9 ?is cupbo>d w hold wat]4 #ag4 #a #b #c b'#a;d#j c#a;d'#j ab#j2 #a #b #c b'd cd' ab ca#j c#a1 i4e4 c#a;a#j - - i4e4 ,^! apples 7 gr[n 9 ! sun4 #ah4 #a #b #c d'#a;b'#j c#a;b#j c'a#j2 #a #b #c d'b' cb c'a d'a#j d'#a1 i4e4 d'#a;a#j - - i4e4 ,puppies1 t w n lie /ill1 nev] c>e to d wor/$-"w4 #ai4 #a #b #c #a #c #b bd'#j a#a;c'#j a'd#j2 bd' a'd ac' bc'#j - - i4e4 ,no "n 9 ?is li/ is unmelodi\s4 #bj4 #a #b #c #a #c #b a#a;b'#j dc#j a'#a;d'#j2 ab' a'd' dc b'c#j - - i4e4 ,no ,m4,p4 %\ld ride 9 a donkey-race1 unless he has p]fect self-comm&4 #ba4 #a #b #c #a #c #b bd#j c'a#j b'c#j2 bd b'c c'a da#j - - i4e4 ,no goods 9 ?is %op1 t are /ill on sale1 may be c>ri$ away4 #bb4 #a #b #c #a #c #b a'b#j cd#j d'a#j2 a'b d'a cd bc#j - - i4e4 ,no acrobatic feat1 :i* involves turn+ a quadruple som]sault1 is ev] attempt$ 9 a circus4 #bc4 #a #b #c dc'#j a#a;b'#j bc#j2 #a #c #b dc' bc ab' da#j a#a1 i4e4 a#a;d#j - - i4e4 ,gu9ea-pigs nev] really appreciate ,bee?ov54 pg#afj #bd4 #a #b #c #a #c #b a#a;d'#j b'#a;c#j ba'#j2 ad' ba' b'c d'c#j - - i4e4 ,no sc5tless fl[]s please me4 #be4 #a #b #c c#a;d'#j ba'#j d#a;a#j2 #a #c #b cd' da ba' cb#j c#a1 i4e4 c#a;b#j - - i4e4 ,%[y talk]s are n really well-in=m$4 #bf4 #a #b #c #d ea#j b#a;d'#j a'#a;c#j e'b'#j2 #a #c #d #b ea a'c e'b' bd' cd'#j -- - i4e4 ,none b r$-hair$ boys le>n ,greek 9 ?is s*ool4 #bg4 #a #b #c #d b#a;d#j ac'#j e#a;d'#j c#a;b'#j2 #a #c #d #b bd ed' cb' ac' ea#j e#a1 i4e4 e#a;a#j -- - i4e4 ,w$d+-cake always disagrees ) me4 #bh4 #a #b #c #d ad#j e'#a;b'#j c#a;d'#j e#a;a'#j2 #a #c #d #b ad cd' ea' e'b' cb'#j c#a1 i4e4 c#a;b'#j -- - i4e4 ,discussions1 t g on :ile ,tomk9s is 9 ! *air1 endang] ! peacefulness ( our ,debat+-,club4 #bi4 #a #b #c #d d#a;a#j e'c#j b#a;a'#j d'e#j2 #a #c #d #b da ba' d'e e'c bc#j b#a1 i4e4 b#a;c#j -- - i4e4 ,all gluttons 9 my family are unheal?y4 #cj4 #a #b #c #d d#a;e#j c'a#j b#a;e'#j c#a;d'#j2 #a #c #d #b de be' cd' c'a ba#j b#a1 i4e4 b#a;a#j -- - i4e4 ,an egg ( ! ,great ,auk is n to be _h = a song4 #ca4 #a #b #c #d d'b#j a#a;c'#j c#a;e'#j a'd#j2 #a #d #b #c d'b a'd ac' ce' be'#j - - - i4e4 ,no books sold "h h gilt edges unless !y are pric$ at #es4 & upw>ds4 #cb4 #a #b #c #d a'#a;c'#j d#a;b#j a#a;e'#j c#a;b'#j2 #a #c #d #b a'c' ae' cb' db e'd#j d#a1 i4e4 d#a;e'#j - - - i4e4 ,:5 y cut y\r f+]1 y w f9d ,t9cture ( ,cal5dula useful4 #cc4 #a #b #c #d d'b#j a#a;e'#j ec#j d#a;a'#j2 #a #d #b #c d'b da' ae' ec bc#j - - - i4e4 ,i h nev] come across a m]maid at sea4 pg#afa #cd4 #a #b #c #d c'#a;b#j a#a;e'#j d#a;b'#j a'#a;c#j2 #a #c #d #b c'b db' a'c ae' de'#j d#a1 i4e4 d#a;e'#j - - - i4e4 ,all ! romances 9 ?is libr>y are well-writt54 #ce4 #a #b #c #d e'd#j c'a#j eb#j d'c#j2 #a #c #d #b e'd eb d'c c'a ba#j - - - i4e4 ,no bird 9 ?is avi>y lives on m9ce-pies4 #cf4 #a #b #c #d d'#a;c'#j e#a;a'#j c#a;b#j e'd#j2 #a #c #d #b d'c' cb e'd ea' ba'#j - - - i4e4 ,no plum-pudd+1 t has n be5 boil$ 9 a clo?1 c be di/+ui%$ f s\p4 #cg4 #a #b #c #d #e ce'#j b'a'#j h#a;d'#j ae#j bd#j2 #a #d #b #e #c ce' ae b'a' bd hd' *#j h#a1 i4e4 h#a;c#j - - - - i4e4 ,all y\r poems are un9t]e/+4 #ch4 #a #b #c #d #e b'#a;a'#j db#j he'#j ec#j a#a;h'#j2 #a #b #e #c #d b'a' db ah' he' ec dc#j - - - - i4e4 ,none ( my pea*es h be5 gr[n 9 a ho?\se4 #ci4 #a #b #c #d #e c#a;d#j h#a;e'#j c'#a;a'#j h'b#j e#a;d'#j2 #a #c #e #b #d cd c'a' ed' he' h'b a'b#j -- - - i4e4 ,no pawnbrok] is di%one/4 #dj4 #a #b #c #d #e bd'#j c'h#j e#a;b'#j da#j e'c#j2 #a #c #d #e #b bd' eb' da e'c c'h ah#j -- - - i4e4 ,no kitt5 ) gre5 eyes w play ) a gorilla4 #da4 #a #b #c #d #e c#a;a'#j h'b#j ae#j d#a;c'#j h#a;e'#j2 #a #c #d #e #b ca' ae dc' he' h'b db#j d#a1 i4e4 d#a;b#j -- - - i4e4 ,all my fri5ds 9 ?is ,college d9e at ! l[] table4 #db4 #a #b #c #d #e ca#j h#a;d'#j c'#a;e'#j b'a'#j d#a;e#j2 #a #c #d #e #b ca c'e' b'a' de hd' b'h#j h#a1 -- - - i4e4 h#a;b'#j i4e4 ,my writ+-desk is full ( live scorpions4 #dc4 #a #b #c #d #e b'#a;e#j ah#j dc#j e'#a;a'#j bc'#j #a #d #b #e #c b'e e'a' ah bc' dc hd#j - - - - i4e4 ,no ,m&>9 ev] reads ,hogg's poems4 pg#afb #dd4 #a #b #c #d #e e#a;b'#j a'd#j c#a;h'#j e'a#j d'h#j2 #a #d #b #e #c eb' e'a a'd d'h *' b'c#j c#a1 - - - - i4e4 c#a;b'#j i4e4 ,%akespe>e 0 clev]4 #de4 #a #b #c #d #e e'#a;c'#j hb'#j d#a;a#j e#a;a'#j c#a;b#j2 #a #d #c #e #b e'c' ea' da cb hb' dh#j d#a1 i4e4 d#a;h#j - - - - i4e4 ,ra9b[s are n wor? writ+ odes to4 #df4 #a #b #c #d #e c'#a;h'#j e#a;a#j bd#j a'#a;h#j d'c#j2 #a #d #b #e #c c'h' a'h ea d'c bd eb#j e#a1 i4e4 e#a;b#j - - - - i4e4 ,^! ,sorites-examples are difficult4 #dg4 #a #b #c #d #e #f a'#a;e'#j bk#j c'a#j eh'#j d#a;b'#j k'h#j2 #a #c #d #f #b #e a'e' c'a eh' k'h bk db' c'd#j d#a1 - - - - - i4e4 d#a;c'#j i4e4 ,all my dreams come true4 #dh4 #a #b #c #d #e #f a'h#j c'k#j a#a;d'#j e#a;h'#j b#ak'#j c#a;e'#j2 #a #c #d #f #b #e a'h ad' eh' ce' c'k bk' d'b#j b#a1 - - - - - i4e4 b#a;d'#j i4e4 ,all ! ,engli% pictures "h are pa9t$ 9 oils4 #di4 #a #b #c #d #e #f k'#a;e#j c#a;h#j b#a;a'#j kd#j h'a#j b'#a;e'#j2 #a #d #f #c #e #b k'e kd b'e' ba' h'a * dc#j c#a1 - - - - - i4e4 c#a;d#j i4e4 ,donkeys are n easy to swall[4 #ej4 #a #b #c #d #e #f ab'#j h'd#j e#a;c#j b#a;d'#j a'k#j c'#a;h#j2 #a #d #b #e #f #c ab' bd' h'd a'k c'h ec ke#j e#a1 -- - - - i4e4 e#ak#j i4e4 ,opium-eat]s nev] we> :ite kid gloves4 #ea4 #a #b #c #d #e #f bc#j k#a;a'#j eh#j d#a;b'#j h'c'#j k'#a;e'#j2 #a #d #e #c #f #b bc db' h'c' eh k'e' ka' da'#j d#a1 -- - - - i4e4 d#a;a'#j i4e4 ,a good husb& always comes home = 8 tea4 #eb4 #a #b #c #d #e #f a'#ak'#j *#j h'k#j b#a;d'#j ea#j d#a;c'#j #a #c #b #f #d #e a'k' h'k * dc' bd' ea be#j b#a1 - - - - - i4e4 b#a;e#j i4e4 ,ba?+-ma*9es are nev] made ( "m-(-pe>l4 pg#afc #ec4 #a #b #c #d #e da'#j k#a;b'#j c#a;h#j d'#ak'#j e#a;c'#j #f a#a;h'#j2 #a #d #b #f #c #e da' d'k' kb' ah' * ec' -- - - - b'e#j e#a1 i4e4 e#a;b'#j i4e4 ,ra9y days are always cl\dy4 #ed4 #a #b #c #d #e #f kb'#j a'#a;c'#j d'b#j k'#a;h'#j ea#j d#a;c#j2 #a #c #d #f #b #e kb' d'b k'h' dc a'c' ea -- - - - h'e#j i4e4 ,no heavy fi% is unk9d to *ildr54 #ee4 #a #b #c #d #e #f k'#a;b'#j eh'#j c'd#j hb#j ac#j kd'#j2 #a #d #b #f #c #e k'b' hb eh' kd' c'd ac ea#j - - - - - i4e4 ,no eng9e-driv] lives on b>ley-sug>4 #ef4 #a #b #c #d #e h#a;b'#j c#a;d'#j k'a#j e#a;h'#j b#a;a'#j #f k#a;c'#j2 #a #d #e #c #f #b hb' eh' ba' k'a kc' cd' -- - - - ed'#j e#a1 i4e4 e#a;d'#j i4e4 ,all ! animals 9 ! y>d gnaw bones4 #eg4 #a #b #c #d #e #f h'#a;d'#j e#a;c'#j k'a#j cb#j d#al'#j e'h#j #g kl#j2 #a #e #g #c #f #b #d h'd' dl' kl k'a e'h ec' cb ab#j - - - - - - i4e4 ,no badg] c guess a conundrum4 #eh4 #a #b #c #d #e #f b'h#j d'#al'#j ca#j d#ak'#j h'#a;e'#j mc'#j #g #h a'b#j ek#j2 #a #e #g #c #f #h #d #b b'h h'e' a'b ca mc' ek dk' d'l' ml'#j - - - - - - - i4e4 ,no *eque ( y\rs1 receiv$ by me1 is payable to ord]4 #ei4 #a #b #c #d #e #f c#al'#j h'e#j kd#j mc'#j b'#a;e'#j n#a;a'#j #g #h #i l#a;d'#j m'b#j ah#j2 #a #d #g #c #h #e #b #i #f cl' mc' ld' kd m'b b'e' h'e ah na' -- - - - - - - kn#j i4e4 ,i _c read any ( ,br[n's lett]s4 #fj4 #a #b #c #d #e #f e#a;c'#j l#an'#j d#a;a'#j m'b#j ck'#j e'r#j #g #h #i #aj h#an#j b'k#j r'#a;d'#j m#al'#j2 #a #e #f #h #d #i #c #aj #b #g ec' ck' e'r b'k m'b r'd' da' ml' ln' hn -- - - - - - - - a'h#j h#a1 i4e4 h#a;a'#j i4e4 ,i always avoid a kang>oo4 pg#afd ,,notes4 7,a7 ,see p4 #hj4 ,"o ( ! fav\rite objections1 br\ght aga9/ ! ,sci5ce ( ,logic by its detractors1 is t a ,syllogism has no real validity z an argum5t1 s9ce x involves ! ,fallacy ( ,petitio ,pr9cipii 7i4e4 ,begg+ ! ,"q1 ! ess5ce ( :i* is t ! :ole ,conclusion is involv$ 9 "o ( ! ,premisses74 ,?is =midable objection is refut$1 ) beautiful cle>ness & simplicity1 by ^! ?ree ,diagrams1 :i* %[ u t1 9 ea* ( ! ?ree ,figures1 ! ,conclusion is really involv$ 9 ! two ,premisses tak5 toge!r1 ea* contribut+ its %>e4 ,?us1 9 ,fig4 ,i41 ! ,premiss xm#j empties ! ,inn] ,cell ( ! ,n4,w4 ,qu>t]1 :ile ! ,premiss ym#j empties its ,out] ,cell4 ,h5ce x ne$s ! two ,premisses to empty ! :ole ( ! ,n4,w4 ,qu>t]1 & ?us to prove ! ,conclusion xy#j4 ,aga91 9 ,fig4 ,,ii41 ! ,premiss xm#j empties ! ,inn] ,cell ( ! ,n4,w4 ,qu>t]4 ,! ,premiss ym#a m]ely tells u t ! ,inn] ,portion ( ! ,w4 ,half is occupi$1 s t we may place a ',i' 9 x1 some:]e2 b1 if ?is 7 ! :ole ( our in=mation1 we %\ld n "k 9 :i* ,cell to place x1 s t x w\ld h to 'sit on ! f5ce'3 x is only :5 we le>n1 f ! o!r ,premiss1 t ! upp] ( ^! two ,cells is empty1 t we feel au?oris$ to place ! ',i' 9 ! l[] ,cell1 & ?us to prove ! ,conclusion x'y#a4 ,la/ly1 9 ,fig4 ,,iii41 ! in=mation1 t m exi/s1 m]ely au?orises u to place a ',i' some:]e 9 ! ,inn] ,squ>e----b x has l>ge *oice ( f5ces to sit ^u6 ,x ne$s ! ,premiss xm#j to drive x out ( ! ,n4 ,half ( t ,squ>e2 & x ne$s ! ,premiss ym#j to drive x out ( ! ,w4 ,half4 ,h5ce x ne$s ! two ,premisses to drive x into ! ,inn] ,portion ( ! ,s4,e4 ,qu>t]1 & ?us to prove ! ,conclusion x'y'#a4 pg#afe ,,app5dix1 ,,address$ ,,to ,,tea*]s4 #a4 ,introductory4 ,!re are sev]al matt]s1 too h>d to discuss ) ,le>n]s1 :i* nev]!less ne$ to be expla9$ to any ,tea*]s1 into ^: h&s ?is book may fall1 9 ord] t !y may ?or\ghly und]/& :at my ,symbolic ,me?od is1 & 9 :at respects x diff]s f ! _m o!r ,me?ods already publi%$4 ,^! matt]s are z foll[s3-- ,! ,exi/5tial ,import ( ,propositions4 ,! use ( is-n 7or are-n7 z a ,copula4 ,! !ory two ,negative ,premisses prove no?