,,fir/ ,,notions ,,( ,,logic 7,,prep>atory ,,to ,,! ,,/udy ,,( ,,geometry7 ,,by ,,augu/us ,,de ,,morgan1 ,,( ,,tr9ity ,,college1 ,,cambridge1 ,,pr(essor ,,( ,,ma!matics ,,9 ,,univ]sity ,,college1 ,,london4 ,! root ( all ! mis*ief 9 ! sci5ces1 is ?is2 t falsely magnify+ & admir+ ! p[]s ( ! m9d1 we seek n its real helps4--,,bacon4 ,,london3 ,,pr9t$ ,,= ,,taylor ,,& ,,walton1 ,,booksell]s ,,& ,,publi%]s ,,to ,,univ]sity ,,college4 #bh ,,upp] ,,g[] ,,/reet4 ,m4,,dccc4,,xxxix4 ,?is ,tract conta9s no m ?an ! au?or has f\nd1 f exp]i5ce1 to be mu* want$ by /ud5ts :o are comm5c+ ) ,euclid4 ,x w ultimately =m an ,app5dix to 8 ,treatise on ,ari?metic4 ,! au?or w\ld n1 by any means1 9 pres5t+ ! m9imum necess>y = a p>ticul> purpose1 be held to imply t he has giv5 en\gh ( ! subject = all ! ends ( education4 ,he has long regrett$ ! neglect ( logic2 a sci5ce1 ! /udy ( :i* w\ld %ew _m ( its oppon5ts t ! light e/eem 9 :i* !y hold x arises f ^? habits ( inf]5ce :i* ?rive be/ 9 its abs5ce4 ,he /rongly recomm5ds any /ud5t to :om ?is tract may be ! fir/ introduction ( ! subject1 to pursue x to a mu* great] ext5t4 ,univ]sity ,college1 ,jan1 #h1 #ahci4 ,,london3--,,pr9t$ ,,by ,,james ,,moyes1 ,ca/le ,/reet1 ,leice/] ,squ>e4 ,,fir/ ,,notions ,,( ,,logic4 ,:at we "h mean by ,logic is ! exam9ation ( t "p ( reason+ :i* dep5ds ^u ! mann] 9 :i* inf]5ces are =m$1 & ! inve/igation ( g5]al maxims & rules = con/ruct+ argum5ts1 s t ! conclusion may conta9 no inaccuracy :i* 0 n previ\sly ass]t$ 9 ! premises4 ,x has no?+ to d ) ! tru? ( ! facts1 op9ions1 or presumptions1 f :i* an inf]5ce is d]iv$2 b simply takes c>e t ! inf]5ce %all c]ta9ly be true1 if ! premises be true4 ,?us1 :5 we say t all m5 w die1 & t all m5 are rational be+s1 & !nce inf] t "s rational be+s w die1 ! logical tru? ( ?is s5t5ce is ! same :e!r x be true or false t m5 are mortal & rational4 ,?is logical tru? dep5ds ^u ! /ructure ( ! s5t5ce1 & n on ! p>ticul> matt]s spok5 (4 ,?us1 ,in/ead (1 ,write1 ,all m5 w die4 ,e ,a is ,b4 ,all m5 are rational be+s4 ,e ,a is ,c4 ,!re=e "s rational be+s w die4 ,!re=e "s ,cs are ,bs4 ,! second ( ^! is ! same proposition1 logically consid]$1 z ! fir/2 ! consequ5ce 9 bo? is virtually conta9$ 91 & rightly inf]r$ f1 ! premises4 ,:e!r ! premises be true or false1 is n a "q ( logic1 b ( morals1 philosophy1 hi/ory1 or any o!r k to :i* _! subject-matt] belongs3 ! "q ( logic is1 does ! conclusion c]ta9ly foll[ if ! premises be true8 ,e act ( reason+ mu/ ma9ly consi/ 9 comp>+ toge!r diff]5t ?+s1 & ei!r f9d+ out1 or recall+ f previ\s k1 ! po9ts 9 :i* !y resemble or diff] f ea* o!r4 ,t p>ticul> "p ( reason+ :i* is call$ inf]5ce1 consi/s 9 ! comp>ison ( sev]al & diff]5t ?+s ) "o & ! same o!r ?+2 & asc]ta9+ ! resemblances1 or diff]5ces1 ( ! sev]al ?+s1 by means ( ! po9ts 9 :i* !y resemble1 or diff] f1 ! ?+ ) :i* all are comp>$4 ,!re mu/ !n be "s propositions already obta9$ be=e any inf]5ce c be drawn4 ,all propositions are ei!r ass]tions or d5ials1 & are ?us divid$ into affirmative & negative4 ,?us1 ,a is ,b1 & ,a is n ,b1 are ! two =ms to :i* all propositions may be r$uc$4 ,^! are1 = our pres5t purpose1 ! mo/ simple =ms2 ?\gh x w frequ5tly happ5 t mu* circumlocution is ne$$ to r$uce propositions to !m4 ,?us1 suppose ! foll[+ ass]tion1 #8,if he %\ld come to-morr[1 he w probably /ay till ,monday'2 h[ is ?is to be r$uc$ to ! =m ,a is ,b8 ,!re is evid5tly some?+ spok5 (1 some?+ said ( x1 & an affirmative connexion betwe5 !m4 ,some?+1 if x happ51 t is1 ! happ5+ ( some?+1 makes ! happ5+ ( ano!r some?+ probable2 or is "o ( ! ?+s :i* r5d] ! happ5+ ( ! second ?+ probable4 ,a is ,b ,! happ5+ ( 8 arrival an ev5t f :i* x may be to-morr[ is inf]r$ z probable t he w /ay till ,monday4 ,! =ms ( language w all[ ! mann] ( ass]t+ to be v>i$ 9 a great numb] ( ways2 b ! r$uction to ! prec$+ =m is always possible4 ,?us1 #8s he said' is an affirmation1 r$ucible z foll[s3 ,:at y h j said 7or is! ?+ :i* he said4 :atev] else #8s' ref]s to7 ,by *ang+ #8is' into #8is n1' we make a negative proposition2 b c>e mu/ always be tak5 to asc]ta9 :e!r a proposition :i* appe>s negative is really s4 ,! pr9cipal dang] is t ( conf\nd+ a proposition :i* is negative ) ano!r :i* is affirmative ( some?+ requir+ a negative to describe x4 ,?us #8he resembles ! man :o 0 n 9 ! room1' is affirmative1 & mu/ n be conf\nd$ ) #8he does n resemble ! man :o 0 9 ! room4' ,aga91 #8if he %\ld come to-morr[1 x is probable he w n /ay till ,monday1' does n mean ! simple d5ial ( ! prec$+ proposition1 b ! affirmation ( ! directly opposite proposition4 ,x is1 ,a is ,b ,! happ5+ ( 8 arrival an ev5t f :i* x may be to-morr[1 is inf]r$ to be improbable t he w /ay till ,monday1 :]eas ! foll[+1 ,! happ5+ ( 8 arrival an ev5t f :i* x may be to-morr[1 is n inf]r$ z probable t he w /ay till ,monday1 w\ld be express$ ?us3 #8,if he %\ld come to-morr[1 t is no reason :y he %\ld /ay till ,monday4' ,moreov]1 ! negative words n1 no1 c41 h two k9ds ( mean+ :i* mu/ be c>efully di/+ui%$4 ,sometimes !y d5y1 & no?+ m3 sometimes !y are us$ to affirm ! direct contr>y4 ,9 cases :i* (f] b two alt]natives1 "o ( :i* is necess>y1 ^! am\nt to ! same ?+1 s9ce ! d5ial ( "o1 & ! affirmation ( ! o!r1 are obvi\sly equival5t propositions4 ,9 _m idioms ( conv]sation1 ! negative implies affirmation ( ! contr>y 9 cases :i* (f] n only alt]natives1 b degrees ( alt]natives4 ,?us1 to ! "q1 #8,is he tall8' ! simple answ]1 #8,no1' mo/ frequ5tly means t he is ! contr>y ( tall1 or consid]ably "u ! av]age4 ,b x mu/ be rememb]$1 t1 9 all logical reason+1 ! negation is simply negation1 & no?+ m1 nev] imply+ affirmation ( ! contr>y4 ,! common proposition t two negatives make an affirmative1 is true only ^u ! supposition t !re are b two possible ?+s1 "o ( :i* is d5i$4 ,grant t a man mu/ be ei!r able or unable to d a p>ticul> ?+1 & !n n unable & able are ! same ?