prior analytics-第18章

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possible　to　refute　a　statement　by　this　method　of　division；　nor　to　draw



a　conclusion　about　an　accident　or　property　of　a　thing；　nor　about　its



genus；　nor　in　cases　in　which　it　is　unknown　whether　it　is　thus　or　thus；



e。g。　whether　the　diagonal　is　incommensurate。　For　if　he　assumes　that



every　length　is　either　commensurate　or　incommensurate；　and　the



diagonal　is　a　length；　he　has　proved　that　the　diagonal　is　either



incommensurate　or　commensurate。　But　if　he　should　assume　that　it　is



incommensurate；　he　will　have　assumed　what　he　ought　to　have　proved。



He　cannot　then　prove　it：　for　this　is　his　method；　but　proof　is　not



possible　by　this　method。　Let　A　stand　for　'incommensurate　or



commensurate'；　B　for　'length'；　C　for　'diagonal'。　It　is　clear　then　that



this　method　of　investigation　is　not　suitable　for　every　inquiry；　nor　is



it　useful　in　those　cases　in　which　it　is　thought　to　be　most　suitable。



　　From　what　has　been　said　it　is　clear　from　what　elements



demonstrations　are　formed　and　in　what　manner；　and　to　what　points　we



must　look　in　each　problem。







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　　Our　next　business　is　to　state　how　we　can　reduce　syllogisms　to　the



