prior analytics-第7章

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universal；　and　one　of　the　premisses　is　assertoric；　the　other



problematic；　whenever　the　minor　premiss　is　problematic　a　syllogism



always　results；　only　sometimes　it　results　from　the　premisses　that



are　taken；　sometimes　it　requires　the　conversion　of　one　premiss。　We



have　stated　when　each　of　these　happens　and　the　reason　why。　But　if



one　of　the　relations　is　universal；　the　other　particular；　then　whenever



the　major　premiss　is　universal　and　problematic；　whether　affirmative　or



negative；　and　the　particular　is　affirmative　and　assertoric；　there　will



be　a　perfect　syllogism；　just　as　when　the　terms　are　universal。　The



demonstration　is　the　same　as　before。　But　whenever　the　major　premiss　is



universal；　but　assertoric；　not　problematic；　and　the　minor　is



particular　and　problematic；　whether　both　premisses　are　negative　or



affirmative；　or　one　is　negative；　the　other　affirmative；　in　all　cases



there　will　be　an　imperfect　syllogism。　Only　some　of　them　will　be　proved



per　impossibile；　others　by　the　conversion　of　the　problematic



premiss；　as　has　been　shown　above。　And　a　syllogism　will　be　possible



by　means　of　conversion　when　the　major　premiss　is　universal　and



assertoric；　whether　positive　or　negative；　and　the　minor　particular；



negative；　and　problematic；　e。g。　if　A　belongs　to　all　B　or　to　no　B；



and　B　may　possibly　not　belong　to　some　C。　For　if　the　premiss　BC　is



converted　in　respect　of　possibility；　a　syllogism　results。　But　whenever



the　particular　premiss　is　assertoric　and　negative；　there　cannot　be　a



syllogism。　As　instances　of　the　positive　relation　we　may　take　the　terms



white…animal…snow；　of　the　negative；　white…animal…pitch。　For　the



demonstration　must　be　made　through　the　indefinite　nature　of　the



particular　premiss。　But　if　the　minor　premiss　is　universal；　and　the



major　particular；　whether　either　premiss　is　negative　or　affirmative；



problematic　or　assertoric；　nohow　is　a　syllogism　possible。　Nor　is　a



syllogism　possible　when　the　premisses　are　particular　or　indefinite；



whether　problematic　or　assertoric；　or　the　one　problematic；　the　other



assertoric。　The　demonstration　is　the　same　as　above。　As　instances　of



the　necessary　and　positive　relation　we　may　take　the　terms



animal…white…man；　of　the　necessary　and　negative　relation；



animal…white…garment。　It　is　evident　then　that　if　the　major　premiss



is　universal；　a　syllogism　always　results；　but　if　the　minor　is



universal　nothing　at　all　can　ever　be　proved。







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　　Whenever　one　premiss　is　necessary；　the　other　problematic；　there　will



be　a　syllogism　when　the　terms　are　related　as　before；　and　a　perfect



syllogism　when　the　minor　premiss　is　necessary。　If　the　premisses　are



affirmative　the　conclusion　will　be　problematic；　not　assertoric；



whether　the　premisses　are　universal　or　not：　but　if　one　is　affirmative；



the　other　negative；　when　the　affirmative　is　necessary　the　conclusion



will　be　problematic；　not　negative　assertoric；　but　when　the　negative　is



necessary　the　conclusion　will　be　problematic　negative；　and



assertoric　negative；　whether　the　premisses　are　universal　or　not。



Possibility　in　the　conclusion　must　be　understood　in　the　same　manner　as



before。　There　cannot　be　an　inference　to　the　necessary　negative



proposition：　for　'not　necessarily　to　belong'　is　different　from



'necessarily　not　to　belong'。



　　If　the　premisses　are　affirmative；　clearly　the　conclusion　which



follows　is　not　necessary。　Suppose　A　necessarily　belongs　to　all　B；



and　let　B　be　possible　for　all　C。　We　shall　have　an　imperfect



syllogism　to　prove　that　A　may　belong　to　all　C。　That　it　is　imperfect　is



clear　from　the　proof：　for　it　will　be　proved　in　the　same　manner　as



above。　Again；　let　A　be　possible　for　all　B；　and　let　B　necessarily



belong　to　all　C。　We　shall　then　have　a　syllogism　to　prove　that　A　may



belong　to　all　C；　not　that　A　does　belong　to　all　C：　and　it　is　perfect；



not　imperfect：　for　it　is　completed　directly　through　the　original



premisses。



　　But　if　the　premisses　are　not　similar　in　quality；　suppose　first



that　the　negative　premiss　is　necessary；　and　let　necessarily　A　not　be



possible　for　any　B；　but　let　B　be　possible　for　all　C。　It　is　necessary



then　that　A　belongs　to　no　C。　For　suppose　A　to　belong　to　all　C　or　to



some　C。　Now　we　assumed　that　A　is　not　possible　for　any　B。　Since　then



the　negative　proposition　is　convertible；　B　is　not　possible　for　any



A。　But　A　is　supposed　to　belong　to　all　C　or　to　some　C。　Consequently　B



will　not　be　possible　for　any　C　or　for　all　C。　But　it　was　originally



laid　down　that　B　is　possible　for　all　C。　And　it　is　clear　that　the



possibility　of　belonging　can　be　inferred；　since　the　fact　of　not



belonging　is　inferred。　Again；　let　the　affirmative　premiss　be



necessary；　and　let　A　possibly　not　belong　to　any　B；　and　let　B



necessarily　belong　to　all　C。　The　syllogism　will　be　perfect；　but　it



will　establish　a　problematic　negative；　not　an　assertoric　negative。　For



the　major　premiss　was　problematic；　and　further　it　is　not　possible　to



prove　the　assertoric　conclusion　per　impossibile。　For　if　it　were



supposed　that　A　belongs　to　some　C；　and　it　is　laid　down　that　A　possibly



does　not　belong　to　any　B；　no　impossible　relation　between　B　and　C



follows　from　these　premisses。　But　if　the　minor　premiss　is　negative；



when　it　is　problematic　a　syllogism　is　possible　by　conversion；　as



above；　but　when　it　is　necessary　no　syllogism　can　be　formed。　Nor



again　when　both　premisses　are　negative；　and　the　minor　is　necessary。



The　same　terms　as　before　serve　both　for　the　positive



relation…white…animal…snow；　and　for　the　negative



relation…white…animal…pitch。



　　The　same　relation　will　obtain　in　particular　syllogisms。　Whenever　the



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。＇







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　　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