prior analytics-第6章

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



beginning。



　　But　if　the　major　premiss　is　the　minor　universal；　whether　both　are



affirmative；　or　negative；　or　different　in　quality；　or　if　both　are



indefinite　or　particular；　in　no　way　will　a　syllogism　be　possible。



For　nothing　prevents　B　from　reaching　beyond　A；　so　that　as　predicates



cover　unequal　areas。　Let　C　be　that　by　which　B　extends　beyond　A。　To　C



it　is　not　possible　that　A　should　belong…either　to　all　or　to　none　or　to



some　or　not　to　some；　since　premisses　in　the　mode　of　possibility　are



convertible　and　it　is　possible　for　B　to　belong　to　more　things　than　A



can。　Further；　this　is　obvious　if　we　take　terms；　for　if　the　premisses



are　as　assumed；　the　major　term　is　both　possible　for　none　of　the



minor　and　must　belong　to　all　of　it。　Take　as　terms　common　to　all　the



cases　under　consideration　'animal'…'white'…'man'；　where　the　major



belongs　necessarily　to　the　minor；　'animal'…'white'…'garment'；　where　it



is　not　possible　that　the　major　should　belong　to　the　minor。　It　is　clear



then　that　if　the　terms　are　related　in　this　manner；　no　syllogism



results。　For　every　syllogism　proves　that　something　belongs　either



simply　or　necessarily　or　possibly。　It　is　clear　that　there　is　no



proof　of　the　first　or　of　the　second。　For　the　affirmative　is



destroyed　by　the　negative；　and　the　negative　by　the　affirmative。



There　remains　the　proof　of　possibility。　But　this　is　impossible。　For　it



has　been　proved　that　if　the　terms　are　related　in　this　manner　it　is



both　necessary　that　the　major　should　belong　to　all　the　minor　and　not



possible　that　it　should　belong　to　any。　Consequently　there　cannot　be



a　syllogism　to　prove　the　possibility；　for　the　necessary　（as　we　stated）



is　not　possible。



　　It　is　clear　that　if　the　terms　are　universal　in　possible　premisses



a　syllogism　always　results　in　the　first　figure；　whether　they　are



affirmative　or　negative；　only　a　perfect　syllogism　results　in　the　first



case；　an　imperfect　in　the　second。　But　possibility　must　be　understood



according　to　the　definition　laid　down；　not　as　covering　necessity。　This



is　sometimes　forgotten。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　15







　　If　one　premiss　is　a　simple　proposition；　the　other　a　problematic；



whenever　the　major　premiss　indicates　possibility　all　the　syllogisms



will　be　perfect　and　establish　possibility　in　the　sense　defined；　but



whenever　the　minor　premiss　indicates　possibility　all　the　syllogisms



will　be　imperfect；　and　those　which　are　negative　will　establish　not



possibility　according　to　the　definition；　but　that　the　major　does　not



necessarily　belong　to　any；　or　to　all；　of　the　minor。　For　if　this　is　so；



we　say　it　is　possible　that　it　should　belong　to　none　or　not　to　all。　Let



A　be　possible　for　all　B；　and　let　B　belong　to　all　C。　Since　C　falls



under　B；　and　A　is　possible　for　all　B；　clearly　it　is　possible　for　all　C



also。　So　a　perfect　syllogism　results。　Likewise　if　the　premiss　AB　is



negative；　and　the　premiss　BC　is　affirmative；　the　former　stating



possible；　the　latter　simple　attribution；　a　perfect　syllogism　results



proving　that　A　possibly　belongs　to　no　C。



　　It　is　clear　that　perfect　syllogisms　result　if　the　minor　premiss



states　simple　belonging：　but　that　syllogisms　will　result　if　the



modality　of　the　premisses　is　reversed；　must　be　proved　per　impossibile。



At　the　same　time　it　will　be　evident　that　they　are　imperfect：　for　the



proof　proceeds　not　from　the　premisses　assumed。　First　we　must　state