+4 ,eul]'s ,me?od ( ,diagrams4 ,v5n's ,me?od ( ,diagrams4 ,my ,me?od ( ,diagrams4 ,! ,solution ( a ,syllogism by v>i\s ,me?ods4 ,my ,me?od ( treat+ ,syllogisms & ,sorites4 ,"s acc\nt ( ,p>ts ,,ii1 ,,iii4 #b4 ,! ,exi/5tial ,import ( ,propositions4 ,! writ]s1 & editors1 ( ! ,logical text-books :i* run 9 ! ord9>y grooves----to :om ,i %all h]eaft] ref] by ! 7,i hope in(f5sive7 title ,! ,logicians----take1 on ?is subject1 :at seems to me to be a m humble position ?an is at all necess>y4 ,!y speak ( ! ,copula ( a ,proposition ) bat$ brea?1 almo/ z if x 7 a liv+1 consci\s ,entity1 capable ( decl>+ = itself :at x *ose to mean1 & t we1 poor human creatures1 _h no?+ to d b to asc]ta9 :at 0 its sov]eign w & pleasure1 & submit to x4 pg#aff ,9 opposition to ?is view1 ,i ma9ta9 t any writ] ( a book is fully au?oris$ 9 atta*+ any mean+ he likes to any ^w or phrase he int5ds to use4 ,if ,i f9d an au?or say+1 at ! beg9n+ ( 8 book1 ,let x be und]/ood t by ! ^w 'black' ,i %all always mean ':ite'1 & t by ! ^w ':ite' ,i %all always mean 'black'1 ,i meekly accept 8 rul+1 h[ev] injudici\s ,i may ?9k x4 ,& s1 ) reg>d to ! "q :e!r a ,proposition is or is n to be und]/ood z ass]t+ ! exi/5ce ( its ,subject1 ,i ma9ta9 t e writ] may adopt 8 own rule1 provid$ ( c\rse t x is consi/5t ) itself & ) ! accept$ facts ( ,logic4 ,let u consid] c]ta9 views t may logically be held1 & ?us settle :i* ( !m may conv5i5tly be held2 aft] :i* ,i %all hold myself free to decl>e :i* ( !m ,i int5d to hold4 ,! k9ds ( ,propositions1 to be consid]$1 are ^? t beg9 ) "s1 ) no1 & ) all4 ,^! are usually call$ ,propositions 9 ,i1 9 ,e1 & 9 ,a4 ,fir/1 !n1 a ,proposition 9 ,i may be und]/ood z ass]t+1 or else z n ass]t+1 ! exi/5ce ( its ,subject4 7,by exi/5ce ,i mean ( c\rse :atev] k9d ( exi/5ce suits its nature4 ,! two ,propositions1 dreams exi/ & drums exi/1 d5ote two totally diff]5t k9ds ( exi/5ce4 ,a dream is an aggregate ( ideas1 & exi/s only 9 ! m9d ( a dream]3 :]eas a drum is an aggregate ( wood & p>*m5t1 & exi/s 9 ! h&s ( a drumm]47 ,fir/1 let u suppose t ,i ass]ts 7i4e4 ass]ts ! exi/5ce ( its ,subject74 ,"h1 ( c\rse1 we mu/ reg>d a ,proposition 9 ,a z mak+ ! same ass]tion1 s9ce x necess>ily conta9s a ,proposition 9 ,i4 ,we n[ h ,i & ,a ass]t+4 ,does ?is leave u free to make :at supposition we *oose z to ,e8 ,my answ] is ,no4 ,we are ti$ d[n to ! supposition t ,e does n ass]t4 ,?is c be prov$ z foll[s3-- ,if possible1 let ,e ass]t4 ,!n 7tak+ x1 y1 & z to repres5t ,attributes7 we see t1 if ! ,proposition ,no xy are z be true1 "s ?+s exi/ ) ! ,attributes x & y3 i4e4 ,"s x are y4 pg#afg ,also we "k t1 if ! ,proposition ,"s xy are z be true1 ! same result foll[s4 ,b ^! two ,propositions are ,contradictories1 s t "o or o!r ( !m mu/ be true4 ,h5ce ?is result is always true3 i4e4 ! ,proposition ,"s x are y is always true6 ,quod e/ absurdum4 7,see ,note 7,a71 p4 #aie74 ,we see1 !n1 t ! supposition ,i ass]ts necess>ily leads to ,a ass]ts1 b ,e does n4 ,& ?is is ! fir/ ( ! v>i\s views t may conceivably be held4 ,next1 let u suppose t ,i does n ass]t4 ,&1 along ) ?is1 let u take ! supposition t ,e does ass]t4 ,h5ce ! ,proposition ,no x are y means ,"s x exi/1 & none ( !m are y3 i4e4 all ( !m are n-y1 :i* is a ,proposition 9 ,a4 ,we also "k1 ( c\rse1 t ! ,proposition ,all x are n-y proves ,no x are y4 ,n[ two ,propositions1 ea* ( :i* proves ! o!r1 are equival5t4 ,h5ce e ,proposition 9 ,a is equival5t to "o 9 ,e1 & !re=e ass]ts4 ,h5ce our second conceivable view is ,e & ,a ass]t1 b ,i does n4 ,?is view does n se5 to involve any necess>y contradiction ) itself or ) ! accept$ facts ( ,logic4 ,b1 :5 we come to te/ x1 z appli$ to ! actual facts ( life1 we %all f9d ,i ?9k1 t x fits 9 ) !m s badly t its adoption w\ld be1 to say ! lea/ ( x1 s+ul>ly inconv5i5t = ord9>y folk4 ,let me record a little dialogue ,i h j held ) my fri5d ,jones1 :o is try+ to =m a new ,club1 to be regulat$ on /rictly ,logical pr9ciples4 ,au?or4 ,well1 ,jones6 ,h y got y\r new ,club />t$ yet8 ,jones 7rubb+ 8 h&s74 ,y'll be glad to he> t "s ( ! ,memb]s 7m9d1 ,i only say '"s'7 are millionaires6 ,roll+ 9 gold1 my boy6 ,au?or4 ,t s\nds well4 ,& h[ _m ,memb]s h ent]$8 ,jones 7/>+74 ,none at all4 ,we hav5't got x />t$ yet4 ,:at makes y ?9k we h8 ,au?or4 ,:y1 ,i ?\ght y said t "s ( ! ,memb]s---- pg#afh ,jones 7contemptu\sly74 ,y don't seem to be aw>e t we're work+ on /rictly ,logical pr9ciples4 ,a ,p>ticul> ,proposition does n ass]t ! exi/5ce ( its ,subject4 ,i m]ely meant to say t we've made a ,rule n to admit any ,memb]s till we h at lea/ ?ree ,c&idates ^: incomes are ov] t5 ?\s& a ye>6 ,au?or4 ,oh1 t's :at y meant1 is x8 ,let's he> "s m ( y\r ,rules4 ,jones4 ,ano!r is1 t no "o1 :o has be5 convict$ sev5 times ( =g]y1 is admissible4 ,au?or4 ,& "h1 aga91 ,i suppose y don't mean to ass]t !re are any su* convicts 9 exi/5ce8 ,jones4 ,:y1 t's exactly :at ,i d mean to ass]t6 ,don't y "k t a ,univ]sal ,negative ass]ts ! exi/5ce ( its ,subject8 ,( c\rse we didn't make t ,rule till we _h satisfi$ ourselves t !re are sev]al su* convicts n[ liv+4 ,! ,read] c n[ decide = himself h[ f> ?is second conceivable view w\ld fit 9 ) ! facts ( life4 ,he w1 ,i ?9k1 agree ) me t ,jones' view1 ( ! ',exi/5tial ,import' ( ,propositions1 w\ld lead to "s inconv5i5ce4 ,?irdly1 let u suppose t nei!r ,i nor ,e ass]ts4 ,n[ ! supposition t ! two ,propositions1 ,"s x are y & ,no x are n-y1 d n ass]t1 necess>ily involves ! supposition t ,all x are y does n ass]t1 s9ce x w\ld be absurd to suppose t !y ass]t1 :5 comb9$1 m ?an !y d :5 tak5 sep>ately4 ,h5ce ! ?ird 7& la/7 ( ! conceivable views is t nei!r ,i1 nor ,e1 nor ,a1 ass]ts4 ,! advocates ( ?is ?ird view w\ld int]pret ! ,proposition ,"s x are y to mean ,if !re 7 any x 9 exi/5ce1 "s ( !m w\ld be y2 & s ) ,e & ,a4 ,x admits ( pro( t ?is view1 z reg>ds ,a1 conflicts ) ! accept$ facts ( ,logic4 ,let u take ! ,syllogism ,d>apti1 :i* is univ]sally accept$ z valid4 ,its =m is ,all m are x2 ,all m are y4 4'4 ,"s y are x4 pg#afi ,?is !y w\ld int]pret z foll[s3-- ,if !re 7 any m 9 exi/5ce1 all ( !m w\ld be x2 ,if !re 7 any m 9 exi/5ce1 all ( !m w\ld be y4 4'4 ,if !re 7 any y 9 exi/5ce1 "s ( !m w\ld be x4 ,t ?is ,conclusion does n foll[ has be5 s briefly & cle>ly expla9$ by ,mr4 ,keynes 79 8 ,=mal ,logic1 dat$ #ahid1 pp4 #cef1 #ceg71 t ,i pref] to quote 8 words3-- ,let no proposition imply ! exi/5ce ei!r ( its subject or ( its pr$icate4 ,take1 z an example1 a syllogism 9 ,d>apti3-- ',all ,m is ,p1 ,all ,m is ,s1 4'4 ,"s ,s is ,p4' ,tak+ ,s1 ,m1 ,p1 z ! m9or1 middle1 & major t]ms respectively1 ! conclusion w imply t1 if !re is an ,s1 !re is "s ,p4 ,w ! premisses also imply ?is8 ,if s1 !n ! syllogism is valid2 b n o!rwise4 ,! conclusion implies t if ,s exi/s ,p exi/s2 b1 consi/5tly ) ! premisses1 ,s may be exi/5t :ile ,m & ,p are bo? non-exi/5t4 ,an implication is1 !re=e1 conta9$ 9 ! conclusion1 :i* is n ju/ifi$ by ! premisses4 ,?is seems to me entirely cle> & conv9c+4 ,/ill1 to make sick]1 ,i may z well ?r[ ! above 7soi-disant7 ,syllogism into a concrete =m1 :i* w be )9 ! grasp ( ev5 a non-logical ,read]4 ,let u suppose t a ,boys' ,s*ool has be5 set up1 ) ! foll[+ sy/em ( ,rules3-- ,all boys 9 ! ,fir/ 7! highe/7 ,class are to d ,fr5*1 ,greek1 & ,lat94 ,all 9 ! ,second ,class are to d ,greek only4 ,all 9 ! ,?ird ,class are to d ,lat9 only4 ,suppose also t !re are boys 9 ! ,?ird ,class1 & 9 ! ,second2 b t no boy has yet ris5 into ! ,fir/4 ,x is evid5t