prior analytics- 第5部分

　　Similar　results　will　obtain　also　in　particular　syllogisms。　For



whenever　the　negative　premiss　is　both　universal　and　necessary；　then



the　conclusion　will　be　necessary：　but　whenever　the　affirmative　premiss



is　universal；　the　negative　particular；　the　conclusion　will　not　be



necessary。　First　then　let　the　negative　premiss　be　both　universal　and



necessary：　let　it　be　possible　for　no　B　that　A　should　belong　to　it；　and



let　A　simply　belong　to　some　C。　Since　the　negative　statement　is



convertible；　it　will　be　possible　for　no　A　that　B　should　belong　to



it：　but　A　belongs　to　some　C；　consequently　B　necessarily　does　not



belong　to　some　of　the　Cs。　Again　let　the　affirmative　premiss　be　both



universal　and　necessary；　and　let　the　major　premiss　be　affirmative。



If　then　A　necessarily　belongs　to　all　B；　but　does　not　belong　to　some　C；



it　is　clear　that　B　will　not　belong　to　some　C；　but　not　necessarily。　For



the　same　terms　can　be　used　to　demonstrate　the　point；　which　were　used



in　the　universal　syllogisms。　Nor　again；　if　the　negative　statement　is



necessary　but　particular；　will　the　conclusion　be　necessary。　The



point　can　be　demonstrated　by　means　of　the　same　terms。







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　　In　the　last　figure　when　the　terms　are　related　universally　to　the