that　if　B's　being　follows　necessarily　from　A's　being；　B's



possibility　will　follow　necessarily　from　A's　possibility。　Suppose；　the



terms　being　so　related；　that　A　is　possible；　and　B　is　impossible。　If



then　that　which　is　possible；　when　it　is　possible　for　it　to　be；　might



happen；　and　if　that　which　is　impossible；　when　it　is　impossible；



could　not　happen；　and　if　at　the　same　time　A　is　possible　and　B



impossible；　it　would　be　possible　for　A　to　happen　without　B；　and　if



to　happen；　then　to　be。　For　that　which　has　happened；　when　it　has



happened；　is。　But　we　must　take　the　impossible　and　the　possible　not



only　in　the　sphere　of　becoming；　but　also　in　the　spheres　of　truth　and



predicability；　and　the　various　other　spheres　in　which　we　speak　of



the　possible：　for　it　will　be　alike　in　all。　Further　we　must



understand　the　statement　that　B's　being　depends　on　A's　being；　not　as



meaning　that　if　some　single　thing　A　is；　B　will　be：　for　nothing　follows



of　necessity　from　the　being　of　some　one　thing；　but　from　two　at



least；　i。e。　when　the　premisses　are　related　in　the　manner　stated　to



be　that　of　the　syllogism。　For　if　C　is　predicated　of　D；　and　D　of　F；



then　C　is　necessarily　predicated　of　F。　And　if　each　is　possible；　the



conclusion　also　is　possible。　If　then；　for　example；　one　should　indicate



the　premisses　by　A；　and　the　conclusion　by　B；　it　would　not　only



result　that　if　A　is　necessary　B　is　necessary；　but　also　that　if　A　is



possible；　B　is　possible。



　　Since　this　is　proved　it　is　evident　that　if　a　false　and　not



impossible　assumption　is　made；　the　consequence　of　the　assumption



will　also　be　false　and　not　impossible：　e。g。　if　A　is　false；　but　not



impossible；　and　if　B　is　the　consequence　of　A；　B　also　will　be　false　but



not　impossible。　For　since　it　has　been　proved　that　if　B's　being　is



the　consequence　of　A's　being；　then　B's　possibility　will　follow　from



A's　possibility　（and　A　is　assumed　to　be　possible）；　consequently　B　will



be　possible：　for　if　it　were　impossible；　the　same　thing　would　at　the



same　time　be　possible　and　impossible。



　　Since　we　have　defined　these　points；　let　A　belong　to　all　B；　and　B



be　possible　for　all　C：　it　is　necessary　then　that　should　be　a



possible　attribute　for　all　C。　Suppose　that　it　is　not　possible；　but



assume　that　B　belongs　to　all　C：　this　is　false　but　not　impossible。　If



then　A　is　not　possible　for　C　but　B　belongs　to　all　C；　then　A　is　not



possible　for　all　B：　for　a　syllogism　is　formed　in　the　third　degree。　But



it　was　assumed　that　A　is　a　possible　attribute　for　all　B。　It　is



necessary　then　that　A　is　possible　for　all　C。　For　though　the　assumption



we　made　is　false　and　not　impossible；　the　conclusion　is　impossible。



It　is　possible　also　in　the　first　figure　to　bring　about　the



impossibility；　by　assuming　that　B　belongs　to　C。　For　if　B　belongs　to



all　C；　and　A　is　possible　for　all　B；　then　A　would　be　possible　for　all



C。　But　the　assumption　was　made　that　A　is　not　possible　for　all　C。



　　We　must　understand　'that　which　belongs　to　all'　with　no　limitation　in



respect　of　time；　e。g。　to　the　present　or　to　a　particular　period；　but



simply　without　qualification。　For　it　is　by　the　help　of　such



premisses　that　we　make　syllogisms；　since　if　the　premiss　is



understood　with　reference　to　the　present　moment；　there　cannot　be　a



syllogism。　For　nothing　perhaps　prevents　'man'　belonging　at　a



particular　time　to　everything　that　is　moving；　i。e。　if　nothing　else



were　moving：　but　'moving'　is　possible　for　every　horse；　yet　'man'　is



possible　for　no　horse。　Further　let　the　major　term　be　'animal'；　the