t !re are no boys 9 ! ,s*ool do+ ,fr5*3 /ill we "k1 by ! ,rules1 :at w\ld happ5 if !re 7 any4 pg#agj ,we are au?oris$1 !n1 by ! ,data1 to ass]t ! foll[+ two ,propositions3-- ,if !re 7 any boys do+ ,fr5*1 all ( !m w\ld be do+ ,greek2 ,if !re 7 any boys do+ ,fr5*1 all ( !m w\ld be do+ ,lat94 ,& ! ,conclusion1 accord+ to ,! ,logicians w\ld be ,if !re 7 any boys do+ ,lat91 "s ( !m w\ld be do+ ,greek4 ,"h1 !n1 we h two true ,premisses & a false ,conclusion 7s9ce we "k t !re are boys do+ ,lat91 & t none ( !m are do+ ,greek74 ,h5ce ! argum5t is invalid4 ,simil>ly x may be %[n t ?is non-exi/5tial int]pretation de/roys ! validity ( ,disamis1 ,datisi1 ,felapton1 & ,fresison4 ,"s ( ,! ,logicians w1 no d\bt1 be ready to reply ,b we are n ,aldri*ians6 ,:y %\ld we be responsible = ! validity ( ! ,syllogisms ( s antiquat$ an au?or z ,aldri*8 ,v good4 ,!n1 = ! special b5efit ( ^! fri5ds ( m9e 7) :at om9\s emphasis t "n is sometimes us$6 ,i mu/ h a private int]view ) y1 my "y fri5d1 says ! bl& ,dr4 ,bir*1 9 my libr>y1 at #i a4m4 tomorr[4 ,& y w please to be punctual671 = _! special b5efit1 ,i say1 ,i w produce ano!r *>ge aga9/ ?is non-exi/5tial int]pretation4 ,x actually invalidates ! ord9>y ,process ( ,conv]sion1 z appli$ to ,proposition 9 ',i'4 ,e logician1 ,aldri*ian or o!rwise1 accepts x z an e/abli%$ fact t ,"s x are y may be legitimately conv]t$ into ,"s y are x4 ,b is x equally cle> t ! ,proposition ,if !re 7 any x1 "s ( !m w\ld be y may be legitimately conv]t$ into ,if !re 7 any y1 "s ( !m w\ld be x8 ,i tr[ n4 ,! example ,i h already us$----( a ,boys' ,s*ool ) a non-exi/5t ,fir/ ,class----w s]ve admirably to illu/rate ?is new flaw 9 ! !ory ( ,! ,logicians4 pg#aga ,let u suppose t !re is yet ano!r ,rule 9 ?is ,s*ool1 viz4 ,9 ea* ,class1 at ! end ( ! ,t]m1 ! head boy & ! second boy %all receive prizes4 ,?is ,rule entirely au?orises u to ass]t 79 ! s5se 9 :i* ,! ,logicians w\ld use ! words7 ,"s boys 9 ! ,fir/ ,class w receive prizes1 = ?is simply means 7accord+ to !m7 ,if !re 7 any boys 9 ! ,fir/ ,class1 "s ( !m w\ld receive prizes4 ,n[ ! ,conv]se ( ?is ,proposition is1 ( c\rse1 ,"s boys1 :o w receive prizes1 are 9 ! ,fir/ ,class1 :i* means 7accord+ to ,! ,logicians7 ,if !re 7 any boys ab\t to receive prizes1 "s ( !m w\ld be 9 ! ,fir/ ,class 7:i* ,class we "k to be empty74 ,( ?is ,pair ( ,conv]se ,propositions1 ! fir/ is und\bt$ly true3 ! second1 z und\bt$ly1 false4 ,x is always sad to see a batsman knock d[n 8 own wicket3 "o pities him1 z a man & a bro!r1 b1 z a cricket]1 "o c b pron\nce him ,out6 ,we see1 !n1 t1 among all ! conceivable views we h "h consid]$1 !re are only two :i* c logically be held1 viz4 ,i & ,a ass]t1 b ,e does n4 ,e & ,a ass]t1 b ,i does n4 ,! second ( ^! ,i h %[n to involve great practical inconv5i5ce4 ,! fir/ is ! "o adopt$ 9 ?is book4 7,see p4 #ai47 ,"s fur!r rem>ks on ?is subject w be f\nd 9 ,note 7,b71 at p4 #aif4 #c4 ,! use ( is-n 7or are-n7 z a ,copula4 ,is x bett] to say ,john is-n 9-!-h\se or ,john is n-9-!-h\se8 ,"s ( my acqua9tances are-n m5-,i-%\ld-l-to-be-se5-) or ,"s ( my acqua9tances are m5-,i-%\ld-n-l-to-be-se5-)8 ,t is ! sort ( "q we h n[ to discuss4 pg#agb ,?is is no "q ( ,logical ,"r & ,wrong3 x is m]ely a matt] ( ta/e1 s9ce ! two =ms mean exactly ! same ?+4 ,& "h1 aga91 ,! ,logicians seem to me to take mu* too humble a position4 ,:5 !y are putt+ ! f9al t\*es to ! gr\p+ ( _! ,proposition1 j be=e ! curta9 goes up1 & :5 ! ,copula----always a r fussy 'heavy fa!r'1 asks !m ,am ,i to h ! 'n'1 or w y tack x on to ! ,pr$icate8 !y are mu* too ready to answ]1 l ! subtle cab-driv]1 ,leave x to y1 ,sir6 ,! result seems to be1 t ! grasp+ ,copula con/antly gets a n t _h bett] h be5 m]g$ 9 ! ,pr$icate1 & t ,propositions are diff]5tiat$ :i* _h bett] h be5 recognis$ z precisely simil>4 ,surely x is simpl] to treat ,"s m5 are ,jews & ,"s m5 are ,g5tiles z be+ bo? ( !m1 affirmative ,propositions1 in/ead ( translat+ ! latt] into ,"s m5 are-n ,jews1 & reg>d+ x z a negative ,propositions8 ,! fact is1 ,! ,logicians h someh[ acquir$ a p]fectly morbid dread ( negative ,attributes1 :i* makes !m %ut _! eyes1 l fright5$ *ildr51 :5 !y come across su* t]rible ,propositions z ,all n-x are y2 & ?us !y exclude f _! sy/em _m v useful =ms ( ,syllogisms4 ,"u ! influ5ce ( ?is unreason+ t]ror1 !y plead t1 9 ,di*otomy by ,contradiction1 ! negative "p is too l>ge to deal )1 s t x is bett] to reg>d ea* ,?+ z ei!r includ$ 91 or exclud$ f1 ! positive "p4 ,i see no =ce 9 ?is plea3 & ! facts (t5 g ! o!r way4 ,z a p]sonal "q1 de> ,read]1 if y 7 to gr\p y\r acqua9tances into ! two ,classes1 m5 t y w\ld l to be se5 )1 & m5 t y w\ld n l to be se5 )1 d y ?9k ! latt] gr\p w\ld be s v mu* ! l>g] ( ! two8 ,= ! purposes ( ,symbolic ,logic1 x is s mu* ! mo/ conv5i5t plan to reg>d ! two sub-divisions1 produc$ by ,di*otomy1 on ! same foot+1 & to say1 ( any ,?+1 ei!r t x is 9 ! "o1 or t x is 9 ! o!r1 t ,i d n ?9k any ,read] ( ?is book is likely to demur to my adopt+ t c\rse4 pg#agc #d4 ,! !ory t two ,negative ,premisses prove no?+4 ,?is ,i consid] to be ano!r craze ( ,! ,logicians1 fully z morbid z _! dread ( a negative ,attribute4 ,x is1 p]haps1 be/ refut$ by ! me?od ( ,in/antia ,contr>ia4 ,take ! foll[+ ,pairs ( ,premisses3-- ,none ( my boys are conceit$2 ,none ( my girls are gre$y4 ,none ( my boys are clev]2 ,none b a clev] boy c\ld solve ?is problem4 ,none ( my boys are le>n$2 ,"s ( my boys are n *ori/]s4 7,?is la/ ,proposition is1 9 my sy/em1 an affirmative "o1 s9ce ,i %\ld read x are n-*ori/]s2 b1 9 deal+ ) ,! ,logicians1 ,i may fairly treat x z a negative "o1 s9ce !y w\ld read x are-n *ori/]s47 ,if y1 de> ,read]1 decl>e1 aft] full consid]ation ( ^! ,pairs ( ,premisses1 t y _c d$uce a ,conclusion f any ( !m----:y1 all ,i c say is t1 l ! ,duke 9 ,pati5ce1 y w h to be cont5t$ ) our he>t-felt sympa?y6 ,see ,note 7,c71 p4 #aif4 #e4 ,eul]'s ,me?od ( ,diagrams4 ,diagrams seem to h be5 us$1 at fir/1 to repres5t ,propositions only4 ,9 ,eul]'s well-kn[n ,circles1 ea* 0 suppos$ to conta9 a class1 & ! ,diagram consi/$ ( two circles1 :i* exhibit$ ! relations1 z to inclusion & exclusion1 exi/+ betwe5 ! two ,classes4 _/ _/ _/ y _/ x _/ _/ ,?us1 ! ,diagram1 "h giv51 exhibits ! two ,classes1 ^: respective ,attributes are x & y1 z s relat$ to ea* o!r t ! foll[+ ,propositions are all simultane\sly true3--,all x are y1 ,no x are n-y1 ,"s x are y1 ,"s y are n-x1 ,"s n-y are n-x1 &1 ( c\rse1 ! ,conv]ses ( ! la/ f\r4 pg#agd _/ _/ _/ y _/ x _/ _/ ,simil>ly1 ) ?is ,diagram1 ! foll[+ ,propositions are true3--,all y are x1 ,no y are n-x1 ,"s y are x1 ,"s x are n-y1 ,"s n-x are n-y1 &1 ( c\rse1 ! ,conv]ses ( ! la/ f\r4 _/ _/ _/ _/ x y _/ _/ _/ _/ ,simil>ly1 ) ?is ,diagram1 ! foll[+ are true3--,all x are n-y1 ,all y are n-x1 ,no x are y1 ,"s x are n-y1 ,"s y are n-x1 ,"s n-x are n-y1 & ! ,conv]ses ( ! la/ f\r4 _/ _/ _/ _/ x y _/ _/ _/ _/ ,simil>ly1 ) ?is ,diagram1 ! foll[+ are true3--,"s x are y1 ,"s x are n-y1 ,"s n-x are y1 ,"s n-x are n-y1 & ( c\rse1 _! f\r ,conv]ses4 ,note t all ,eul]'s ,diagrams ass]t ,"s n-x are n-y4 ,app>5tly x nev] occur$ to him t x might sometimes fail to be true6 ,n[1 to repres5t ,all x are y1 ! fir/ ( ^! ,diagrams w\ld suffice4 ,simil>ly1 to repres5t ,no x are y1 ! ?ird w\ld suffice4 ,b to repres5t any ,p>ticul> ,proposition1 at lea/ ?ree ,diagrams w\ld be ne$$ 79 ord] to include all ! possible cases71 &1 = ,"s n-x are n-y1 all ! f\r4 #f4 ,v5n's ,me?od ( ,diagrams4 ,let u repres5t n-x by x'4 ,mr4 ,v5n's ,me?od ( ,diagrams is a great advance on ! above ,me?od4 ,he uses ! la/ ( ! above ,diagrams to repres5t any desir$ relation betwe5 x & y1 by simply %ad+ a ,comp>tm5t kn[n to be empty1 & plac+ a 9 "o kn[n to be occupi$4 ,?us1 he w\ld repres5t ! ?ree ,propositions ,"s x are y1 ,no x are y1 & ,all x are y1 z foll[s3-- _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/ _/_/ _/ _/ _/ _/ pg#age ,x w be se5 t1 ( ! f\r ,classes1 ^: peculi> ,sets ( ,attributes are xy1 xy'1 x'y1 & x'y'1 only ?ree are "h provid$ ) clos$ ,comp>tm5ts1 :ile ! f\r? is all[$ ! re/ ( ! ,inf9ite ,plane to range ab\t 96 ,?is arrangem5t w\ld involve u 9 v s]i\s tr\ble1 if we ev] attempt$ to repres5t ,no x' are y'4 ,mr4 ,v5n once 7at p4 #bha7 enc\nt]s ?is awful task2 b evades x1 9 a q ma/]ly fa%ion1 by ! simple foot-note ,we h n tr\bl$ to %ade ! outside ( ?is diagram6 ,to repres5t two ,propositions 7conta9+ a common ,t]m7 toge!r1 a ?ree-lett] ,diagram is ne$$4 ,?is is ! "o us$ by ,mr4 ,v5n4 _/ _/ x _/ _/ _/ _/ _/ _/ m _/ y _/ _/ _/ ,"h1 aga91 we h only sev5 clos$ ,comp>tm5ts1 to accommodate ! eight ,classes ^: peculi> ,sets ( ,attributes are xym1 xym'1 c4 ,) f\r t]ms 9 reque/1 ,mr4 ,v5n says1 ! mo/ simple & symmetrical diagram seems to me t produc$ by mak+ f\r ellipses int]sect "o ano!r 9 ! desir$ mann]4 ,?is1 h[ev]1 provides only fifte5 clos$ comp>tm5ts4 b c _/ _/ a _/ _/ d _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/ _/ _/_/_/ _/ _/_/ ,= five lett]s1 ! simple/ diagram ,i c sugge/1 ,mr4 ,v5n says1 is "o l ?is 7! small ellipse 9 ! c5tre is to be reg>d$ z a portion ( ! outside ( c2 i4e4 its f\r compon5t portions are inside b & d b are no "p ( c74 ,x mu/ be admitt$ t su* a diagram is n q s simple to draw z "o might wi% x to be2 b !n consid] :at ! alt]native is ( "o und]takes to deal ) five t]ms & all _! comb9ations--no?