prior analytics-第10章

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negative　proposition　is　necessary；　the　conclusion　will　be　negative



assertoric：　e。g。　if　it　is　not　possible　that　A　should　belong　to　any



B；　but　B　may　belong　to　some　of　the　Cs；　it　is　necessary　that　A　should



not　belong　to　some　of　the　Cs。　For　if　A　belongs　to　all　C；　but　cannot



belong　to　any　B；　neither　can　B　belong　to　any　A。　So　if　A　belongs　to　all



C；　to　none　of　the　Cs　can　B　belong。　But　it　was　laid　down　that　B　may



belong　to　some　C。　But　when　the　particular　affirmative　in　the



negative　syllogism；　e。g。　BC　the　minor　premiss；　or　the　universal



proposition　in　the　affirmative　syllogism；　e。g。　AB　the　major　premiss；



is　necessary；　there　will　not　be　an　assertoric　conclusion。　The



demonstration　is　the　same　as　before。　But　if　the　minor　premiss　is



universal；　and　problematic；　whether　affirmative　or　negative；　and　the



major　premiss　is　particular　and　necessary；　there　cannot　be　a



syllogism。　Premisses　of　this　kind　are　possible　both　where　the　relation



is　positive　and　necessary；　e。g。　animal…white…man；　and　where　it　is



necessary　and　negative；　e。g。　animal…white…garment。　But　when　the



universal　is　necessary；　the　particular　problematic；　if　the　universal



is　negative　we　may　take　the　terms　animal…white…raven　to　illustrate　the



positive　relation；　or　animal…white…pitch　to　illustrate　the　negative；



and　if　the　universal　is　affirmative　we　may　take　the　terms



animal…white…swan　to　illustrate　the　positive　relation；　and



animal…white…snow　to　illustrate　the　negative　and　necessary　relation。



Nor　again　is　a　syllogism　possible　when　the　premisses　are　indefinite；



or　both　particular。　Terms　applicable　in　either　case　to　illustrate



the　positive　relation　are　animal…white…man：　to　illustrate　the



negative；　animal…white…inanimate。　For　the　relation　of　animal　to　some



white；　and　of　white　to　some　inanimate；　is　both　necessary　and



positive　and　necessary　and　negative。　Similarly　if　the　relation　is



problematic：　so　the　terms　may　be　used　for　all　cases。



　　Clearly　then　from　what　has　been　said　a　syllogism　results　or　not　from



similar　relations　of　the　terms　whether　we　are　dealing　with　simple



existence　or　necessity；　with　this　exception；　that　if　the　negative



premiss　is　assertoric　the　conclusion　is　problematic；　but　if　the



negative　premiss　is　necessary　the　conclusion　is　both　problematic　and



negative　assertoric。　＇It　is　clear　also　that　all　the　syllogisms　are



imperfect　and　are　perfected　by　means　of　the　figures　above　mentioned。＇







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　17







　　In　the　second　figure　whenever　both　premisses　are　problematic；　no



syllogism　is　possible；　whether　the　premisses　are　affirmative　or



negative；　universal　or　particular。　But　when　one　premiss　is　assertoric；



the　other　problematic；　if　the　affirmative　is　assertoric　no　syllogism



is　possible；　but　if　the　universal　negative　is　assertoric　a



conclusion　can　always　be　drawn。　Similarly　when　one　premiss　is



necessary；　the　other　problematic。　Here　also　we　must　understand　the



term　'possible'　in　the　conclusion；　in　the　same　sense　as　before。



　　First　we　must　point　out　that　the　negative　problematic　proposition　is



not　convertible；　e。g。　if　A　may　belong　to　no　B；　it　does　not　follow　that



B　may　belong　to　no　A。　For　suppose　it　to　follow　and　assume　that　B　may



belong　to　no　A。　Since　then　problematic　affirmations　are　convertible



with　negations；　whether　they　are　contraries　or　contradictories；　and



since　B　may　belong　to　no　A；　it　is　clear　that　B　may　belong　to　all　A。



But　this　is　false：　for　if　all　this　can　be　that；　it　does　not　follow



that　all　that　can　be　this：　consequently　the　negative　proposition　is



not　convertible。　Further；　these　propositions　are　not　incompatible；



'A　may　belong　to　no　B'；　'B　necessarily　does　not　belong　to　some　of



the　As'；　e。g。　it　is　possible　that　no　man　should　be　white　（for　it　is



