prior analytics-第24节

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the　conclusion　is　retained；　B　will　belong　to　some　C：　for　we　obtain　the



first　figure　and　A　is　middle。　But　if　the　syllogism　is　negative；　it



is　not　possible　to　prove　the　universal　premiss；　for　the　reason　given



above。　But　it　is　possible　to　prove　the　particular　premiss；　if　the



proposition　AB　is　converted　as　in　the　universal　syllogism；　i。e　'B



belongs　to　some　of　that　to　some　of　which　A　does　not　belong'：　otherwise



no　syllogism　results　because　the　particular　premiss　is　negative。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　6







　　In　the　second　figure　it　is　not　possible　to　prove　an　affirmative



proposition　in　this　way；　but　a　negative　proposition　may　be　proved。



An　affirmative　proposition　is　not　proved　because　both　premisses　of　the



new　syllogism　are　not　affirmative　（for　the　conclusion　is　negative）　but



an　affirmative　proposition　is　（as　we　saw）　proved　from　premisses



which　are　both　affirmative。　The　negative　is　proved　as　follows。　Let　A



belong　to　all　B；　and　to　no　C：　we　conclude　that　B　belongs　to　no　C。　If



then　it　is　assumed　that　B　belongs　to　all　A；　it　is　necessary　that　A



should　belong　to　no　C：　for　we　get　the　second　figure；　with　B　as　middle。



But　if　the　premiss　AB　was　negative；　and　the　other　affirmative；　we



shall　have　the　first　figure。　For　C　belongs　to　all　A　and　B　to　no　C；



consequently　B　belongs　to　no　A：　neither　then　does　A　belong　to　B。



Through　the　conclusion；　therefore；　and　one　premiss；　we　get　no



syllogism；　but　if　another　premiss　is　assumed　in　addition；　a



syllogism　will　be　possible。　But　if　the　syllogism　not　universal；　the



universal　premiss　cannot　be　proved；　for　the　same　reason　as　we　gave



above；　but　the　particular　premiss　can　be　proved　whenever　the　universal



statement　is　affirmative。　Let　A　belong　to　all　B；　and　not　to　all　C：　the



conclusion　is　BC。　If　then　it　is　assumed　that　B　belongs　to　all　A；　but



not　to　all　C；　A　will　not　belong　to　some　C；　B　being　middle。　But　if



the　universal　premiss　is　negative；　the　premiss　AC　will　not　be



demonstrated　by　the　conversion　of　AB：　for　it　turns　out　that　either



both　or　one　of　the　premisses　is　negative；　consequently　a　syllogism



will　not　be　possible。　But　the　proof　will　proceed　as　in　the　universal



syllogisms；　if　it　is　assumed　that　A　belongs　to　some　of　that　to　some　of



which　B　does　not　belong。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　7







　　In　the　third　figure；　when　both　premisses　are　taken　universally；　it



is　not　possible　to　prove　them　reciprocally：　for　that　which　is



universal　is　proved　through　statements　which　are　universal；　but　the



conclusion　in　this　figure　is　always　particular；　so　that　it　is　clear



that　it　is　not　possible　at　all　to　prove　through　this　figure　the



universal　premiss。　But　if　one　premiss　is　universal；　the　other



particular；　proof　of　the　latter　will　sometimes　be　possible；



sometimes　not。　When　both　the　premisses　assumed　are　affirmative；　and



the　universal　concerns　the　minor　extreme；　proof　will　be　possible；



but　when　it　concerns　the　other　extreme；　impossible。　Let　A　belong　to



all　C　and　B　to　some　C：　the　conclusion　is　the　statement　AB。　If　then



it　is　assumed　that　C　belongs　to　all　A；　it　has　been　proved　that　C



belongs　to　some　B；　but　that　B　belongs　to　some　C　has　not　been　proved。



And　yet　it　is　necessary；　if　C　belongs　to　some　B；　that　B　should



belong　to　some　C。　But　it　is　not　the　same　that　this　should　belong　to



that；　and　that　to　this：　but　we　must　assume　besides　that　if　this



belongs　to　some　of　that；　that　belongs　to　some　of　this。　But　if　this



is　assumed　the　syllogism　no　longer　results　from　the　conclusion　and　the



other　premiss。　But　if　B　belongs　to　all　C；　and　A　to　some　C；　it　will



be　possible　to　prove　the　proposition　AC；　when　it　is　assumed　that　C



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



to　some　B；　it　is　necessary　that　A　should　belong　to　some　C；　B　being



middle。　And　whenever　one　premiss　is　affirmative　the　other　negative；



and　the　affirmative　is　universal；　the　other　premiss　can　be　proved。　Let



B　belong　to　all　C；　and　A　not　to　some　C：　the　conclusion　is　that　A



does　not　belong　to　some　B。　If　then　it　is　assumed　further　that　C



belongs　to　all　B；　it　is　necessary　that　A　should　not　belong　to　some



C；　B　being　middle。　But　when　the　negative　premiss　is　universal；　the