+ %ort ( ! disagreeable task ( writ+ out1 or 9 "s way putt+ be=e u1 all ! #cb comb9ations involv$4 b c d _/ _/ _/ a _/ _/ _/ _/ _/ e _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/_/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/ _/_/_/_/ _/ _/ _/ _/ _/ pg#agf ,?is ,diagram gives u #ca clos$ comp>tm5ts4 ,= six lett]s1 ,mr4 ,v5n sugge/s t we might use two ,diagrams1 l ! above1 "o = ! f-"p1 & ! o!r = ! n-f-"p1 ( all ! o!r comb9ations4 ,?is1 he says1 w\ld give ! desir$ #fd subdivisions4 ,?is1 h[ev]1 w\ld only give #fb clos$ ,comp>tm5ts1 & "o inf9ite area1 :i* ! two ,classes1 a'b'c'd'e'f & a'b'c'd'e'f'1 w\ld h to %>e betwe5 !m4 ,beyond six lett]s ,mr4 ,v5n does n g4 #g4 ,my ,me?od ( ,diagrams4 ,my ,me?od ( ,diagrams resembles ,mr4 ,v5n's1 9 hav+ sep>ate ,comp>tm5ts assign$ to ! v>i\s ,classes1 & 9 m>k+ ^! ,comp>tm5ts z occupi$ or z empty2 b x diff]s f 8 ,me?od1 9 assign+ a clos$ area to ! ,univ]se ( ,disc\rse1 s t ! ,class :i*1 "u ,mr4 ,v5n's lib]al sway1 has be5 rang+ at w ?r\gh ,inf9ite ,space1 is sudd5ly dismay$ to f9d itself cab9'd1 cribb'd1 conf9$1 9 a limit$ ,cell l any o!r ,class6 ,also ,i use rectil9e>1 in/ead ( curvil9e>1 ,figures2 & ,i m>k an occupi$ ,cell ) a ',i' 7mean+ t !re is at lea/ "o ,?+ 9 x71 & an empty ,cell ) a ',o' 7mean+ t !re is no ,?+ 9 x74 ,= two lett]s1 ,i use ?is ,diagram1 9 :i* ! ,nor? ,half is assign$ to 'x'1 ! ,s\? to 'n-x' 7or 'x''71 ! ,we/ to y1 & ! ,ea/ to y'4 ,?us ! ,n4,w4 ,cell conta9s ! xy-,class1 ! ,n4,e4 ,cell ! xy'-,class1 & s on4 ------- ------ ------- ,= ?ree lett]s1 ,i subdivide ^! f\r ,cells1 by draw+ an ,inn] ,squ>e1 :i* ,i assign to m1 ! ,out] ,bord] be+ assign$ to m'4 ,i ?us get eight ,cells t are ne$$ to accommodate ! eight ,classes1 ^: peculi> ,sets ( ,attributes are xym1 xym'1 c4 --------------- ------ ------------ ------ --------------- ,?is la/ ,diagram is ! mo/ complex t ,i use 9 ! ,elem5t>y ,"p ( my ',symbolic ,logic4' ,b ,i may z well take ?is opportunity ( describ+ ! m complex ones :i* w appe> 9 ,"p ,,ii4 pg#agg ,= f\r lett]s 7:i* ,i call a1 b1 c1 d7 ,i use ?is ,diagram2 assign+ ! ,nor? ,half to a 7& ( c\rse ! re/ ( ! ,diagram to a'71 ! ,we/ ,half to b1 ! ,horizontal ,oblong to c1 & ! ,upright ,oblong to d4 ,we h n[ got #af ,cells4 --------------------- ------ ------------ ---------------- ------------ ------ --------------------- ,= five lett]s 7add+ e7 ,i subdivide ! #af ,cells ( ! previ\s ,diagram by oblique p>titions1 assign+ all ! upp] portions to e1 & all ! l[] portions to e'4 ,"h1 ,i admit1 we lose ! advantage ( hav+ ! e-,class all toge!r1 9 a r+-f5ce1 l ! o!r #d ,classes4 ,/ill1 x is v easy to f9d2 & ! op]ation1 ( eras+ x1 is ne>ly z easy z t ( eras+ any o!r ,class4 ,we h n[ got #cb ,cells4 --------------------- _/ _/ _/ ------ _/ _/ _/ _/ _/ ------------ _/ _/ _/ _/ ---------------- _/ _/ _/ _/ ------------ _/ _/ _/ _/ _/ ------ _/ _/ _/ --------------------- ,= six lett]s 7add+ h1 z ,i avoid tail$ lett]s7 ,i sub/itute upright crosses = ! oblique p>titions1 assign+ ! #d portions1 into :i* ea* ( ! #af ,cells is ?us divid$1 to ! f\r ,classes eh1 eh'1 e'h1 e'h'4 ,we h n[ got #fd ,cells4 ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h-------,h----,h----,h-------,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----,h----,h----,h----,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h,h,h,h--,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----,h----,h----,h----,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h-------,h----,h----,h-------,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h pg#agh ,= sev5 lett]s 7add+ k7 ,i add1 to ea* upright cross1 a little inn] squ>e4 ,all ^! #af little squ>es are assign$ to ! k-,class1 & all outside !m to ! k'-,class2 s t #h little ,cells 7into :i* ea* ( ! #af ,cells is divid$7 are respectively assign$ to ! #h ,classes ehk1 ehk'1 c4 ,we h n[ got #abh ,cells4 ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h-----------,h--------,h--------,h----- ------,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h--------,h--------,h--------,h-------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h,h,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h--------,h--------,h--------,h-------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h-----------,h--------,h--------,h----- ------,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,= eight lett]s 7add+ l7 ,i place1 9 ea* ( ! #af ,cells1 a lattice1 :i* is a r$uc$ copy ( ! :ole ,diagram2 &1 j z ! #af l>ge ,cells ( ! :ole ,diagram are assign$ to ! #af ,classes abcd1 abcd'1 c41 s ! #af little ,cells ( ea* lattice are assign$ to ! #af ,classes ehkl1 ehkl'1 c4 ,?us1 ! lattice 9 ! ,n4,w4 corn] s]ves to accommodate ! #af ,classes abc'd'ehkl1 abc'd'eh'kl'1 c4 ,?is ,octolit]al ,diagram 7see next page7 conta9s #bef ,cells4 ,= n9e lett]s1 ,i place #b ,octolit]al ,diagrams side by side1 assign+ "o ( !m to m1 & ! o!r to m'4 ,we h n[ got #eab ,cells4 pg#agi ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h-------------,h----------,h----------, h-------------,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----------,h----------,h----------,h-- --------,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h,h,h,h,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h----------,h----------,h----------,h-- --------,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h,h,h ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h-------------,h----------,h----------, h-------------,h ,h ,h ,h ,h ,h ,h -------- ,h -------- ,h -------- ,h -------- ,h ,h ,h ,h ,h ,h ,h ---- ,h ---- ,h ---- ,h ---- ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,h ,f9ally1 = t5 lett]s1 ,i arrange #d ,octolit]al ,diagrams1 l ! above1 9 a squ>e1 assign+ !m to ! #d ,classes mn1 mn'1 m'n1 m'n'4 ,we h n[ got #ajbd ,cells4 #h4 ,solution ( a ,syllogism by v>i\s ,me?ods4 ,! be/ way1 ,i ?9k1 to exhibit ! diff]5ces betwe5 ^! v>i\s ,me?ods ( solv+ ,syllogisms1 w be to take a concrete example1 & solve x by ea* ,me?od 9 turn4 ,let u take1 z our example1 ,no4 #bi 7see p4 #ajb74 ,no philosoph]s are conceit$2 ,"s conceit$ p]sons are n gambl]s4 4'4 ,"s p]sons1 :o are n gambl]s1 are n philosoph]s4 pg#ahj 7#a7 ,solution by ord9>y ,me?od4 ,^! ,premisses1 z !y /&1 w give no ,conclusion1 z !y are bo? negative4 ,if by ',p]mutation' or ',obv]sion'1 we write ! ,m9or ,premiss ?us1 ',"s conceit$ p]sons are n-gambl]s1' we c get a ,conclusion 9 ,fresison1 viz4 ,no philosoph]s are conceit$2 ,"s conceit$ p]sons are n-gambl]s4 4'4 ,"s n-gambl]s are n philosoph]s ,?is c be prov$ by r$uction to ,f]io1 ?us3-- ,no conceit$ p]sons are philosoph]s2 ,"s n-gambl]s are conceit$4 4'4 ,"s n-gambl]s are n philosoph]s4 ,! validity ( ,f]io foll[s directly f ! ,axiom ',de ,omni et ,nullo'4 7#b7 ,symbolic ,repres5tation4 ,be=e proce$+ to discuss o!r ,me?ods ( ,solution1 x is necess>y to translate our ,syllogism into an ab/ract =m4 ,let u take p]sons z our ',univ]se ( ,disc\rse'2 & let x philosoph]s1 m conceit$1 & y gambl]s4 ,!n ! ,syllogism may be writt5 ?us3-- ,no x are m2 ,"s m are y'4 4'4 ,"s y' are x'4 7#c7 ,solution by ,eul]'s ,me?od ( ,diagrams4 ,! ,major ,premiss requires only "o ,diagram1 viz4 #a _/ _/ _/ _/ x m _/ _/ _/ _/ pg#aha ,! ,m9or requires ?ree1 viz4 #b _/ _/ _/ _/ y m _/ _/ _/ _/ #c _/ _/ _/ _/ y m _/ _/ _/ _/ #d _/ _/ _/ y _/ m _/ _/ ,! comb9ation ( ,major & ,m9or1 9 e possible way