prior analytics-第25节

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converted　into　its　contrary。　For　if　A　does　not　belong　to　some　C；　but



to　all　B；　then　B　will　not　belong　to　some　C。　But　the　original　premiss



is　not　yet　refuted：　for　it　is　possible　that　B　should　belong　to　some　C；



and　should　not　belong　to　some　C。　The　universal　premiss　AB　cannot　be



affected　by　a　syllogism　at　all：　for　if　A　does　not　belong　to　some　of



the　Cs；　but　B　belongs　to　some　of　the　Cs；　neither　of　the　premisses　is



universal。　Similarly　if　the　syllogism　is　negative：　for　if　it　should　be



assumed　that　A　belongs　to　all　C；　both　premisses　are　refuted：　but　if



the　assumption　is　that　A　belongs　to　some　C；　neither　premiss　is



refuted。　The　proof　is　the　same　as　before。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　9







　　In　the　second　figure　it　is　not　possible　to　refute　the　premiss



which　concerns　the　major　extreme　by　establishing　something　contrary　to



it；　whichever　form　the　conversion　of　the　conclusion　may　take。　For



the　conclusion　of　the　refutation　will　always　be　in　the　third　figure；



and　in　this　figure　（as　we　saw）　there　is　no　universal　syllogism。　The



other　premiss　can　be　refuted　in　a　manner　similar　to　the　conversion：



I　mean；　if　the　conclusion　of　the　first　syllogism　is　converted　into　its



contrary；　the　conclusion　of　the　refutation　will　be　the　contrary　of　the



minor　premiss　of　the　first；　if　into　its　contradictory；　the



contradictory。　Let　A　belong　to　all　B　and　to　no　C：　conclusion　BC。　If



then　it　is　assumed　that　B　belongs　to　all　C；　and　the　proposition　AB



stands；　A　will　belong　to　all　C；　since　the　first　figure　is　produced。　If



B　belongs　to　all　C；　and　A　to　no　C；　then　A　belongs　not　to　all　B：　the



figure　is　the　last。　But　if　the　conclusion　BC　is　converted　into　its



contradictory；　the　premiss　AB　will　be　refuted　as　before；　the



premiss；　AC　by　its　contradictory。　For　if　B　belongs　to　some　C；　and　A　to



no　C；　then　A　will　not　belong　to　some　B。　Again　if　B　belongs　to　some



C；　and　A　to　all　B；　A　will　belong　to　some　C；　so　that　the　syllogism



results　in　the　contradictory　of　the　minor　premiss。　A　similar　proof　can



be　given　if　the　premisses　are　transposed　in　respect　of　their　quality。



　　If　the　syllogism　is　particular；　when　the　conclusion　is　converted



into　its　contrary　neither　premiss　can　be　refuted；　as　also　happened



in　the　first　figure；'　if　the　conclusion　is　converted　into　its



contradictory；　both　premisses　can　be　refuted。　Suppose　that　A　belongs



to　no　B；　and　to　some　C：　the　conclusion　is　BC。　If　then　it　is　assumed



that　B　belongs　to　some　C；　and　the　statement　AB　stands；　the



conclusion　will　be　that　A　does　not　belong　to　some　C。　But　the



original　statement　has　not　been　refuted：　for　it　is　possible　that　A



should　belong　to　some　C　and　also　not　to　some　C。　Again　if　B　belongs



to　some　C　and　A　to　some　C；　no　syllogism　will　be　possible：　for



neither　of　the　premisses　taken　is　universal。　Consequently　the



proposition　AB　is　not　refuted。　But　if　the　conclusion　is　converted　into



its　contradictory；　both　premisses　can　be　refuted。　For　if　B　belongs



to　all　C；　and　A　to　no　B；　A　will　belong　to　no　C：　but　it　was　assumed



to　belong　to　some　C。　Again　if　B　belongs　to　all　C　and　A　to　some　C；　A



will　belong　to　some　B。　The　same　proof　can　be　given　if　the　universal



statement　is　affirmative。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　10