+s4 ,b if we suppose v>i\s degrees ( p]=mance1 & !re=e degrees ( ability1 x is false1 9 ! common s5se ( ! words1 t two negatives make an affirmative4 ,?us1 x w\ld be errone\s to say1 #8,john is able to translate ,virgil1 & ,?omas is n unable2 !re=e1 :at ,john c d ,?omas c d1' = x is evid5t t ! premises mean t ,john is s ne> to ! be/ sort ( translation t an affirmation ( 8 ability may be made1 :ile ,?omas is consid]ably l[] ?an ,john1 b n s ne> to absolute defici5cy t 8 ability may be altoge!r d5i$4 ,x w g5]ally be f\nd t two negatives imply an affirmative ( a weak] degree ?an ! positive affirmation4 ,ea* ( ! propositions1 #8,a is ,b1' & #8,a is n ,b1' may be subdivid$ into two species3 ! univ]sal1 9 :i* e possible case is includ$2 & ! p>ticul>1 9 :i* x is n meant to be ass]t$ t ! affirmation or negation is univ]sal4 ,! f\r species ( propositions are !n z foll[s1 ea* be+ m>k$ ) ! lett] by :i* writ]s on logic h always di/+ui%$ x4 ,a ,univ]sal ,affirmative ,e ,a is ,b ,e ,univ]sal ,negative ,no ,a is ,b ,i ,p>ticul> ,affirmative ,"s ,a is ,b ,o ,p>ticul> ,negative ,"s ,a is n ,b ,9 common conv]sation ! affirmation ( a "p is meant to imply ! d5ial ( ! rema9d]4 ,?us1 by #8"s ( ! apples are ripe1' x is always int5d$ to signify t "s are n ripe4 ,?is is n ! case 9 logical language1 b e proposition is int5d$ to make its am\nt ( affirmation or d5ial1 & no m4 ,:5 we say1 #8,"s ,a is ,b1' or1 m grammatically1 #8,"s ,z are ,bs1' we d n mean to imply t "s are n3 ?is may or may n be4 ,aga91 ! ^w "s means1 #8"o or m1 possibly all4' ,! foll[+ table w %ew ! be>+ ( ea* proposition on ! re/4 ,e ,a is ,b affirms & conta9s ,"s ,a is ,b &,no ,a is ,b d5ies ,"s ,a is n ,b ,no ,a is ,b affirms & conta9s ,"s ,a is n ,b ,e ,a is ,b & d5ies ,"s ,a is ,b ,"s ,a is ,b does n ,e ,a is ,b b d5ies ,no ,a is ,b contradict ,"s ,a is n ,b ,"s ,a is n ,b does n ,no ,a is ,b b d5ies ,e ,a is ,b contradict ,"s ,a is ,b ,contradictory propositions are ^? 9 :i* "o d5ies any ?+ t ! o!r affirms2 contr>y propositions are ^? 9 :i* "o d5ies e ?+ :i* ! o!r affirms1 or affirms e ?+ :i* ! o!r d5ies4 ,! foll[+ pair are contr>ies4 ,e ,a is ,b & ,no ,a is ,b & ! foll[+ are contradictories1 ,e ,a is ,b to ,"s ,a is n ,b ,no ,a is ,b to ,"s ,a is ,b ,a contr>y1 !re=e1 is a complete & total contradictory2 & a little consid]ation w make x appe> t ! decisive di/9ction betwe5 contr>ies & contradictories lies 9 ?is1 t contr>ies may bo? be false1 b ( contradictories1 "o mu/ be true & ! o!r false4 ,we may say1 #8,ei!r ,p is true1 or some?+ 9 contradiction ( x is true2' b we _c say1 #8,ei!r ,p is true1 or e ?+ 9 contradiction ( x is true4' ,x is a v common mi/ake to imag9e t ! d5ial ( a proposition gives a "r to affirm ! contr>y2 :]eas x %\ld be1 t ! affirmation ( a proposition gives a "r to d5y ! contr>y4 ,?us1 if we d5y t ,e ,a is ,b1 we d n affirm t ,no ,a is ,b1 b only t ,"s ,a is n ,b2 :ile1 if we affirm t ,e ,a is ,b1 we d5y ,no ,a is ,b1 & also ,"s ,a is n ,b4 ,b1 z to contradictories1 affirmation ( "o is a d5ial ( ! o!r1 & d5ial ( "o is affirmation ( ! o!r4 ,?us1 ei!r ,e ,a is ,b1 or ,"s ,a is n ,b3 affirmation ( ei!r is d5ial ( ! o!r1 & vice v]s4 ,let ! /ud5t n[ endeav\r to satisfy himself ( ! foll[+4 ,tak+ ! f\r prec$+ propositions1 ,a1 ,e1 ,i1 ,o1 let ! simple lett] signify ! affirmation1 ! same lett] 9 p>5!ses ! d5ial1 & ! abs5ce ( ! lett]1 t !re is nei!r affirmation nor d5ial4 ,f ,a foll[7,e71 ,i1 7,o7,f 7,a7 foll[ ,o ,f ,e 7,a71 7,i71 ,o,f 7,e7 ,i ,f ,i 7,e7 ,f 7,i7 7,a71 ,e1 ,o ,f ,o 7,a7 ,f 7,o7 ,a1 7,e71 ,i ,^! may be ?us summ$ up3 ,! affirmation ( a univ]sal proposition1 & ! d5ial ( a p>ticul> "o1 enable u to affirm or d5y all ! o!r ?ree2 b ! d5ial ( a univ]sal proposition1 & ! affirmation ( a p>ticul> "o1 leave u unable to affirm or d5y two ( ! o!rs4 ,9 su* propositions z #8,e ,a is ,b1' #8,"s ,a is n ,b1' c41 ,a is call$ ! subject1 & ,b ! pr$icate1 :ile ! v]b #8is' or #8is n1' is call$ ! copula4 ,x is obvi\s t ! words ( ! proposition po9t out :e!r ! subject is spok5 ( univ]sally or p>tially1 b n s ( ! pr$icate1 :i* x is !re=e important to exam9e4 ,logical writ]s g5]ally give ! "n ( di/ribut$ subjects or pr$icates to ^? :i* are spok5 ( univ]sally2 b z ?is ^w is r te*nical1 ,i %all say t a subject or pr$icate ent]s :olly or p>tially1 accord+ z x is univ]sally or p>ticul>ly spok5 (4 #a4 ,9 ,a1 or #8,e ,a is ,b1' ! subject ent]s :olly1 b ! pr$icate only p>tially4 ,= x obvi\sly says1 #8,among ! ,bs are all ! ,z1' #8,e ,a is "p ( ! collection ( ,bs1 s t all ! ,z make a "p ( ! ,bs1 ! :ole x may be4' ,?us1 #8,e horse is an animal1' does n speak ( all animals1 b /ates t all ! horses make up a portion ( ! animals4 #b4 ,9 ,e1 or #8,no ,a is ,b1' bo? subject & pr$icate ent] :olly4 #8,no ,a :atsoev] is any "o out ( all ! ,bs2' #8se>* ! :ole collection ( ,bs1 & e ,b %all be f\nd to be some?+ :i* is n ,a4' #c4 ,9 ,i1 or #8,"s ,a is ,b1' bo? subject & pr$icate ent] p>tially4 #8,"s ( ! ,z are f\nd among ! ,bs1 or make up a "p 7! :ole possibly1 b n kn[n f ! prec$+7 ( ! ,bs4' #d4 ,9 ,o1 or #8,"s ,a is n ,b1' ! subject ent]s p>tially1 & ! pr$icate :olly4 #8,"s ,z are none ( !m any :atsoev] ( ! ,bs2 e ,b w be f\nd to be no "o out ( a c]ta9 portion ( ! ,z4' ,x appe>s !n t1 ,9 affirmatives1 ! pr$icate ent]s p>tially4 ,9 negatives1 ! pr$icate ent]s :olly4 ,9 contradictory propositions1 bo? subject & pr$icate ent] diff]5tly 9 ! two4 ,! conv]se ( a proposition is t :i* is made by int]*ang+ ! subject & pr$icate1 z foll[s3 ,! proposition4 ,its conv]se4 ,a ,e ,a is ,b ,e ,b is ,a ,e ,no ,a is ,b ,no ,b is ,a ,i ,"s ,a is ,b ,"s ,b is ,a ,o ,"s ,a is n ,b ,"s ,b is n ,a ,n[1 x is a fundam5tal & self-evid5t proposition1 t no consequ5ce mu/ be all[$ to ass]t m widely ?an its premises2 s t1 = in/ance1 an ass]tion :i* is only ( "s ,bs c nev] lead to a result :i* is true ( all ,bs4 ,b if a proposition ass]t agreem5t or disagreem5t1 any o!r proposition :i* ass]ts ! same1 to ! same ext5t & no fur!r1 mu/ be a legitimate consequ5ce2 or1 if y please1 mu/ am\nt to ! :ole1 or "p1 ( ! orig9al ass]tion 9 ano!r =m4 ,?us1 ! conv]se ( ,a is n true3 =1 9 #8,e ,a is ,b1' ! pr$icate