requires n9e1 viz4 ,figs4 #a & #b give #e _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #f _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #g _/ _/ _/ _/ xy m _/ _/ _/ _/ #h _/ _/ _/ _/ x _/ _/ m y _/ _/ _/ _/ #i _/ _/ _/ _/ y _/ _/ m x _/ _/ _/ _/ ,figs4 #a & #c give #aj _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #aa _/ _/ _/ _/ _/ _/ x y m _/ _/ _/ _/ _/ _/ #ab _/ _/ _/ _/ x _/ _/ m y _/ _/ _/ _/ ,figs4 #a & #d give #ac _/ _/ _/ _/ _/ y x _/ _/ m _/ _/ _/ ,f ?is gr\p 7,figs4 #e to #ac7 we h1 by disreg>d+ m1 to f9d ! relation ( x & y4 ,on exam9ation we f9d t ,figs4 #e1 #aj1 #ac express ! relation ( entire mutual exclusion2 t ,figs4 #f1 #aa express p>tial inclusion & p>tial exclusion2 t ,fig4 #g expresses co9cid5ce2 t ,figs4 #h1 #ab express entire inclusion ( x 9 y2 & t ,fig4 #i expresses entire inclusion ( y 9 x4 pg#ahb ,we ?us get five ,bilit]al ,diagrams = x & y1 viz4 #ad _/ _/ _/ _/ x y _/ _/ _/ _/ #ae _/ _/ _/ _/ x y _/ _/ _/ _/ #af _/ _/ xy _/ _/ #ag _/ _/ _/ x _/ y _/ _/ #ah _/ _/ _/ y _/ x _/ _/ :]e ! only ,proposition1 repres5t$ by !m all1 is ,"s n-y are n-x1 i4e4 ,"s p]sons1 :o are n gambl]s1 are n philosoph]s----a result :i* ,eul] w\ld h>dly h reg>d$ z a valuable "o1 s9ce he seems to h assum$ t a ,proposition ( ?is =m is always true6 7#d7 ,solution by ,v5n's ,me?od ( ,diagrams4 ,! foll[+ ,solution has be5 k9dly suppli$ to me ,mr4 ,v5n himself4 ,! ,m9or ,premiss decl>es t "s ( ! con/itu5ts 9 my' mu/ be sav$3 m>k ^! con/itu5ts ) a cross4 _/ _/ _/_/ _/ _/ _/ _/ m _/ y _/ _/ _/ ,! ,major decl>es t all xm mu/ be de/roy$2 erase x4 ,!n1 z "s my' is to be sav$1 x mu/ cle>ly be my'x'4 ,t is1 !re mu/ exi/ my'x'2 or elim9at+ m1 y'x'4 ,9 common phraseology1 ',"s y' are x'1' or1 ',"s n-gambl]s are n-philosoph]s4' pg#ahc 7#e7 ,solution by my ,me?od ( ,diagrams4 ,! fir/ ,premiss ass]ts t no xm exi/3 s we m>k ! xm-,comp>tm5t z empty1 by plac+ a ',o' 9 ea* ( its ,cells4 ,! second ass]ts t "s my' exi/3 s we m>k ! my'-,comp>tm5t z occupi$1 by plac+ a ',i' 9 its only available ,cell4 --------------- ------ 7,o77,o7 ------------ 7,i7 ------ --------------- ,! only in=mation1 t ?is gives u z to x & y1 is t ! x'y'-,comp>tm5t is occupi$1 i4e4 t "s x'y' exi/4 ,h5ce ,"s x' are y'3 i4e4 ,"s p]sons1 :o are n philosoph]s1 are n gambl]s4 7#f7 ,solution by my ,me?od ( ,subscripts4 xm#j my'#a x'y'#a i4e4 ,"s p]sons1 :o are n philosoph]s1 are n gambl]s4 #i4 ,my ,me?od ( treat+ ,syllogisms & ,sorites4 ,( all ! /range ?+s1 t are to be met ) 9 ! ord9>y text-books ( ,=mal ,logic1 p]haps ! /range/ is ! viol5t contra/ "o f9ds to exi/ betwe5 _! ways ( deal+ ) ^! two subjects4 ,:ile !y h elaborately discuss$ no less ?an n9ete5 diff]5t =ms ( ,syllogisms----ea* ) its own special & exasp]at+ ,rules1 :ile ! :ole con/itute an almo/ useless ma*9e1 = practical purposes1 _m ( ! ,conclusions be+ incomplete1 & _m q legitimate =ms be+ ignor$----!y h limit$ ,sorites to two =ms only1 ( *ildi% simplicity2 & ^! !y h dignifi$ ) special names1 app>5tly "u ! impression t no o!r possible =ms exi/$6 ,z to ,syllogisms1 ,i f9d t _! n9ete5 =ms1 ) ab\t a score ( o!rs :i* !y h ignor$1 c all be arrang$ "u ?ree =ms1 ea* ) a v simple ,rule ( its own2 & ! only "q ! ,read] has to settle1 9 work+ any "o ( ! #aja ,examples giv5 at p4 #aja ( ?is book1 is ,does x belong to ,fig4 ,i41 ,,ii41 or ,,iii48 pg#ahd ,z to ,sorites1 ! only two =ms1 recognis$ by ! text-books1 are ! ,ari/otelian1 ^: ,premisses are a s]ies ( ,propositions 9 ,a1 s arrang$ t ! ,pr$icate ( ea* is ! ,subject ( ! next1 & ! ,gocl5ian1 ^: ,premisses are ! v same s]ies1 writt5 backw>ds4 ,gocl5ius1 x seems1 0 ! fir/ :o notic$ ! />tl+ fact t x does n affect ! =ce ( a ,syllogism to inv]t ! ord] ( its ,premisses1 & :o appli$ ?is discov]y to a ,sorites4 ,if we assume 7z surely we may87 t he is ! same man z t transc5d5t g5ius :o fir/ notic$ t #d times #e is ! same ?+ z #e times #d1 we may apply to him :at somebody 7,edmund ,yates1 ,i ?9k x 07 has said ( ,tupp]1 viz41 "h is a man :o1 beyond all o!rs ( 8 g5]ation1 has be5 fav\r$ ) ,glimpses ( ! ,obvi\s6 ,^! pu]ile----n to say infant9e----=ms ( a ,sorites ,i h1 9 ?is book1 ignor$ f ! v fir/1 & h n only admitt$ freely ,propositions 9 ,e1 b h purposely /at$ ! ,premisses 9 r&om ord]1 leav+ to ! ,read] ! useful task ( arrang+ !m1 = himself1 9 an ord] :i* c be work$ z a s]ies ( regul> ,syllogisms4 ,9 do+ ?is1 he c beg9 ) any "o ( !m he likes4 ,i h tabulat$1 = curiosity1 ! v>i\s ord]s 9 :i* ! ,premisses ( ! ,ari/otelian ,sorites #a4 ,all a are b2 #b4 ,all b are c2 #c4 ,all c are d2 #d4 ,all d are e2 #e4 ,all e are h4 4'4 ,all a are h4 may be syllogi/ically arrang$1 & ,i f9d !re are no less ?an sixte5 su* ord]s1 viz41 #abcde1 #bacde1 #bcade1 #bcdae1 #bcdea1 #cbade1 #cbdae1 #cbdea1 #cdbae1 #cdbea1 #cdeba1 #dcbae1 #dcbea1 #dceba1 #decba1 #edcba4 ,( ^! ! fir/ & ! la/ h be5 dignifi$ ) names2 b ! o!r f\rte5----fir/ enum]at$ by an obscure ,writ] on ,logic1 t[>ds ! end ( ! ,n9ete5? ,c5tury----rema9 )\t a "n6 pg#ahe #aj4 ,"s acc\nt ( ,p>ts ,,ii1 ,,iii4 ,9 ,"p ,,ii4 w be f\nd "s ( ! matt]s m5tion$ 9 ?is ,app5dix1 viz41 ! ,exi/5tial ,import ( ,propositions1 ! use ( a negative ,copula1 & ! !ory t two negative ,premisses prove no?+4 ,i %all also ext5d ! range ( ,syllogisms1 by introduc+ ,propositions conta9+ alt]natives 7su* z ,n-all x are y71 ,propositions conta9+ #c or m ,t]ms 7su* z ,all ab are c1 :i*1 tak5 along ) ,"s bc' are d1 w\ld prove ,"s d are a'71 c4 ,i %all also discuss ,sorites conta9+ ,entities1 & ! v puzzl+ subjects ( ,hypo!ticals & ,dilemmas4 ,i hope1 9 ! c\rse ( ,"p ,,ii41 to g ov] all ! gr\nd usually trav]s$ 9 ! text-books us$ 9 our ,s*ools & ,univ]sities1 & to enable my ,read]s to solve ,problems ( ! same k9d z1 & f> h>d] ?an1 ^? t are at pres5t set 9 _! ,exam9ations4 ,9 ,"p ,,iii4 ,i hope to deal ) _m curi\s & out-(-!-way subjects1 "s ( :i* are n ev5 allud$ to 9 any ( ! treatises ,i h met )4 ,9 ?is ,"p w be f\nd su* matt]s z ! ,analysis ( ,propositions into _! ,elem5ts 7let ! ,read]1 :o has nev] gone into ?is bran* ( ! subject1 try to make out = himself :at additional ,proposition w\ld be ne$$ to conv]t ,"s a are b into ,"s a are bc71 ! treatm5t ( ,num]ical & ,geometrical ,problems1 ! con/ruction ( ,problems1 & ! solution ( ,syllogisms & ,sorites conta9+ ,propositions m complex ?an any t ,i h us$ 9 ,"p ,,ii4 ,i w conclude ) eight ,problems1 z a ta/e ( :at is com+ 9 ,"p ,,ii4 ,i %all be v glad to receive1 f any ,read]1 :o ?9ks he has solv$ any "o ( !m 7m especially if he has done s )\t us+ any ,me?od ( ,symbols71 :at he conceives to be its complete ,conclusion4 ,x may be well to expla9 :at ,i mean by ! complete ,conclusion ( a ,syllogism or a ,sorites4 ,i di/+ui% _! ,t]ms z be+ ( two k9ds----^? :i* c be elim9at$ 7e4g4 ! ,middle ,t]m ( a ,syllogism71 :i* ,i call ! ,elim9&s1 & ^? :i* _c1 :i* ,i call ! ,ret95ds2 & ,i d n call ! ,conclusion complete1 unless x /ates all ! relations among ! ,ret95ds only1 :i* c be d$uc$ f ! ,premisses4 pg#ahf #a4 ,all ! boys1 9 a c]ta9 ,s*ool1 sit toge!r 9 "o l>ge room e ev5+4 ,!y are ( no less ?an five nationalities----,engli%1 ,scot*1 ,wel%1 ,iri%1 & ,g]man4 ,"o ( ! ,monitors 7:o is a great read] ( ,wilkie ,coll9s' novels7 is v obs]vant1 & takes ,,ms4 notes ( almo/ ev]y?