prior analytics-第3章

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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　might　be　proved　also　per　impossibile；　as　in　the　former　cases。　But



if　R　belongs　to　no　S；　P　to　all　S；　there　will　be　no　syllogism。　Terms



for　the　positive　relation　are　animal；　horse；　man：　for　the　negative



relation　animal；　inanimate；　man。



　　Nor　can　there　be　a　syllogism　when　both　terms　are　asserted　of　no　S。



Terms　for　the　positive　relation　are　animal；　horse；　inanimate；　for



the　negative　relation　man；　horse；　inanimate…inanimate　being　the　middle



term。



　　It　is　clear　then　in　this　figure　also　when　a　syllogism　will　be



possible　and　when　not；　if　the　terms　are　related　universally。　For



whenever　both　the　terms　are　affirmative；　there　will　be　a　syllogism



to　prove　that　one　extreme　belongs　to　some　of　the　other；　but　when



they　are　negative；　no　syllogism　will　be　possible。　But　when　one　is



negative；　the　other　affirmative；　if　the　major　is　negative；　the　minor



affirmative；　there　will　be　a　syllogism　to　prove　that　the　one　extreme



does　not　belong　to　some　of　the　other：　but　if　the　relation　is　reversed；



no　syllogism　will　be　possible。　If　one　term　is　related　universally　to



the　middle；　the　other　in　part　only；　when　both　are　affirmative　there



must　be　a　syllogism；　no　matter　which　of　the　premisses　is　universal。



For　if　R　belongs　to　all　S；　P　to　some　S；　P　must　belong　to　some　R。　For



since　the　affirmative　statement　is　convertible　S　will　belong　to　some



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



belong　to　some　P：　therefore　P　must　belong　to　some　R。



　　Again　if　R　belongs　to　some　S；　and　P　to　all　S；　P　must　belong　to



some　R。　This　may　be　demonstrated　in　the　same　way　as　the　preceding。　And



it　is　possible　to　demonstrate　it　also　per　impossibile　and　by



exposition；　as　in　the　former　cases。　But　if　one　term　is　affirmative；



the　other　negative；　and　if　the　affirmative　is　universal；　a　syllogism



will　be　possible　whenever　the　minor　term　is　affirmative。　For　if　R



belongs　to　all　S；　but　P　does　not　belong　to　some　S；　it　is　necessary



that　P　does　not　belong　to　some　R。　For　if　P　belongs　to　all　R；　and　R



belongs　to　all　S；　then　P　will　belong　to　all　S：　but　we　assumed　that



it　did　not。　Proof　is　possible　also　without　reduction　ad　impossibile；



if　one　of　the　Ss　be　taken　to　which　P　does　not　belong。



　　But　whenever　the　major　is　affirmative；　no　syllogism　will　be



possible；　e。g。　if　P　belongs　to　all　S　and　R　does　not　belong　to　some



S。　Terms　for　the　universal　affirmative　relation　are　animate；　man；



animal。　For　the　universal　negative　relation　it　is　not　possible　to



get　terms；　if　R　belongs　to　some　S；　and　does　not　belong　to　some　S。



For　if　P　belongs　to　all　S；　and　R　to　some　S；　then　P　will　belong　to　some



R：　but　we　assumed　that　it　belongs　to　no　R。　We　must　put　the　matter　as



before。'　Since　the　expression　'it　does　not　belong　to　some'　is



indefinite；　it　may　be　used　truly　of　that　also　which　belongs　to　none。



But　if　R　belongs　to　no　S；　no　syllogism　is　possible；　as　has　been　shown。



Clearly　then　no　syllogism　will　be　possible　here。



　　But　if　the　negative　term　is　universal；　whenever　the　major　is



negative　and　the　minor　affirmative　there　will　be　a　syllogism。　For　if　P



belongs　to　no　S；　and　R　belongs　to　some　S；　P　will　not　belong　to　some　R：



for　we　shall　have　the　first　figure　again；　if　the　premiss　RS　is



converted。



　　But　when　the　minor　is　negative；　there　will　be　no　syllogism。　Terms



for　the　positive　relation　are　animal；　man；　wild：　for　the　negative



relation；　animal；　science；　wild…the　middle　in　both　being　the　term



wild。



　　Nor　is　a　syllogism　possible　when　both　are　stated　in　the　negative；



but　one　is　universal；　the　other　particular。　When　the　minor　is



related　universally　to　the　middle；　take　the　terms　animal；　science；



wild；　animal；　man；　wild。　When　the　major　is　related　universally　to



the　middle；　take　as　terms　for　a　negative　relation　raven；　snow；



white。　For　a　positive　relation　terms　cannot　be　found；　if　R　belongs



to　some　S；　and　does　not　belong　to　some　S。　For　if　P　belongs　to　all　R；



and　R　to　some　S；　then　P　belongs　to　some　S：　but　we　assumed　that　it



belongs　to　no　S。　Our　point；　then；　must　be　proved　from　the　indefinite



nature　of　the　particular　statement。



　　Nor　is　a　syllogism　possible　anyhow；　if　each　of　the　extremes



belongs　to　some　of　the　middle　or　does　not　belong；　or　one　belongs　and