middle；　and　both　premisses　are　affirmative；　if　one　of　the　two　is



necessary；　then　the　conclusion　will　be　necessary。　But　if　one　is



negative；　the　other　affirmative；　whenever　the　negative　is　necessary



the　conclusion　also　will　be　necessary；　but　whenever　the　affirmative　is



necessary　the　conclusion　will　not　be　necessary。　First　let　both　the



premisses　be　affirmative；　and　let　A　and　B　belong　to　all　C；　and　let



AC　be　necessary。　Since　then　B　belongs　to　all　C；　C　also　will　belong



to　some　B；　because　the　universal　is　convertible　into　the　particular：



consequently　if　A　belongs　necessarily　to　all　C；　and　C　belongs　to



some　B；　it　is　necessary　that　A　should　belong　to　some　B　also。　For　B



is　under　C。　The　first　figure　then　is　formed。　A　similar　proof　will　be



given　also　if　BC　is　necessary。　For　C　is　convertible　with　some　A：



consequently　if　B　belongs　necessarily　to　all　C；　it　will　belong



necessarily　also　to　some　A。



　　Again　let　AC　be　negative；　BC　affirmative；　and　let　the　negative



premiss　be　necessary。　Since　then　C　is　convertible　with　some　B；　but　A



necessarily　belongs　to　no　C；　A　will　necessarily　not　belong　to　some　B



either：　for　B　is　under　C。　But　if　the　affirmative　is　necessary；　the



conclusion　will　not　be　necessary。　For　suppose　BC　is　affirmative　and



necessary；　while　AC　is　negative　and　not　necessary。　Since　then　the



affirmative　is　convertible；　C　also　will　belong　to　some　B



necessarily：　consequently　if　A　belongs　to　none　of　the　Cs；　while　C



belongs　to　some　of　the　Bs；　A　will　not　belong　to　some　of　the　Bs…but　not



of　necessity；　for　it　has　been　proved；　in　the　case　of　the　first　figure；



that　if　the　negative　premiss　is　not　necessary；　neither　will　the



conclusion　be　necessary。　Further；　the　point　may　be　made　clear　by



considering　the　terms。　Let　the　term　A　be　'good'；　let　that　which　B



signifies　be　'animal'；　let　the　term　C　be　'horse'。　It　is　possible



then　that　the　term　good　should　belong　to　no　horse；　and　it　is　necessary



that　the　term　animal　should　belong　to　every　horse：　but　it　is　not



necessary　that　some　animal　should　not　be　good；　since　it　is　possible



for　every　animal　to　be　good。　Or　if　that　is　not　possible；　take　as　the



term　'awake'　or　'asleep'：　for　every　animal　can　accept　these。



　　If；　then；　the　premisses　are　universal；　we　have　stated　when　the



conclusion　will　be　necessary。　But　if　one　premiss　is　universal；　the



other　particular；　and　if　both　are　affirmative；　whenever　the



universal　is　necessary　the　conclusion　also　must　be　necessary。　The



demonstration　is　the　same　as　before；　for　the　particular　affirmative



also　is　convertible。　If　then　it　is　necessary　that　B　should　belong　to



all　C；　and　A　falls　under　C；　it　is　necessary　that　B　should　belong　to



some　A。　But　if　B　must　belong　to　some　A；　then　A　must　belong　to　some



B：　for　conversion　is　possible。　Similarly　also　if　AC　should　be



necessary　and　universal：　for　B　falls　under　C。　But　if　the　particular



premiss　is　necessary；　the　conclusion　will　not　be　necessary。　Let　the



premiss　BC　be　both　particular　and　necessary；　and　let　A　belong　to　all



C；　not　however　necessarily。　If　the　proposition　BC　is　converted　the



first　figure　is　formed；　and　the　universal　premiss　is　not　necessary；



but　the　particular　is　necessary。　But　when　the　premisses　were　thus；　the



conclusion　（as　we　proved　was　not　necessary：　consequently　it　is　not



here　either。　Further；　the　point　is　clear　if　we　look　at　the　terms。



Let　A　be　waking；　B　biped；　and　C　animal。　It　is　necessary　that　B



should　belong　to　some　C；　but　it　is　possible　for　A　to　belong　to　C；



and　that　A　should　belong　to　B　is　not　necessary。　For　there　is　no



necessity　that　some　biped　should　be　asleep　or　awake。　Similarly　and



by　means　of　the　same　terms　proof　can　be　made；　should　the　proposition



AC　be　both　particular　and　necessary。



　　But　if　one　premiss　is　affirmative；　the　other　negative；　whenever



the　universal　is　both　negative　and　necessary　the　conclusion　also



will　be　necessary。　For　if　it　is　not　possible　that　A　should　belong　to



any　C；　but　B　belongs　to　some　C；　it　is　necessary　that　A　should　not



belong　to　some　B。　But　whenever　the　affirmative　proposition　is



necessary；　whether　universal　or　particular；　or　the　negative　is



particular；　the　conclusion　will　not　be　necessary。　The　proof　of　this　by



reduction　will　be　the　same　as　before；　but　if　terms　are　wanted；　when



the　universal　affirmative　is　necessary；　take　the　terms



'waking'…'animal'…'man'；　'man'　being　middle；　and　when　the



affirmative　is　particular　and　necessary；　take　the　terms



'waking'…'animal'…'white'：　for　it　is　necessary　that　animal　should



belong　to　some　white　thing；　but　it　is　possible　that　waking　should



belong　to　none；　and　it　is　not　necessary　that　waking　should　not



belong　to　some　animal。　But　when　the　negative　proposition　being



particular　is　necessary；　take　the　terms　'biped'；　'moving'；　'animal'；



'animal'　being　middle。



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　　It　is　clear　then　that　a　simple　conclusion　is　not　reached　unless　both



premisses　are　simple　assertions；　but　a　necessary　conclusion　is



possible　although　one　only　of　the　premisses　is　necessary。　But　in



both　cases；　whether　the　syllogisms　are　affirmative　or　negative；　it



is　necessary　that　one　premiss　should　be　similar　to　the　conclusion。　I



mean　by　'similar'；　if　the　conclusion　is　a　simple　assertion；　the



premiss　must　be　simple；　if　the　conclusion　is　necessary；　the　premiss



must　be　necessary。　Consequently　this　also　is　clear；　that　the



conclusion　will　be　neither　necessary　nor　simple　unless　a　necessary



or　simple　premiss　is　assumed。







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　　Perhaps　enough　has　been　said　about　the　proof　of　necessity；　how　it



comes　about　and　how　it　differs　from　the　proof　of　a　simple　statement。



We　proceed　to　discuss　that　which　is　possible；　when　and　how　and　by　what



means　it　can　be　proved。　I　use　the　terms　'to　be　possible'　and　'the



possible'　of　that　which　is　not　necessary　but；　being　assumed；　results



in　nothing　impossible。　We　say　indeed　ambiguously　of　the　necessary　that



it　is　possible。　But　that　my　definition　of　the　possible　is　correct　is



clear　from　the　phrases　by　which　we　deny　or　on　the　contrary　affirm



possibility。　For　the　expressions　'it　is　not　possible　to　belong'；　'it



is　impossible　to　belong'；　and　'it　is　necessary　not　to　belong'　are



either　identical　or　follow　from　one　another；　consequently　their



opposites　also；　'it　is　possible　to　belong'；　'it　is　not　impossible　to



belong'；　and　'it　is　not　necessary　not　to　belong'；　will　either　be



identical　or　follow　from　one　another。　For　of　everything　the



affirmation　or　the　denial　holds　good。　That　which　is　possible　then　will



be　not　necessary　and　that　which　is　not　necessary　will　be　possible。



It　results　that　all　premisses　in　the　mode　of　possibility　are



convertible　into　one　another。　I　mean　not　that　the　affirmative　are



convertible　into　the　negative；　but　that　those　which　are　affirmative　in



form　admit　of　conversion　by　opposition；　e。g。　'it　is　possible　to



belong'　may　be　converted　into　'it　is　possible　not　to　belong'；　and



'it　is　possible　for　A　to　belong　to　all　B'　into　'it　is　possible　for　A



to　belong　to　no　B'　or　'not　to　all　B'；　and　'it　is　possible　for　A　to



belong　to　some　B'　into　'it　is　possible　for　A　not　to　belong　to　some　B'。



And　similarly　the　other　propositions　in　this　mode　can　be　converted。



For　since　that　which　is　possible　is　not　necessary；　and　that　which　is



not　necessary　may　possibly　not　belong；　it　is　clear　that　if　it　is



possible　that　A　should　belong　to　B；　it　is　possible　also　that　it　should



not　belong　to　B：　and　if　it　is　possible　that　it　should　belong　to　all；



it　is　also　possible　that　it　should　not　belong　to　all。　The　same　holds



good　in　the　case　of　particular　affirmations：　for　the　proof　is



identical。　And　such　premisses　are　affirmative　and　not　negative；　for



'to　be　possible'　is　in　the　same　rank　as　'to　be'；　as　was　said　above。



　　Having　made　these　distinctions　we　next　point　out　that　the　expression



'to　be　possible'　is　used　in　two　ways。　In　one　it　means　to　happen



generally　and　fall　short　of　necessity；　e。g。　man's　turning　grey　or



growing　or　decaying；　or　generally　what　naturally　belongs　to　a　thing



（for　this　has　not　its　necessity　unbroken；　since　man's　existence　is　not



continuous　for　ever；　although　if　a　man　does　exist；　it　comes　about



either　necessarily　o