prior analytics-第23章

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　　In　the　third　figure　an　affirmative　syllogism　can　never　be　made　out



of　opposite　premisses；　for　the　reason　given　in　reference　to　the



first　figure；　but　a　negative　syllogism　is　possible　whether　the　terms



are　universal　or　not。　Let　B　and　C　stand　for　science；　A　for　medicine。



If　then　one　should　assume　that　all　medicine　is　science　and　that　no



medicine　is　science；　he　has　assumed　that　B　belongs　to　all　A　and　C　to



no　A；　so　that　a　particular　science　will　not　be　a　science。　Similarly　if



the　premiss　BA　is　not　assumed　universally。　For　if　some　medicine　is



science　and　again　no　medicine　is　science；　it　results　that　some　science



is　not　science；　The　premisses　are　contrary　if　the　terms　are　taken



universally；　if　one　is　particular；　they　are　contradictory。



　　We　must　recognize　that　it　is　possible　to　take　opposites　in　the　way



we　said；　viz。　'all　science　is　good'　and　'no　science　is　good'　or



'some　science　is　not　good'。　This　does　not　usually　escape　notice。　But



it　is　possible　to　establish　one　part　of　a　contradiction　through



other　premisses；　or　to　assume　it　in　the　way　suggested　in　the　Topics。



Since　there　are　three　oppositions　to　affirmative　statements；　it



follows　that　opposite　statements　may　be　assumed　as　premisses　in　six



ways；　we　may　have　either　universal　affirmative　and　negative；　or



universal　affirmative　and　particular　negative；　or　particular



affirmative　and　universal　negative；　and　the　relations　between　the



terms　may　be　reversed；　e。g。　A　may　belong　to　all　B　and　to　no　C；　or　to



all　C　and　to　no　B；　or　to　all　of　the　one；　not　to　all　of　the　other；　here



too　the　relation　between　the　terms　may　be　reversed。　Similarly　in　the



third　figure。　So　it　is　clear　in　how　many　ways　and　in　what　figures　a



syllogism　can　be　made　by　means　of　premisses　which　are　opposed。



　　It　is　clear　too　that　from　false　premisses　it　is　possible　to　draw　a



true　conclusion；　as　has　been　said　before；　but　it　is　not　possible　if



the　premisses　are　opposed。　For　the　syllogism　is　always　contrary　to　the



fact；　e。g。　if　a　thing　is　good；　it　is　proved　that　it　is　not　good；　if　an



animal；　that　it　is　not　an　animal　because　the　syllogism　springs　out



of　a　contradiction　and　the　terms　presupposed　are　either　identical　or



related　as　whole　and　part。　It　is　evident　also　that　in　fallacious



reasonings　nothing　prevents　a　contradiction　to　the　hypothesis　from



resulting；　e。g。　if　something　is　odd；　it　is　not　odd。　For　the



syllogism　owed　its　contrariety　to　its　contradictory　premisses；　if　we



assume　such　premisses　we　shall　get　a　result　that　contradicts　our



hypothesis。　But　we　must　recognize　that　contraries　cannot　be　inferred



from　a　single　syllogism　in　such　a　way　that　we　conclude　that　what　is



not　good　is　good；　or　anything　of　that　sort　unless　a　self…contradictory



premiss　is　at　once　assumed；　e。g。　'every　animal　is　white　and　not



white'；　and　we　proceed　'man　is　an　animal'。　Either　we　must　introduce



the　contradiction　by　an　additional　assumption；　assuming；　e。g。；　that



every　science　is　supposition；　and　then　assuming　'Medicine　is　a



science；　but　none　of　it　is　supposition'　（which　is　the　mode　in　which



refutations　are　made）；　or　we　must　argue　from　two　syllogisms。　In　no



other　way　than　this；　as　was　said　before；　is　it　possible　that　the



premisses　should　be　really　contrary。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　16







