prior analytics-第8节

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we　have　a　syllogism　in　the　third　figure：　but　this　is　impossible。



Thus　it　will　be　possible　for　A　to　belong　to　no　C；　for　if　at　is



supposed　false；　the　consequence　is　an　impossible　one。　This　syllogism



then　does　not　establish　that　which　is　possible　according　to　the



definition；　but　that　which　does　not　necessarily　belong　to　any　part



of　the　subject　（for　this　is　the　contradictory　of　the　assumption



which　was　made：　for　it　was　supposed　that　A　necessarily　belongs　to　some



C；　but　the　syllogism　per　impossibile　establishes　the　contradictory



which　is　opposed　to　this）。　Further；　it　is　clear　also　from　an　example



that　the　conclusion　will　not　establish　possibility。　Let　A　be



'raven'；　B　'intelligent'；　and　C　'man'。　A　then　belongs　to　no　B：　for



no　intelligent　thing　is　a　raven。　But　B　is　possible　for　all　C：　for



every　man　may　possibly　be　intelligent。　But　A　necessarily　belongs　to　no



C：　so　the　conclusion　does　not　establish　possibility。　But　neither　is　it



always　necessary。　Let　A　be　'moving'；　B　'science'；　C　'man'。　A　then　will



belong　to　no　B；　but　B　is　possible　for　all　C。　And　the　conclusion　will



not　be　necessary。　For　it　is　not　necessary　that　no　man　should　move；



rather　it　is　not　necessary　that　any　man　should　move。　Clearly　then



the　conclusion　establishes　that　one　term　does　not　necessarily　belong



to　any　instance　of　another　term。　But　we　must　take　our　terms　better。



　　If　the　minor　premiss　is　negative　and　indicates　possibility；　from　the



actual　premisses　taken　there　can　be　no　syllogism；　but　if　the



problematic　premiss　is　converted；　a　syllogism　will　be　possible；　as



before。　Let　A　belong　to　all　B；　and　let　B　possibly　belong　to　no　C。　If



the　terms　are　arranged　thus；　nothing　necessarily　follows：　but　if　the



proposition　BC　is　converted　and　it　is　assumed　that　B　is　possible　for



all　C；　a　syllogism　results　as　before：　for　the　terms　are　in　the　same



relative　positions。　Likewise　if　both　the　relations　are　negative；　if



the　major　premiss　states　that　A　does　not　belong　to　B；　and　the　minor



premiss　indicates　that　B　may　possibly　belong　to　no　C。　Through　the



premisses　actually　taken　nothing　necessary　results　in　any　way；　but



if　the　problematic　premiss　is　converted；　we　shall　have　a　syllogism。



Suppose　that　A　belongs　to　no　B；　and　B　may　possibly　belong　to　no　C。



Through　these　comes　nothing　necessary。　But　if　B　is　assumed　to　be



possible　for　all　C　（and　this　is　true）　and　if　the　premiss　AB　remains　as



before；　we　shall　again　have　the　same　syllogism。　But　if　it　be　assumed



that　B　does　not　belong　to　any　C；　instead　of　possibly　not　belonging；



there　cannot　be　a　syllogism　anyhow；　whether　the　premiss　AB　is　negative



or　affirmative。　As　common　instances　of　a　necessary　and　positive



relation　we　may　take　the　terms　white…animal…snow：　of　a　necessary　and



negative　relation；　white…animal…pitch。　Clearly　then　if　the　terms　are



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。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　16







　　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　shou