prior analytics-第5章

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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。



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　12







　　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。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　13







　　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　or　generally）。　In　another　sense　the　expression



means　the　indefinite；　which　can　be　both　thus　and　not　thus；　e。g。　an



animal's　walking　or　an　earthquake's　taking　place　while　it　is



walking；　or　generally　what　happens　by　chance：　for　none　of　these



inclines　by　nature　in　the　one　way　more　than　in　the　opposite。



　　That　which　is　possible　in　each　of　its　two　senses　is　convertible　into



its　opposite；　not　however　in　the　same　way：　but　what　is　natural　is



convertible　because　it　does　not　necessarily　belong　（for　in　this



sense　it　is　possible　that　a　man　should　not　grow　grey）　and　what　is



indefinite　is　convertible　because　it　inclines　this　way　no　more　than



that。　Science　and　demonstrative　syllogism　are　not　concerned　with



things　which　are　indefinite；　because　the　middle　term　is　uncertain；　but



they　are　concerned　with　things　that　are　natural；　and　as　a　rule



arguments　and　inquiries　are　made　about　things　which　are　possible　in



this　sense。　Syllogisms　indeed　can　be　made　about　the　former；　but　it



is　unusual　at　any　rate　to　inquire　about　them。



　　These　matters　will　be　treated　more　definitely　in　the　sequel；　our



business　at　present　is　to　state　the　moods　and　nature　of　the



syllogism　made　from　possible　premisses。　The　expression　'it　is　possible



for　this　to　belong　to　that'　may　be　understood　in　two　senses：　'that'



may　mean　either　that　to　which　'that'　belongs　or　that　to　which　it　may



belong；　for　the　expression　'A　is　possible　of　the　subject　of　B'　means



that　it　is　possible　either　of　that　of　which　B　is　stated　or　of　that



of　which　B　may　possibly　be　stated。　It　makes　no　difference　whether　we



say；　A　is　possible　of　the　subject　of　B；　or　all　B　admits　of　A。　It　is



clear　then　that　the　expression　'A　may　possibly　belong　to　all　B'



might　be　used　in　two　senses。　First　then　we　must　state　the　nature　and



characteristics　of　the　syllogism　which　arises　if　B　is　possible　of



the　subject　of　C；　and　A　is　possible　of　the　subject　of　B。　For　thus　both



premisses　are　assumed　in　the　mode　of　possibility；　but　whenever　A　is



possible　of　that　of　which　B　is　true；　one　premiss　is　a　simple



assertion；　the　other　a　problematic。　Consequently　we　must　start　from



premisses　which　are　similar　in　form；　as　in　the　other　cases。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　14







　　Whenever　A　may　possibly　belong　to　all　B；　and　B　to　all　C；　there



will　be　a　perfect　syllogism　to　prove　that　A　may　possibly　belong　to　all



C。　This　is　clear　from　the　definition：　for　it　was　in　this　way　that　we



explained　'to　be　possible　for　one　term　to　belong　to　all　of　another'。



Similarly　if　it　is　possible　for　A　to　belong　no　B；　and　for　B　to



belong　to　all　C；　then　it　is　possible　for　A　to　belong　to　no　C。　For



the　statement　that　it　is　possible　for　A　not　to　belong　to　that　of　which



B　may　be　true　means　（as　we　saw）　that　none　of　those　things　which　can



possibly　fall　under　the　term　B　is　left　out　of　account。　But　whenever



A　may　belong　to　all　B；　and　B　may　belong　to　no　C；　then　indeed　no



syllogism　results　from　the　premisses　assumed；　but　if　the　premiss　BC　is



converted　after　the　manner　of　problematic　propositions；　the　same



syllogism　results　as　before。　For　since　it　is　possible　that　B　should



belong　to　no　C；　it　is　possible　also　that　it　should　belong　to　all　C。



This　has　been　stated　above。　Consequently　if　B　is　possible　for　all　C；



and　A　is　possible　for　all　B；　the　same　syllogism　again　results。



Similarly　if　in　both　the　premisses　the　negative　is　joined　with　'it



is　possible'：　e。g。　if　A　may　belong　to　none　of　the　Bs；　and　B　to　none　of



the　Cs。　No　syllogism　results　from　the　assumed　premisses；　but　if　they



are　converted　we　shall　have　the　same　syllogism　as　before。　It　is



clear　then　that　if　the　minor　premiss　is　negative；　or　if　both　premisses



are　negative；　either　no　syllogism　results；　or　if　one　it　is　not



perfect。　For　the　necessity　results　from　the　conversion。



　　But　if　one　of　the　premisses　is　universal；　the　other　particular；　when



the　major　premiss　is　universal　there　will　be　a　perfect　syllogism。



For　if　A　is　possible　for　all　B；　and　B　for　some　C；　then　A　is　possible



for　some　C。　This　is　clear　from　the　definition　of　being　possible。　Again



if　A　may　belong　to　no　B；　and　B　may　belong　to　some　of　the　Cs；　it　is



necessary　that　A　may　possibly　not　belong　to　some　of　the　Cs。　The



proof　is　the　same　as　above。　But　if　the　particular　premiss　is　negative；



and　the　universal　is　affirmative；　the　major　still　being　universal



and　the　minor　particular；　e。g。　A　is　possible　for　all　B；　B　may　possibly



not　belong　to　some　C；　then　a　clear　syllogism　does　not　result　from



the　assumed　premisses；　but　if　the　particular　premiss　is　converted



and　it　is　laid　down　that　B　possibly　may　belong　to　some　C；　we　shall



have　the　same　conclusion　as　before；　as　in　the　cases　given　at　the



beginning。



　　But　if　the　major　premiss　is　the　m