ent]s p>tially2 :ile 9 #8,e ,b is ,a1' ! subject ent]s :olly4 #8,all ! ,z make up a "p ( ! ,bs1 !n a "p ( ! ,bs are among ! ,z1 or "s ,b is ,a4' ,h5ce1 ! only legitimate conv]se ( #8,e ,a is ,b' is1 #8,"s ,b is ,a4' ,b 9 #8,no ,a is ,b1' bo? subject & pr$icate ent] :olly1 & #8,no ,b is ,a' is1 9 fact1 ! same proposition z #8,no ,a is ,b4' ,& #8,"s ,a is ,b' is also ! same z its conv]se #8,"s ,b is ,a2' "h bo? t]ms ent] p>tially4 ,b #8,"s ,a is n ,b' admits ( no conv]se :atev]2 x is p]fectly consi/5t ) all ass]tions ^u ,b & ,a 9 :i* ,b is ! subject4 ,?us nei!r ( ! f\r foll[+ l9es is inconsi/5t ) itself4 ,"s ,a is n ,b & ,e ,b is ,a ,"s ,a is n ,b & ,no ,b is ,a ,"s ,a is n ,b & ,"s ,b is ,a ,"s ,a is n ,b & ,"s ,b is n ,a4 ,we f9d !n1 includ+ conv]ses1 :i* are n id5tical ) _! direct propositions1 six diff]5t ways ( ass]t+ or d5y+1 ) respect to agreem5t or non-agreem5t1 total or p>tial1 betwe5 ,a &1 say ,x3 ^! we write d[n1 designat+ ! additional ass]tions by ,u & ,y4 ,id5tical4 ,id5tical4 ,a ,e ,a is ,x,e ,no ,a is ,x,i ,"s ,a is ,x,o ,"s ,a is n ,x ,u ,e ,x is ,a ,no ,x is ,a ,"s ,x is ,a,y ,"s ,x is n ,a ,we %all n[ repeat & ext5d ! table ( page #h 7,a71 c41 mean+1 z be=e1 ! d5ial ( ,a1 c4 ,f ,a or 7,o7 foll[ ,a1 7,e71 ,i 7,o7 ,f ,e or 7,i7 7,a71 ,e1 7,i71 ,o1 7,u71 ,y ,f ,i or 7,e7 7,e7 ,i ,f ,o or 7,a7 7,a71 ,o ,f ,u or 7,y7 7,e7 ,i1 ,u 7,y7 ,f ,y or 7,u7 7,u7 ,y ,hav+ ?us discuss$ ! pr9cipal po9ts connect$ ) ! simple ass]tion1 we pass to ! mann] ( mak+ two ass]tions give a ?ird4 ,e in/ance ( ?is is call$ a syllogism1 ! two ass]tions :i* =m ! basis ( ! ?ird are call$ premises1 & ! ?ird itself ! conclusion4 ,if two ?+s bo? agree ) a ?ird 9 any p>ticul>1 !y agree ) ea* o!r 9 ! same2 z1 if ,a be ( ! same col\r z ,x1 & ,b ( ! same col\r z ,x1 !n ,a is ( ! same col\r z ,b4 ,aga91 if ,a diff] f ,x 9 any p>ticul> 9 :i* ,b agrees ) ,x1 !n ,a & ,b diff] 9 t p>ticul>4 ,if ,a be n ( ! same col\r z ,x1 & ,b be ( ! same col\r z ,x1 !n ,a is n ( ! col\r ( ,b4 ,b if ,a & ,b bo? diff] f ,x 9 any p>ticul>1 no?+ c be inf]r$2 !y may ei!r diff] 9 ! same way & to ! same ext5t1 or n4 ,?us1 if ,a & ,b be bo? ( diff]5t col\rs f ,x1 x nei!r foll[s t !y agree1 nor diff]1 9 _! own col\rs4 ,! p>agraph prec$+ conta9s ! ess5tial p>ts ( all inf]5ce1 :i* consi/s 9 comp>+ two ?+s ) a ?ird1 & f9d+ f _! agreem5t or diff]5ce ) t ?ird1 _! agreem5t or diff]5ce ) "o ano!r4 ,?us1 ,e ,a is ,x1 e ,b is ,x1 all[s u to inf] t ,a & ,b h all ^? qualities 9 common :i* are necess>y to ,x4 ,aga91 f ,e ,a is ,x1 & #8,no ,b is ,x1' we inf] t ,a & ,b diff] f "o ano!r 9 all p>ticul>s :i* are ess5tial to ,x4 ,! prec$+ =ms1 h[ev]1 ?\gh !y repres5t common reason+ bett] ?an ! ord9>y syllogism1 to :i* we are n[ com+1 d n con/itute ! ultimate =ms ( inf]5ce4 ,simple id5tity or non-id5tity is ! ultimate /ate to :i* e ass]tion may be r$uc$2 & we %all1 !re=e1 fir/ ask1 f :at id5tities1 c41 c o!r id5tities1 c41 be produc$8 ,aga91 s9ce we "n objects 9 species1 ea* species consi/+ ( a numb] ( individuals1 & s9ce our ass]tion may include all or only "p ( a species1 x is fur!r necess>y to ask1 9 e in/ance1 to :at ext5t ! conclusion drawn is true1 :e!r ( all1 or only ( "p8 ,let u take ! simple ass]tion1 #8,e liv+ man respires2' or1 e liv+ man is "o ( ! ?+s 7h[ev] v>i$ !y may be7 :i* respire4 ,if we 7 to inclose all liv+ m5 9 a l>ge triangle1 & all respir+ objects 9 a l>ge circle1 ! prec$+ ass]tion1 if true1 w\ld require t ! :ole ( ! triangle %\ld be conta9$ 9 ! circle4 ,& 9 ! same way we may r$uce any ass]tion to ! expression ( a co9cid5ce1 total or p>tial1 betwe5 two figures4 ,?us1 a po9t 9 a circle may repres5t an individual ( "o species1 & a po9t 9 a triangle an individual ( ano!r species3 & we may express t ! :ole ( "o species is ass]t$ to be conta9$ or n conta9$ 9 ! o!r by su* =ms z1 #8,all ! is 9 ! '2 #8,none ( ! is 9 ! '4 ,any two ass]tions ab\t ,a & ,b1 ea* express+ agreem5t or disagreem5t1 total or p>tial1 ) or f ,x1 & lead+ to a conclusion ) respect to ,a or ,b1 is call$ a syllogism1 ( :i* ,x is call$ ! middle t]m4 ,! pla9e/ syllogism is ! foll[+3-- ,e ,a is ,x ,all ! is 9 ! ,e ,x is ,b ,all ! is 9 ! ,!re=e ,e ,a is ,b,!re=e ,all ! is 9 ! ,9 ord] to f9d all ! possible =ms ( syllogism1 we mu/ make a table ( all ! elem5ts ( :i* !y c consi/2 namely-- ,a & ,x ,b & ,x ,e ,a is ,x ,a ,e ,b is ,x ,no ,a is ,x ,e ,no ,b is ,x ,"s ,a is ,x ,i ,"s ,b is ,x ,"s ,a is n ,x ,o ,"s ,b is n ,x ,e ,x is ,a ,u ,e ,x is ,b ,"s ,x is n ,a ,y ,"s ,x is n ,b ,or _! synonymes1 & & ,all ! is 9 ! ,a ,all ! is 9 ! ,none ( ! is 9 ! ,e ,none ( ! is 9 ! ,"s ( ! is 9 ! ,i ,"s ( ! is 9 ! ,"s ( ! is n 9 ! ,o ,"s ( ! is n 9 ! ,all ! is 9 ! ,u ,all ! is 9 ! ,"s ( ! is n 9 ! ,y ,"s ( ! is n 9 ! ,n[1 tak+ any "o ( ! six relations betwe5 ,a & ,x1 & comb9+ x ) ei!r ( ^? betwe5 ,b & ,x1 we h six pairs ( premises1 & ! same numb] repeat$ = e diff]5t relation ( ,a & ,x4 ,we h !n ?irty-six =ms to consid]3 b1 ?irty ( ^! 7namely1 all b 7,a1 ,a7 7,e1 ,e71 c47 are half ( !m repetitions ( ! o!r half4 ,?us1 #8,e ,a is ,x1 no ,b is ,x1' & #8,e ,b is ,x1 no ,a is ,x1' are ( ! same =m1 & only diff] by *ang+ ,a into ,b & ,b into ,a4 ,!re are !n only #ae #f1 or #ba di/9ct =ms1 "s ( :i* give a necess>y conclusion1 :ile o!rs d n4 ,we %all select ! =m] ( ^!1 classify+ !m by _! conclusions2 t is1 accord+ z ! inf]5ce is ( ! =m ,a1 ,e1 ,i1 or ,o4 ,i4 ,9 :at mann] c a univ]sal affirmative conclusion be drawn2 namely1 t "o figure is entirely conta9$ 9 ! o!r8 ,?is we c only ass]t :5 we "k t "o figure is entirely conta9$ 9 ! circle1 :i* itself is entirely conta9$ 9 ! o!r figure4 ,?us1 ,e ,a is ,x ,all ! is 9 ! ,a ,e ,x is ,b ,all ! is 9 ! ,a ,e ,a is ,b ,all ! is 9 ! ,a is ! only way 9 :i* a univ]sal affirmative conclusion c be drawn4 ,,ii4 ,9 :at mann] c a univ]sal negative conclusion be drawn2 namely1 t "o figure is entirely ext]ior to ! o!r8 ,only :5 we are able to ass]t t "o figure is entirely )91 & ! o!r entirely )\t1 ! circle4 ,?us1 ,e ,a is ,x,all ! is 9 ! ,a ,no ,b is ,x,none ( ! is 9 ,e ! ,no ,a is ,b,none ( ! is 9 ,e ! is ! only way 9 :i* a univ]sal negative conclusion c be drawn4 ,,iii4 ,9 :at mann] c a p>ticul> affirmative conclusion be drawn2 namely1 t "p or all ( "o figure is conta9$ 9 ! o!r8 ,only :5 we are able to ass]t t ! :ole circle is "p ( "o ( ! figures1 & t ! :ole1 or "p ( ! circle1 is "p ( ! o!r figure4 ,we h !n two =ms4 ,e ,x is ,a ,all ! is 9 ! ,a ,e ,x is ,b ,all ! is 9 ! ,a ,"s ,a is ,b ,"s ( ! is 9 ,i ! ,e ,x is ,a ,all ! is 9 ! ,a ,"s ,x is ,b ,"s ( ! is 9 ,i ! ,"s ,a is ,b ,"s ( ! is 9 ,i ! ,! second ( ^! conta9s all t is /rictly necess>y to ! conclusion1 & ! fir/ may be omitt$4 ,t :i* foll[s :5 an ass]tion c be made z to "s1 mu/ foll[ :5 ! same ass]tion c be made ( all4 ,,iv4 ,h[ c a p>ticul> negative proposition be inf]r$2 namely1 t "p1 or all ( "o figure1 is n conta9$ 9 ! o!r8 ,x w\ld seem at fir/ sight1 :5ev] we are able to ass]t t "p or all ( "o figure is 9 ! circle1 & t "p or all ( ! o!r figure is n4 ,! weake/ syllogism f :i* su* an inf]5ce c be drawn w\ld !n seem to be z foll[s4 ,"s ,a is ,x ,"s ( ! is 9 ! ,"s ,b is n ,x ,"s ( ! is n 9 ! ,"s ,b is n ,a ,"s ( ! is n 9 ! ,b "h x w appe>1 on a little consid]ation1 t ! conclusion is only ?us f> true2 t ^? ,z :i* are ,xs _c be ^? ,bs :i* are n ,xs2 b !y may be o!r ,bs1 ab\t :i* no?+ is ass]t$ :5 we say t "s ,bs are n ,xs4 ,& fur!r consid]ation w make x evid5t1 t a conclusion ( ?is =m c only be arriv$ at :5 "o ( ! figures is entirely )9 ! circle1 & ! :ole or "p ( ! o!r )\t2 or else :5 ! :ole ( "o ( ! figures is )\t ! circle1 & ! :ole or "p ( ! o!r )92 or la/ly1 :5 ! circle lies entirely )9 "o ( ! figures1 & n entirely )9 ! o!r4 ,t is1 ! foll[+ are ! di/9ct =ms :i* all[ ( a p>ticul> negative conclusion1 9 :i* x %\ld be rememb]$ t a p>ticul> proposition 9 ! premises may always be *ang$ into a univ]sal "o1 )\t affect+ ! conclusion4 ,= t :i* necess>ily foll[s f 8"s10 foll[s f 8all40 ,e ,a is ,x ,all ! is 9 ! ,a ,"s ,b is n ,x ,"s ( ! is n 9 ! ,o ,"s ,b is n ,a ,"s ( ! is n 9 ! ,o ,no ,a ,is ,x ,none ( ! is 9 ! ,e ,"s ,b is ,x ,"s ( ! is 9 ! ,i ,"s ,b is n ,a ,"s ( ! is n 9 ! ,o ,e ,x is ,a ,all ! is 9 ! ,a ,"s ,x is n ,b ,"s ( ! is n 9 ! ,o ,"s ,a is n ,b ,"s ( ! is n 9 ! ,o ,x appe>s1 !n1 t !re are b six di/9ct syllogisms4 ,all o!rs are made f !m by /r5g!n+ "o ( ! premises1 or conv]t+ "o or bo? ( ! premises1 :]e su* conv]sion is all[able2 or else by fir/ mak+ ! conv]sion1 & !n /r5g!n+ "o ( ! premises4 ,& ! foll[+ arrangem5t w %ew t two ( !m are univ]sal1 ?ree ( ! o!rs be+ d]iv$ f !m by weak5+ "o ( ! premises 9 a mann] :i* does n de/roy1 b only weak5s1 ! conclusion4 #a4 ,e ,a is ,x #c4 ,e ,a is ,x ,e ,x is ,b ,no ,b is ,x 444444444 ------------------------ ------------------------ ,e ,a is ,b ,no ,a is ,b #b4 ,"s ,a is ,x #d4 ,"s ,a is ,x #e4 ,e ,a is ,x #f4 ,e ,x is ,a ,e ,x is ,b ,no ,b is ,x ,"s ,b is n ,x ,"s ,x is n ,b ------------------------ ------------------------------ -------------------------------- ------------------------------ ,"s ,a is ,b ,"s ,a is n ,b ,"s ,b is n ,a ,"s ,a is n ,b ,we may see h[ x arises t "o ( ! p>tial syllogisms is n imm$iately d]iv$1 l ! o!rs1 f a univ]sal "o4 ,9 ! prec$+1 ,,aee may be consid]$ z d]iv$ f ,,aaa1 by *ang+ ! t]m 9 :i* ,x ent]s univ]sally into its contr>y4 ,if ?is be done ) ! o!r t]m in/ead1 we h ,no ,a is ,xf :i* univ]sal premises we _c d$uce a univ]sal conclusion1 b only ,"s ,b is n ,a4 ,e ,x is ,b ,if we weak5 "o & ! o!r ( ^! premises1 z !y /&1 we obta9 ,"s ,a is n ,x ,no ,a is ,x ,e ,x is ,b & ,"s ,x is ,b -------------------------------- ------------------------------ ,no conclusion ,"s ,b is n ,a equival5t to ! f\r? ( ! prec$+3 b if we conv]t ! fir/ premiss1 & proce$ 9 ! same mann]1 ,no ,x is ,a ,"s ,x is n ,a ,f ,e ,x is ,b we obta9 ,e ,x is ,b -------------------------------- -------------------------------- ,"s ,b is n ,a ,"s ,b is n ,a :i* is legitimate1 & is ! same z ! la/ ( ! prec$+ li/1 ) ,a & ,b int]*ang$4 ,be=e proce$+ to %ew t all ! usual =ms are conta9$ 9 ! prec$+1 let ! read] rem>k ! foll[+ rules1 :i* may be prov$ ei!r by collect+ !m f ! prec$+ cases1 or by indep5d5t reason+4 #a4 ,! middle t]m mu/ ent] univ]sally into "o or ! o!r premiss4 ,if x 7 n s1 ! "o premiss might speak ( "o "p ( ! middle t]m1 & ! o!r ( ! o!r2 s t !re w\ld1 9 fact1 be no middle t]m4 ,?us1 #8,e ,a is ,x1 ,e ,b is ,x1' gives no conclusion3 x may be ?us /at$2 ,all ! ,z make up a "p ( ! ,xs ,all ! ,bs make up a "p ( ! ,xs ,&1 be=e we c "k t !re is any common t]m ( comp>ison at all1 we mu/ h "s means ( %ew+ t ! two p>ts are ! same2 or ! prec$+ premises by !mselves are inconclusive4 #b4 ,no t]m mu/ ent] ! conclusion m g5]ally ?an x is f\nd 9 ! premises2 ?us1 if ,a be spok5 ( p>tially 9 ! premises1 x mu/ ent] p>tially into ! conclusion4 ,?is is obvi\s1 s9ce ! conclusion mu/ ass]t no m ?an ! premises imply4 #c4 ,f premises bo? negative no conclusion c be drawn4 ,= x is obvi\s1 t ! m]e ass]tion ( disagreem5t betwe5 ea* ( two ?+s & a ?ird1 c be no reason = inf]r+ ei!r agreem5t or disagreem5t betwe5 ^! two ?+s4 ,x w n be difficult to r$uce any case :i* falls "u ?is rule to a brea* ( ! fir/ rule3 ?us1 ,no ,a is ,x1 ,no ,b is ,x1 gives ,e ,a is 7some?+ :i* is n ,x7 ,e ,b is 7some?+ :i* is n ,x7 9 :i* ! middle t]m is n spok5 ( univ]sally 9 ei!r4 ,aga91 #8,no ,x is ,a1 ,"s ,x is n ,b1' may be conv]t$ into ,e ,a is 7a ?+ :i* is n ,x7 ,"s 7?