　　To　beg　and　assume　the　original　question　is　a　species　of　failure　to



demonstrate　the　problem　proposed；　but　this　happens　in　many　ways。　A　man



may　not　reason　syllogistically　at　all；　or　he　may　argue　from



premisses　which　are　less　known　or　equally　unknown；　or　he　may　establish



the　antecedent　by　means　of　its　consequents；　for　demonstration　proceeds



from　what　is　more　certain　and　is　prior。　Now　begging　the　question　is



none　of　these：　but　since　we　get　to　know　some　things　naturally



through　themselves；　and　other　things　by　means　of　something　else　（the



first　principles　through　themselves；　what　is　subordinate　to　them



through　something　else）；　whenever　a　man　tries　to　prove　what　is　not



self…evident　by　means　of　itself；　then　he　begs　the　original　question。



This　may　be　done　by　assuming　what　is　in　question　at　once；　it　is　also



possible　to　make　a　transition　to　other　things　which　would　naturally　be



proved　through　the　thesis　proposed；　and　demonstrate　it　through　them；



e。g。　if　A　should　be　proved　through　B；　and　B　through　C；　though　it　was



natural　that　C　should　be　proved　through　A：　for　it　turns　out　that　those



who　reason　thus　are　proving　A　by　means　of　itself。　This　is　what　those



persons　do　who　suppose　that　they　are　constructing　parallel　straight



lines：　for　they　fail　to　see　that　they　are　assuming　facts　which　it　is



impossible　to　demonstrate　unless　the　parallels　exist。　So　it　turns



out　that　those　who　reason　thus　merely　say　a　particular　thing　is；　if　it



is：　in　this　way　everything　will　be　self…evident。　But　that　is



impossible。



　　If　then　it　is　uncertain　whether　A　belongs　to　C；　and　also　whether　A



belongs　to　B；　and　if　one　should　assume　that　A　does　belong　to　B；　it



is　not　yet　clear　whether　he　begs　the　original　question；　but　it　is



evident　that　he　is　not　demonstrating：　for　what　is　as　uncertain　as



the　question　to　be　answered　cannot　be　a　principle　of　a



demonstration。　If　however　B　is　so　related　to　C　that　they　are



identical；　or　if　they　are　plainly　convertible；　or　the　one　belongs　to



the　other；　the　original　question　is　begged。　For　one　might　equally　well



prove　that　A　belongs　to　B　through　those　terms　if　they　are　convertible。



But　if　they　are　not　convertible；　it　is　the　fact　that　they　are　not　that



prevents　such　a　demonstration；　not　the　method　of　demonstrating。　But　if



one　were　to　make　the　conversion；　then　he　would　be　doing　what　we　have



described　and　effecting　a　reciprocal　proof　with　three　propositions。



　　Similarly　if　he　should　assume　that　B　belongs　to　C；　this　being　as



uncertain　as　the　question　whether　A　belongs　to　C；　the　question　is



not　yet　begged；　but　no　demonstration　is　made。　If　however　A　and　B　are



identical　either　because　they　are　convertible　or　because　A　follows



B；　then　the　question　is　begged　for　the　same　reason　as　before。　For　we



have　explained　the　meaning　of　begging　the　question；　viz。　proving



that　which　is　not　self…evident　by　means　of　itself。



　　If　then　begging　the　question　is　proving　what　is　not　self…evident



by　means　of　itself；　in　other　words　failing　to　prove　when　the　failure



is　due　to　the　thesis　to　be　proved　and　the　premiss　through　which　it



is　proved　being　equally　uncertain；　either　because　predicates　which　are



identical　belong　to　the　same　subject；　or　because　the　same　predicate



belongs　to　subjects　which　are　identical；　the　question　may　be　begged　in



the　middle　and　third　figures　in　both　ways；　though；　if　the　syllogism　is



affirmative；　only　in　the　third　and　first　figures。　If　the　syllogism



is　negative；　the　question　is　begged　when　identical　predicates　are



denied　of　the　same　subject；　and　both　premisses　do　not　beg　the　question