also　possible　that　every　man　should　be　white）；　but　it　is　not　true　to



say　that　it　is　possible　that　no　white　thing　should　be　a　man：　for



many　white　things　are　necessarily　not　men；　and　the　necessary　（as　we



saw）　other　than　the　possible。



　　Moreover　it　is　not　possible　to　prove　the　convertibility　of　these



propositions　by　a　reductio　ad　absurdum；　i。e。　by　claiming　assent　to　the



following　argument：　'since　it　is　false　that　B　may　belong　to　no　A；　it



is　true　that　it　cannot　belong　to　no　A；　for　the　one　statement　is　the



contradictory　of　the　other。　But　if　this　is　so；　it　is　true　that　B



necessarily　belongs　to　some　of　the　As：　consequently　A　necessarily



belongs　to　some　of　the　Bs。　But　this　is　impossible。'　The　argument



cannot　be　admitted；　for　it　does　not　follow　that　some　A　is



necessarily　B；　if　it　is　not　possible　that　no　A　should　be　B。　For　the



latter　expression　is　used　in　two　senses；　one　if　A　some　is



necessarily　B；　another　if　some　A　is　necessarily　not　B。　For　it　is　not



true　to　say　that　that　which　necessarily　does　not　belong　to　some　of　the



As　may　possibly　not　belong　to　any　A；　just　as　it　is　not　true　to　say



that　what　necessarily　belongs　to　some　A　may　possibly　belong　to　all



A。　If　any　one　then　should　claim　that　because　it　is　not　possible　for



C　to　belong　to　all　D；　it　necessarily　does　not　belong　to　some　D；　he



would　make　a　false　assumption：　for　it　does　belong　to　all　D；　but



because　in　some　cases　it　belongs　necessarily；　therefore　we　say　that　it



is　not　possible　for　it　to　belong　to　all。　Hence　both　the　propositions



'A　necessarily　belongs　to　some　B'　and　'A　necessarily　does　not　belong



to　some　B'　are　opposed　to　the　proposition　'A　belongs　to　all　B'。



Similarly　also　they　are　opposed　to　the　proposition　'A　may　belong　to　no



B'。　It　is　clear　then　that　in　relation　to　what　is　possible　and　not



possible；　in　the　sense　originally　defined；　we　must　assume；　not　that



A　necessarily　belongs　to　some　B；　but　that　A　necessarily　does　not



belong　to　some　B。　But　if　this　is　assumed；　no　absurdity　results：



consequently　no　syllogism。　It　is　clear　from　what　has　been　said　that



the　negative　proposition　is　not　convertible。



　　This　being　proved；　suppose　it　possible　that　A　may　belong　to　no　B　and



to　all　C。　By　means　of　conversion　no　syllogism　will　result：　for　the



major　premiss；　as　has　been　said；　is　not　convertible。　Nor　can　a　proof



be　obtained　by　a　reductio　ad　absurdum：　for　if　it　is　assumed　that　B　can



belong　to　all　C；　no　false　consequence　results：　for　A　may　belong　both



to　all　C　and　to　no　C。　In　general；　if　there　is　a　syllogism；　it　is　clear



that　its　conclusion　will　be　problematic　because　neither　of　the



premisses　is　assertoric；　and　this　must　be　either　affirmative　or



negative。　But　neither　is　possible。　Suppose　the　conclusion　is



affirmative：　it　will　be　proved　by　an　example　that　the　predicate　cannot



belong　to　the　subject。　Suppose　the　conclusion　is　negative：　it　will



be　proved　that　it　is　not　problematic　but　necessary。　Let　A　be　white；



B　man；　C　horse。　It　is　possible　then　for　A　to　belong　to　all　of　the



one　and　to　none　of　the　other。　But　it　is　not　possible　for　B　to　belong



nor　not　to　belong　to　C。　That　it　is　not　possible　for　it　to　belong；　is



clear。　For　no　horse　is　a　man。　Neither　is　it　possible　for　it　not　to



belong。　For　it　is　necessary　that　no　horse　should　be　a　man；　but　the



necessary　we　found　to　be　different　from　the　possible。　No　syllogism



then　results。　A　similar　proof　can　be　given　if　the　major　premiss　is



negative；　the　minor　affirmative；　or　if　both　are　affirmative　or



negative。　The　demonstration　can　be　made　by　means　of　the　same　terms。



And　whenever　one　premiss　is　universal；　the　other　particular；　or　both



are　particular　or　indefinite；　or　in　whatever　other　way　the　premisses



can　be　altered；　the　proof　will　always　proceed　through　the　same



terms。　Clearly　then；　if　both　the　premisses　are　problematic；　no



syllogism　results。