prior analytics-第2节

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　　Whenever　three　terms　are　so　related　to　one　another　that　the　last



is　contained　in　the　middle　as　in　a　whole；　and　the　middle　is　either



contained　in；　or　excluded　from；　the　first　as　in　or　from　a　whole；　the



extremes　must　be　related　by　a　perfect　syllogism。　I　call　that　term



middle　which　is　itself　contained　in　another　and　contains　another　in



itself：　in　position　also　this　comes　in　the　middle。　By　extremes　I



mean　both　that　term　which　is　itself　contained　in　another　and　that　in



which　another　is　contained。　If　A　is　predicated　of　all　B；　and　B　of



all　C；　A　must　be　predicated　of　all　C：　we　have　already　explained　what



we　mean　by　'predicated　of　all'。　Similarly　also；　if　A　is　predicated



of　no　B；　and　B　of　all　C；　it　is　necessary　that　no　C　will　be　A。



　　But　if　the　first　term　belongs　to　all　the　middle；　but　the　middle　to



none　of　the　last　term；　there　will　be　no　syllogism　in　respect　of　the



extremes；　for　nothing　necessary　follows　from　the　terms　being　so



related；　for　it　is　possible　that　the　first　should　belong　either　to　all



or　to　none　of　the　last；　so　that　neither　a　particular　nor　a　universal



conclusion　is　necessary。　But　if　there　is　no　necessary　consequence；



there　cannot　be　a　syllogism　by　means　of　these　premisses。　As　an　example



of　a　universal　affirmative　relation　between　the　extremes　we　may　take



the　terms　animal；　man；　horse；　of　a　universal　negative　relation；　the



terms　animal；　man；　stone。　Nor　again　can　syllogism　be　formed　when



neither　the　first　term　belongs　to　any　of　the　middle；　nor　the　middle　to



any　of　the　last。　As　an　example　of　a　positive　relation　between　the



extremes　take　the　terms　science；　line；　medicine：　of　a　negative



relation　science；　line；　unit。



　　If　then　the　terms　are　universally　related；　it　is　clear　in　this



figure　when　a　syllogism　will　be　possible　and　when　not；　and　that　if　a



syllogism　is　possible　the　terms　must　be　related　as　described；　and　if



they　are　so　related　there　will　be　a　syllogism。



　　But　if　one　term　is　related　universally；　the　other　in　part　only；　to



its　subject；　there　must　be　a　perfect　syllogism　whenever　universality



is　posited　with　reference　to　the　major　term　either　affirmatively　or



negatively；　and　particularity　with　reference　to　the　minor　term



affirmatively：　but　whenever　the　universality　is　posited　in　relation　to



the　minor　term；　or　the　terms　are　related　in　any　other　way；　a　syllogism



is　impossible。　I　call　that　term　the　major　in　which　the　middle　is



contained　and　that　term　the　minor　which　comes　under　the　middle。　Let



all　B　be　A　and　some　C　be　B。　Then　if　'predicated　of　all'　means　what　was



said　above；　it　is　necessary　that　some　C　is　A。　And　if　no　B　is　A　but



some　C　is　B；　it　is　necessary　that　some　C　is　not　A。　The　meaning　of



'predicated　of　none'　has　also　been　defined。　So　there　will　be　a　perfect



syllogism。　This　holds　good　also　if　the　premiss　BC　should　be



indefinite；　provided　that　it　is　affirmative：　for　we　shall　have　the



same　syllogism　whether　the　premiss　is　indefinite　or　particular。



　　But　if　the　universality　is　posited　with　respect　to　the　minor　term



either　affirmatively　or　negatively；　a　syllogism　will　not　be



possible；　whether　the　major　premiss　is　positive　or　negative；



indefinite　or　particular：　e。g。　if　some　B　is　or　is　not　A；　and　all　C



is　B。　As　an　example　of　a　positive　relation　between　the　extremes　take



the　terms　good；　state；　wisdom：　of　a　negative　relation；　good；　state；



ignorance。　Again　if　no　C　is　B；　but　some　B　is　or　is　not　A　or　not



every　B　is　A；　there　cannot　be　a　syllogism。　Take　the　terms　white；



horse；　swan：　white；　horse；　raven。　The　same　terms　may　be　taken　also



if　the　premiss　BA　is　indefinite。



　　Nor　when　the　major　premiss　is　universal；　whether　affirmative　or



negative；　and　the　minor　premiss　is　negative　and　particular；　can



there　be　a　syllogism；　whether　the　minor　premiss　be　indefinite　or



particular：　e。g。　if　all　B　is　A　and　some　C　is　not　B；　or　if　not　all　C　is



B。　For　the　major　term　may　be　predicable　both　of　all　and　of　none　of　the



minor；　to　some　of　which　the　middle　term　cannot　be　attributed。



Suppose　the　terms　are　animal；　man；　white：　next　take　some　of　the



white　things　of　which　man　is　not　predicated…swan　and　snow：　animal　is



predicated　of　all　of　the　one；　but　of　none　of　the　other。　Consequently



there　cannot　be　a　syllogism。　Again　let　no　B　be　A；　but　let　some　C　not



