prior analytics-第25章

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actual　exercise；　nor　on　the　other　hand　has　his　thought　caused　an　error



contrary　to　his　knowledge：　for　the　error　contrary　to　the　knowledge



of　the　universal　would　be　a　syllogism。



　　But　he　who　thinks　the　essence　of　good　is　the　essence　of　bad　will



think　the　same　thing　to　be　the　essence　of　good　and　the　essence　of　bad。



Let　A　stand　for　the　essence　of　good　and　B　for　the　essence　of　bad；



and　again　C　for　the　essence　of　good。　Since　then　he　thinks　B　and　C



identical；　he　will　think　that　C　is　B；　and　similarly　that　B　is　A；



consequently　that　C　is　A。　For　just　as　we　saw　that　if　B　is　true　of



all　of　which　C　is　true；　and　A　is　true　of　all　of　which　B　is　true；　A



is　true　of　C；　similarly　with　the　word　'think'。　Similarly　also　with　the



word　'is'；　for　we　saw　that　if　C　is　the　same　as　B；　and　B　as　A；　C　is　the



same　as　A。　Similarly　therefore　with　'opine'。　Perhaps　then　this　is



necessary　if　a　man　will　grant　the　first　point。　But　presumably　that



is　false；　that　any　one　could　suppose　the　essence　of　good　to　be　the



essence　of　bad；　save　incidentally。　For　it　is　possible　to　think　this　in



many　different　ways。　But　we　must　consider　this　matter　better。







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　　Whenever　the　extremes　are　convertible　it　is　necessary　that　the



