prior analytics-第15节

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It　turns　out　then　that　those　who　inquire　in　this　manner　are　looking



gratuitously　for　some　other　way　than　the　necessary　way　because　they



have　failed　to　observe　the　identity　of　the　Bs　with　the　Hs。







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　　Syllogisms　which　lead　to　impossible　conclusions　are　similar　to



ostensive　syllogisms；　they　also　are　formed　by　means　of　the　consequents



and　antecedents　of　the　terms　in　question。　In　both　cases　the　same



inquiry　is　involved。　For　what　is　proved　ostensively　may　also　be



concluded　syllogistically　per　impossibile　by　means　of　the　same



terms；　and　what　is　proved　per　impossibile　may　also　be　proved



ostensively；　e。g。　that　A　belongs　to　none　of　the　Es。　For　suppose　A　to



belong　to　some　E：　then　since　B　belongs　to　all　A　and　A　to　some　of　the



Es；　B　will　belong　to　some　of　the　Es：　but　it　was　assumed　that　it



belongs　to　none。　Again　we　may　prove　that　A　belongs　to　some　E：　for　if　A



belonged　to　none　of　the　Es；　and　E　belongs　to　all　G；　A　will　belong　to



none　of　the　Gs：　but　it　was　assumed　to　belong　to　all。　Similarly　with



the　other　propositions　requiring　proof。　The　proof　per　impossibile　will



always　and　in　all　cases　be　from　the　consequents　and　antecedents　of　the



terms　in　question。　Whatever　the　problem　the　same　inquiry　is



necessary　whether　one　wishes　to　use　an　ostensive　syllogism　or　a



reduction　to　impossibility。　For　both　the　demonstrations　start　from　the



same　terms；　e。g。　suppose　it　has　been　proved　that　A　belongs　to　no　E；



because　it　turns　out　that　otherwise　B　belongs　to　some　of　the　Es　and



this　is　impossible…if　now　it　is　assumed　that　B　belongs　to　no　E　and



to　all　A；　it　is　clear　that　A　will　belong　to　no　E。　Again　if　it　has　been



proved　by　an　ostensive　syllogism　that　A　belongs　to　no　E；　assume　that　A



belongs　to　some　E　and　it　will　be　proved　per　impossibile　to　belong　to



no　E。　Similarly　with　the　rest。　In　all　cases　it　is　necessary　to　find



some　common　term　other　than　the　subjects　of　inquiry；　to　which　the



syllogism　establishing　the　false　conclusion　may　relate；　so　that　if



this　premiss　is　converted；　and　the　other　remains　as　it　is；　the



syllogism　will　be　ostensive　by　means　of　the　same　terms。　For　the



ostensive　syllogism　differs　from　the　reductio　ad　impossibile　in



this：　in　the　ostensive　syllogism　both　remisses　are　laid　down　in



accordance　with　the　truth；　in　the　reductio　ad　impossibile　one　of　the



premisses　is　assumed　falsely。



　　These　points　will　be　made　clearer　by　the　sequel；　when　we　discuss　the



reduction　to　impossibility：　at　present　this　much　must　be　clear；　that



we　must　look　to　terms　of　the　kinds　mentioned　whether　we　wish　to　use　an



ostensive　syllogism　or　a　reduction　to　impossibility。　In　the　other



hypothetical　syllogisms；　I　mean　those　which　proceed　by　substitution；



or　by　positing　a　certain　quality；　the　inquiry　will　be　directed　to



the　terms　of　the　problem　to　be　proved…not　the　terms　of　the　original



problem；　but　the　new　terms　introduced；　and　the　method　of　the　inquiry



will　be　the　same　as　before。　But　we　must　consider　and　determine　in



how　many　ways　hypothetical　syllogisms　are　possible。



　　Each　of　the　problems　then　can　be　proved　in　the　manner　described；　but



it　is　possible　to　establish　some　of　them　syllogistically　in　another



way；　e。g。　universal　problems　by　the　inquiry　which　leads　up　to　a



particular　conclusion；　with　the　addition　of　an　hypothesis。　For　if



the　Cs　and　the　Gs　should　be　identical；　but　E　should　be　assumed　to



belong　to　the　Gs　only；　then　A　would　belong　to　every　E：　and　again　if



the　Ds　and　the　Gs　should　be　identical；　but　E　should　be　predicated　of



the　Gs　only；　it　follows　that　A　will　belong　to　none　of　the　Es。



Clearly　then　we　must　consider　the　matter　in　this　way　also。　The



method　is　the　same　whether　the　relation　is　necessary　or　possible。



For　the　inquiry　will　be　the　same；　and　the　syllogism　will　proceed



through　terms　arranged　in　the　same　order　whether　a　possible　or　a



pure　proposition　is　proved。　We　must　find　in　the　case　of　possible



relations；　as　well　as　terms　that　belong；　terms　which　can　belong　though



they　actually　do　not：　for　we　have　proved　that　the　syllogism　which



establishes　a　possible　relation　proceeds　through　these　terms　as



well。　Similarly　also　with　the　other　modes　of　predication。



　　It　is　clear　then　from　what　has　been　said　not　only　that　all



syllogisms　can　be　formed　in　this　way；　but　also　that　they　cannot　be



formed　in　any　other。　For　every　syllogism　has　been　proved　to　be



formed　through　one　of　the　aforementioned　figures；　and　these　cannot



be　composed　through　other　terms　than　the　consequents　and　antecedents



of　the　terms　in　question：　for　from　these　we　obtain　the　premisses　and



find　the　middle　term。　Consequently　a　syllogism　cannot　be　formed　by



means　of　other　terms。







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　　The　method　is　the　same　in　all　cases；　in　philosophy；　in　any　art　or



study。　We　must　look　for　the　attributes　and　the　subjects　of　both　our



terms；　and　we　must　supply　ourselves　with　as　many　of　these　as　possible；



and　consider　them　by　means　of　the　three　terms；　refuting　statements



in　one　way；　confirming　them　in　another；　in　the　pursuit　of　truth



starting　from　premisses　in　which　the　arrangement　of　the　terms　is　in



accordance　with　truth；　while　if　we　look　for　dialectical　syllogisms



we　must　start　from　probable　premisses。　The　principles　of　syllogisms



have　been　stated　in　general　terms；　both　how　they　are　characterized　and



how　we　must　hunt　for　them；　so　as　not　to　look　to　everything　that　is



said　about　the　terms　of　the　problem　or　to　the　same　points　whether　we



are　confirming　or　refuting；　or　again　whether　we　are　confirming　of



all　or　of　some；　and　whether　we　are　refuting　of　all　or　some。　we　must



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　fo