indifferently　（in　a　similar　way　the　question　may　be　begged　in　the



middle　figure）；　because　the　terms　in　negative　syllogisms　are　not



convertible。　In　scientific　demonstrations　the　question　is　begged



when　the　terms　are　really　related　in　the　manner　described；　in



dialectical　arguments　when　they　are　according　to　common　opinion　so



related。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　17







　　The　objection　that　'this　is　not　the　reason　why　the　result　is　false'；



which　we　frequently　make　in　argument；　is　made　primarily　in　the　case　of



a　reductio　ad　impossibile；　to　rebut　the　proposition　which　was　being



proved　by　the　reduction。　For　unless　a　man　has　contradicted　this



proposition　he　will　not　say；　'False　cause'；　but　urge　that　something



false　has　been　assumed　in　the　earlier　parts　of　the　argument；　nor



will　he　use　the　formula　in　the　case　of　an　ostensive　proof；　for　here



what　one　denies　is　not　assumed　as　a　premiss。　Further　when　anything



is　refuted　ostensively　by　the　terms　ABC；　it　cannot　be　objected　that



the　syllogism　does　not　depend　on　the　assumption　laid　down。　For　we



use　the　expression　'false　cause'；　when　the　syllogism　is　concluded　in



spite　of　the　refutation　of　this　position；　but　that　is　not　possible



in　ostensive　proofs：　since　if　an　assumption　is　refuted；　a　syllogism



can　no　longer　be　drawn　in　reference　to　it。　It　is　clear　then　that　the



expression　'false　cause'　can　only　be　used　in　the　case　of　a　reductio　ad



impossibile；　and　when　the　original　hypothesis　is　so　related　to　the



impossible　conclusion；　that　the　conclusion　results　indifferently



whether　the　hypothesis　is　made　or　not。　The　most　obvious　case　of　the



irrelevance　of　an　assumption　to　a　conclusion　which　is　false　is　when



a　syllogism　drawn　from　middle　terms　to　an　impossible　conclusion　is



independent　of　the　hypothesis；　as　we　have　explained　in　the　Topics。　For



to　put　that　which　is　not　the　cause　as　the　cause；　is　just　this：　e。g。　if



a　man；　wishing　to　prove　that　the　diagonal　of　the　square　is



incommensurate　with　the　side；　should　try　to　prove　Zeno's　theorem



that　motion　is　impossible；　and　so　establish　a　reductio　ad　impossibile：



for　Zeno's　false　theorem　has　no　connexion　at　all　with　the　original



assumption。　Another　case　is　where　the　impossible　conclusion　is



connected　with　the　hypothesis；　but　does　not　result　from　it。　This　may



happen　whether　one　traces　the　connexion　upwards　or　downwards；　e。g。



if　it　is　laid　down　that　A　belongs　to　B；　B　to　C；　and　C　to　D；　and　it



should　be　false　that　B　belongs　to　D：　for　if　we　eliminated　A　and



assumed　all　the　same　that　B　belongs　to　C　and　C　to　D；　the　false



conclusion　would　not　depend　on　the　original　hypothesis。　Or　again　trace



the　connexion　upwards；　e。g。　suppose　that　A　belongs　to　B；　E　to　A　and



F　to　E；　it　being　false　that　F　belongs　to　A。　In　this　way　too　the



impossible　conclusion　would　result；　though　the　original　hypothesis



were　eliminated。　But　the　impossible　conclusion　ought　to　be　connected



with　the　original　terms：　in　this　way　it　will　depend　on　the　hypothesis；



e。g。　when　one　traces　the　connexion　downwards；　the　impossible



conclusion　must　be　connected　with　that　term　which　is　predicate　in



the　hypothesis：　for　if　it　is　impossible　that　A　should　belong　to　D；　the



false　conclusion　will　no　longer　result　after　A　has　been　eliminated。　If



one　traces　the　connexion　upwards；　the　impossible　conclusion　must　be



connected　with　that　term　which　is　subject　in　the　hypothesis：　for　if　it



is　impossible　that　F　should　belong　to　B；　the　impossible　conclusion



will　disappear　if　B　is　eliminated。　Similarly　when　the　syllogisms　are



negative。



　　I