prior analytics-第20节

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made。　That　whatever　is　a　man　is　not　musical　is　proved　destructively　in



the　three　ways　mentioned。



　　In　general　whenever　A　and　B　are　such　that　they　cannot　belong　at



the　same　time　to　the　same　thing；　and　one　of　the　two　necessarily



belongs　to　everything；　and　again　C　and　D　are　related　in　the　same



way；　and　A　follows　C　but　the　relation　cannot　be　reversed；　then　D



must　follow　B　and　the　relation　cannot　be　reversed。　And　A　and　D　may



belong　to　the　same　thing；　but　B　and　C　cannot。　First　it　is　clear　from



the　following　consideration　that　D　follows　B。　For　since　either　C　or



D　necessarily　belongs　to　everything；　and　since　C　cannot　belong　to　that



to　which　B　belongs；　because　it　carries　A　along　with　it　and　A　and　B



cannot　belong　to　the　same　thing；　it　is　clear　that　D　must　follow　B。



Again　since　C　does　not　reciprocate　with　but　A；　but　C　or　D　belongs　to



everything；　it　is　possible　that　A　and　D　should　belong　to　the　same



thing。　But　B　and　C　cannot　belong　to　the　same　thing；　because　A



follows　C；　and　so　something　impossible　results。　It　is　clear　then



that　B　does　not　reciprocate　with　D　either；　since　it　is　possible　that　D



and　A　should　belong　at　the　same　time　to　the　same　thing。



　　It　results　sometimes　even　in　such　an　arrangement　of　terms　that　one



is　deceived　through　not　apprehending　the　opposites　rightly；　one　of



which　must　belong　to　everything；　e。g。　we　may　reason　that　'if　A　and　B



cannot　belong　at　the　same　time　to　the　same　thing；　but　it　is



necessary　that　one　of　them　should　belong　to　whatever　the　other　does



not　belong　to：　and　again　C　and　D　are　related　in　the　same　way；　and



follows　everything　which　C　follows：　it　will　result　that　B　belongs



necessarily　to　everything　to　which　D　belongs'：　but　this　is　false。



'Assume　that　F　stands　for　the　negation　of　A　and　B；　and　again　that　H



stands　for　the　negation　of　C　and　D。　It　is　necessary　then　that　either　A



or　F　should　belong　to　everything：　for　either　the　affirmation　or　the



denial　must　belong。　And　again　either　C　or　H　must　belong　to　everything：



for　they　are　related　as　affirmation　and　denial。　And　ex　hypothesi　A



belongs　to　everything　ever　thing　to　which　C　belongs。　Therefore　H



belongs　to　everything　to　which　F　belongs。　Again　since　either　F　or　B



belongs　to　everything；　and　similarly　either　H　or　D；　and　since　H



follows　F；　B　must　follow　D：　for　we　know　this。　If　then　A　follows　C；　B



must　follow　D'。　But　this　is　false：　for　as　we　proved　the　sequence　is



reversed　in　terms　so　constituted。　The　fallacy　arises　because　perhaps



it　is　not　necessary　that　A　or　F　should　belong　to　everything；　or　that　F



or　B　should　belong　to　everything：　for　F　is　not　the　denial　of　A。　For



not　good　is　the　negation　of　good：　and　not…good　is　not　identical　with



'neither　good　nor　not…good'。　Similarly　also　with　C　and　D。　For　two



negations　have　been　assumed　in　respect　to　one　term。











　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　Book　II



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1







　　WE　have　already　explained　the　number　of　the　figures；　the　character



and　number　of　the　premisses；　when　and　how　a　syllogism　is　formed；



further　what　we　must　look　for　when　a　refuting　and　establishing



propositions；　and　how　we　should　investigate　a　given　problem　in　any



branch　of　inquiry；　also　by　what　means　we　shall　obtain　principles



appropriate　to　each　subject。　Since　some　syllogisms　are　universal；



others　particular；　all　the　universal　syllogisms　give　more　than　one



result；　and　of　particular　syllogisms　the　affirmative　yield　more　than



one；　the　negative　yield　only　the　stated　conclusion。　For　all



propositions　are　convertible　save　only　the　particular　negative：　and



the　conclusion　states　one　definite　thing　about　another　definite　thing。



Consequently　all　syllogisms　save　the　particular　negative　yield　more



than　one　conclusion；　e。g。　if　A　has　been　proved　to　to　all　or　to　some　B；



then　B　must　belong　to　some　A：　and　if　A　has　been　proved　to　belong　to　no



B；　then　B　belongs　to　no　A。　This　is　a　different　conclusion　from　the



former。　But　if　A　does　not　belong　to　some　B；　it　is　not　necessary　that　B



should　not　belong　to　some　A：　for　it　may　possibly　belong　to　all　A。



　　This　then　is　the　reason　common　to　all　syllogisms　whether　universal



or　particular。　But　it　is　possible　to　give　another　reason　concerning