+ :i* is n ,b7 is ,x 9 :i* !re is no middle t]m4 #d4 ,f premises bo? p>ticul> no conclusion c be drawn4 ,?is is suffici5tly obvi\s :5 ! fir/ or second rule is brok51 z 9 #8,"s ,a is ,x1 ,"s ,b is ,x4' ,b x is n imm$iately obvi\s :5 ! middle t]m ent]s "o ( ! premises univ]sally4 ,! foll[+ reason+ w s]ve = ex]cise 9 ! prec$+ results4 ,s9ce bo? premises are p>ticul> 9 =m1 ! middle t]m c only ent] "o ( !m univ]sally by be+ ! pr$icate ( a negative proposition2 consequ5tly 7,rule #c7 ! o!r premiss mu/ be affirmative1 &1 be+ p>ticul>1 nei!r ( its t]ms is univ]sal4 ,consequ5tly bo? ! t]ms z to :i* ! conclusion is to be drawn ent] p>tially1 & ! conclusion 7,rule #b7 c only be a p>ticul> affirmative proposition4 ,b if "o ( ! premises be negative1 ! conclusion mu/ be negative 7z we %all imm$iately see74 ,?is contradiction %ews t ! supposition ( p>ticul> premises produc+ a legitimate result is inadmissible4 #e4 ,if "o premiss be negative1 ! conclusion1 if any1 mu/ be negative4 ,if "o t]m agree ) a second & disagree ) a ?ird1 no agreem5t c be inf]r$ betwe5 ! second & ?ird4 #f4 ,if "o premiss be p>ticul>1 ! conclusion mu/ be p>ticul>4 ,?is is n v obvi\s1 s9ce ! middle t]m may be univ]sally spok5 ( 9 a p>ticul> proposition1 z 9 ,"s ,b is n ,x4 ,b ?is requires "o negative proposition1 :5ce 7,rule #c7 ! o!r mu/ be affirmative4 ,aga91 s9ce ! conclusion mu/ be negative 7,rule #e7 its pr$icate is spok5 ( univ]sally1 &1 !re=e1 mu/ ent] univ]sally2 ! o!r t]m ,a mu/ ent]1 !n1 9 a univ]sal affirmative proposition1 :i* is aga9/ ! supposition4 ,9 ! prec$+ set ( syllogisms we obs]ve "o =m only :i* produces ,a1 or ,e1 or ,i1 b ?ree :i* produce ,o4 ,let an ass]tion be said to be weak5$ :5 x is r$uc$ f univ]sal to p>ticul>1 & /r5g!n$ 9 ! contr>y case4 ,?us1 #8,e ,a is ,b' is call$ /rong] ?an #8,"s ,a is ,b4' ,e =m ( syllogism :i* c give a legitimate result is ei!r "o ( ! prec$+ six1 or ano!r =m$ f "o ( ! six1 ei!r by *ang+ "o ( ! ass]tions into its conv]se1 if t be all[able1 or by /r5g!n+ "o ( ! premises )\t alt]+ ! conclusion1 or bo?4 ,?us1 ,"s ,a is ,x may be writt5 ,"s ,x is ,a ,e ,x is ,b ,e ,x is ,b ,:at foll[s w /ill foll[ f ,e ,x is ,a ,e ,x is ,b = all :i* is true :5 #8,"s ,x is ,a1' is n less true :5 #8,e ,x is ,a4' ,x w\ld be possible also to =m a legitimate syllogism by weak5+ ! conclusion1 :5 x is univ]sal1 s9ce t :i* is true ( all is true ( "s4 ,?us1 #8,e ,a is ,x1 ,e ,x is ,b1' :i* yields #8,e ,a is ,b1' also yields #8,"s ,a is ,b4' ,b writ]s on logic h always consid]$ ^! syllogisms z useless1 conceiv+ x bett] to draw f any premises _! /ronge/ conclusion4 ,9 ?is !y 7 und\bt$ly "r2 & ! only "q is1 :e!r x w\ld n h be5 advisable to make ! premises z weak z possible1 & n to admit any syllogisms 9 :i* m appe>$ ?an 0 absolutely necess>y to ! conclusion4 ,if su* _h be5 ! practice1 !n ,e ,x is ,a1 ,e ,x is ,b1 !re=e ,"s ,a is ,b w\ld h be5 consid]$ z =m$ by a spuri\s & unnecess>y excess ( ass]tion4 ,! m9imum ( ass]tion w\ld be conta9$ 9 ei!r ( ! foll[+1 ,e ,x is ,a1 ,"s ,x is ,b1 !re=e ,"s ,a is ,b ,"s ,x is ,a1 ,e ,x is ,b1 !re=e ,"s ,a is ,b ,9 ?is tract1 syllogisms h be5 divid$ into two classes3 fir/1 ^? :i* prove a univ]sal conclusion2 secondly1 ^? :i* prove a p>tial conclusion1 & :i* are 7all b "o7 d]iv$ f ! fir/ by weak5+ "o ( ! premises1 9 su* mann] z to produce a legitimate b weak5$ conclusion4 ,^? ( ! fir/ class are plac$ 9 ! fir/ column1 & ! o!r 9 ! second4 ,univ]sal4 ,p>ticul>4 ,a ,e ,a is ,x ,"s ,a is ,x ,i ,a ,e ,x is ,b ,e ,x is ,b ,a ------------------------ -------------------------- ,a ,e ,a is ,b ,"s ,a is ,b ,i ,"s ,a is ,x ,i ,no ,x is ,b ,e ------------------------------ ,a ,e ,a is ,x ,"s ,a is n ,b ,o ,e ,no ,x is ,b ,e ,a is ,x ,a ------------------------ ,e ,no ,a is ,b ,"s ,b is n ,x ,o ------------------------------ ,"s ,b is n ,a ,o ,e ,x is ,a ,a 444444 ,"s ,x is n ,b ,o ------------------------------ ,"s ,a is n ,b ,o ,9 all works on logic1 x is cu/om>y to write t premiss fir/ :i* conta9s ! pr$icate ( ! conclusion4 ,?us1 ,e ,x is ,b ,e ,a is ,x ,e ,a is ,x w\ld be writt51 & n ,e ,x is ,b ------------------------ ------------------------ ,e ,a is ,b ,e ,a is ,b ,! premises ?us arrang$ are call$ major & m9or2 ! pr$icate ( ! conclusion be+ call$ ! major t]m1 & its subject ! m9or4 ,aga91 9 ! prec$+ case we see ! v>i\s subjects com+ 9 ! ord] ,x1 ,b2 ,a1 ,x2 ,a1 ,b3 & ! numb] ( diff]5t ord]s :i* c appe> is f\r1 namely-- ,,xb ,,bx ,,xb ,,bx ,,ax ,,ax ,,xa ,,xa ---- ---- ---- ---- ,,ab ,,ab ,,ab ,,ab :i* are call$ ! f\r figures1 & e k9d ( syllogism 9 ea* figure is call$ a mood4 ,i n[ put d[n ! v>i\s moods ( ea* figure1 ! lett]s ( :i* w be a guide to f9d out ^? ( ! prec$+ li/ f :i* !y are d]iv$4 ,co means t a premiss ( ! prec$+ li/ has be5 conv]t$2 t x has be5 /r5g!n$2 ,co 1 t bo? *anges h tak5 place4 ,?us1 ,a ,e ,x is ,b ,a ,e ,x is ,b ,i ,"s ,a is ,x becomes ,a ,e ,x is ,a3 7,co 7 ------------------------ ------------------------ ,i ,"s ,a is ,b ,i ,"s ,a is ,b ,& ,co abbreviates ! foll[+3 ,if "s ,a be ,x1 !n "s ,x is ,a 7,co72 & all t is true :5 ,"s ,x is ,a1 is true :5 ,e ,x is ,a 772 !re=e ! second is legitimate1 if ! fir/ be s4 ,fir/ ,figure4 ,a ,e ,x is ,b ,a ,e ,x is ,b ,a ,e ,a is ,x ,i ,"s ,a is ,x ------------------------ ---------------------------- ,a ,e ,a is ,b ,i ,"s ,a is ,b ,e ,no ,x is ,b ,e ,no ,x is ,b ,a ,e ,a is ,x ,i ,"s ,a is ,x ------------------------ -------------------------------- ,e ,no ,a is ,b ,o ,"s ,a is n ,b ,second ,figure4 ,e ,no ,b is ,x 7,co7 ,e ,no ,b is ,x 7,co7 ,a ,e ,a is ,x ,i ,"s ,a is ,x ------------------------ ---------------------------------- ,e ,no ,a is ,b ,o ,"s ,a is n ,b ,a ,e ,b is ,x ,a ,e ,b is ,x ,e ,no ,a is ,x 7,co7 ,o ,"s ,a is n ,x ------------------------ -------------------------------- ,e ,no ,a is ,b ,o ,"s ,a is n ,b ,?ird ,figure4 ,a ,e ,x is ,b ,e ,no ,x is ,b ,a ,e ,x is ,a 7,co7 ,a ,e ,x is ,a 7,co7 ------------------------ ------------------------------------ ,i ,"s ,a is ,b ,o ,"s ,a is n ,b ,i ,"s ,x is ,b 7,co7 ,o ,"s ,x is n ,b ,a ,e ,x is ,a ,a ,e ,x is ,a ------------------------ -------------------------------- ,i ,"s ,a is ,b ,o ,"s ,a is n ,b ,a ,e ,x is ,b ,e ,no ,x is ,b ,i ,"s ,x is ,a 7,co7 ,i ,"s ,x is ,a 7,co7 ------------------------ ---------------------------------- ,i ,"s ,a is ,b ,o ,"s ,a is n ,b ,f\r? ,figure4 ,a ,e ,b is ,x 77 ,i ,"s ,b is ,x ,a ,e ,x is ,a ,a ,e ,x is ,a ------------------------ ------------------------ ,i ,"s ,a is ,b ,i ,"s ,b is ,a ,a ,e ,b is ,x ,e ,no ,b is ,x 7,co7 ,e ,no ,x is ,a ,a ,e ,x is ,a 7,co7 ------------------------ ------------------------------------ ,e ,no ,a is ,b ,o ,"s ,a is n ,b ,e ,no ,b is ,x 7,co7 ,i ,"s ,x is ,a 7,co7 -------------------------------- ,o ,"s ,a is n ,b ,! above is ! anci5t me?od ( divid+ syllogisms2 b1 = ! pres5t purpose1 x w be suffici5t to consid] ! six f :i* ! re/ c be obta9$4 ,& s9ce "s ( ! six h ,a 9 ! pr$icate ( ! conclusion1 & n ,b1 we %all jo9 to !m ! six o!r syllogisms :i* are f\nd by transpos+ ,b & ,a4 ,! complete li/1 !re=e1 ( syllogisms ) ! weake/ premises & ! /ronge/ conclusions1 9 :i* a comp>ison ( ,a & ,b is obta9$ by comp>ison ( bo? ) ,x1 is z foll[s3 ,e ,a is ,x ,e ,b is ,x ,"s ,a is ,x ,"s ,b is ,x ,e ,x is ,b ,e ,x is ,a ,no ,x is ,b ,no ,x is ,a ------------------------ ------------------------ -------------------------------- -------------------------------- ,e ,a is ,b ,e ,b is ,a ,"s ,a is n ,b ,"s ,b is n ,a ,e ,a is ,x ,e ,b is ,x ,e ,a is ,x ,e ,b is ,x ,no ,x is ,b ,no ,x is ,a ,"s ,b is n ,x ,"s ,a is n ,x ------------------------ ------------------------ -------------------------------- -------------------------------- ,no ,a is ,b ,no ,b is ,a ,"s ,b is n ,a ,"s ,a is n ,b ,"s ,a is ,x ,"s ,b is ,x ,e ,x is ,a ,e ,x is ,b ,e ,x is ,b ,e ,x is ,a ,"s ,x is n ,b ,"s ,x is n ,a ------------------------ ------------------------ -------------------------------- -------------------------------- ,"s ,a is ,b ,"s ,b is ,a ,"s ,a is n ,b ,"s ,b is n ,a ,9 ! li/ ( page #ai1 !re 0 no?+ b recapitulation ( =ms1 ea* =m admitt+ a v>iation by int]*ang+ ,a & ,b4 ,?is int]*ange hav+ be5 made1 & ! results collect$ z above1 if we take e case 9 :i* ,b is ! pr$icate1 or c be made ! pr$icate by all[able conv]sion1 we h a collection ( all possible weake/ =ms 9 :i* ! result is "o ( ! f\r #8,e ,a is ,b1' #8,no ,a is ,b1' #8,"s ,a is ,b1' #8,"s ,a is n ,b'2 z foll[s4 ,! premises are writt5 9 :at appe>$ ! mo/ natural ord]1 )\t di/9ction ( major or m9or2 & ! lett]s prefix$ are accord+ to ! =ms ( ! sev]al premises1 z 9 page #aj4 ,a ,e ,a is ,x ,u ,e ,x is ,b ------------------------ ,a ,e ,a is ,b ,i ,"s ,a is ,x ,i ,"s ,b is ,x ,u ,e ,x is ,b ,u ,e ,x is ,a ------------------------ ------------------------ ,i ,"s ,a is ,b ,i ,"s ,a is ,b ,a ,e ,a is ,x ,a ,e ,b is ,x ,e ,no ,b is ,x ,e ,no ,a is ,x ------------------------ ------------------------ ,e ,no ,a is ,b ,e ,no ,a is ,b ,i ,"s ,a is ,x ,a ,e ,b is ,x ,u ,e ,x is ,a ,e ,no ,b is ,x ,o ,"s ,a is n ,x ,y ,"s ,x is n ,b -------------------------------- -------------------------------- -------------------------------- ,o ,"s ,a is n ,b ,o ,"s ,a is n ,b ,o ,"s ,a is n ,b ,e ass]tion :i* c be made ^u two ?+s by comp>ison ) any ?ird1 t is1 e simple inf]5ce1 c be r$uc$ to "o ( ! prec$+ =ms4 ,g5]ally speak+1 "o ( ! premises is omitt$1 z obvi\s f ! conclusion2 t is1 "o premiss be+ nam$ & ! conclusion1 t premiss is impli$ :i* is necess>y to make ! conclusion good4 ,?us1 if ,i say1 8,t race mu/ h possess$ "s ( ! arts ( life1 = !y came f ,asia10 x is obvi\sly meant to be ass]t$1 t all races com+ f ,asia mu/ h possess$ "s ( ! arts ( life4 ,! prec$+ is !n a syllogism1 z foll[s3 #8,t race' is #8a race ( ,asiatic orig93' ,e #8race ( ,asiatic orig9' is #8a race :i* mu/ h possess$ "s ( ! arts ( life3' ,!re=e1 ,t race is a race :i* mu/ h possess$ "s ( ! arts ( life4 ,a p]son :o makes ! prec$+ ass]tion ei!r means to imply1 antec$5tly to ! conclusion1 t all ,asiatic races mu/ h possess$ arts1 or he talks nons5se if he ass]ts ! conclusion positively4 #8,a mu/ be ,b1 = x is ,x1' c only be true :5 #8,e ,x is ,b4' ,?is latt] proposition may be call$ ! suppress$ premiss2 & x is 9 su* suppress$ propositions t ! greate/ dang] ( error lies4 ,x is also 9 su* propositions t m5 convey op9ions :i* !y w\ld n will+ly express4 ,?us1 ! hone/ witness :o said1 #8,i always ?\ght him a respectable man--he kept 8 gig1' w\ld probably n h admitt$ 9 direct t]ms1 #8,e man :o keeps a gig mu/ be respectable4' ,i %all n[ give a few deta*$ illu/rations ( :at prec$es4 8,8 imbecility ( "* might h be5 inf]r$ f 8 pron5ess to fav\rites2 = all weak pr9ces h ?is fail+40 ,! prec$+ w\ld /& v well 9 a hi/ory1 & _m w\ld pass x ov] z conta9+ v good inf]5ce4 ,writt51 h[ev]1 9 ! =m ( a syllogism1 x is1 ,all weak pr9ces are prone to fav\rites ,he 0 prone to fav\rites -------------------------------- ---------------------------------------- ------ ,!re=e ,he 0 a weak pr9ce :i* is palpably wrong4 7,rule #a47 ,! writ] ( su* a s5t5ce z ! prec$+ might h meant to say1 #8= all :o h ?is fail+ are weak pr9ces2' 9 :i* case he w\ld h inf]r$ rightly4 ,e "o %\ld be aw>e t !re is mu* false inf]5ce aris+ out ( badness ( /yle1 :i* is j z injuri\s to ! habits ( ! untra9$ read] z if ! errors 7 mi/akes ( logic 9 ! m9d ( ! writ]4 #8,a is less ?an ,b2 ,b is less ?an ,c3 !re=e ,a is less ?an ,c4' ,?is1 at fir/ sight1 appe>s to be a syllogism2 b1 on r$uc+ x to ! usual =m1 we f9d x to be1 ,a is 7a magnitude less ?an ,b7 ,b is 7a magnitude less ?an ,c7 ,!re=e ,a is 7a magnitude less ?an ,c7 :i* is n a syllogism1 s9ce !re is no middle t]m4 ,evid5t z ! prec$+ is1 ! foll[+ additional proposition mu/ be =m$ be=e x c be made explicitly logical4 #8,if ,b be a magnitude less ?an ,c1 !n e magnitude less ?an ,b is also less ?an ,c4' ,!re is1 !n1 be=e ! prec$+ c be r$uc$ to a syllogi/ic =m1 ! necessity ( a d$uction f ! second premiss1 & ! sub/itution ( ! result in/ead ( t premiss4 ,?us1 ,a is less ?an ,b ,less ?an ,b is less ?an ,c3 foll[+ f ,b is less ?an ,c4 ------------------ ---------------------------------- ,!re=e ,a is less ?an ,c ,b1 if ! additional argum5t be exam9$--namely1 if ,b be less ?an ,c1 !n t :i* is less ?an ,b is less ?an ,c--x w be f\nd to require precisely ! same consid]ations repeat$2 = ! orig9al inf]5ce 0 no?+ m4 ,9 fact1 x may easily be se5 z foll[s1 t ! proposition be=e u involves m ?an any simple syllogism c express4 ,:5 we say t ,a is less ?an ,b1 we say t if ,a 7 appli$ to ,b1 e "p ( ,a w\ld mat* a "p ( ,b1 & !re w\ld be p>ts ( ,b rema9+ ov]4 ,b :5 we say1 #8,e ,a is ,b1' mean+ ! premiss ( a common syllogism1 we say t e in/ance ( ,a is an in/ance ( ,b1 )\t say+ any ?