prior analytics-第16章

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antecedents　of　E　by　G；　and　attributes　which　cannot　belong　to　E　by　H。



If　then　one　of　the　Cs　should　be　identical　with　one　of　the　Fs；　A　must



belong　to　all　E：　for　F　belongs　to　all　E；　and　A　to　all　C；



consequently　A　belongs　to　all　E。　If　C　and　G　are　identical；　A　must



belong　to　some　of　the　Es：　for　A　follows　C；　and　E　follows　all　G。　If　F



and　D　are　identical；　A　will　belong　to　none　of　the　Es　by　a



prosyllogism：　for　since　the　negative　proposition　is　convertible；　and　F



is　identical　with　D；　A　will　belong　to　none　of　the　Fs；　but　F　belongs　to



all　E。　Again；　if　B　and　H　are　identical；　A　will　belong　to　none　of　the



Es：　for　B　will　belong　to　all　A；　but　to　no　E：　for　it　was　assumed　to



be　identical　with　H；　and　H　belonged　to　none　of　the　Es。　If　D　and　G



are　identical；　A　will　not　belong　to　some　of　the　Es：　for　it　will　not



belong　to　G；　because　it　does　not　belong　to　D：　but　G　falls　under　E：



consequently　A　will　not　belong　to　some　of　the　Es。　If　B　is　identical



with　G；　there　will　be　a　converted　syllogism：　for　E　will　belong　to



all　A　since　B　belongs　to　A　and　E　to　B　（for　B　was　found　to　be　identical



with　G）：　but　that　A　should　belong　to　all　E　is　not　necessary；　but　it



must　belong　to　some　E　because　it　is　possible　to　convert　the



universal　statement　into　a　particular。



　　It　is　clear　then　that　in　every　proposition　which　requires　proof　we



must　look　to　the　aforesaid　relations　of　the　subject　and　predicate　in



question：　for　all　syllogisms　proceed　through　these。　But　if　we　are



seeking　consequents　and　antecedents　we　must　look　for　those　which　are



primary　and　most　universal；　e。g。　in　reference　to　E　we　must　look　to



KF　rather　than　to　F　alone；　and　in　reference　to　A　we　must　look　to　KC



rather　than　to　C　alone。　For　if　A　belongs　to　KF；　it　belongs　both　to　F



and　to　E：　but　if　it　does　not　follow　KF；　it　may　yet　follow　F。　Similarly



we　must　consider　the　antecedents　of　A　itself：　for　if　a　term　follows



the　primary　antecedents；　it　will　follow　those　also　which　are



subordinate；　but　if　it　does　not　follow　the　former；　it　may　yet　follow



the　latter。



　　It　is　clear　too　that　the　inquiry　proceeds　through　the　three　terms



and　the　two　premisses；　and　that　all　the　syllogisms　proceed　through　the



aforesaid　figures。　For　it　is　proved　that　A　belongs　to　all　E；



whenever　an　identical　term　is　found　among　the　Cs　and　Fs。　This　will



be　the　middle　term；　A　and　E　will　be　the　extremes。　So　the　first



figure　is　formed。　And　A　will　belong　to　some　E；　whenever　C　and　G　are



apprehended　to　be　the　same。　This　is　the　last　figure：　for　G　becomes　the



middle　term。　And　A　will　belong　to　no　E；　when　D　and　F　are　identical。



Thus　we　have　both　the　first　figure　and　the　middle　figure；　the　first；



because　A　belongs　to　no　F；　since　the　negative　statement　is



convertible；　and　F　belongs　to　all　E：　the　middle　figure　because　D



belongs　to　no　A；　and　to　all　E。　And　A　will　not　belong　to　some　E；



whenever　D　and　G　are　identical。　This　is　the　last　figure：　for　A　will



belong　to　no　G；　and　E　will　belong　to　all　G。　Clearly　then　all



syllogisms　proceed　through　the　aforesaid　figures；　and　we　must　not



select　consequents　of　all　the　terms；　because　no　syllogism　is



produced　from　them。　For　（as　we　saw）　it　is　not　possible　at　all　to



establish　a　proposition　from　consequents；　and　it　is　not　possible　to



refute　by　means　of　a　consequent　of　both　the　terms　in　question：　for　the



middle　term　must　belong　to　the　one；　and　not　belong　to　the　other。



　　It　is　clear　too　that　other　methods　of　inquiry　by　selection　of　middle



terms　are　useless　to　produce　a　syllogism；　e。g。　if　the　consequents　of



the　terms　in　question　are　identical；　or　if　the　antecedents　of　A　are



identical　with　those　attributes　which　cannot　possibly　belong　to　E；



or　if　those　attributes　are　identical　which　cannot　belong　to　either



term：　for　no　syllogism　is　produced　by　means　of　these。　For　if　the



consequents　are　identical；　e。g。　B　and　F；　we　have　the　middle　figure



with　both　premisses　affirmative：　if　the　antecedents　of　A　are　identical



with　attributes　which　cannot　belong　to　E；　e。g。　C　with　H；　we　have　the



first　figure　with　its　minor　premiss　negative。　If　attributes　which



cannot　belong　to　either　term　are　identical；　e。g。　C　and　H；　both



premisses　are　negative；　either　in　the　first　or　in　the　middle　figure。



But　no　syllogism　is　possible　in　this　way。



　　It　is　evident　too　that　we　must　find　out　which　terms　in　this



inquiry　are　identical；　not　which　are　different　or　contrary；　first



because　the　object　of　our　investigation　is　the　middle　term；　and　the



middle　term　must　be　not　diverse　but　identical。　Secondly；　wherever　it



happens　that　a　syllogism　results　from　taking　contraries　or　terms　which



cannot　belong　to　the　same　thing；　all　arguments　can　be　reduced　to　the



aforesaid　moods；　e。g。　if　B　and　F　are　contraries　or　cannot　belong　to



the　same　thing。　For　if　these　are　taken；　a　syllogism　will　be　formed



to　prove　that　A　belongs　to　none　of　the　Es；　not　however　from　the



premisses　taken　but　in　the　aforesaid　mood。　For　B　will　belong　to　all



A　and　to　no　E。　Consequently　B　must　be　identical　with　one　of　the　Hs。



Again；　if　B　and　G　cannot　belong　to　the　same　thing；　it　follows　that　A



will　not　belong　to　some　of　the　Es：　for　then　too　we　shall　have　the



middle　figure：　for　B　will　belong　to　all　A　and　to　no　G。　Consequently



B　must　be　identical　with　some　of　the　Hs。　For　the　fact　that　B　and　G



cannot　belong　to　the　same　thing　differs　in　no　way　from　the　fact　that　B



is　identical　with　some　of　the　Hs：　for　that　includes　everything　which



cannot　belong　to　E。



　　It　is　clear　then　that　from　the　inquiries　taken　by　themselves　no



syllogism　results；　but　if　B　and　F　are　contraries　B　must　be　identical



with　one　of　the　Hs；　and　the　syllogism　results　through　these　terms。



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　establ