those　which　are　universal。　For　all　the　things　that　are　subordinate



to　the　middle　term　or　to　the　conclusion　may　be　proved　by　the　same



syllogism；　if　the　former　are　placed　in　the　middle；　the　latter　in　the



conclusion；　e。g。　if　the　conclusion　AB　is　proved　through　C；　whatever　is



subordinate　to　B　or　C　must　accept　the　predicate　A：　for　if　D　is



included　in　B　as　in　a　whole；　and　B　is　included　in　A；　then　D　will　be



included　in　A。　Again　if　E　is　included　in　C　as　in　a　whole；　and　C　is



included　in　A；　then　E　will　be　included　in　A。　Similarly　if　the



syllogism　is　negative。　In　the　second　figure　it　will　be　possible　to



infer　only　that　which　is　subordinate　to　the　conclusion；　e。g。　if　A



belongs　to　no　B　and　to　all　C；　we　conclude　that　B　belongs　to　no　C。　If



then　D　is　subordinate　to　C；　clearly　B　does　not　belong　to　it。　But



that　B　does　not　belong　to　what　is　subordinate　to　A　is　not　clear　by



means　of　the　syllogism。　And　yet　B　does　not　belong　to　E；　if　E　is



subordinate　to　A。　But　while　it　has　been　proved　through　the　syllogism



that　B　belongs　to　no　C；　it　has　been　assumed　without　proof　that　B



does　not　belong　to　A；　consequently　it　does　not　result　through　the



syllogism　that　B　does　not　belong　to　E。



　　But　in　particular　syllogisms　there　will　be　no　necessity　of　inferring



what　is　subordinate　to　the　conclusion　（for　a　syllogism　does　not　result



when　this　premiss　is　particular）；　but　whatever　is　subordinate　to　the



middle　term　may　be　inferred；　not　however　through　the　syllogism；　e。g。



if　A　belongs　to　all　B　and　B　to　some　C。　Nothing　can　be　inferred　about



that　which　is　subordinate　to　C；　something　can　be　inferred　about　that



which　is　subordinate　to　B；　but　not　through　the　preceding　syllogism。



Similarly　in　the　other　figures。　That　which　is　subordinate　to　the



conclusion　cannot　be　proved；　the　other　subordinate　can　be　proved；　only



not　through　the　syllogism；　just　as　in　the　universal　syllogisms　what　is



subordinate　to　the　middle　term　is　proved　（as　we　saw）　from　a　premiss



which　is　not　demonstrated：　consequently　either　a　conclusion　is　not



possible　in　the　case　of　universal　syllogisms　or　else　it　is　possible



also　in　the　case　of　particular　syllogisms。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　2







　　It　is　possible　for　the　premisses　of　the　syllogism　to　be　true；　or



to　be　false；　or　to　be　the　one　true；　the　other　false。　The　conclusion　is



either　true　or　false　necessarily。　From　true　premisses　it　is　not



possible　to　draw　a　false　conclusion；　but　a　true　conclusion　may　be



drawn　from　false　premisses；　true　however　only　in　respect　to　the



fact；　not　to　the　reason。　The　reason　cannot　be　established　from　false



premisses：　why　this　is　so　will　be　explained　in　the　sequel。



　　First　then　that　it　is　not　possible　to　draw　a　false　conclusion　from



true　premisses；　is　made　clear　by　this　consideration。　If　it　is



necessary　that　B　should　be　when　A　is；　it　is　necessary　that　A　should



not　be　when　B　is　not。　If　then　A　is　true；　B　must　be　true：　otherwise



it　will　turn　out　that　the　same　thing　both　is　and　is　not　at　the　same



time。　But　this　is　impossible。　Let　it　not；　because　A　is　laid　down　as



a　single　term；　be　supposed　that　it　is　possible；　when　a　single　fact



is　given；　that　something　should　necessarily　result。　For　that　is　not



possible。　For　what　results　necessarily　is　the　conclusion；　and　the



means　by　which　this　comes　about　are　at　the　least　three　terms；　and



two　relations　of　subject　and　predicate　or　premisses。　If　then　it　is



true　that　A　belongs　to　all　that　to　which　B　belongs；　and　that　B　belongs



to　all　that　to　which　C　belongs；　it　is　necessary　that　A　should　belong



to　all　that　to　which　C　belongs；　and　this　cannot　be　false：　for　then　the



same　thing　will　belong　and　not　belong　at　the　same　time。　So　A　is



posited　as　one　thing；　being　two　premisses　taken　together。　The　same



holds　good　of　negative　syllogisms：　it　is　not　possible　to　prove　a　false



conclusion　from　true　premisses。



　　But　from　what　is　false　a　true　conclusion　may　be　drawn；　whether



both　the　premisses　are　false　or　only　one；　provided　that　this　is　not



either　of　the　premisses　indifferently；　if　it　is　taken　as　wholly　false：



but　if　the　premiss　is　not　taken　as　wholly　false；　it　does　not　matter



which　of　the　two　is　false。　（1）　Let　A　belong　to　the　whole　of　C；　but



to　none　of　the　Bs；　neither　let　B　belong　to　C。　This　is　possible；　e。g。



animal　belongs　to　no　stone；　nor　stone　to　any　man。　If　then　A　is　taken