+ t happ5s1 ) ! view ( be+ a good s5sational witness1 9 case any conspiracy to commit a murd] %\ld be on foot4 ,! foll[+ are "s ( 8 notes3-- 7#a7 ,:5ev] "s ( ! ,engli% boys are s++ ,rule ,britannia1 & "s n1 "s ( ! ,monitors are wide-awake2 7#b7 ,:5ev] "s ( ! ,scot* are danc+ reels1 & "s ( ! ,iri% fight+1 "s ( ! ,wel% are eat+ toa/$ *eese2 7#c7 ,:5ev] all ! ,g]mans are play+ *ess1 "s ( ! ,elev5 are n oil+ _! bats2 7#d7 ,:5ev] "s ( ! ,monitors are asleep1 & "s n1 "s ( ! ,iri% are fight+2 7#e7 ,:5ev] "s ( ! ,g]mans are play+ *ess1 & none ( ! ,scot* are danc+ reels1 "s ( ! ,wel% are n eat+ toa/$ *eese2 7#f7 ,:5ev] "s ( ! ,scot* are n danc+ reels1 & "s ( ! ,iri% n fight+1 "s ( ! ,g]mans are play+ *ess2 7#g7 ,:5ev] "s ( ! ,monitors are awake1 & "s ( ! ,wel% are eat+ toa/$ *eese1 none ( ! ,scot* are danc+ reels2 7#h7 ,:5ev] "s ( ! ,g]mans are n play+ *ess1 & "s ( ! ,wel% are n eat+ toa/$ *eese1 none ( ! ,iri% are fight+2 pg#ahg 7#i7 ,:5ev] all ! ,engli% are s++ ,rule ,britannia1 & "s ( ! ,scot* are n danc+ reels1 none ( ! ,g]mans are play+ *ess2 7#aj7 ,:5ev] "s ( ! ,engli% are s++ ,rule ,britannia1 & "s ( ! ,monitors are asleep1 "s ( ! ,iri% are n fight+2 7#aa7 ,:5ev] "s ( ! ,monitors are awake1 & "s ( ! ,elev5 are n oil+ _! bats1 "s ( ! ,scot* are danc+ reels2 7#ab7 ,:5ev] "s ( ! ,engli% are s++ ,rule ,britannia1 & "s ( ! ,scot* are n danc+ reels1 99 99 99 99 ,"h ! ,,ms4 breaks (f sudd5ly4 ,! ,problem is to complete ! s5t5ce1 if possible4 ,n4,b4 ,9 solv+ ?is ,problem1 x is necess>y to rememb] t ! ,proposition ,all x are y is a ,d\ble ,proposition1 & is equival5t to ,"s x are y1 & none are y'4 ,see p4 #ag4 #b4 7#a7 ,a logician1 :o eats pork-*ops = supp]1 w probably lose money2 7#b7 ,a gambl]1 ^: appetite is n rav5\s1 w probably lose money2 7#c7 ,a man :o is depress$1 hav+ lo/ money & be+ likely to lose m1 always rises at #e a4m42 7#d7 ,a man1 :o nei!r gambles nor eats pork-*ops = supp]1 is sure to h a rav5\s appetite2 7#e7 ,a lively man1 :o goes to b$ be=e #d a4m41 _h bett] take to cab-driv+2 7#f7 ,a man ) a rav5\s appetite1 :o has n lo/ money & does n rise at #e a4m41 always eats pork-*ops = supp]2 7#g7 ,a logician1 :o is 9 dang] ( los+ money1 _h bett] take to cab-driv+2 7#h7 ,an e>ne/ gambl]1 :o is depress$ ?\gh he has n lo/ money1 is 9 no dang] ( los+ any2 7#i7 ,a man1 :o does n gamble1 & ^: appetite is n rav5\s1 is always lively2 pg#ahh 7#aj7 ,a lively logician1 :o is really 9 e>ne/1 is 9 no dang] ( los+ money2 7#aa7 ,a man ) a rav5\s appetite has no ne$ to take to cab-driv+1 if he is really 9 e>ne/2 7#ab7 ,a gambl]1 :o is depress$ ?\gh 9 no dang] ( los+ money1 sits up till #d a4m4 7#ac7 ,a man1 :o has lo/ money & does n eat pork-*ops = supp]1 _h bett] take to cab-driv+1 unless he gets up at #e a4m4 7#ad7 ,a gambl]1 :o goes to b$ be=e #d a4m41 ne$ n take to cab-driv+1 unless he has a rav5\s appetite2 7#ae7 ,a man ) a rav5\s appetite1 :o is depress$ ?\gh 9 no dang] ( los+1 is a gambl]4 ,univ4 m52 a e>ne/2 b eat+ pork-*ops = supp]2 c gambl]s2 d gett+ up at #e2 e hav+ lo/ money2 h hav+ a rav5\s appetite2 k likely to lose money2 l lively2 m logicians2 n m5 :o _h bett] take to cab-driv+2 r sitt+ up till #d4 ,n4,b4 ,9 ?is ,problem1 clauses1 beg9n+ ) ?\gh1 are int5d$ to be treat$ z ess5tial p>ts ( ! ,propositions 9 :i* !y occur1 j z if !y _h begun ) &4 #c4 7#a7 ,:5 ! day is f9e1 ,i tell ,froggy ,y're q ! d&y1 old *ap62 7#b7 ,:5ev] ,i let ,froggy =get t #aj he owes me1 & he beg9s to /rut ab\t l a peacock1 8 "m decl>es ,he %all n g out a-woo+62 7#c7 ,n[ t ,froggy's hair is out ( curl1 he has put away 8 gorge\s wai/coat2 7#d7 ,:5ev] ,i g out on ! ro( to enjoy a quiet cig>1 ,i'm sure to discov] t my purse is empty2 7#e7 ,:5 my tailor calls ) 8 little bill1 & ,i rem9d ,froggy ( t #aj he owes me1 he does n gr9 l a hyna2 pg#ahi 7#f7 ,:5 x is v hot1 ! !rmomet] is high2 7#g7 ,:5 ! day is f9e1 & ,i'm n 9 ! hum\r = a cig>1 & ,froggy is gr9n+ l a hyna1 ,i nev] v5ture to h9t t he's q ! d&y2 7#h7 ,:5 my tailor calls ) 8 little bill & f9ds me ) an empty purse1 ,i rem9d ,froggy ( t #aj he owes me2 7#i7 ,my railway-%>es are go+ up l any?+6 7#aj7 ,:5 my purse is empty1 & :51 notic+ t ,froggy has got 8 gorge\s wai/coat on1 ,i v5ture to rem9d him ( t #aj he owes me1 ?+s are apt to get r w>m2 7#aa7 ,n[ t x looks l ra91 & ,froggy is gr9n+ l a hyna1 ,i c d )\t my cig>2 7#ab7 ,:5 ! !rmomet] is high1 y ne$ n tr\ble y\rself to take an umbrella2 7#ac7 ,:5 ,froggy has 8 gorge\s wai/coat on1 b is n /rutt+ ab\t l a peacock1 ,i betake myself to a quiet cig>2 7#ad7 ,:5 ,i tell ,froggy t he's q ! d&y1 he gr9s l a hyna2 7#ae7 ,:5 my purse is tol]ably full1 & ,froggy's hair is "o mass ( curls1 & :5 he is n /rutt+ ab\t l a peacock1 ,i g out on ! ro(2 7#af7 ,:5 my railway-%>es are go+ up1 & :5 x is *illy & looks l ra91 ,i h a quiet cig>2 7#ag7 ,:5 ,froggy's "m lets him g a-woo+1 he seems ne>ly mad ) joy1 & puts on a wai/coat t is gorge\s beyond words2 7#ah7 ,:5 x is go+ to ra91 & ,i am hav+ a quiet cig>1 & ,froggy is n int5d+ to g a-woo+1 y _h bett] take an umbrella2 7#ai7 ,:5 my railway-%>es are go+ up1 & ,froggy seems ne>ly mad ) joy1 t is ! "t my tailor always *ooses = call+ ) 8 little bill2 7#bj7 ,:5 ! day is cool & ! !rmomet] l[1 & ,i say no?+ to ,froggy ab\t 8 be+ q ! d&y1 & !re's n ! gho/ ( a gr9 on 8 face1 ,i hav5't ! he>t = my cig>6 pg#aij #d4 7#a7 ,any "o1 fit to be an ,m4,p41 :o is n always speak+1 is a public b5efactor2 7#b7 ,cle>-head$ p1 :o express !mselves well1 h _h a good education2 7#c7 ,a woman1 :o des]ves praise1 is "o :o c keep a secret2 7#d7 ,p1 :o b5efit ! public1 b d n use _! influ5ce = good purpose1 are n fit to g into ,p>liam5t2 7#e7 ,p1 :o are wor? _! weight 9 gold & :o des]ve praise1 are always unassum+2 7#f7 ,public b5efactors1 :o use _! influ5ce = good objects1 des]ve praise2 7#g7 ,p1 :o are unpopul> & n wor? _! weight 9 gold1 nev] c keep a secret2 7#h7 ,p1 :o c talk = ev] & are fit to be ,memb]s ( ,p>liam5t1 des]ve praise2 7#i7 ,any "o1 :o c keep a secret & :o is unassum+1 is a nev]-to-be-=gott5 public b5efactor2 7#aj7 ,a woman1 :o b5efits ! public1 is always popul>2 7#aa7 ,p1 :o are wor? _! weight 9 gold1 :o nev] leave (f talk+1 & :om x is impossible to =get1 are j ! p ^: photographs are 9 all ! %op-w9d[s2 7#ab7 ,an ill-educat$ woman1 :o is n cle>-head$1 is n fit to g into ,p>liam5t2 7#ac7 ,any "o1 :o c keep a secret & is n = ev] talk+1 is sure to be unpopul>2 7#ad7 ,a cle>-head$ p]son1 :o has influ5ce & uses x = good objects1 is a public b5efactor2 7#ae7 ,a public b5efactor1 :o is unassum+1 is n ! sort ( p]son ^: photograph is 9 e %op-w9d[2 7#af7 ,p1 :o c keep a secret & :o use _! influ5ce = good purposes1 are wor? _! weight 9 gold2 7#ag7 ,a p]son1 :o has no p[] ( expression & :o _c influ5ce o!rs1 is c]ta9ly n a woman2 pg#aia 7#ah7 ,p1 :o are popul> & wor?y ( praise1 ei!r are public b5efactors or else are unassum+4 ,univ4 p]sons2 a able to keep a secret2 b cle>-head$2 c con/antly talk+2 d des]v+ praise2 e exhibit$ 9 %op-w9d[s2 h express+ oneself well2 k fit to be an ,m4,p42 l influ5tial2 m nev]-to-be-=gott52 n popul>2 r public b5efactors2 s unassum+2 t us+ "o's influ5ce = good objects2 v well-educat$2 w wom52 z wor? "o's weight 9 gold4 #e4 ,six fri5ds1 & _! six wives1 are /ay+ 9 ! same hotel2 & !y all walk out daily1 9 p>ties ( v>i\s size & composition4 ,to ensure v>iety 9 ^! daily walks1 !y h agree to obs]ve ! foll[+ ,rules3-- 7#a7 ,if ,acres is ) 7i4e4 is 9 ! same p>ty )7 8 wife1 & ,b>ry ) 81 & ,ed5 ) ,mrs4 ,hall1 ,cole mu/ be ) ,mrs4 ,dix2 7#b7 ,if ,acres is ) 8 wife1 & ,hall ) 81 & ,b>ry ) ,mrs4 ,cole1 ,dix mu/ n be ) ,mrs4 ,ed52 7#c7 ,if ,cole & ,dix & _! wives are all 9 ! same p>ty1 & ,acres n ) ,mrs4 ,b>ry1 ,ed5 mu/ n be ) ,mrs4 ,hall2 7#d7 ,if ,acres is ) 8 wife1 & ,dix ) 81 & ,b>ry n ) ,mrs4 ,cole1 ,ed5 mu/ be ) ,mrs4 ,hall2 7#e7 ,if ,ed5 is ) 8 wife1 & ,hall ) 81 & ,cole ) ,mrs4 ,dix1 ,acres mu/ n be ) ,mrs4 ,b>ry2 7#f7 ,if ,b>ry & ,cole & _! wives are all 9 ! same p>ty1 & ,ed5 n ) ,mrs4 ,hall1 ,dix mu/ be ) ,mrs4 ,ed54 ,! ,problem is to prove t !re mu/ be1 e day1 at lea/ "o m>ri$ c\ple :o are n 9 ! same p>ty4 pg#aib #f4 ,aft] ! six fri5ds1 nam$ 9 ,problem #e1 _h return$ f _! t\r1 ?ree ( !m1 ,b>ry1 ,cole1 & ,dix1 agre$1 ) two o!r fri5ds ( !irs1 ,lang & ,mill1 t ! five %\ld meet1 e day1 at a c]ta9 table d'hte4 ,rememb]+ h[ mu* amusem5t !y _h d]iv$ f _! code ( rules = walk+-p>ties1 !y devis$ ! foll[+ rules to be obs]v$ :5ev] beef appe>$ on ! table3-- 7#a7 ,if ,b>ry takes salt1 !n ei!r ,cole or ,lang takes "o only ( ! two condim5ts1 salt & mu/>d3 if he takes mu/>d1 !n ei!r ,dix takes nei!r condim5t1 or ,mill takes bo?4 7#b7 ,if ,cole takes salt1 !n ei!r ,b>ry takes only "o condim5t1 or ,mill takes nei!r3 if he takes mu/>d1 !n ei!r ,dix or ,lang takes bo?4 7#c7 ,if ,dix takes salt1 !n ei!r ,b>ry takes nei!r condim5t or ,cole take bo?3 if he takes mu/>d1 !n ei!r ,lang or ,mill takes nei!r4 7#d7 ,if ,lang takes salt1 !n ,b>ry or ,dix takes only "o condim5t3 if he takes mu/>d1 !n ei!r ,cole or ,mill takes nei!r4 7#e7 ,if ,mill takes salt1 !n ei!r ,b>ry or ,lang takes bo? condim5ts3 if he takes mu/>d1 !n ei!r ,cole or ,dix takes only "o4 ,! ,problem is to discov] :e!r ^! rules are compatible2 &1 if s1 :at arrangem5ts are possible4 ,n4,b4 ,9 ?is ,problem1 x is assum$ t ! phrase if ,b>ry takes salt all[s ( two possible cases1 viz4 7#a7 he takes salt only2 7#b7 he takes bo? condim5ts4 ,& s ) all simil> phrases4 ,x is also assum$ t ! phrase ei!r ,cole or ,lang takes "o only ( ! two condim5ts all[s ?ree possible cases1 viz4 7#a7 ,cole takes "o only1 ,lang takes bo? or nei!r2 7#b7 ,cole takes bo? or nei!r1 ,lang takes "o only2 7#c7 ,cole takes "o only1 ,lang takes "o only4 ,& s ) all simil> phrases4 ,x is also assum$ t e rule is to be und]/ood z imply+ ! words & vice v]s4 ,?us ! fir/ rule w\ld imply ! addition &1 if ei!r ,cole or ,lang takes only "o condim5t1 !n ,b>ry takes salt4 pg#aic #g4 7#a7 ,bro!rs1 :o are mu* admir$1 are apt to be self-consci\s2 7#b7 ,:5 two m5 ( ! same height are on opposite sides 9 ,politics1 if "o ( !m has 8 admir]s1 s also has ! o!r2 7#c7 ,bro!rs1 :o avoid g5]al ,society1 look well :5 walk+ toge!r2 7#d7 ,:5ev] y f9d two m51 :o diff] 9 ,politics & 9 _! views ( ,society1 & :o are n bo? ( !m ugly1 y may be sure t !y look well :5 walk+ toge!r2 7#e7 ,ugly m51 :o look well :5 walk+ toge!r1 are n bo? ( !m free f self-consci\sness2 7#f7 ,bro!rs1 :o diff]s 9 ,politics1 & are n bo? ( !m h&some1 nev] give !mselves airs2 7#g7 ,john decl9es to g into ,society1 b nev] gives himself airs2 7#h7 ,bro!rs1 :o are apt to be self-consci\s1 ?