prior analytics-第10节

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they　stand；　but　if　the　problematic　premiss　is　converted　into　its



complementary　affirmative　a　syllogism　is　formed　to　prove　that　B　may



belong　to　no　C；　as　before：　for　we　shall　again　have　the　first　figure。



But　if　both　premisses　are　affirmative；　no　syllogism　will　be



possible。　This　arrangement　of　terms　is　possible　both　when　the　relation



is　positive；　e。g。　health；　animal；　man；　and　when　it　is　negative；　e。g。



health；　horse；　man。



　　The　same　will　hold　good　if　the　syllogisms　are　particular。　Whenever



the　affirmative　proposition　is　assertoric；　whether　universal　or



particular；　no　syllogism　is　possible　（this　is　proved　similarly　and



by　the　same　examples　as　above）；　but　when　the　negative　proposition　is



assertoric；　a　conclusion　can　be　drawn　by　means　of　conversion；　as



before。　Again　if　both　the　relations　are　negative；　and　the　assertoric



proposition　is　universal；　although　no　conclusion　follows　from　the



actual　premisses；　a　syllogism　can　be　obtained　by　converting　the



problematic　premiss　into　its　complementary　affirmative　as　before。



But　if　the　negative　proposition　is　assertoric；　but　particular；　no



syllogism　is　possible；　whether　the　other　premiss　is　affirmative　or



negative。　Nor　can　a　conclusion　be　drawn　when　both　premisses　are



indefinite；　whether　affirmative　or　negative；　or　particular。　The



proof　is　the　same　and　by　the　same　terms。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　19







