prior analytics-第4节

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indefinite；　it　may　be　used　truly　of　that　also　which　belongs　to　none。



But　if　R　belongs　to　no　S；　no　syllogism　is　possible；　as　has　been　shown。



Clearly　then　no　syllogism　will　be　possible　here。



　　But　if　the　negative　term　is　universal；　whenever　the　major　is



negative　and　the　minor　affirmative　there　will　be　a　syllogism。　For　if　P



belongs　to　no　S；　and　R　belongs　to　some　S；　P　will　not　belong　to　some　R：



for　we　shall　have　the　first　figure　again；　if　the　premiss　RS　is



converted。



　　But　when　the　minor　is　negative；　there　will　be　no　syllogism。　Terms



for　the　positive　relation　are　animal；　man；　wild：　for　the　negative



relation；　animal；　science；　wild…the　middle　in　both　being　the　term



wild。



　　Nor　is　a　syllogism　possible　when　both　are　stated　in　the　negative；



but　one　is　universal；　the　other　particular。　When　the　minor　is



related　universally　to　the　middle；　take　the　terms　animal；　science；



wild；　animal；　man；　wild。　When　the　major　is　related　universally　to



the　middle；　take　as　terms　for　a　negative　relation　raven；　snow；



white。　For　a　positive　relation　terms　cannot　be　found；　if　R　belongs



to　some　S；　and　does　not　belong　to　some　S。　For　if　P　belongs　to　all　R；



and　R　to　some　S；　then　P　belongs　to　some　S：　but　we　assumed　that　it



belongs　to　no　S。　Our　point；　then；　must　be　proved　from　the　indefinite



nature　of　the　particular　statement。



　　Nor　is　a　syllogism　possible　anyhow；　if　each　of　the　extremes



belongs　to　some　of　the　middle　or　does　not　belong；　or　one　belongs　and



the　other　does　not　to　some　of　the　middle；　or　one　belongs　to　some　of



the　middle；　the　other　not　to　all；　or　if　the　premisses　are



indefinite。　Common　terms　for　all　are　animal；　man；　white：　animal；



inanimate；　white。



　　It　is　clear　then　in　this　figure　also　when　a　syllogism　will　be



possible；　and　when　not；　and　that　if　the　terms　are　as　stated；　a



syllogism　results　of　necessity；　and　if　there　is　a　syllogism；　the　terms



must　be　so　related。　It　is　clear　also　that　all　the　syllogisms　in　this



figure　are　imperfect　（for　all　are　made　perfect　by　certain



supplementary　assumptions）；　and　that　it　will　not　be　possible　to



reach　a　universal　conclusion　by　means　of　this　figure；　whether　negative



or　affirmative。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　7







　　It　is　evident　also　that　in　all　the　figures；　whenever　a　proper



syllogism　does　not　result；　if　both　the　terms　are　affirmative　or



negative　nothing　necessary　follows　at　all；　but　if　one　is



affirmative；　the　other　negative；　and　if　the　negative　is　stated



universally；　a　syllogism　always　results　relating　the　minor　to　the



major　term；　e。g。　if　A　belongs　to　all　or　some　B；　and　B　belongs　to　no　C：



for　if　the　premisses　are　converted　it　is　necessary　that　C　does　not



belong　to　some　A。　Similarly　also　in　the　other　figures：　a　syllogism



always　results　by　means　of　conversion。　It　is　evident　also　that　the



substitution　of　an　indefinite　for　a　particular　affirmative　will　effect



the　same　syllogism　in　all　the　figures。



　　It　is　clear　too　that　all　the　imperfect　syllogisms　are　made　perfect



by　means　of　the　first　figure。　For　all　are　brought　to　a　conclusion



either　ostensively　or　per　impossibile。　In　both　ways　the　first　figure



is　formed：　if　they　are　made　perfect　ostensively；　because　（as　we　saw）



all　are　brought　to　a　conclusion　by　means　of　conversion；　and　conversion



produces　the　first　figure：　if　they　are　proved　per　impossibile；　because



on　the　assumption　of　the　false　statement　the　syllogism　comes　about



by　means　of　the　first　figure；　e。g。　in　the　last　figure；　if　A　and　B



belong　to　all　C；　it　follows　that　A　belongs　to　some　B：　for　if　A



belonged　to　no　B；　and　B　belongs　to　all　C；　A　would　belong　to　no　C：



but　（as　we　stated）　it　belongs　to　all　C。　Similarly　also　with　the　rest。



　　It　is　possible　also　to　reduce　all　syllogisms　to　the　universal



syllogisms　in　the　first　figure。　Those　in　the　second　figure　are　clearly



made　perfect　by　these；　though　not　all　in　the　same　way；　the　universal



syllogisms　are　made　perfect　by　converting　the　negative　premiss；　each



of　the　particular　syllogisms　by　reductio　ad　impossibile。　In　the



first　figure　particular　syllogisms　are　indeed　made　perfect　by



themselves；　but　it　is　possible　also　to　prove　them　by　means　of　the



second　figure；　reducing　them　ad　impossibile；　e。g。　if　A　belongs　to



all　B；　and　B　to　some　C；　it　follows　that　A　belongs　to　some　C。　For　if　it



belonged　to　no　C；　and　belongs　to　all　B；　then　B　will　belong　to　no　C：



this　we　know　by　means　of　the　second　figure。　Similarly　also



demonstration　will　be　possible　in　the　case　of　the　negative。　For　if　A



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



for　if　it　belonged　to　all　C；　and　belongs　to　no　B；　then　B　will　belong



to　no　C：　and　this　（as　we　saw）　is　the　middle　figure。　Consequently；



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　i