+ z to :e!r !re are or are n in/ances ( ,b /ill left1 aft] ^? :i* are also ,a are tak5 away4 ,if1 !n1 we wi% to write an ord9>y syllogism 9 a mann] :i* %all correspond ) #8,a is less ?an ,b1 ,b is less ?an ,c1 !re=e ,a is less ?an ,c1' we mu/ introduce a m def9ite am\nt ( ass]tion ?an 0 made 9 ! prec$+ =ms4 ,?us1 ,e ,a is ,b1 & !re are ,bs :i* are n ,z ,e ,b is ,c1 & !re are ,cs :i* are n ,bs ---------------------------------------- ---------------------------------------- -------------- ,!re=e ,e ,a is ,c1 & !re are ,cs :i* are n ,z ,or ?us3 ,! ,bs conta9 all ! ,z1 & m ,! ,cs conta9 all ! ,bs1 & m ---------------------------------------- ------------------------------ ,! ,cs conta9 all ! ,z1 & m ,! mo/ te*nical =m1 h[ev]1 is1 ,f ,e ,a is ,b2 ,"s ,b is n ,a ,e ,b is ,c2 ,"s ,c is n ,b ,foll[s ,e ,a is ,c2 ,"s ,c is n ,a ,?is sort ( argum5t is call$ =tiori argum5t1 because ! premises are m ?an suffici5t to prove ! conclusion1 & ! ext5t ( ! conclusion is !reby great] ?an its m]e =m w\ld indicate4 ,?us1 #8,a is less ?an ,b1 ,b is less ?an ,c1 !re=e1 =tiori1 ,a is less ?an ,c1' means t ! ext5t to :i* ,a is less ?an ,c mu/ be great] ?an t to :i* ,a is less ?an ,b1 or ,b ?an ,c4 ,9 ! syllogism la/ writt51 ei!r ( ! bracket$ premises might be /ruck out )\t de/roy+ ! conclusion2 :i* la/ w\ld1 h[ev]1 be weak5$4 ,z x /&s1 !n1 ! "p ( ! conclusion1 #8,"s ,c is n ,a1' foll[s x =tiori4 ,! argum5t =tiori1 may !n be def9$ z a univ]sally affirmative syllogism1 9 :i* bo? ( ! premises are %ewn to be less ?an ! :ole tru?1 or great]4 ,?us1 9 #8,e ,a is ,x1 ,e ,x is ,b1 !re=e ,e ,a is ,b1' we d n c]ta9ly imply t !re are m ,xs ?an ,z1 or m ,bs ?an ,xs1 s t we d n "k t !re are m ,bs ?an ,z4 ,b if we are at lib]ty to /ate ! syllogism z foll[s1 ,all ! ,z make up "p 7& "p only7 ( ! ,xs ,e ,x is ,b2 !n we are c]ta9 t ,all ! ,z make up "p 7& "p only7 ( ! ,bs4 ,b if we are at lib]ty fur!r to say t ,all ! ,z make up "p 7& "p only7 ( ! ,xs ,all ! ,xs make up "p 7& "p only7 ( ! ,bs !n we conclude t ,all ! ,z make up "p ( "p 7only7 ( ! ,bs & ! words 9 ,italics m>k t quality ( ! conclusion f :i* ! argum5t is call$ =tiori4 ,mo/ syllogisms :i* give an affirmative conclusion are g5]ally meant to imply =tiori argum5ts1 except only 9 ma!matics4 ,x is seldom1 except 9 ! exact sci5ces1 t we meet ) a proposition1 #8,e ,a is ,b1' :i* we _c imm$iately c\ple ) #8,"s ,bs are n ,z4' ,:5 an argum5t is completely e/abli%$1 ) ! exception ( "o ass]tion only1 s t ! inf]5ce may be drawn z soon z t "o ass]tion is e/abli%$1 ! result is /at$ 9 a =m :i* be>s ! "n ( an hypo!tical syllogism4 ,! ^w hypo!sis means no?+ b supposition2 & ! species ( syllogism j m5tion$ fir/ lays d[n ! ass]tion t a consequ5ce w be true if a c]ta9 condition be fulfill$1 & !n ei!r ass]ts ! fulfilm5t ( ! condition1 & !nce ! consequ5ce1 or else d5ies ! consequ5ce1 & !nce d5ies ! fulfilm5t ( ! condition4 ,?us1 if we "k t ,:5 ,a is ,b1 x foll[s t ,p is ,q2 !n1 z soon z we c asc]ta9 t ,a is ,b1 we c conclude t ,p is ,q2 or1 if we c %ew t ,p is n ,q1 we "k t ,a is n ,b4 ,b if we f9d t ,a is n ,b1 we c inf] no?+2 = ! prec$+ does n ass]t t ,p is ,q only :5 ,a is ,b4 ,& if we f9d out t ,p is ,q1 we c inf] no?+4 ,?is conditional syllogism may be conv]t$ into an ord9>y syllogism1 z foll[s4 ,let ,k be any #8case 9 :i* ,a is ,b1' & ,z a #8case 9 :i* ,p is ,q'2 !n ! prec$+ ass]tion am\nts to #8,e ,k is ,z4' ,let ,l be a p>ticul> in/ance1 ! ,a ( :i* may or may n be ,b4 ,if ,a be ,b 9 ! in/ance "u discussion1 or if ,a be n ,b1 we h1 9 ! "o case & ! o!r1 ,e ,k is ,z ,e ,k is ,z ,l is a ,k ,l is n a ,k ---------------- -------------------------- ,!re=e ,l is a ,z ,no conclusion ,simil>ly1 accord+ z a p>ticul> case 7,m7 is or is n ,z1 we h ,e ,k is ,z ,e ,k is ,z ,m is a ,z ,m is n a ,z -------------------------- ------------------------ ,no conclusion ,m is n a ,k ,t is to say3 ,! ass]tion ( an hypo!sis is ! ass]tion ( its necess>y consequ5ce1 & ! d5ial ( ! necess>y consequ5ce is ! d5ial ( ! hypo!sis2 b ! ass]tion ( ! necess>y consequ5ce gives no "r to ass]t ! hypo!sis1 nor does ! d5ial ( ! hypo!sis give any "r to d5y ! tru? ( t :i* w\ld 77 ! hypo!sis true7 be its necess>y consequ5ce4 ,demon/ration is ( two k9ds3 :i* arises f ?is1 t e proposition has a contradictory2 & ( ^! two1 "o mu/ be true & ! o!r mu/ be false4 ,we may !n ei!r prove a proposition to be true1 or its contradictory to be false4 #8,x is true t ,e ,a is ,b1' &1 #8x is false t !re are "s ,z :i* are n ,bs1' are ! same proposition2 & ! pro( ( ei!r is call$ ! indirect pro( ( ! o!r4 ,b h[ is any proposition to be prov$ false1 except by prov+ a contradiction to be true8 ,by prov+ a necess>y consequ5ce ( ! proposition to be false4 ,b ?is is n a complete answ]1 s9ce x involves ! necessity ( do+ ! same ?+2 or1 s f> z ?is answ] goes1 "o proposition _c be prov$ false unless by prov+ ano!r to be false4 ,b x may happ51 t a necess>y consequ5ce c be obta9$ :i* is obvi\sly & self-evid5tly false1 9 :i* case no fur!r pro( ( ! falsehood ( ! hypo!sis is necess>y4 ,?us ! pro( :i* ,euclid gives t all equiangul> triangles are equilat]al is ( ! foll[+ /ructure1 logically consid]$4 7#a47 ,if !re be an equiangul> triangle n equilat]al1 x foll[s t a :ole c be f\nd :i* is n great] ?an its "p4#a ,footnote #a3 ,?is is ! proposition 9 pro( ( :i* ne>ly ! :ole ( ! demon/ration ( ,euclid is sp5t4 7#b47 ,x is false t !re c be any :ole :i* is n great] ?an its "p 7self evid5t74 7#c47 ,!re=e x is false t !re is any equiangul> triangle :i* is n equilat]al2 or all equiangul> triangles are equilat]al4 ,:5 a proposition is e/abli%$ by prov+ ! tru? ( ! matt]s x conta9s1 ! demon/ration is call$ direct2 :5 by prov+ ! falsehood ( e contradictory proposition1 x is call$ indirect4 ,! latt] species ( demon/ration is z logical z ! =m]1 b n ( s simple a k9d2 :5ce x is desirable to use ! =m] :5ev] x c be obta9$4 ,! use ( indirect demon/ration 9 ! ,elem5ts ( ,euclid is almo/ entirely conf9$ to ^? propositions 9 :i* ! conv]ses ( simple propositions are prov$4 ,x frequ5tly happ5s t an e/abli%$ ass]tion ( ! =m ,e ,a is ,b 7#a7 may be easily made ! means ( d$uc+1 ,e 7?