\gh n bo? ( !m h&some1 usually dislike ,society2 7#i7 ,m5 ( ! same height1 :o d n give !mselves airs1 are free f self-consci\sness2 7#aj7 ,m51 :o agree on que/ions ( ,art1 ?\gh !y diff] 9 ,politics1 & :o are n bo? ( !m ugly1 are always admir$2 7#aa7 ,m51 :o hold opposite views ab\t ,art & are n admir$1 always give !mselves airs2 7#ab7 ,bro!rs ( ! same height always diff] 9 ,politics2 7#ac7 ,two h&some m51 :o are nei!r bo? ( !m admir$ nor bo? ( !m self-consci\s1 are no d\bt ( diff]5t heights2 7#ad7 ,bro!rs1 :o are self-consci\s1 & d n bo? ( !m l ,society1 nev] look well :5 walk+ toge!r4 ,n4,b4 ,see ,note at end ( ,problem #b4 pg#aid #h4 7#a7 ,a man c always ma/] 8 fa!r2 7#b7 ,an inf]ior ( a man's uncle owes t man money2 7#c7 ,! fa!r ( an enemy ( a fri5d ( a man owes t man no?+2 7#d7 ,a man is always p]secut$ by 8 son's cr$itors2 7#e7 ,an inf]ior ( ! ma/] ( a man's son is s5ior to t man2 7#f7 ,a gr&son ( a man's junior is n 8 nephew2 7#g7 ,a s]vant ( an inf]ior ( a fri5d ( a man's enemy is nev] p]secut$ by t man2 7#h7 ,a fri5d ( a sup]ior ( ! ma/] ( a man's victim is t man's enemy2 7#i7 ,an enemy ( a p]secutor ( a s]vant ( a man's fa!r is t man's fri5d4 ,! ,problem is to d$uce "s fact ab\t great-gr&sons4 ,n4,b4 ,9 ?is ,problem1 x is assum$ t all ! m51 "h ref]r$ to1 live 9 ! same t[n1 & t e pair ( !m are ei!r fri5ds or enemies1 t e pair are relat$ z s5ior & junior1 sup]ior & inf]ior1 & t c]ta9 pairs are relat$ z cr$itor & debtor1 fa!r & son1 ma/] & s]vant1 p]secutor & victim1 uncle & nephew4 #i4 ,jack ,sprat c\ld eat no fat3 ,8 wife c\ld eat no lean3 ,& s1 betwe5 !m bo?1 ,!y lick$ ! platt] clean4 ,solve ?is z a ,sorites-,problem1 tak+ l9es #c & #d z ! ,conclusion to be prov$4 ,x is p]mitt$ to use1 z ,premisses1 n only all t is "h ass]t$1 b also all t we may reasonably und]/& to be impli$4 pg#aie ,,notes ,,to ,,app5dix4 7,a7 ,see p4 #afg1 l9e #f4 ,x may1 p]haps1 occur to ! ,read]1 :o has /udi$ ,=mal ,logic t ! argum5t1 "h appli$ to ! ,propositions ,i & ,e1 w apply equally well to ! ,propositions ,i & ,a 7s9ce1 9 ! ord9>y text-books1 ! ,propositions ,all xy are z & ,"s xy are n z are reg>d$ z ,contradictories74 ,h5ce x may appe> to him t ! argum5t might h be5 put z foll[s3-- ,we n[ h ,i & ,a 'ass]t+4' ,h5ce1 if ! ,proposition ',all xy are z' be true1 "s ?+s exi/ ) ! ,attributes x & y3 i4e4 ',"s x are y4' ,also we "k t1 if ! ,proposition ',"s xy are n-z' be true ! same result foll[s4 ,b ^! two ,propositions are ,contradictories1 s t "o or o!r ( !m mu/ be true4 ,h5ce ?is result is always true3 i4e4 ! ,proposition ',"s x are y' is always true6 ,quod e/ absurdum4 ,h5ce ,i _c ass]t4 ,?is matt] w be discuss$ 9 ,"p ,,ii2 b ,i may z well give "h :at seems to me to be an irresi/able pro( t ?is view 7t ,a & ,i are ,contradictories71 ?\gh adopt$ 9 ! ord9>y text-books1 is unt5able4 ,! pro( is z foll[s3-- ,) reg>d to ! relation%ip exi/+ betwe5 ! ,class 'xy' & ! two ,classes 'z' & 'n-z'1 !re are f\r conceivable /ates ( ?+s1 viz4 7#a7 ,"s xy are z1 & "s are n-z2 7#b7 none 7#c7 ,no xy "s 7#d7 none ,( ^! f\r1 ,no4 7#b7 is equival5t to ,all xy are z1 ,no4 7#c7 is equival5t to ,all xy are n-z1 & ,no4 7#d7 is equival5t to ,no xy exi/4 ,n[ x is q und5iable t1 ( ^! f\r /ates ( ?+s1 ea* is1 a priori1 possible1 "s "o mu/ be true1 & ! o!r ?ree mu/ be false4 ,h5ce ! ,contradictory to 7#b7 is ,ei!r 7#a7 or 7#c7 or 7#d7 is true4 ,n[ ! ass]tion ,ei!r 7#a7 or 7#c7 is true is equival5t to ,"s xy are n-z2 & ! ass]tion 7#d7 is true is equival5t to ,no xy exi/4 ,h5ce ! ,contradictory to ,all xy are z may be express$ z ! ,alt]native ,proposition ,ei!r "s xy are n-z1 or no xy exi/1 b n z ! ,categorical ,proposition ,"s y are n-z4 pg#aif 7,b7 ,see p4 #aga1 at end ( ,section #b4 ,!re are yet o!r views curr5t among ,! ,logicians1 z to ! ,exi/5tial ,import ( ,propositions1 :i* h n be5 m5tion$ 9 ?is ,section4 ,"o is1 t ! ,proposition "s x are y is to be int]pret$1 nei!r z ,"s x exi/ & are y1 nor yet z ,if !re 7 any x 9 exi/5ce1 "s ( !m w\ld be y1 b m]ely z ,"s x c be y2 i4e4 ! ,attributes x & y are compatible4 ,on ?is !ory1 !re w\ld be no?+ (f5sive 9 my tell+ my fri5d ,jones ,"s ( y\r bro!rs are sw9dl]s2 s9ce1 if he indignantly retort$ ,:at d y mean by su* insult+ language1 y sc\ndrel81 ,i %\ld calmly reply ,i m]ely mean t ! ?+ is conceivable----t "s ( y\r bro!rs might possibly be sw9dl]s4 ,b x may well be d\bt$ :e!r su* an explanation w\ld entirely appease ! wra? ( ,jones6 ,ano!r view is1 t ! ,proposition ,all x are y sometimes implies ! actual exi/5ce ( x1 & sometimes does n imply x2 & t we _c tell1 )\t hav+ x 9 concrete =m1 :i* int]pretation we are to give to x4 ,?is view is1 ,i ?9k1 /rongly support$ by common usage2 & x w be fully discuss$ 9 ,"p ,,ii3 b ! difficulties1 :i* x introduces1 seem to me too =midable to be ev5 allud$ to 9 ,"p ,i1 :i* ,i am try+ to make1 z f> z possible1 easily intelligible to m]e beg9n]s4 7,c7 ,see p4 #agc1 #d4 ,! ?ree ,conclusions are ,no conceit$ *ild ( m9e is gre$y2 ,none ( my boys c\ld solve ?is problem2 ,"s unle>n$ boys are n *ori/]s4 pg#aig ,,index4 #a4 ,tables4 ,i4 ,bilit]al ,diagram4 ,attributes ( ,classes1 & ,comp>tm5ts1 or ,cells1 assign$ to !m #be ,,ii4 d4 ,repres5tation ( ,unilit]al ,propositions ( ,exi/5ce #cd ,,iii4 d4 ,repres5tation ( ,bilit]al ,propositions ( ,exi/5ce & ( ,relation #ce ,,iv4 ,trilit]al ,diagram4 ,attributes ( ,classes1 & ,comp>tm5ts1 or ,cells1 assign$ to !m #db ,v4 d4 ,repres5tation ( ,p>ticul> & ,univ]sal ,negative ,propositions1 ( ,exi/5ce & ( ,relation1 9 t]ms ( x & m #df ,,vi4 d4 d41 9 t]ms ( y & m #dg ,,vii4 d4 ,repres5tation ( ,univ]sal ,affirmative ,propositions ( ,relation1 9 t]ms ( x & m #dh ,,viii4 d4 d4 9 t]ms ( y & m #di ,,ix4 ,me?od ( ,subscripts4 ,=mul & ,rules = ,syllogisms #gh #b4 ,words c4 expla9$4 ',ab/ract' ,proposition #ei ',adjuncts' #a ',affirmative' ,proposition #aj ',attributes' #a ',bilit]al' ,diagram #bb ,proposition #bg ',class' #a ,classes1 arbitr>y limits ( #c 1 subdivision ( #d pg#aih ',classification' #a ',codivisional' ,classes #c ',complete' ,conclusion ( a ,sorites #he ',conclusion' ( a ,sorites ,syllogism #ef ',concrete' ,proposition #ei ',consequ5t' 9 a ,sorites #he ,syllogism #ef ',conv]se' ,propositions #ca ',conv]sion' ( a ,proposition ',copula' ( a ,proposition #i ',def9ition' #f ',di*otomy' #c ',diff]5tia' #a ',division' #c ',elim9&s' ( a ,sorites #he ,syllogism #ef ',entity' #gj ',equival5t' ,propositions #ag ',fallacy' #ha ',g5us' #a ',imag9>y' ,class ,"n #d ',individual' #b ',l'1 & ',unlike'1 ,signs ( ,t]ms #gj ',"n' #d ',negative' ,proposition #aj ',normal' =m ( a ,proposition #i ( ,exi/5ce #aa ( ,relation #ab ',nullity' #gj ',p>tial' ,conclusion ( a ,sorites #he ',p>ticul>' ,proposition #i ',peculi>' ,attributes #a ',pr$icate' ( a ,proposition #i ( a ,proposition ( ,exi/5ce #aa ,relation #ab ',premisses' ( a ,sorites #he ,syllogism #ef pg#aii ',proposition' #h '9 ,i'1 '9 ,e'1 & '9 ,a' #i '9 t]ms (' c]ta9 ,lett]s #bg ( ,exi/5ce #aa ( ,relation #ab ',real' ,class #a ',ret95ds' ( a ,sorites #he ,syllogism #ef ',sign ( ,quantity' 9 a ,proposition #i ',sitt+ on ! ,f5ce' #bf ',"s'1 te*nical mean+ ( #h ',sorites' #he ',species' #a ',subject' ( a ,proposition #i ( ,exi/5ce #aa ( ,relation #ab ',subscripts' ( ,t]ms #gj ',syllogism' #ef ,symbol 4'4 & #gj ',t]ms' ( a ,proposition #i ',?