middle　'moving'；　the　the　minor　'man'。　The　premisses　then　will　be　as



before；　but　the　conclusion　necessary；　not　possible。　For　man　is



necessarily　animal。　It　is　clear　then　that　the　universal　must　be



understood　simply；　without　limitation　in　respect　of　time。



　　Again　let　the　premiss　AB　be　universal　and　negative；　and　assume



that　A　belongs　to　no　B；　but　B　possibly　belongs　to　all　C。　These



propositions　being　laid　down；　it　is　necessary　that　A　possibly



belongs　to　no　C。　Suppose　that　it　cannot　belong；　and　that　B　belongs



to　C；　as　above。　It　is　necessary　then　that　A　belongs　to　some　B：　for



we　have　a　syllogism　in　the　third　figure：　but　this　is　impossible。



Thus　it　will　be　possible　for　A　to　belong　to　no　C；　for　if　at　is



supposed　false；　the　consequence　is　an　impossible　one。　This　syllogism



then　does　not　establish　that　which　is　possible　according　to　the



definition；　but　that　which　does　not　necessarily　belong　to　any　part



of　the　subject　（for　this　is　the　contradictory　of　the　assumption



which　was　made：　for　it　was　supposed　that　A　necessarily　belongs　to　some



C；　but　the　syllogism　per　impossibile　establishes　the　contradictory



which　is　opposed　to　this）。　Further；　it　is　clear　also　from　an　example



that　the　conclusion　will　not　establish　possibility。　Let　A　be



'raven'；　B　'intelligent'；　and　C　'man'。　A　then　belongs　to　no　B：　for



no　intelligent　thing　is　a　raven。　But　B　is　possible　for　all　C：　for



every　man　may　possibly　be　intelligent。　But　A　necessarily　belongs　to　no



C：　so　the　conclusion　does　not　establish　possibility。　But　neither　is　it



always　necessary。　Let　A　be　'moving'；　B　'science'；　C　'man'。　A　then　will



belong　to　no　B；　but　B　is　possible　for　all　C。　And　the　conclusion　will



not　be　necessary。　For　it　is　not　necessary　that　no　man　should　move；



rather　it　is　not　necessary　that　any　man　should　move。　Clearly　then



the　conclusion　establishes　that　one　term　does　not　necessarily　belong



to　any　instance　of　another　term。　But　we　must　take　our　terms　better。



　　If　the　minor　premiss　is　negative　and　indicates　possibility；　from　the



actual　premisses　taken　there　can　be　no　syllogism；　but　if　the



problematic　premiss　is　converted；　a　syllogism　will　be　possible；　as



before。　Let　A　belong　to　all　B；　and　let　B　possibly　belong　to　no　C。　If



the　terms　are　arranged　thus；　nothing　necessarily　follows：　but　if　the



proposition　BC　is　converted　and　it　is　assumed　that　B　is　possible　for



all　C；　a　syllogism　results　as　before：　for　the　terms　are　in　the　same



relative　positions。　Likewise　if　both　the　relations　are　negative；　if



the　major　premiss　states　that　A　does　not　belong　to　B；　and　the　minor



premiss　indicates　that　B　may　possibly　belong　to　no　C。　Through　the



premisses　actually　taken　nothing　necessary　results　in　any　way；　but



if　the　problematic　premiss　is　converted；　we　shall　have　a　syllogism。



Suppose　that　A　belongs　to　no　B；　and　B　may　possibly　belong　to　no　C。



Through　these　comes　nothing　necessary。　But　if　B　is　assumed　to　be



possible　for　all　C　（and　this　is　true）　and　if　the　premiss　AB　remains　as



before；　we　shall　again　have　the　same　syllogism。　But　if　it　be　assumed



that　B　does　not　belong　to　any　C；　instead　of　possibly　not　belonging；



there　cannot　be　a　syllogism　anyhow；　whether　the　premiss　AB　is　negative



or　affirmative。　As　common　instances　of　a　necessary　and　positive



relation　we　may　take　the　terms　white…animal…snow：　of　a　necessary　and



negative　relation；　white…animal…pitch。　Clearly　then　if　the　terms　are



universal；　and　one　of　the　premisses　is　assertoric；　the　other



problematic；