prior analytics-第13章

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look　to　fewer　points　and　they　must　be　definite。　We　have　also　stated



how　we　must　select　with　reference　to　everything　that　is；　e。g。　about



good　or　knowledge。　But　in　each　science　the　principles　which　are



peculiar　are　the　most　numerous。　Consequently　it　is　the　business　of



experience　to　give　the　principles　which　belong　to　each　subject。　I　mean



for　example　that　astronomical　experience　supplies　the　principles　of



astronomical　science：　for　once　the　phenomena　were　adequately



apprehended；　the　demonstrations　of　astronomy　were　discovered。



Similarly　with　any　other　art　or　science。　Consequently；　if　the



attributes　of　the　thing　are　apprehended；　our　business　will　then　be



to　exhibit　readily　the　demonstrations。　For　if　none　of　the　true



attributes　of　things　had　been　omitted　in　the　historical　survey；　we



should　be　able　to　discover　the　proof　and　demonstrate　everything



which　admitted　of　proof；　and　to　make　that　clear；　whose　nature　does　not



admit　of　proof。



　　In　general　then　we　have　explained　fairly　well　how　we　must　select



premisses：　we　have　discussed　the　matter　accurately　in　the　treatise



concerning　dialectic。







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　　It　is　easy　to　see　that　division　into　classes　is　a　small　part　of



the　method　we　have　described：　for　division　is；　so　to　speak；　a　weak



syllogism；　for　what　it　ought　to　prove；　it　begs；　and　it　always



establishes　something　more　general　than　the　attribute　in　question。



First；　this　very　point　had　escaped　all　those　who　used　the　method　of



division；　and　they　attempted　to　persuade　men　that　it　was　possible　to



make　a　demonstration　of　substance　and　essence。　Consequently　they　did



not　understand　what　it　is　possible　to　prove　syllogistically　by



division；　nor　did　they　understand　that　it　was　possible　to　prove



syllogistically　in　the　manner　we　have　described。　In　demonstrations；



when　there　is　a　need　to　prove　a　positive　statement；　the　middle　term



through　which　the　syllogism　is　formed　must　always　be　inferior　to　and



not　comprehend　the　first　of　the　extremes。　But　division　has　a



contrary　intention：　for　it　takes　the　universal　as　middle。　Let　animal



be　the　term　signified　by　A；　mortal　by　B；　and　immortal　by　C；　and　let



man；　whose　definition　is　to　be　got；　be　signified　by　D。　The　man　who



divides　assumes　that　every　animal　is　either　mortal　or　immortal：　i。e。



whatever　is　A　is　all　either　B　or　C。　Again；　always　dividing；　he　lays　it



down　that　man　is　an　animal；　so　he　assumes　A　of　D　as　belonging　to　it。



Now　the　true　conclusion　is　that　every　D　is　either　B　or　C；　consequently



man　must　be　either　mortal　or　immortal；　but　it　is　not　necessary　that



man　should　be　a　mortal　animal…this　is　begged：　and　this　is　what　ought



to　have　been　proved　syllogistically。　And　again；　taking　A　as　mortal



animal；　B　as　footed；　C　as　footless；　and　D　as　man；　he　assumes　in　the



same　way　that　A　inheres　either　in　B　or　in　C　（for　every　mortal　animal



is　either　footed　or　footless）；　and　he　assumes　A　of　D　（for　he　assumed



man；　as　we　saw；　to　be　a　mortal　animal）；　consequently　it　is　necessary



that　man　should　be　either　a　footed　or　a　footless　animal；　but　it　is　not



necessary　that　man　should　be　footed：　this　he　assumes：　and　it　is　just



this　again　which　he　ought　to　have　demonstrated。　Always　dividing　then



in　this　way　it　turns　out　that　these　logicians　assume　as　middle　the



universal　term；　and　as　extremes　that　which　ought　to　have　been　the



subject　of　demonstration　and　the　differentiae。　In　conclusion；　they



do　not　make　it　clear；　and　show　it　to　be　necessary；　that　this　is　man　or



whatever　the　subject　of　inquiry　may　be：　for　they　pursue　the　other



method　altogether；　never　even　suspecting　the　presence　of　the　rich



supply　of　evidence　which　might　be　used。　It　is　clear　that　it　is　neither



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　ha