+s' #a ,translation ( ,proposition f 'concrete' to 'ab/ract' #ei 'ab/ract' to 'subscript' #gb ',trilit]al' ,diagram #ci ',und]scor+' ( lett]s #ia ',unilit]al' ,proposition #bg ',univ]sal' #aj ',univ]se ( ,disc\rse' 7or ',univ4'7 #ab ',unreal' ,class #a ',unreal' ,"n #d pg#bjj ,,! ,,end4 px-#a ,,works ,,by ,,lewis ,,c>roll4 99 99 99 99 99 ,,publi%$ ,,by ,,macmillan ,,& ,,co41 ,,ltd41 ,,london4 99 99 99 99 99 ,,alice',s ,,adv5tures ,,9 ,,wond]l&4 ,) ,=ty-two ,illu/rations by ,,t5niel4 7,fir/ publi%$ 9 #ahfe47 ,cr4 #hvo1 clo?1 gilt edges1 price #fs4 net4 ,eighty-six? ,?\s&4 ,,! ,,same2 ,,p',s ,,edition4 7,fir/ publi%$ 9 #ahhg47 ,cr4 #hvo1 clo?1 price #bs4 #f;d4 net4 ,=ty-eigh? ,?\s&4 ,,av5tures ,d',,alice ,,au ,,pays ,,des ,,m]veilles4 ,traduit de l',anglais p> ,,h5ri ,,bu4 ,ouvrage illu/r de #db ,vignettes p> ,,john ,,t5niel4 7,fir/ publi%$ 9 #ahfi47 ,cr4 #hvo1 clo?1 gilt edges1 price #fs4 net4 ,second ,?\s&4 ,alice's ,ab5teu] im ,wund]l&4 ,aus dem ,englis*5 von ,antonie ,zimm]mann4 ,mit #db ,illu/ration5 von ,,john ,,t5niel4 7,fir/ publi%$ 9 #ahfi47 ,cr[n #hvo1 clo?1 gilt edges1 price #fs4 net4 ,,le ,,avv5ture ,d',,alice ,,nel ,,paese ,,delle ,,m]aviglie4 ,tradotte dall' ,+lese da ,t4 ,,pietrocola-,,rossetti4 ,con #db ,vignette di ,,giovanni ,,t5niel4 7,fir/ publi%$ 9 #ahgb47 ,cr[n #hvo1 clo?1 gilt edges1 price #fs4 net4 ,,alice',s ,,adv5tures ,,"u ,,gr\nd4 ,be+ a ,facsimile ( ! orig9al ,,ms4 ,book1 :i* 0 aft]w>ds develop$ into ,alice's ,adv5tures 9 ,wond]l&4 ,) ,?irty-sev5 ,illu/rations by ! ,au?or4 7,begun1 ,july #ahfb2 f9i%$1 ,feb4 #ahfc2 fir/ publi%$1 9 facsimile1 9 #ahhf47 ,cr[n #hvo1 clo?1 gilt edges1 price #ds4 net4 ,?ird ,?\s&4 ,,! ,,nurs]y ,,alice4 ,conta9+ ,tw5ty ,col\r$ ,enl>gem5ts f ,,t5niel',s ,illu/rations to ,alice's ,adv5tures 9 ,wond]l&4 ,) text adapt$ to ,nurs]y ,read]s4 ,cov] design$ by ,e4 ,,g]trude ,,?omson4 7,fir/ publi%$ 9 #ahij47 #dto1 bo>ds1 price #as4 net4 ,elev5? ,?\s&4 px-#b ,,?r\gh ,,! ,,look+-,,glass1 ,,& ,,:at ,,alice ,,f\nd ,,!re4 ,) ,fifty ,illu/ration by ,,t5niel4 7,fir/ publi%$ 9 #ahga47 ,cr4 #hvo1 clo?1 gilt edges1 price #fs4 net4 ,sixty-fir/ ,?\s&4 ,,?r\gh ,,! ,,look+-,,glass1 ,,& ,,:at ,,alice ,,f\nd ,,!re2 ,,p',s ,,edition4 7,fir/ publi%$ 9 #ahhg47 ,cr[n #hvo1 clo?1 gilt edges1 price #bs4 #f;d4 net4 ,?irtie? ,?\s&4 ,,alice',s ,,adv5tures ,,9 ,,wond]l&2 ,,& ,,?r\gh ,,! ,,look+-,,glass2 ,,p',s ,,editions4 ,bo? ,books toge!r 9 ,"o ,volume4 7,fir/ publi%$ 9 #ahhg47 ,cr[n #hvo1 clo?1 gilt edges1 price #ds4 #f;d4 net4 ,twelf? ,?\s&4 ,,! ,,hunt+ ,,( ,,! ,,sn>k4 ,an ,agony 9 ,eight ,fits4 ,) ,n9e ,illu/rations1 & two l>ge gilt designs on cov]1 by ,,h5ry ,,holiday4 7,fir/ publi%$ 9 #ahgf47 ,cr[n #hvo1 clo?1 gilt edges1 price #ds4 #f;d4 net4 ,tw5tie? ,?\s&4 ,,rhyme8 ,,& ,,reason8 ,) ,sixty-five ,illu/rations by ,,ar?ur ,b4 ,,fro/1 & n9e by ,,h5ry ,,holiday4 7,fir/ publi%$ 9 #ahhc1 be+ a repr9t1 ) a few additions1 ( ! comic portion ( ,phantasmagoria & o!r ,poems1 publi%$ 9 #ahfi1 & ( ,! ,hunt+ ( ! ,sn>k1 publi%$ 9 #ahgf47 ,cr[n #hvo1 clo?1 gilt edges1 price #ds4 #f;d4 net4 ,six? ,?\s&4 ,,symbolic ,,logic4 ,9 ?ree ,p>ts1 :i* w be issu$ sep>ately3-- ,,"p ,i4 ,elem5t>y4 7,fir/ publi%$ 9 #ahif47 ,cr[n #hvo1 limp clo?1 price #bs4 net4 ,second ,?\s&1 ,f\r? ,edition4 ,,"p ,,ii4 ,advanc$4 ,,"p ,,iii4 ,transc5d5tal4 ,9 prep>ation4 ,n4,b4--,an envelope1 conta9+ two blank ,diagrams 7,bilit]al & ,trilit]al7 & #i ,c\nt]s 7#d ,r$ & #e ,grey7 c be _h = #c;d41 by po/ #d;d4 px-#c ,a ,,tangl$ ,,tale4 ,repr9t$ f ,! ,mon?ly ,packet4 ,) ,six ,illu/rations by ,,ar?ur ,b4 ,,fro/4 7,fir/ publi%$ 9 #ahhe47 ,cr[n #hvo1 clo?1 gilt edges1 price #ds4 #f;d4 net4 ,f\r? ,?\s&4 ,,sylvie ,,& ,,bruno4 ,) ,=ty-six ,illu/rations by ,,h>ry ,,furniss4 7,fir/ publi%$ 9 #ahhi47 ,cr[n #hvo1 clo?1 gilt edges1 price #gs4 #f;d4 net4 ,twelf? ,?\s&4 ,n4,b4--,?is book conta9s #cie pages--ne>ly z mu* z ! two ,alice' books put toge!r4 ,,sylvie ,,& ,,bruno ,,conclud$4 ,) ,=ty-six ,illu/rations by ,,h>ry ,,furniss4 7,fir/ publi%$ 9 #ahic47 ,cr[n #hvo1 clo?1 gilt edges1 price #gs4 #f;d4 net4 ,?ird ,?\s&4 ,n4,b4--,?is book conta9s #daa pages4 ,,orig9al ,,games ,,& ,,puzzles4 ,cr[n #hvo1 clo?1 gilt edges4 ,9 prep>ation4 ,,?ree ,,sunsets1 & ,o!r ,poems4 ,) ,twelve ,illu/rations by ,e4 ,,g]trude ,,?omson4 ,fcap4 #dto1 clo?1 gilt edges4 ,n4,b4--,?is w be a repr9t1 possibly ) a few additions1 ( ! s]i\s portion ( ,phantasmagoria1 & o!r ,poems1 publi%$ 9 #ahfi4 99 99 99 99 99 ,,advice ,,to ,,writ]s4 ,buy ,,! ,,wond]l& ,,case ,,= ,,po/age-,,/amps1 inv5t$ by ,,lewis ,,c>rol1 ,oct4 #bi1 #ahhh1 size #d in*es by #c1 conta9+ #ab sep>ate pockets = /amps ( diff]5t values1 #b ,col\r$ ,pictorial ,surprises tak5 f ,alice 9 ,wond]l&1 & #h or #i ,wise ,words ab\t ,lett]-,writ+4 ,x is publi%$ by ,messrs4 ,,emb]l9 ,,son1 #d ,magdal5e ,/reet1 ,ox=d4 ,price #as4 ,n4,b4--,if ord]$ by ,po/1 an additional paym5t w be requir$1 to cov] co/ ( po/age1 z foll[s3-- ,"o copy1 #a;d4 ,two or ?ree d41 #b;d4 ,f\r d41 #b;d4 ,five to f\rte5 d41 #c;d4 ,ea* subsequ5t f\rte5 or fraction !re(1 #a;d4 99 99 99 99 99 99 99 99 99 99 ,transcrib]'s ,note ,?is book makes ext5sive use ( page ref]5ces4 ,to assi/ ! read]1 page m>k]s 9 ! =ms pg-ix1 pg#aic px-#c h be5 includ$ 9 ! "r m>g9 at po9ts correspond+ closely to ! tops ( ! orig9al pages4 ,^! may be se>*$ = to locate ! mat]ial ref]r$ to4 ,9 ! ma9 section1 ^! page m>k]s are always giv5 ) #c digits includ+1 if necess>y1 lead+ z]oes4 ,?is book conta9s a l>ge numb] ( l9e drawn illu/rations :i* are un-cr$it$4 ,z ^! _c be r5d]$ "h 9 ! orig9al mann] !y h be5 reproduc$ z well z possible 9 ! mann] kn[n z ,,ascii art4 ,a numb] ( transcription errors 7 f\nd 9 ! orig9al book4 ,z ^! 7 cle>ly n "p ( ! ,au?or's int5tion !y h1 z f> z possible1 be5 id5tifi$ & correct$ 9 accordance ) ! me?ods giv5 by ! ,au?or4 ,^! corrections are li/$ "h bel[ ) _! locations & orig9al text4 ,9 ^! notes ! ^w 'natural' id5tifies a lett] symbol occurr+ )\t a prime m>k4 ,page viii3 #ahi correct$ to #aid4 ,page viii3 #ahh correct$ to #aib4 ,page xv1 ',real' & ',unreal'1 or ',imag9>y'1 ,classes3 #a correct$ to #b4 ,page xix1 ,propositions beg9n+ ) ,"s3 #ah correct$ to #ai4 ,page xix1 ,rules3 #ai correct$ to #bj4 ,page xix1 ,! ,we/ & ,ea/ ,halves 4443 #bd correct$ to #bc4 ,page xxi1 ,! ,proposition ,all x are y 4443 0 orig9ally %[n z occurr+ 9 page #cd4 ,page xxii1 ,& ( ?ree o!r simil> arrangem5ts3 #cg correct$ to #cf4 ,page xxiii1 ,! ,proposition ',no xm exi/'3 #dc correct$ to #dd4 ,page #jfj3 contruct correct$ to con/ruct4 ,page #jid1 ,pap] ,v3 miss+ ^w x suppli$4 ,page #aaa1 #bh3 ,no h are k-natural correct$ to ,no h are k-prime4 ,page #aaa1 #cj3 ,no a are h-natural correct$ to ,no a are h-prime4 ,page #aaa1 #cj3 ,no c are n-natural correct$ to ,no c are n-prime4 ,page #abc1 #eg 7d73 mortally (f5d$ if ,i fail to notice !m correct$ to mortally (f5d$4 ,page #abh1 #cd3 ,"s x-prime are y correct$ to ,"s x-natural are y4 ,page #adf1 #cj3 x#am-prime#j correct$ to x#am-natural#j4 ,page #adg1 #cb3 xm-natural#j correct$ to xm-prime#j4 ,page #aef1 #ah 7#d_/a73 be correct$ to be-sub3z]o4 ,page #aef1 #bb 7#e_/a73 * correct$ to *-sub3z]o4 ,page #aeg1 #bc 7#e_/b73 second und]l9e correct$ f s+le to d\ble4 ,page #aeg1 #bc 7#b_/b73 fir/ und]l9e correct$ f s+le to d\ble4 ,page #aeg1 #bc 7#b73 h#a;c correct$ to h#a;c-sub3z]o4 ,page #aeg1 #bf 7#e_/a73 a#a;c-natural#j correct$ to a#a;c-prime#j4 ,page #aeg1 #bf 7#b73 e#a;c-natural#j correct$ to e#a;c-prime#j4 ,page #aeg1 #bi 7#h_/b73 fir/ und]l9e correct$ f s+le to d\ble4 ,page #afa1 #cf 7#d_/b73 e'd-prime correct$ to e'd-natural4 ,page #afa1 #ci 7#a_/b73 c-primed correct$ to c-naturald4 ,page #afa1 #dj3 a & b int]*ang$4 ,page #afa1 #dc 7#a_/a73 b-natural#a;e#j correct$ to b-prime#a;e#j4 ,page #afb1 #eb 7#c_/a73 h'k-prime#j correct$ to h'k-natural#j4 ,page #afc1 #ee 7#c_/b73 c'd-prime correct$ to c'd-natural4 ,page #afc1 #eg 7#a_/b73 h-naturald' correct$ to h-primed'4 ,9 ! orig9al book at ! top ( page #ig1 ! foll[+ text occurr$3 ,n4,b4 ,! numb]s at ! foot ( ea* page indicate ! pages :]e ! correspond+ matt] may be f\nd4 ,9 accordance ) ! un-pag$ m$ium "h ?is has be5 *ang$ to3 ,n4,b4 ,ref]5ce tags = ,examples1 ,answ]s ,solutions w be f\nd 9 ! 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