prior analytics-第35章

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latter　proves　the　major　term　to　belong　to　the　third　term　by　means　of



the　middle；　the　former　proves　the　major　to　belong　to　the　middle　by



means　of　the　third。　In　the　order　of　nature；　syllogism　through　the



middle　term　is　prior　and　better　known；　but　syllogism　through　induction



is　clearer　to　us。







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　　We　have　an　'example'　when　the　major　term　is　proved　to　belong　to



the　middle　by　means　of　a　term　which　resembles　the　third。　It　ought　to



be　known　both　that　the　middle　belongs　to　the　third　term；　and　that



the　first　belongs　to　that　which　resembles　the　third。　For　example　let　A



be　evil；　B　making　war　against　neighbours；　C　Athenians　against　Thebans；



D　Thebans　against　Phocians。　If　then　we　wish　to　prove　that　to　fight



with　the　Thebans　is　an　evil；　we　must　assume　that　to　fight　against



neighbours　is　an　evil。　Evidence　of　this　is　obtained　from　similar



cases；　e。g。　that　the　war　against　the　Phocians　was　an　evil　to　the



Thebans。　Since　then　to　fight　against　neighbours　is　an　evil；　and　to



fight　against　the　Thebans　is　to　fight　against　neighbours；　it　is



clear　that　to　fight　against　the　Thebans　is　an　evil。　Now　it　is　clear



that　B　belongs　to　C　and　to　D　（for　both　are　cases　of　making　war　upon



one's　neighbours）　and　that　A　belongs　to　D　（for　the　war　against　the



Phocians　did　not　turn　out　well　for　the　Thebans）：　but　that　A　belongs　to



B　will　be　proved　through　D。　Similarly　if　the　belief　in　the　relation　of



the　middle　term　to　the　extreme　should　be　produced　by　several　similar



cases。　Clearly　then　to　argue　by　example　is　neither　like　reasoning　from



part　to　whole；　nor　like　reasoning　from　whole　to　part；　but　rather



reasoning　from　part　to　part；　when　both　particulars　are　subordinate



to　the　same　term；　and　one　of　them　is　known。　It　differs　from　induction；



because　induction　starting　from　all　the　particular　cases　proves　（as　we



saw）　that　the　major　term　belongs　to　the　middle；　and　does　not　apply　the



syllogistic　conclusion　to　the　minor　term；　whereas　argument　by



example　does　make　this　application　and　does　not　draw　its　proof　from



all　the　particular　cases。







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　　By　reduction　we　mean　an　argument　in　which　the　first　term　clearly



belongs　to　the　middle；　but　the　relation　of　the　middle　to　the　last　term



is　uncertain　though　equally　or　more　probable　than　the　conclusion；　or



again　an　argument　in　which　the　terms　intermediate　between　the　last



term　and　the　middle　are　few。　For　in　any　of　these　cases　it　turns　out



that　we　approach　more　nearly　to　knowledge。　For　example　let　A　stand　for



what　can　be　taught；　B　for　knowledge；　C　for　justice。　Now　it　is　clear



that　knowledge　can　be　taught：　but　it　is　uncertain　whether　virtue　is



knowledge。　If　now　the　statement　BC　is　equally　or　more　probable　than



AC；　we　have　a　reduction：　for　we　are　nearer　to　knowledge；　since　we　have



taken　a　new　term；　being　so　far　without　knowledge　that　A　belongs　to



C。　Or　again　suppose　that　the　terms　intermediate　between　B　and　C　are



few：　for　thus　too　we　are　nearer　knowledge。　For　example　let　D　stand　for



squaring；　E　for　rectilinear　figure；　F　for　circle。　If　there　were　only



one　term　intermediate　between　E　and　F　（viz。　that　the　circle　is　made



equal　to　a　rectilinear　figure　by　the　help　of　lunules）；　we　should　be



near　to　knowledge。　But　when　BC　is　not　more　probable　than　AC；　and　the



intermediate　terms　are　not　few；　I　do　not　call　this　reduction：　nor



again　when　the　statement　BC　is　immediate：　for　such　a　statement　is



knowledge。







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　　An　objection　is　a　premiss　contrary　to　a　premiss。　It　differs　from　a