other　premiss　is　not　except　as　before；　viz。　if　it　is　assumed　that　that



belongs　to　some　of　that；　to　some　of　which　this　does　not　belong；　e。g。



if　A　belongs　to　no　C；　and　B　to　some　C：　the　conclusion　is　that　A　does



not　belong　to　some　B。　If　then　it　is　assumed　that　C　belongs　to　some



of　that　to　some　of　which　does　not　belong；　it　is　necessary　that　C



should　belong　to　some　of　the　Bs。　In　no　other　way　is　it　possible　by



converting　the　universal　premiss　to　prove　the　other：　for　in　no　other



way　can　a　syllogism　be　formed。



　　It　is　clear　then　that　in　the　first　figure　reciprocal　proof　is　made



both　through　the　third　and　through　the　first　figure…if　the



conclusion　is　affirmative　through　the　first；　if　the　conclusion　is



negative　through　the　last。　For　it　is　assumed　that　that　belongs　to



all　of　that　to　none　of　which　this　belongs。　In　the　middle　figure；



when　the　syllogism　is　universal；　proof　is　possible　through　the



second　figure　and　through　the　first；　but　when　particular　through　the



second　and　the　last。　In　the　third　figure　all　proofs　are　made　through



itself。　It　is　clear　also　that　in　the　third　figure　and　in　the　middle



figure　those　syllogisms　which　are　not　made　through　those　figures



themselves　either　are　not　of　the　nature　of　circular　proof　or　are



imperfect。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　8







　　To　convert　a　syllogism　means　to　alter　the　conclusion　and　make



another　syllogism　to　prove　that　either　the　extreme　cannot　belong　to



the　middle　or　the　middle　to　the　last　term。　For　it　is　necessary；　if　the



conclusion　has　been　changed　into　its　opposite　and　one　of　the　premisses



stands；　that　the　other　premiss　should　be　destroyed。　For　if　it　should



stand；　the　conclusion　also　must　stand。　It　makes　a　difference　whether



the　conclusion　is　converted　into　its　contradictory　or　into　its



contrary。　For　the　same　syllogism　does　not　result　whichever　form　the



conversion　takes。　This　will　be　made　clear　by　the　sequel。　By



contradictory　opposition　I　mean　the　opposition　of　'to　all'　to　'not



to　all'；　and　of　'to　some'　to　'to　none'；　by　contrary　opposition　I



mean　the　opposition　of　'to　all'　to　'to　none'；　and　of　'to　some'　to　'not



to　some'。　Suppose　that　A　been　proved　of　C；　through　B　as　middle　term。



If　then　it　should　be　assumed　that　A　belongs　to　no　C；　but　to　all　B；　B



will　belong　to　no　C。　And　if　A　belongs　to　no　C；　and　B　to　all　C；　A



will　belong；　not　to　no　B　at　all；　but　not　to　all　B。　For　（as　we　saw）　the



universal　is　not　proved　through　the　last　figure。　In　a　word　it　is　not



possible　to　refute　universally　by　conversion　the　premiss　which



concerns　the　major　extreme：　for　the　refutation　always　proceeds　through



the　third　since　it　is　necessary　to　take　both　premisses　in　reference　to



the　minor　extreme。　Similarly　if　the　syllogism　is　negative。　Suppose



it　has　been　proved　that　A　belongs　to　no　C　through　B。　Then　if　it　is



assumed　that　A　belongs　to　all　C；　and　to　no　B；　B　will　belong　to　none　of



the　Cs。　And　if　A　and　B　belong　to　all　C；　A　will　belong　to　some　B：　but



in　the　original　premiss　it　belonged　to　no　B。



　　If　the　conclusion　is　converted　into　its　contradictory；　the



syllogisms　will　be　contradictory　and　not　universal。　For　one　premiss　is



particular；　so　that　the　conclusion　also　will　be　particular。　Let　the



syllogism　be　affirmative；　and　let　it　be　converted　as　stated。　Then　if　A



belongs　not　to　all　C；　but　to　all　B；　B　will　belong　not　to　all　C。　And　if



A　belongs　not　to　all　C；　but　B　belongs　to　all　C；　A　will　belong　not　to



all　B。　Similarly　if　the　syllogism　is　negative。　For　if　A　belongs　to



some　C；　and　to　no　B；　B　will　belong；　not　to　no　C　at　all；　but…not　to



some　C。　And　if　A　belongs　to　some　C；　and　B　to　all　C；　as　was



originally　assumed；　A　will　belong　to　some　B。



　　In　particular　syllogisms　when　the　conclusion　is　converted　into　its



contradictory；　both　premisses　may　be　refuted；　but　when　it　is　converted



into　its　contrary；　neither。　For　the　result　is　no　longer；　as　in　the



universal　syllogisms；　refutation　in　which　the　conclusion　reached　by　O；



conversion　lacks　universality；　but　no　refutation　at　all。　Suppose



that　A　has　been　proved　of　some　C。　If　then　it　is　assumed　that　A　belongs



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



belongs　to　no　C；　but　to　all　B；　B　will　belong　to　no　C。　Thus　both



premisses　are　refuted。　But　neither　can　be　refuted　if　the　conclusion　is



converted　into　its　contrary。　For　if　A　does　not