aforementioned　figures：　for　this　part　of　the　inquiry　still　remains。　If



we　should　investigate　the　production　of　the　syllogisms　and　had　the



power　of　discovering　them；　and　further　if　we　could　resolve　the



syllogisms　produced　into　the　aforementioned　figures；　our　original



problem　would　be　brought　to　a　conclusion。　It　will　happen　at　the　same



time　that　what　has　been　already　said　will　be　confirmed　and　its　truth



made　clearer　by　what　we　are　about　to　say。　For　everything　that　is



true　must　in　every　respect　agree　with　itself　First　then　we　must



attempt　to　select　the　two　premisses　of　the　syllogism　（for　it　is　easier



to　divide　into　large　parts　than　into　small；　and　the　composite　parts



are　larger　than　the　elements　out　of　which　they　are　made）；　next　we　must



inquire　which　are　universal　and　which　particular；　and　if　both



premisses　have　not　been　stated；　we　must　ourselves　assume　the　one　which



is　missing。　For　sometimes　men　put　forward　the　universal　premiss；　but



do　not　posit　the　premiss　which　is　contained　in　it；　either　in　writing



or　in　discussion：　or　men　put　forward　the　premisses　of　the　principal



syllogism；　but　omit　those　through　which　they　are　inferred；　and



invite　the　concession　of　others　to　no　purpose。　We　must　inquire　then



whether　anything　unnecessary　has　been　assumed；　or　anything　necessary



has　been　omitted；　and　we　must　posit　the　one　and　take　away　the　other；



until　we　have　reached　the　two　premisses：　for　unless　we　have　these；



we　cannot　reduce　arguments　put　forward　in　the　way　described。　In　some



arguments　it　is　easy　to　see　what　is　wanting；　but　some　escape　us；　and



appear　to　be　syllogisms；　because　something　necessary　results　from　what



has　been　laid　down；　e。g。　if　the　assumptions　were　made　that　substance



is　not　annihilated　by　the　annihilation　of　what　is　not　substance；　and



that　if　the　elements　out　of　which　a　thing　is　made　are　annihilated；



then　that　which　is　made　out　of　them　is　destroyed：　these　propositions



being　laid　down；　it　is　necessary　that　any　part　of　substance　is



substance；　this　has　not　however　been　drawn　by　syllogism　from　the



propositions　assumed；　but　premisses　are　wanting。　Again　if　it　is



necessary　that　animal　should　exist；　if　man　does；　and　that　substance



should　exist；　if　animal　does；　it　is　necessary　that　substance　should



exist　if　man　does：　but　as　yet　the　conclusion　has　not　been　drawn



syllogistically：　for　the　premisses　are　not　in　the　shape　we　required。



We　are　deceived　in　such　cases　because　something　necessary　results　from



what　is　assumed；　since　the　syllogism　also　is　necessary。　But　that　which



is　necessary　is　wider　than　the　syllogism：　for　every　syllogism　is



necessary；　but　not　everything　which　is　necessary　is　a　syllogism。



Consequently；　though　something　results　when　certain　propositions　are



assumed；　we　must　not　try　to　reduce　it　directly；　but　must　first　state



the　two　premisses；　then　divide　them　into　their　terms。　We　must　take



that　term　as　middle　which　is　stated　in　both　the　remisses：　for　it　is



necessary　that　the　middle　should　be　found　in　both　premisses　in　all　the



figures。



　　If　then　the　middle　term　is　a　predicate　and　a　subject　of　predication；



or　if　it　is　a　predicate；　and　something　else　is　denied　of　it；　we



shall　have　the　first　figure：　if　it　both　is　a　predicate　and　is　denied



of　something；　the　middle　figure：　if　other　things　are　predicated　of　it；



or　one　is　denied；　the　other　predicated；　the　last　figure。　For　it　was



thus　that　we　found　the　middle　term　placed　in　each　figure。　It　is　placed



similarly　too　if　the　premisses　are　not　universal：　for　the　middle



term　is　determined　in　the　same　way。　Clearly　then；　if　the　same　term



is　not　stated　more　than　once　in　the　course　of　an　argument；　a　syllogism



cannot　be　made：　for　a　middle　term　has　not　been　taken。　Since　we　know



what　sort　of　thesis　is　established　in　each　figure；　and　in　which　the



universal；　in　what　sort　the　particular　is　described；　clearly　we　must



not　look　for　all　the　figures；　but　for　that　which　is　appropriate　to　the



thesis　in　hand。　If　the　thesis　is　established　in　more　figures　than　one；



we　shall　recognize　the　figure　by　the　position　of　the　middle　term。







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　　Men　are　frequently　deceived　about　syllogisms　because　the　inference



is　necessary；　as　has　been　said　above；　sometimes　they　are　deceived　by



the　similarity　in　the　positing　of　the　terms；　and　this　ought　not　to



escape　our　notice。　E。g。　if　A　is　stated　of　B；　and　B　of　C：　it　would　seem



that　a　syllogism　is　possible　since　the　terms　stand　thus：　but　nothing



necessary　results；　nor　does　a　syllogism。　Let　A　represent　the　term



'being　eternal'；　B　'Aristomenes　as　an　object　of　thought'；　C



'Aristomenes'。　It　is　true　then　that　A　belongs　to　B。　For　Aristomenes　as



an　object　of　thought　is　eternal。　But　B　also　belongs　to　C：　for



Aristomenes　is　Aristomenes　as　an　object　of　thought。　But　A　does　not



belong　to　C：　for　Aristomenes　is　perishable。　For　no　syllogism　was



made　although　the　terms　stood　thus：　that　required　that　the　premiss



AB　should　be　stated　universally。　But　this　is　false；　that　every



Aristomenes　who　is　an　object　of　thought　is　eternal；　since



Aristomenes　is　perishable。　Again　let　C　stand　for　'Miccalus'；　B　for



'musical　Miccalus'；　A　for　'perishing　to…morrow'。　It　is　true　to



predicate　B　of　C：　for　Miccalus　is　musical　Miccalus。　Also　A　can　be



predicated　of　B：　for　musical　Miccalus　might　perish　to…morrow。　But　to



state　A　of　C　is　false　at　any　rate。　This　argument　then　is　identical



with　the　former；　for　it　is　not　true　universally　that　musical



Miccalus　perishes　to…morrow：　but　unless　this　is　assumed；　no



syllogism　（as　we　have　shown）　is　possible。



　　This　deception　then　arises　through　ignoring　a　small　distinction。　For



if　we　accept　the　conclusion　as　though　it　made　no　difference　whether　we



said　'This　belong　to　that'　or　'This　belongs　to　all　of　that'。







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　　Men　will　frequently　fall　into　fallacies　through　not　setting　out



the　terms　of　the　premiss　well；　e。g。　suppose　A　to　be　health；　B　disease；



C　man。　It　is　true　to　say　that　A　cannot　belong　to　any　B　（for　health



belongs　to　no　disease）　and　again　that　B　belongs　to　every　C　（for



every　man　is　capable　of　disease）。　It　would　seem　to　follow　that



health　cannot　belong　to　any　man。　The　reason　for　this　is　that　the　terms



are　not　set　out　well　in　the　statement；　since　if　the　things　which　are



in　the　conditions　are　substituted；　no　syllogism　can　be　made；　e。g。　if



'healthy'　is　substituted　for　'health'　and　'diseased'　for　'disease