　　If　one　of　the　premisses　is　necessary；　the　other　problematic；　then　if



the　negative　is　necessary　a　syllogistic　conclusion　can　be　drawn；　not



merely　a　negative　problematic　but　also　a　negative　assertoric



conclusion；　but　if　the　affirmative　premiss　is　necessary；　no　conclusion



is　possible。　Suppose　that　A　necessarily　belongs　to　no　B；　but　may



belong　to　all　C。　If　the　negative　premiss　is　converted　B　will　belong　to



no　A：　but　A　ex　hypothesi　is　capable　of　belonging　to　all　C：　so　once



more　a　conclusion　is　drawn　by　the　first　figure　that　B　may　belong　to　no



C。　But　at　the　same　time　it　is　clear　that　B　will　not　belong　to　any　C。



For　assume　that　it　does：　then　if　A　cannot　belong　to　any　B；　and　B



belongs　to　some　of　the　Cs；　A　cannot　belong　to　some　of　the　Cs：　but　ex



hypothesi　it　may　belong　to　all。　A　similar　proof　can　be　given　if　the



minor　premiss　is　negative。　Again　let　the　affirmative　proposition　be



necessary；　and　the　other　problematic；　i。e。　suppose　that　A　may　belong



to　no　B；　but　necessarily　belongs　to　all　C。　When　the　terms　are　arranged



in　this　way；　no　syllogism　is　possible。　For　（1）　it　sometimes　turns



out　that　B　necessarily　does　not　belong　to　C。　Let　A　be　white；　B　man；



C　swan。　White　then　necessarily　belongs　to　swan；　but　may　belong　to　no



man；　and　man　necessarily　belongs　to　no　swan；　Clearly　then　we　cannot



draw　a　problematic　conclusion；　for　that　which　is　necessary　is



admittedly　distinct　from　that　which　is　possible。　（2）　Nor　again　can



we　draw　a　necessary　conclusion：　for　that　presupposes　that　both



premisses　are　necessary；　or　at　any　rate　the　negative　premiss。　（3）



Further　it　is　possible　also；　when　the　terms　are　so　arranged；　that　B



should　belong　to　C：　for　nothing　prevents　C　falling　under　B；　A　being



possible　for　all　B；　and　necessarily　belonging　to　C；　e。g。　if　C　stands



for　'awake'；　B　for　'animal'；　A　for　'motion'。　For　motion　necessarily



belongs　to　what　is　awake；　and　is　possible　for　every　animal：　and



everything　that　is　awake　is　animal。　Clearly　then　the　conclusion　cannot



be　the　negative　assertion；　if　the　relation　must　be　positive　when　the



terms　are　related　as　above。　Nor　can　the　opposite　affirmations　be



established：　consequently　no　syllogism　is　possible。　A　similar　proof　is



possible　if　the　major　premiss　is　affirmative。



　　But　if　the　premisses　are　similar　in　quality；　when　they　are



negative　a　syllogism　can　always　be　formed　by　converting　the



problematic　premiss　into　its　complementary　affirmative　as　before。



Suppose　A　necessarily　does　not　belong　to　B；　and　possibly　may　not



belong　to　C：　if　the　premisses　are　converted　B　belongs　to　no　A；　and　A



may　possibly　belong　to　all　C：　thus　we　have　the　first　figure。　Similarly



if　the　minor　premiss　is　negative。　But　if　the　premisses　are　affirmative



there　cannot　be　a　syllogism。　Clearly　the　conclusion　cannot　be　a



negative　assertoric　or　a　negative　necessary　proposition　because　no



negative　premiss　has　been　laid　down　either　in　the　assertoric　or　in　the



necessary　mode。　Nor　can　the　conclusion　be　a　problematic　negative



proposition。　For　if　the　terms　are　so　related；　there　are　cases　in　which



B　necessarily　will　not　belong　to　C；　e。g。　suppose　that　A　is　white；　B



swan；　C　man。　Nor　can　the　opposite　affirmations　be　established；　since



we　have　shown　a　case　in　which　B　necessarily　does　not　belong　to　C。　A



syllogism　then　is　not　possible　at　all。



　　Similar　relations　will　obtain　in　particular　syllogisms。　For　whenever



the　negative　proposition　is　universal　and　necessary；　a　syllogism



will　always　be　possible　to　prove　both　a　problematic　and　a　negative



assertoric　proposition　（the　proof　proceeds　by　conversion）；　but　when



the　affirmative　proposition　is　universal　and　necessary；　no　syllogistic



conclusion　can　be　drawn。　This　can　be　proved　in　the　same　way　as　for



universal　propositions；　and　by　the　same　terms。　Nor　is　a　syllogistic



conclusion　possible　when　both　premisses　are　affirmative：　this　also　may



be　proved　as　above。　But　when　both　premisses　are　negative；　and　the



premiss　that　definitely　disconnects　two　terms　is　universal　and



necessary；　though　nothing　follows　necessarily　from　the　premisses　as



they　are　stated；　a　conclusion　can　be　drawn　as　above　if　the　problematic



premiss　is　converted　into　its　complementary　affirmative。　But　if　both



are　indefinite　or　particular；　no　syllogism　can　be　formed。　The　same



proof　will　serve；　and　the　same　terms。



　　It　is　clear　then　from　what　has　been　said　that　if　the　universal　and



negative　premiss　is　necessary；　a　syllogism　is　always　possible；　proving



not　merely　a　negative　problematic；　but　also　a　negative　assertoric



proposition；　but　if　the　affirmative　premiss　is　necessary　no　conclusion



can　be　drawn。　It　is　clear　too　that　a　syllogism　is　possible　or　not



under　the　same　conditions　whether　the　mode　of　the　premisses　is



assertoric　or　necessary。　And　it　is　clear　that　all　the　syllogisms　are



imperfect；　and　are　completed　by　means　of　the　figures　mentioned。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　20



　　In　the　last　figure　a　syllogism　is　possible　whether　both　or　only



one　of　the　premisses　is　problematic。　When　the　premisses　are



problematic　the　conclusion　will　be　problematic；　and　also　when　one



premiss　is　problematic；　the　other　assertoric。　But　when　the　other



premiss　is　necessary；　if　it　is　affirmative　the　conclusion　will　be



neither　necessary　or　assertoric；　but　if　it　is　negative　the　syllogism



will　result　in　a　negative　assertoric　proposition；　as　above。　In　these



also　we　must　understand　the　expression　'possible'　in　the　conclusion　in



the　same　way　as　before。



　　First　let　the　premisses　be　problematic　and　suppose　that　both　A　and　B



may　possibly　belong　to　every　C。　Since　then　the　affirmative　proposition



is　convertible　into　a　particular；　and　B　may　possibly　belong　to　every



C；　it　follows　that　C　may　possibly　belong　to　some　B。　So；　if　A　is



possible　for　every　C；　and　C　is　possible　for　some　of　the　Bs；　then　A



is　possible　for　some　of　the　Bs。　For　we　have　got　the　first　figure。



And　A　if　may　possibly　belong　to　no　C；　but　B　may　possibly　belong　to　all



C；　it　follows　that　A　may　possibly　not　belong　to　some　B：　for　we　shall



have　the　first　figure　again　by　conversion。　But　if　both　premisses



should　be　negative　no　necessary　consequence　will　follow　from　them　as



they　are　stated；　but　if　the　premisses　are　converted　into　their



corresponding　affirmatives　there　will　be　a　syllogism　as　before。　For　if



A　and　B　may　possibly　not　belong　to　C；　if　'may　possibly　belong'　is



substituted　we　shall　again　have　the　first　figure　by　means　of



conversion。　But　if　one　of　the　premisses　is　universal；　the　other



particular；　a　syllogism　will　be　possible；　or　not；　under　the



arrangement　of　the　terms　as　in　the　case　of　assertoric　propositions。



Suppose　that　A　may　possibly　belong　to　all　C；　and　B　to　some　C。　We　shall



have　the　first　figure　again　if　the　particular　premiss　is　converted。



For　if　A　is　possible　for　all　C；　and　C　for　some　of　the　Bs；　then　A　is



possible　for　some　of　the　Bs。　Similarly　if　the　proposition　BC　is



universal。　Likewise　also　if　the　proposition　AC　is　negative；　and　the



proposition　BC　affirmative：　for　we　shall　again　have　the　first　figure



by　conversion。　But　if　both　premisses　should　be　negative…the　one



universal　and　the　other　particular…although　no