be　B。　Take　the　terms　inanimate；　man；　white：　then　take　some　white



things　of　which　man　is　not　predicated…swan　and　snow：　the　term



inanimate　is　predicated　of　all　of　the　one；　of　none　of　the　other。



　　Further　since　it　is　indefinite　to　say　some　C　is　not　B；　and　it　is



true　that　some　C　is　not　B；　whether　no　C　is　B；　or　not　all　C　is　B；　and



since　if　terms　are　assumed　such　that　no　C　is　B；　no　syllogism　follows



（this　has　already　been　stated）　it　is　clear　that　this　arrangement　of



terms　will　not　afford　a　syllogism：　otherwise　one　would　have　been



possible　with　a　universal　negative　minor　premiss。　A　similar　proof



may　also　be　given　if　the　universal　premiss　is　negative。



　　Nor　can　there　in　any　way　be　a　syllogism　if　both　the　relations　of



subject　and　predicate　are　particular；　either　positively　or　negatively；



or　the　one　negative　and　the　other　affirmative；　or　one　indefinite　and



the　other　definite；　or　both　indefinite。　Terms　common　to　all　the



above　are　animal；　white；　horse：　animal；　white；　stone。



　　It　is　clear　then　from　what　has　been　said　that　if　there　is　a



syllogism　in　this　figure　with　a　particular　conclusion；　the　terms



must　be　related　as　we　have　stated：　if　they　are　related　otherwise；　no



syllogism　is　possible　anyhow。　It　is　evident　also　that　all　the



syllogisms　in　this　figure　are　perfect　（for　they　are　all　completed　by



means　of　the　premisses　originally　taken）　and　that　all　conclusions



are　proved　by　this　figure；　viz。　universal　and　particular；



affirmative　and　negative。　Such　a　figure　I　call　the　first。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　5







　　Whenever　the　same　thing　belongs　to　all　of　one　subject；　and　to　none



of　another；　or　to　all　of　each　subject　or　to　none　of　either；　I　call



such　a　figure　the　second；　by　middle　term　in　it　I　mean　that　which　is



predicated　of　both　subjects；　by　extremes　the　terms　of　which　this　is



said；　by　major　extreme　that　which　lies　near　the　middle；　by　minor



that　which　is　further　away　from　the　middle。　The　middle　term　stands



outside　the　extremes；　and　is　first　in　position。　A　syllogism　cannot



be　perfect　anyhow　in　this　figure；　but　it　may　be　valid　whether　the



terms　are　related　universally　or　not。



　　If　then　the　terms　are　related　universally　a　syllogism　will　be



possible；　whenever　the　middle　belongs　to　all　of　one　subject　and　to



none　of　another　（it　does　not　matter　which　has　the　negative



relation）；　but　in　no　other　way。　Let　M　be　predicated　of　no　N；　but　of



all　O。　Since；　then；　the　negative　relation　is　convertible；　N　will



belong　to　no　M：　but　M　was　assumed　to　belong　to　all　O：　consequently　N



will　belong　to　no　O。　This　has　already　been　proved。　Again　if　M



belongs　to　all　N；　but　to　no　O；　then　N　will　belong　to　no　O。　For　if　M



belongs　to　no　O；　O　belongs　to　no　M：　but　M　（as　was　said）　belongs　to　all



N：　O　then　will　belong　to　no　N：　for　the　first　figure　has　again　been



formed。　But　since　the　negative　relation　is　convertible；　N　will



belong　to　no　O。　Thus　it　will　be　the　same　syllogism　that　proves　both



conclusions。



　　It　is　possible　to　prove　these　results　also　by　reductio　ad



impossibile。



　　It　is　clear　then　that　a　syllogism　is　formed　when　the　terms　are　so



related；　but　not　a　perfect　syllogism；　for　necessity　is　not　perfectly



established　merely　from　the　original　premisses；　others　also　are



needed。



　　But　if　M　is　predicated　of　every　N　and　O；　there　cannot　be　a



syllogism。　Terms　to　illustrate　a　positive　relation　between　the



extremes　are　substance；　animal；　man；　a　negative　relation；　substance；





animal；　number…substance　being　the　middle　term。



　　Nor　is　a　syllogism　possible　when　M　is　predicated　neither　of　any　N



nor　of　any　O。　Terms　to　illustrate　a　positive　relation　are　line；



animal；　man：　a　negative　relation；　line；　animal；　stone。



　　It　is　clear　then　that　if　a　syllogism　is　formed　when　the　terms　are



universally　related；　the　terms　must　be　related　as　we　stated　at　the



outset：　for　if　they　are　otherwise　related　no　necessary　consequence



follows。



　　If　the　middle　term　is　related　universally　to　one　of　the　extremes；



a　particular　negative　syllogism　must　result　whenever　the　middle　term



is　related　universally　to　the　major　whether　positively　or



negatively；　and　particularly　to　the　minor　and　in　a　manner　opposite



to　that　of　the　universal　statement：　by　'an　opposite　manner'　I　mean；　if



the　universal