premiss；　because　it　may　be　particular；　but　a　premiss　either　cannot



be　particular　at　all　or　not　in　universal　syllogisms。　An　objection　is



brought　in　two　ways　and　through　two　figures；　in　two　ways　because　every



objection　is　either　universal　or　particular；　by　two　figures　because



objections　are　brought　in　opposition　to　the　premiss；　and　opposites　can



be　proved　only　in　the　first　and　third　figures。　If　a　man　maintains　a



universal　affirmative；　we　reply　with　a　universal　or　a　particular



negative；　the　former　is　proved　from　the　first　figure；　the　latter



from　the　third。　For　example　let　stand　for　there　being　a　single



science；　B　for　contraries。　If　a　man　premises　that　contraries　are



subjects　of　a　single　science；　the　objection　may　be　either　that



opposites　are　never　subjects　of　a　single　science；　and　contraries　are



opposites；　so　that　we　get　the　first　figure；　or　that　the　knowable　and



the　unknowable　are　not　subjects　of　a　single　science：　this　proof　is



in　the　third　figure：　for　it　is　true　of　C　（the　knowable　and　the



unknowable）　that　they　are　contraries；　and　it　is　false　that　they　are



the　subjects　of　a　single　science。



　　Similarly　if　the　premiss　objected　to　is　negative。　For　if　a　man



maintains　that　contraries　are　not　subjects　of　a　single　science；　we



reply　either　that　all　opposites　or　that　certain　contraries；　e。g。



what　is　healthy　and　what　is　sickly；　are　subjects　of　the　same



science：　the　former　argument　issues　from　the　first；　the　latter　from



the　third　figure。



　　In　general　if　a　man　urges　a　universal　objection　he　must　frame　his



contradiction　with　reference　to　the　universal　of　the　terms　taken　by



his　opponent；　e。g。　if　a　man　maintains　that　contraries　are　not　subjects



of　the　same　science；　his　opponent　must　reply　that　there　is　a　single



science　of　all　opposites。　Thus　we　must　have　the　first　figure：　for



the　term　which　embraces　the　original　subject　becomes　the　middle　term。



　　If　the　objection　is　particular；　the　objector　must　frame　his



contradiction　with　reference　to　a　term　relatively　to　which　the　subject



of　his　opponent's　premiss　is　universal；　e。g。　he　will　point　out　that



the　knowable　and　the　unknowable　are　not　subjects　of　the　same



science：　'contraries'　is　universal　relatively　to　these。　And　we　have



the　third　figure：　for　the　particular　term　assumed　is　middle；　e。g。



the　knowable　and　the　unknowable。　Premisses　from　which　it　is　possible



to　draw　the　contrary　conclusion　are　what　we　start　from　when　we　try



to　make　objections。　Consequently　we　bring　objections　in　these



figures　only：　for　in　them　only　are　opposite　syllogisms　possible；　since



the　second　figure　cannot　produce　an　affirmative　conclusion。



　　Besides；　an　objection　in　the　middle　figure　would　require　a　fuller



argument；　e。g。　if　it　should　not　be　granted　that　A　belongs　to　B；



because　C　does　not　follow　B。　This　can　be　made　clear　only　by　other



premisses。　But　an　objection　ought　not　to　turn　off　into　other　things；



but　have　its　new　premiss　quite　clear　immediately。　For　this　reason　also



this　is　the　only　figure　from　which　proof　by　signs　cannot　be　obtained。



　　We　must　consider　later　the　other　kinds　of　objection；　namely　the



objection　from　contraries；　from　similars；　and　from　common　opinion；　and



inquire　whether　a　particular　objection　cannot　be　elicited　from　the



first　figure　or　a　negative　objection　from　the　second。







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　　A　probability　and　a　sign　are　not　identical；　but　a　probability　is　a



generally　approved　proposition：　what　men　know　to　happen　or　not　to



happen；　to　be　or　not　to　be；　for　the　most　part　thus　and　thus；　is　a



probability；　e。g。　'the　envious　hate'；　'the　beloved　show　affection'。



A　sign　means　a　demonstrative　proposition　necessary　or　generally



approved：　for　anything　such　that　when　it　is　another　thing　is；　or



when　it　has　come　into　being　the　other　has　come　into　being　before　or



after；　is　a　sign　of　the　other's　being　or　having　come　into　being。　Now



an　enthymeme　is　a　syllogism　starting　from　probabilities　or　signs；



and　a　sign　may　be　taken　in　thre