the　other　does　not　to　some　of　the　middle；　or　one　belongs　to　some　of



the　middle；　the　other　not　to　all；　or　if　the　premisses　are



indefinite。　Common　terms　for　all　are　animal；　man；　white：　animal；



inanimate；　white。



　　It　is　clear　then　in　this　figure　also　when　a　syllogism　will　be



possible；　and　when　not；　and　that　if　the　terms　are　as　stated；　a



syllogism　results　of　necessity；　and　if　there　is　a　syllogism；　the　terms



must　be　so　related。　It　is　clear　also　that　all　the　syllogisms　in　this



figure　are　imperfect　（for　all　are　made　perfect　by　certain



supplementary　assumptions）；　and　that　it　will　not　be　possible　to



reach　a　universal　conclusion　by　means　of　this　figure；　whether　negative



or　affirmative。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　7







　　It　is　evident　also　that　in　all　the　figures；　whenever　a　proper



syllogism　does　not　result；　if　both　the　terms　are　affirmative　or



negative　nothing　necessary　follows　at　all；　but　if　one　is



affirmative；　the　other　negative；　and　if　the　negative　is　stated



universally；　a　syllogism　always　results　relating　the　minor　to　the



major　term；　e。g。　if　A　belongs　to　all　or　some　B；　and　B　belongs　to　no　C：



for　if　the　premisses　are　converted　it　is　necessary　that　C　does　not



belong　to　some　A。　Similarly　also　in　the　other　figures：　a　syllogism



always　results　by　means　of　conversion。　It　is　evident　also　that　the



substitution　of　an　indefinite　for　a　particular　affirmative　will　effect



the　same　syllogism　in　all　the　figures。



　　It　is　clear　too　that　all　the　imperfect　syllogisms　are　made　perfect



by　means　of　the　first　figure。　For　all　are　brought　to　a　conclusion



either　ostensively　or　per　impossibile。　In　both　ways　the　first　figure



is　formed：　if　they　are　made　perfect　ostensively；　because　（as　we　saw）



all　are　brought　to　a　conclusion　by　means　of　conversion；　and　conversion



produces　the　first　figure：　if　they　are　proved　per　impossibile；　because



on　the　assumption　of　the　false　statement　the　syllogism　comes　about



by　means　of　the　first　figure；　e。g。　in　the　last　figure；　if　A　and　B



belong　to　all　C；　it　follows　that　A　belongs　to　some　B：　for　if　A



belonged　to　no　B；　and　B　belongs　to　all　C；　A　would　belong　to　no　C：



but　（as　we　stated）　it　belongs　to　all　C。　Similarly　also　with　the　rest。



　　It　is　possible　also　to　reduce　all　syllogisms　to　the　universal



syllogisms　in　the　first　figure。　Those　in　the　second　figure　are　clearly



made　perfect　by　these；　though　not　all　in　the　same　way；　the　universal



syllogisms　are　made　perfect　by　converting　the　negative　premiss；　each



of　the　particular　syllogisms　by　reductio　ad　impossibile。　In　the



first　figure　particular　syllogisms　are　indeed　made　perfect　by



themselves；　but　it　is　possible　also　to　prove　them　by　means　of　the



second　figure；　reducing　them　ad　impossibile；　e。g。　if　A　belongs　to



all　B；　and　B　to　some　C；　it　follows　that　A　belongs　to　some　C。　For　if　it



belonged　to　no　C；　and　belongs　to　all　B；　then　B　will　belong　to　no　C：



this　we　know　by　means　of　the　second　figure。　Similarly　also



demonstration　will　be　possible　in　the　case　of　the　negative。　For　if　A



belongs　to　no　B；　and　B　belongs　to　some　C；　A　will　not　belong　to　some　C：



for　if　it　belonged　to　all　C；　and　belongs　to　no　B；　then　B　will　belong



to　no　C：　and　this　（as　we　saw）　is　the　middle　figure。　Consequently；



since　all　syllogisms　in　the　middle　figure　can　be　reduced　to



universal　syllogisms　in　the　first　figure；　and　since　particular



syllogisms　in　the　first　figure　can　be　reduced　to　syllogisms　in　the



middle　figure；　it　is　clear　that　particular　syllogisms　can　be　reduced



to　universal　syllogisms　in　the　first　figure。　Syllogisms　in　the　third



figure；　if　the　terms　are　universal；　are　directly　made　perfect　by　means



of　those　syllogisms；　but；　when　one　of　the　premisses　is　particular；



by　means　of　the　particular　syllogisms　in　the　first　figure：　and　these



（we　have　seen）　may　be　reduced　to　the　universal　syllogisms　in　the　first



figure：　consequently　also　the　particular　syllogisms　in　the　third



figure　may　be　so　reduced。　It　is　clear　then　that　all　syllogisms　may



be　reduced　to　the　universal　syllogisms　in　the　first　figure。



　　We　have　stated　then　how　syllogisms　which　prove　that　something



belongs　or　does　not　belong　to　something　else　are　constituted；　both　how



syllogisms　of　the　same　figure　are　constituted　in　themselves；　and　how



syllogisms　of　di