prior analytics-第5章

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since　all　syllogisms　in　the　middle　figure　can　be　reduced　to



universal　syllogisms　in　the　first　figure；　and　since　particular



syllogisms　in　the　first　figure　can　be　reduced　to　syllogisms　in　the



middle　figure；　it　is　clear　that　particular　syllogisms　can　be　reduced



to　universal　syllogisms　in　the　first　figure。　Syllogisms　in　the　third



figure；　if　the　terms　are　universal；　are　directly　made　perfect　by　means



of　those　syllogisms；　but；　when　one　of　the　premisses　is　particular；



by　means　of　the　particular　syllogisms　in　the　first　figure：　and　these



（we　have　seen）　may　be　reduced　to　the　universal　syllogisms　in　the　first



figure：　consequently　also　the　particular　syllogisms　in　the　third



figure　may　be　so　reduced。　It　is　clear　then　that　all　syllogisms　may



be　reduced　to　the　universal　syllogisms　in　the　first　figure。



　　We　have　stated　then　how　syllogisms　which　prove　that　something



belongs　or　does　not　belong　to　something　else　are　constituted；　both　how



syllogisms　of　the　same　figure　are　constituted　in　themselves；　and　how



syllogisms　of　different　figures　are　related　to　one　another。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　8







　　Since　there　is　a　difference　according　as　something　belongs；



necessarily　belongs；　or　may　belong　to　something　else　（for　many



things　belong　indeed；　but　not　necessarily；　others　neither



necessarily　nor　indeed　at　all；　but　it　is　possible　for　them　to　belong）；



it　is　clear　that　there　will　be　different　syllogisms　to　prove　each　of



these　relations；　and　syllogisms　with　differently　related　terms；　one



syllogism　concluding　from　what　is　necessary；　another　from　what　is；　a



third　from　what　is　possible。



　　There　is　hardly　any　difference　between　syllogisms　from　necessary



premisses　and　syllogisms　from　premisses　which　merely　assert。　When



the　terms　are　put　in　the　same　way；　then；　whether　something　belongs



or　necessarily　belongs　（or　does　not　belong）　to　something　else；　a



syllogism　will　or　will　not　result　alike　in　both　cases；　the　only



difference　being　the　addition　of　the　expression　'necessarily'　to　the



terms。　For　the　negative　statement　is　convertible　alike　in　both



cases；　and　we　should　give　the　same　account　of　the　expressions　'to　be



contained　in　something　as　in　a　whole'　and　'to　be　predicated　of　all



of　something'。　With　the　exceptions　to　be　made　below；　the　conclusion



will　be　proved　to　be　necessary　by　means　of　conversion；　in　the　same



manner　as　in　the　case　of　simple　predication。　But　in　the　middle



figure　when　the　universal　statement　is　affirmative；　and　the　particular



negative；　and　again　in　the　third　figure　when　the　universal　is



affirmative　and　the　particular　negative；　the　demonstration　will　not



take　the　same　form；　but　it　is　necessary　by　the　'exposition'　of　a



part　of　the　subject　of　the　particular　negative　proposition；　to　which



the　predicate　does　not　belong；　to　make　the　syllogism　in　reference　to



this：　with　terms　so　chosen　the　conclusion　will　necessarily　follow。　But



if　the　relation　is　necessary　in　respect　of　the　part　taken；　it　must



hold　of　some　of　that　term　in　which　this　part　is　included：　for　the　part



taken　is　just　some　of　that。　And　each　of　the　resulting　syllogisms　is　in



the　appropriate　figure。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　9







　　It　happens　sometimes　also　that　when　one　premiss　is　necessary　the



conclusion　is　necessary；　not　however　when　either　premiss　is　necessary；



but　only　when　the　major　is；　e。g。　if　A　is　taken　as　necessarily



belonging　or　not　belonging　to　B；　but　B　is　taken　as　simply　belonging　to



C：　for　if　the　premisses　are　taken　in　this　way；　A　will　necessarily



belong　or　not　belong　to　C。　For　since　necessarily　belongs；　or　does



not　belong；　to　every　B；　and　since　C　is　one　of　the　Bs；　it　is　clear　that



for　C　also　the　positive　or　the　negative　relation　to　A　will　hold



