prior analytics-第3章

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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　statement　is　negative；　the　particular　is　affirmative：　if



the　universal　is　affirmative；　the　particular　is　negative。　For　if　M



belongs　to　no　N；　but　to　some　O；　it　is　necessary　that　N　does　not　belong



to　some　O。　For　since　the　negative　statement　is　convertible；　N　will



belong　to　no　M：　but　M　was　admitted　to　belong　to　some　O：　therefore　N



will　not　belong　to　some　O：　for　the　result　is　reached　by　means　of　the



first　figure。　Again　if　M　belongs　to　all　N；　but　not　to　some　O；　it　is



necessary　that　N　does　not　belong　to　some　O：　for　if　N　belongs　to　all　O；



and　M　is　predicated　also　of　all　N；　M　must　belong　to　all　O：　but　we



assumed　that　M　does　not　belong　to　some　O。　And　if　M　belongs　to　all　N



but　not　to　all　O；　we　shall　conclude　that　N　does　not　belong　to　all　O：



the　proof　is　the　same　as　the　above。　But　if　M　is　predicated　of　all　O；



but　not　of　all　N；　there　will　be　no　syllogism。　Take　the　terms　animal；



substance；　raven；　animal；　white；　raven。　Nor　will　there　be　a　conclusion



when　M　is　predicated　of　no　O；　but　of　some　N。　Terms　to　illustrate　a



positive　relation　between　the　extremes　are　animal；　substance；　unit：



a　negative　relation；　animal；　substance；　science。



　　If　then　the　universal　statement　is　opposed　to　the　particular；　we



have　stated　when　a　syllogism　will　be　possible　and　when　not：　but　if　the



premisses　are　similar　in　form；　I　mean　both　negative　or　both



affirmative；　a　syllogism　will　not　be　possible　anyhow。　First　let　them



be　negative；　and　let　the　major　premiss　be　universal；　e。g。　let　M　belong



to　no　N；　and　not　to　some　O。　It　is　possible　then　for　N　to　belong　either



to　all　O　or　to　no　O。　Terms　to　illustrate　the　negative　relation　are



black；　snow；　animal。　But　it　is　not　possible　to　find　terms　of　which　the



extremes　are　related　positively　and　universally；　if　M　belongs　to



some　O；　and　does　not　belong　to　some　O。　For　if　N　belonged　to　all　O；　but



M　to　no　N；　then　M　would　belong　to　no　O：　but　we　assumed　that　it　belongs



to　some　O。　In　this　way　then　it　is　not　admissible　to　take　terms：　our



point　must　be　proved　from　the　indefinite　nature　of　the　particular



statement。　For　since　it　is　true　that　M　does　not　belong　to　some　O；　even



if　it　belongs　to　no　O；　and　since　if　it　belongs　to　no　O　a　syllogism



is　（as　we　have　seen）　not　possible；　clearly　it　will　not　be　possible　now



either。



　　Again　let　the　premisses　be　affirmative；　and　let　the　major　premiss　as



before　be　universal；　e。g。　let　M　belong　to　all　N　and　to　some　O。　It　is



possible　then　for　N　to　belong　to　all　O　or　to　no　O。　Terms　to　illustrate



the　negative　relation　are　white；　swan；　stone。　But　it　is　not　possible



to　take　terms　to　illustrate　the　universal　affirmative　relation；　for



the　reason　already　stated：　the　point　must　be　proved　from　the



indefinite　nature　of　the　particular　statement。　But　if　the　minor



premiss　is　universal；　and　M　belongs　to　no　O；　and　not　to　some　N；　it



is　possible　for　N　to　belong　either　to　all　O　or　to　no　O。　Terms　for



the　positive　relation　are　white；　animal；　raven：　for　the　negative



relation；　white；　stone；　raven。　If　the　premisses　are　affirmative；　terms



for　the　negative　relation　are　white；　animal；　snow；　for　the　positive



relation；　white；　animal；　swan。　Evidently　then；　whenever　the



premisses　are　similar　in　form；　and　one　is　universal；　the　other



particular；　a　syllogism　can；　not　be　formed　anyhow。　Nor　is　one　possible



if　the　middle　term　belongs　to　some　of　each　of　the　extremes；　or　does



not　belong　to　some　of　either；　or　belongs　to　some　of　the　one；　not　to



some　of　the　other；　or　belongs　to　neither　universally；　or　is　related　to



them　indefinitely。　Common　terms　for　all　the　above　are　white；　animal；



man：　white；　animal；　inanimate。



It　is　clear　then　from　what　has　been　said　that　if　the　terms　are　related



to　one　another　in　the　way　stated；　a　syllogism　results　of　necessity；



and　if　there　is　a　syllogism；　the　terms　must　be　so　related。　But　it　is



evident　also　that　all　the　syllogisms　in　this　figure　are　imperfect：　for



all　are　made　perfect　by　certain　supplementary　statements；　which　either



are　contained　in　the　terms　of　necessity　or　are　assumed　as



hypotheses；　i。e。　when　we　prove　per　impossibile。　And　it　is　evident　that



an　affirmative　conclusion　is　not　attained　by　means　of　this　figure；　but



all　are　negative；　whether　universal　or　particular。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　6







　　But　if　one　term　belongs　to　all；　and　another　to　none；　of　a　third；



or　if　both　belong　to　all；　or　to　none；　of　it；　I　call　such　a　figure



the　third；　by　middle　term　in　it　I　mean　that　of　which　both　the



predicates　are　predicated；　by　extremes　I　mean　the　predicates；　by　the



major　extreme　that　which　is　further　from　the　middle；　by　the　minor　that



which　is　nearer　to　it。　The　middle　term　stands　outside　the　extremes；



and　is　last　in　position。　A　syllogism　cannot　be　perfect　in　this



figure　either；　but　it　may　be　valid　whether　the　terms　are　related



universally　or　not　to　the　middle　term。



　　If　they　are　universal；　whenever　both　P　and　R　belong　to　S；　it　follows



that　P　will　necessarily　belong　to　some　R。　For；　since　the　affirmative



statement　is　convertible；　S　will　belong　to　some　R：　consequently



since　P　belongs　to　all　S；　and　S　to　some　R；　P　must　belong　to　some　R：



for　a　syllogism　in　the　first　figure　is　produced。　It　is　possible　to



demonstrate　this　also　per　impossibile　and　by　exposition。　For　if　both　P



and　R　belong　to　all　S；　should　one　of　the　Ss；　e。g。　N；　be　taken；　both



P　and　R　will　belong　to　this；　and　thus　P　will　belong　to　some　R。



　　If　R　belongs　to　all　S；　and　P　to　no　S；　there　will　be　a　syllogism　to



prove　that　P　will　necessarily　not　belong　to　some　R。　This　may　be



demonstrated　in　the　same　way　as　before　by　converting　the　premiss　RS。



It　migh