　　In　the　third　figure　when　the　conclusion　is　converted　into　its



contrary；　neither　of　the　premisses　can　be　refuted　in　any　of　the



syllogisms；　but　when　the　conclusion　is　converted　into　its



contradictory；　both　premisses　may　be　refuted　and　in　all　the　moods。



Suppose　it　has　been　proved　that　A　belongs　to　some　B；　C　being　taken



as　middle；　and　the　premisses　being　universal。　If　then　it　is　assumed



that　A　does　not　belong　to　some　B；　but　B　belongs　to　all　C；　no　syllogism



is　formed　about　A　and　C。　Nor　if　A　does　not　belong　to　some　B；　but



belongs　to　all　C；　will　a　syllogism　be　possible　about　B　and　C。　A



similar　proof　can　be　given　if　the　premisses　are　not　universal。　For



either　both　premisses　arrived　at　by　the　conversion　must　be　particular；



or　the　universal　premiss　must　refer　to　the　minor　extreme。　But　we　found



that　no　syllogism　is　possible　thus　either　in　the　first　or　in　the



middle　figure。　But　if　the　conclusion　is　converted　into　its



contradictory；　both　the　premisses　can　be　refuted。　For　if　A　belongs



to　no　B；　and　B　to　all　C；　then　A　belongs　to　no　C：　again　if　A　belongs　to



no　B；　and　to　all　C；　B　belongs　to　no　C。　And　similarly　if　one　of　the



premisses　is　not　universal。　For　if　A　belongs　to　no　B；　and　B　to　some　C；



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



belong　to　no　C。



　　Similarly　if　the　original　syllogism　is　negative。　Suppose　it　has　been



proved　that　A　does　not　belong　to　some　B；　BC　being　affirmative；　AC



being　negative：　for　it　was　thus　that；　as　we　saw；　a　syllogism　could



be　made。　Whenever　then　the　contrary　of　the　conclusion　is　assumed　a



syllogism　will　not　be　possible。　For　if　A　belongs　to　some　B；　and　B　to



all　C；　no　syllogism　is　possible　（as　we　saw）　about　A　and　C。　Nor；　if　A



belongs　to　some　B；　and　to　no　C；　was　a　syllogism　possible　concerning



B　and　C。　Therefore　the　premisses　are　not　refuted。　But　when　the



contradictory　of　the　conclusion　is　assumed；　they　are　refuted。　For　if　A



belongs　to　all　B；　and　B　to　C；　A　belongs　to　all　C：　but　A　was　supposed



originally　to　belong　to　no　C。　Again　if　A　belongs　to　all　B；　and　to　no



C；　then　B　belongs　to　no　C：　but　it　was　supposed　to　belong　to　all　C。　A



similar　proof　is　possible　if　the　premisses　are　not　universal。　For　AC



becomes　universal　and　negative；　the　other　premiss　particular　and



affirmative。　If　then　A　belongs　to　all　B；　and　B　to　some　C；　it　results



that　A　belongs　to　some　C：　but　it　was　supposed　to　belong　to　no　C。　Again



if　A　belongs　to　all　B；　and　to　no　C；　then　B　belongs　to　no　C：　but　it　was



assumed　to　belong　to　some　C。　If　A　belongs　to　some　B　and　B　to　some　C；



no　syllogism　results：　nor　yet　if　A　belongs　to　some　B；　and　to　no　C。



Thus　in　one　way　the　premisses　are　refuted；　in　the　other　way　they　are



not。



　　From　what　has　been　said　it　is　clear　how　a　syllogism　results　in



each　figure　when　the　conclusion　is　converted；　when　a　result　contrary



to　the　premiss；　and　when　a　result　contradictory　to　the　premiss；　is



obtained。　It　is　clear　that　in　the　first　figure　the　syllogisms　are



formed　through　the　middle　and　the　last　figures；　and　the　premiss



which　concerns　the　minor　extreme　is　alway　refuted　through　the　middle



figure；　the　premiss　which　concerns　the　major　through　the　last



figure。　In　the　second　figure　syllogisms　proceed　through　the　first



and　the　last　figures；　and　the　premiss　which　concerns　the　minor　extreme



is　always　refuted　through　the　first　figure；　the　premiss　which　concerns



the　major　extreme　through　the　last。　In　the　third　figure　the　refutation



proceeds　through　the　first　and　the　middle　figures；　the　premiss　which



concerns　the　major　is　always　refuted　through　the　first　figure；　the



premiss　which　concerns　the　minor　through　the　middle　figure。



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　11







　　It　is　clear　then　what　conversion　is；　how　it　is　effected　in　each



figure；　and　what　syllogism　results。　The　syllogism　per　impossibile　is



proved　when　the　contradictory　of　the　conclusion　stated　and　another



premiss　is　assumed；　it　can　be　made　in　all　the　figures。　For　it



resembles　conversion；　differing　only　in　this：　conversion　takes　place



after　a　syllogism　has　been　formed　and　both　the　premisses　have　been



taken；　but　a　reduction　to　the　impossible　takes　place　not　because　the



contradictory　has　been　agreed　to　already；　but　because　it　is　clear　that



it　is　true。　The　terms　are　alike　in　both；　and　the　premisses　of　both　are



taken　in　the　same　way。　For　example　if　A　belongs　to　all　B；　C　being



middle；　then　if　it　is　supposed　that　A　does　not　belong　to　all　B　or



belongs　to　no　B；　but　to　all　C　（which　was　admitted　to　be　true）；　it



follows　that　C　belongs　to　no　B　or　not　to　all　B。　But　this　is



impossible：　consequently　the　supposition　is　false：　its　contradictory



then　is　true。　Similarly　in　the　other　figures：　for　whatever　moods　admit



of　conversion　admit　also　of　the　reduction　per　impossibile。



　　All　the　problems　can　be　proved　per　impossibile　in　all　the　figures；



excepting　the　universal　affirmative；　which　is　proved　in　the　middle　and



third　figures；　but　not　in　the　first。　Suppose　that　A　belongs　not　to　all



B；　or　to　no　B；　and　take　besides　another　premiss　concerning　either　of



the　terms；　viz。　that　C　belongs　to　all　A；　or　that　B　belongs　to　all　D；



thus　we　get　the　first　figure。　If　then　it　is　supposed　that　A　does　not



belong　to　all　B；　no　syllogism　results　whichever　term　the　assumed



premiss　concerns；　but　if　it　is　suppos