necessarily。　But　if　the　major　premiss　is　not　necessary；　but　the



minor　is　necessary；　the　conclusion　will　not　be　necessary。　For　if　it



were；　it　would　result　both　through　the　first　figure　and　through　the



third　that　A　belongs　necessarily　to　some　B。　But　this　is　false；　for　B



may　be　such　that　it　is　possible　that　A　should　belong　to　none　of　it。



Further；　an　example　also　makes　it　clear　that　the　conclusion　not　be



necessary；　e。g。　if　A　were　movement；　B　animal；　C　man：　man　is　an



animal　necessarily；　but　an　animal　does　not　move　necessarily；　nor



does　man。　Similarly　also　if　the　major　premiss　is　negative；　for　the



proof　is　the　same。



　　In　particular　syllogisms；　if　the　universal　premiss　is　necessary；



then　the　conclusion　will　be　necessary；　but　if　the　particular；　the



conclusion　will　not　be　necessary；　whether　the　universal　premiss　is



negative　or　affirmative。　First　let　the　universal　be　necessary；　and　let



A　belong　to　all　B　necessarily；　but　let　B　simply　belong　to　some　C：　it



is　necessary　then　that　A　belongs　to　some　C　necessarily：　for　C　falls



under　B；　and　A　was　assumed　to　belong　necessarily　to　all　B。　Similarly



also　if　the　syllogism　should　be　negative：　for　the　proof　will　be　the



same。　But　if　the　particular　premiss　is　necessary；　the　conclusion



will　not　be　necessary：　for　from　the　denial　of　such　a　conclusion



nothing　impossible　results；　just　as　it　does　not　in　the　universal



syllogisms。　The　same　is　true　of　negative　syllogisms。　Try　the　terms



movement；　animal；　white。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　10







　　In　the　second　figure；　if　the　negative　premiss　is　necessary；　then　the



conclusion　will　be　necessary；　but　if　the　affirmative；　not　necessary。



First　let　the　negative　be　necessary；　let　A　be　possible　of　no　B；　and



simply　belong　to　C。　Since　then　the　negative　statement　is



convertible；　B　is　possible　of　no　A。　But　A　belongs　to　all　C；



consequently　B　is　possible　of　no　C。　For　C　falls　under　A。　The　same



result　would　be　obtained　if　the　minor　premiss　were　negative：　for　if



A　is　possible　be　of　no　C；　C　is　possible　of　no　A：　but　A　belongs　to





all　B；　consequently　C　is　possible　of　none　of　the　Bs：　for　again　we　have



obtained　the　first　figure。　Neither　then　is　B　possible　of　C：　for



conversion　is　possible　without　modifying　the　relation。



　　But　if　the　affirmative　premiss　is　necessary；　the　conclusion　will　not



be　necessary。　Let　A　belong　to　all　B　necessarily；　but　to　no　C　simply。



If　then　the　negative　premiss　is　converted；　the　first　figure　results。



But　it　has　been　proved　in　the　case　of　the　first　figure　that　if　the



negative　major　premiss　is　not　necessary　the　conclusion　will　not　be



necessary　either。　Therefore　the　same　result　will　obtain　here。　Further；



if　the　conclusion　is　necessary；　it　follows　that　C　necessarily　does　not



belong　to　some　A。　For　if　B　necessarily　belongs　to　no　C；　C　will



necessarily　belong　to　no　B。　But　B　at　any　rate　must　belong　to　some　A；



if　it　is　true　（as　was　assumed）　that　A　necessarily　belongs　to　all　B。



Consequently　it　is　necessary　that　C　does　not　belong　to　some　A。　But



nothing　prevents　such　an　A　being　taken　that　it　is　possible　for　C　to



belong　to　all　of　it。　Further　one　might　show　by　an　exposition　of



terms　that　the　conclusion　is　not　necessary　without　qualification；



though　it　is　a　necessary　conclusion　from　the　premisses。　For　example



let　A　be　animal；　B　man；　C　white；　and　let　the　premisses　be　assumed　to



correspond　to　what　we　had　before：　it　is　possible　that　animal　should



belong　to　nothing　white。　Man　then　will　not　belong　to　anything　white；



but　not　necessarily：　for　it　is　possible　for　man　to　be　born　white；



not　however　so　long　as　animal　belongs　to　nothing　white。　Consequently



under　these　conditions　the　conclusion　will　be　necessary；　but　it　is　not



necessary　without　qualification。



　　Similar　results　will　obtain　also　in　particular　syllogisms。　For



whenever　the　negative　premiss　is　both　un