middle　should　be　convertible　with　both。　For　if　A　belongs　to　C



through　B；　then　if　A　and　C　are　convertible　and　C　belongs　everything　to



which　A　belongs；　B　is　convertible　with　A；　and　B　belongs　to



everything　to　which　A　belongs；　through　C　as　middle；　and　C　is



convertible　with　B　through　A　as　middle。　Similarly　if　the　conclusion　is



negative；　e。g。　if　B　belongs　to　C；　but　A　does　not　belong　to　B；



neither　will　A　belong　to　C。　If　then　B　is　convertible　with　A；　C　will　be



convertible　with　A。　Suppose　B　does　not　belong　to　A；　neither　then



will　C：　for　ex　hypothesi　B　belonged　to　all　C。　And　if　C　is



convertible　with　B；　B　is　convertible　also　with　A；　for　C　is　said　of



that　of　all　of　which　B　is　said。　And　if　C　is　convertible　in　relation　to



A　and　to　B；　B　also　is　convertible　in　relation　to　A。　For　C　belongs　to



that　to　which　B　belongs：　but　C　does　not　belong　to　that　to　which　A



belongs。　And　this　alone　starts　from　the　conclusion；　the　preceding



moods　do　not　do　so　as　in　the　affirmative　syllogism。　Again　if　A　and　B



are　convertible；　and　similarly　C　and　D；　and　if　A　or　C　must　belong　to



anything　whatever；　then　B　and　D　will　be　such　that　one　or　other　belongs



to　anything　whatever。　For　since　B　belongs　to　that　to　which　A



belongs；　and　D　belongs　to　that　to　which　C　belongs；　and　since　A　or　C



belongs　to　everything；　but　not　together；　it　is　clear　that　B　or　D



belongs　to　everything；　but　not　together。　For　example　if　that　which



is　uncreated　is　incorruptible　and　that　which　is　incorruptible　is



uncreated；　it　is　necessary　that　what　is　created　should　be



corruptible　and　what　is　corruptible　should　have　been　created。　For



two　syllogisms　have　been　put　together。　Again　if　A　or　B　belongs　to



everything　and　if　C　or　D　belongs　to　everything；　but　they　cannot　belong



together；　then　when　A　and　C　are　convertible　B　and　D　are　convertible。



For　if　B　does　not　belong　to　something　to　which　D　belongs；　it　is



clear　that　A　belongs　to　it。　But　if　A　then　C：　for　they　are　convertible。



Therefore　C　and　D　belong　together。　But　this　is　impossible。　When　A



belongs　to　the　whole　of　B　and　to　C　and　is　affirmed　of　nothing　else；



and　B　also　belongs　to　all　C；　it　is　necessary　that　A　and　B　should　be



convertible：　for　since　A　is　said　of　B　and　C　only；　and　B　is　affirmed



both　of　itself　and　of　C；　it　is　clear　that　B　will　be　said　of　everything



of　which　A　is　said；　except　A　itself。　Again　when　A　and　B　belong　to



the　whole　of　C；　and　C　is　convertible　with　B；　it　is　necessary　that　A



should　belong　to　all　B：　for　since　A　belongs　to　all　C；　and　C　to　B　by



conversion；　A　will　belong　to　all　B。



　　When；　of　two　opposites　A　and　B；　A　is　preferable　to　B；　and



similarly　D　is　preferable　to　C；　then　if　A　and　C　together　are



preferable　to　B　and　D　together；　A　must　be　preferable　to　D。　For　A　is　an



object　of　desire　to　the　same　extent　as　B　is　an　object　of　aversion；



since　they　are　opposites：　and　C　is　similarly　related　to　D；　since



they　also　are　opposites。　If　then　A　is　an　object　of　desire　to　the



same　extent　as　D；　B　is　an　object　of　aversion　to　the　same　extent　as　C



（since　each　is　to　the　same　extent　as　each…the　one　an　object　of



aversion；　the　other　an　object　of　desire）。　Therefore　both　A　and　C



together；　and　B　and　D　together；　will　be　equally　objects　of　desire　or



aversion。　But　since　A　and　C　are　preferable　to　B　and　D；　A　cannot　be



equally　desirable　with　D；　for　then　B　along　with　D　would　be　equally



desirable　with　A　along　with　C。　But　if　D　is　preferable　to　A；　then　B



must　be　less　an　object　of　aversion　than　C：　for　the　less　is　opposed



to　the　less。　But　the　greater　good　and　lesser　evil　are　preferable　to



the　lesser　good　and　greater　evil：　the　whole　BD　then　is　preferable　to



the　whole　AC。　But　ex　hypothesi　this　is　not　so。　A　then　is　preferable　to



D；　and　C　consequently　is　less　an　object　of　aversion　than　B。　If　then



every　lover　in　virtue　of　his　love　would　prefer　A；　viz。　that　the



beloved　should　be　such　as　to　grant　a　favour；　and　yet　should　not



grant　it　（for　which　C　stands）；　to　the　beloved's　granting　the　favour



（represented　by　D）　without　being　such　as　to　grant　it　（represented　by



B）；　it　is　clear　that　A　（being　of　such　a　nature）　is　preferable　to



granting　the　favour。　To　receive　affection　then　is　preferable　in　love



to　sexual　intercourse。　Love　then　is　more　dependent　on　friendship



than　on　intercourse。　And　if　it　is　most　dependent　on　receiving



affection；　then　this　is　its　end。　Intercourse　then　either　is　not　an　end



at　all　or　is　an　end　relative　to　the　further　end；　the　receiving　of



affection。　And　indeed　the　same　is　true　of　the　other　desires　and　arts。







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　　It　is　clear　then　how　the　terms　are　related　in　conversion；　and　in



respect　of　being　in　a　higher　degree　objects　of　aversion　or　of



desire。　We　must　now　state　that　not　only　dialectical　and



demonstrative　syllogisms　are　formed　by　means　of　the　aforesaid　figures；



but　also　rhetorical　syllogisms　and　in　general　any　form　of



persuasion；　however　it　may　be　presented。　For　every　belief　comes　either



through　syllogism　or　from　induction。



　　Now　induction；　or　rather　the　syllogism　which　springs　out　of



induction；　consists　in　establishing　syllogistically　a　relation　between



one　extreme　and　the　middle　by　means　of　the　other　extreme；　e。g。　if　B　is



the　middle　term　between　A　and　C；　it　consists　in　proving　through　C　that



A　belongs　to　B。　For　this　is　the　manner　in　which　we　make　inductions。



For　example　let　A　stand　for　long…lived；　B　for　bileless；　and　C　for



the　particular　long…lived　animals；　e。g。　man；　horse；　mule。　A　then



belongs　to　the　whole　of　C：　for　whatever　is　bileless　is　long…lived。　But



B　also　（'not　possessing　bile'）　belongs　to　all　C。　If　then　C　is



convertible　with　B；　and　the　middle　term　is　not　wider　in　extension；



it　is　necessary　that　A　should　belong　to　B。　For　it　has　already　been



proved　that　if　two　things　belong　to　the　same　thing；　and　the　extreme　is



convertible　with　one　of　them；　then　the　other　predicate　will　belong



to　the　predicate　that　is　converted。　But　we　must　apprehend　C　as　made　up



of　all　the　particulars。　For　induction　proceeds　through　an



enumeration　of　all　the　cases。



　　Such　is　the　syllogism　which　establishes　the　first　and　immediate



premiss：　for　where　there　is　a　middle　term　the　syllogism　proceeds



through　the　middle　term；　when　there　is　no　middle　term；　through



induction。　And　in　a　way　induction　is　opposed　to　syllogism：　for　the



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。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　24







　　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。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　25







　　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；