+ n ,a7 is n ,b 7#b7 :i* la/ gives ,e ,b is ,a 7#c7 ,! conv]sion ( ! second proposition into ! ?ird is usually made by an indirect demon/ration1 9 ! foll[+ mann]4 ,if possible1 let !re be "o ,b :i* is n ,a1 7#b7 be+ true4 ,!n !re is "o ?+ :i* is n ,a & is ,b2 b e ?+ n ,a is n ,b2 !re=e !re is "o ?+ :i* is ,b & is n ,b3 :i* is absurd4 ,x is !n absurd t !re %\ld be "o s+le ,b :i* is n ,a2 or1 ,e ,b is ,a4 ,! foll[+ proposition conta9s a me?od :i* is ( frequ5t use4 ,,hypo!sis4--,let !re be any numb] ( propositions or ass]tions1--?ree = in/ance1 ,a1 ,b1 & ,c1--( :i* x is ! prop]ty t "o or ! o!r mu/ be true1 & "o only4 ,let !re be ?ree o!r propositions1 ,p1 ,q1 & ,r1 ( :i* x is also ! prop]ty t "o1 & "o only1 mu/ be true4 ,let x also be a connexion ( ^? ass]tions1 t ,:5 ,a is true1 ,p is true ,:5 ,b is true1 ,q is true ,:5 ,c is true1 ,r is true ,,consequ5ce3 !n x foll[s t ,:5 ,p is true1 ,a is true ,:5 ,q is true1 ,b is true ,:5 ,r is true1 ,c is true ,=1 :5 ,p is true1 !n ,q & ,r mu/ be false2 consequ5tly1 nei!r ,b nor ,c c be true1 = !n ,q or ,r w\ld be true4 ,b ei!r ,a1 ,b1 or ,c mu/ be true1 !re=e ,a mu/ be true2 or1 :5 ,p is true1 ,a is true4 ,9 a simil> way ! rema9+ ass]tions may be prov$4 ,case #a4 ,if ,:5 ,p is ,q1 ,a is ,b ,:5 ,p is n ,q1 ,a is n ,b ,x foll[s t,:5 ,a is ,b1 ,p is ,q ,:5 ,a is n ,b1 ,p is n ,q ,case #b4 ,if ,:5 ,a is great] ?an ,b1 ,p is great] ?an ,q ,:5 ,a is equal to ,b1 ,p is equal to ,q ,:5 ,a is less ?an ,b1 ,p is less ?an ,q ,x foll[s t,:5 ,p is great] ?an ,q1 ,a is great] ?an ,b ,:5 ,p is equal to ,q1 ,a is equal to ,b ,:5 ,p is less ?an ,q1 ,a is less ?an ,b 99 99 99 99 99 ,we h hi!rto suppos$ t ! premises are actually true2 &1 9 su* a case1 ! logical conclusion is z c]ta9 z ! premises4 ,x rema9s to say a few words ^u ! case 9 :i* ! premises are probably1 b n c]ta9ly1 true4 ,! probability ( an ev5t be+ ab\t to happ51 & t ( an argum5t be+ true1 may be s connect$ t ! usual me?od ( measur+ ! fir/ may be made to give an easy me?od ( express+ ! second4 ,suppose an urn1 or lott]y1 ) a l>ge numb] ( balls1 black or :ite2 !n1 if !re be twelve :ite balls to "o black1 we say x is twelve to "o t a :ite ball w be drawn1 or t a :ite ball is twelve times z probable z a black "o4 ,a c]ta9 ass]tion may be 9 ! same condition z to ! =ce ( probability ) :i* x /rikes ! m9d3 t is1 ! que/ions ,is ! ass]tion true8 ,w a :ite ball be drawn8 may be su* t ! answ]1 #8mo/ probably1' expresses ! same degree ( likelihood 9 bo? cases4 ,we h be=e expla9$ t logic has no?+ to d ) ! tru? or falsehood ( ass]tions1 b only pr(esses1 suppos+ !m true1 to collect & classify ! legitimate me?ods ( draw+ inf]5ces4 ,simil>ly1 9 ?is "p ( ! subject1 we d n tr\ble ourselves ) ! "q1 ,h[ are we to f9d ! probability due to premises8 b we ask3 ,suppos+ 7happ5 h[ x may7 t we h f\nd ! probability ( ! premises1 requir$ ! probability ( ! conclusion4 ,:5 ! odds 9 fav\r ( a conclusion are1 say #f to #a1 !re are1 out ( e #g possible *ances1 #f 9 fav\r ( ! conclusion1 & #a aga9/ x4 ,h5ce & w repres5t ! proportions1 = & aga9/1 ( all ! possible cases :i* exi/4 ,?us we h ! succession ( su* results z 9 ! foll[+ table3-- ,odds 9 fav\r ( an ev5t ,probability = ,probability aga9/ #a to #a #b to #a #c to #a #c to #b #d to #a #d to #c #e to #a c4 c4 c4 ,let ! probability ( a conclusion1 z d]iv$ f ! premises 7t is on ! supposition t x 0 nev] imag9$ to be possible till ! argum5t 0 he>d71 be call$ ! intr9sic probability ( ! argum5t4 ,?is is f\nd by multiply+ toge!r ! probabilities ( all ! ass]tions :i* are necess>y to ! argum5t4 ,?us1 suppose t a conclusion 0 held to be impossible until an argum5t ( a s+le syllogism 0 produc$1 ! premises ( :i* h sev]ally five to "o & eight to "o 9 _! fav\r4 ,!n 1 or 1 is ! intr9sic probability ( ! argum5t1 & ! odds 9 its fav\r are #dj to #ad1 or #bj to #g4 ,b ?is intr9sic probability is n always t ( ! conclusion2 ! latt]1 ( c\rse1 dep5d+ 9 "s degree on ! likelihood :i* ! conclusion 0 suppos$ to h be=e ! argum5t 0 produc$4 ,a syllogism ( #bj to #g 9 its fav\r1 advanc$ 9 fav\r ( a conclusion :i* 0 be=eh& z likely z n1 produces a mu* m probable result ?an if ! conclusion _h be5 ?\ght absolutely false until ! argum5t produc$ a c]ta9 belief 9 ! possibility ( its be+ true4 ,! *ange made 9 ! probability ( a conclusion by ! introduction ( an argum5t 7or ( a new argum5t1 if "s h already prec$$7 is f\nd by ! foll[+ rule4 ,f ! sum ( ! exi/+ probability ( ! conclusion & ! intr9sic probability ( ! new argum5t1 take _! product2 ! rema9d] is ! probability ( ! conclusion1 z re9=c$ by ! argum5t4 ,?us1 a b ab is ! probability ( ! tru? ( a conclusion aft] ! introduction ( an argum5t ( ! intr9sic probability b1 ! previ\s probability ( ! said conclusion hav+ be5 a4 ,?us1 a conclusion :i* has at pres5t ! *ance 9 its fav\r1 :5 re9=c$ by an argum5t ^: intr9sic probability is 1 acquires ! probability or1 1 or 2 or1 hav+ #b to #a 9 its fav\r be=e1 x has #aa to #a 9 its fav\r aft]1 ! argum5t4 ,:5 ! conclusion 0 nei!r likely nor unlikely be=eh& 7or _h ! probability 71 ! %orte/ way ( apply+ ! prec$+ rule 79 :i* a b ab becomes b7 is to divide ! sum ( ! num]ator & d5om9ator ( ! intr9sic probability ( ! argum5t by twice ! d5om9ator4 ,?us1 an argum5t ( :i* ! intr9sic probability is 1 gives to a conclusion on :i* no bias previ\sly exi/$1 ! probability or 7#c #d7_/7b #d74 ,,! ,,end4 ,,london3--,,pr9t$ ,,by ,,james ,,moyes1 ,ca/le ,/reet1 ,leice/] ,squ>e4 ---------------------------------------- -------------------------------- ,,transcrib]',s ,,notes #a4 ,sil5tly correct$ obvi\s typographical errors & v>iations 9 spell+4 #b4 ,reta9$ ar*aic1 non-/&>d1 & unc]ta9 spell+s z pr9t$4 #c4 ,enclos$ italics font 9 und]scores4