prior analytics-第14章

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mean　not　only　in　being　affirmative　or　negative；　but　also　in　being



necessary；　pure；　problematic。　We　must　consider　also　the　other　forms　of



predication。



　　It　is　clear　also　when　a　syllogism　in　general　can　be　made　and　when　it



cannot；　and　when　a　valid；　when　a　perfect　syllogism　can　be　formed；



and　that　if　a　syllogism　is　formed　the　terms　must　be　arranged　in　one　of



the　ways　that　have　been　mentioned。







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　　It　is　clear　too　that　every　demonstration　will　proceed　through



three　terms　and　no　more；　unless　the　same　conclusion　is　established



by　different　pairs　of　propositions；　e。g。　the　conclusion　E　may　be



established　through　the　propositions　A　and　B；　and　through　the



propositions　C　and　D；　or　through　the　propositions　A　and　B；　or　A　and　C；



or　B　and　C。　For　nothing　prevents　there　being　several　middles　for　the



same　terms。　But　in　that　case　there　is　not　one　but　several



syllogisms。　Or　again　when　each　of　the　propositions　A　and　B　is　obtained



by　syllogistic　inference；　e。g。　by　means　of　D　and　E；　and　again　B　by



means　of　F　and　G。　Or　one　may　be　obtained　by　syllogistic；　the　other



by　inductive　inference。　But　thus　also　the　syllogisms　are　many；　for　the



conclusions　are　many；　e。g。　A　and　B　and　C。　But　if　this　can　be　called



one　syllogism；　not　many；　the　same　conclusion　may　be　reached　by　more



than　three　terms　in　this　way；　but　it　cannot　be　reached　as　C　is



established　by　means　of　A　and　B。　Suppose　that　the　proposition　E　is



inferred　from　the　premisses　A；　B；　C；　and　D。　It　is　necessary　then



that　of　these　one　should　be　related　to　another　as　whole　to　part：　for



it　has　already　been　proved　that　if　a　syllogism　is　formed　some　of　its



terms　must　be　related　in　this　way。　Suppose　then　that　A　stands　in



this　relation　to　B。　Some　conclusion　then　follows　from　them。　It　must



either　be　E　or　one　or　other　of　C　and　D；　or　something　other　than　these。



　　（1）　If　it　is　E　the　syllogism　will　have　A　and　B　for　its　sole



premisses。　But　if　C　and　D　are　so　related　that　one　is　whole；　the



other　part；　some　conclusion　will　follow　from　them　also；　and　it　must　be



either　E；　or　one　or　other　of　the　propositions　A　and　B；　or　something



other　than　these。　And　if　it　is　（i）　E；　or　（ii）　A　or　B；　either　（i）　the



syllogisms　will　be　more　than　one；　or　（ii）　the　same　thing　happens　to　be



inferred　by　means　of　several　terms　only　in　the　sense　which　we　saw　to



be　possible。　But　if　（iii）　the　conclusion　is　other　than　E　or　A　or　B；



the　syllogisms　will　be　many；　and　unconnected　with　one　another。　But



if　C　is　not　so　related　to　D　as　to　make　a　syllogism；　the　propositions



will　have　been　assumed　to　no　purpose；　unless　for　the　sake　of　induction



or　of　obscuring　the　argument　or　something　of　the　sort。



　　（2）　But　if　from　the　propositions　A　and　B　there　follows　not　E　but



some　other　conclusion；　and　if　from　C　and　D　either　A　or　B　follows　or



something　else；　then　there　are　several　syllogisms；　and　they　do　not



establish　the　conclusion　proposed：　for　we　assumed　that　the　syllogism



proved　E。　And　if　no　conclusion　follows　from　C　and　D；　it　turns　out　that



these　propositions　have　been　assumed　to　no　purpose；　and　the



syllogism　does　not　prove　the　original　proposition。



　　So　it　is　clear　that　every　demonstration　and　every　syllogism　will



proceed　through　three　terms　only。



　　This　being　evident；　it　is　clear　that　a　syllogistic　conclusion



follows　from　two　premisses　and　not　from　more　than　two。　For　the　three



terms　make　two　premisses；　unless　a　new　premiss　is　assumed；　as　was　said



at　the　beginning；　to　perfect　the　syllogisms。　It　is　clear　therefore



that　in　whatever　syllogistic　argument　the　premisses　through　which



the　main　conclusion　follows　（for　some　of　the　preceding　conclusions



must　be　premisses）　are　not　even　in　number；　this　argument　either　has



not　been　drawn　syllogistically　or　it　has　assumed　more　than　was



necessary　to　establish　its　thesis。



　　If　then　syllogisms　are　taken　with　respect　to　their　main　premisses；



every　syllogism　will　consist　of　an　even　number　of　premisses　and　an　odd



number　of　terms　（for　the　terms　exceed　the　premisses　by　one）；　and　the



conclusions　will　be　half　the　number　of　the　premisses。　But　whenever　a



conclusion　is　reached　by　means　of　prosyllogisms　or　by　means　of　several



continuous　middle　terms；　e。g。　the　proposition　AB　by　means　of　the



middle　terms　C　and　D；　the　number　of　the　terms　will　similarly　exceed



that　of　the　premisses　by　one　（for　the　extra　term　must　either　be



added　outside　or　inserted：　but　in　either　case　it　follows　that　the



relations　of　predication　are　one　fewer　than　the　terms　related）；　and



the　premisses　will　be　equal　in　number　to　the　relations　of　predication。



The　premisses　however　will　not　always　be　even；　the　terms　odd；　but　they



will　alternate…when　the　premisses　are　even；　the　terms　must　be　odd；



when　the　terms　are　even；　the　premisses　must　be　odd：　for　along　with　one



term　one　premiss　is　added；　if　a　term　is　added　from　any　quarter。



Consequently　since　the　premisses　were　（as　we　saw）　even；　and　the



terms　odd；　we　must　make　them　alternately　even　and　odd　at　each



addition。　But　the　conclusions　will　not　follow　the　same　arrangement



either　in　respect　to　the　terms　or　to　the　premisses。　For　if　one　term　is



added；　conclusions　will　be　added　less　by　one　than　the　pre…existing



terms：　for　the　conclusion　is　drawn　not　in　relation　to　the　single



term　last　added；　but　in　relation　to　all　the　rest；　e。g。　if　to　ABC　the



term　D　is　added；　two　conclusions　are　thereby　added；　one　in　relation　to



A；　the　other　in　relation　to　B。　Similarly　with　any　further　additions。



And　similarly　too　if　the　term　is　inserted　in　the　middle：　for　in



relation　to　one　term　only；　a　syllogism　will　not　be　constructed。



Consequently　the　conclusions　will　be　much　more　numerous　than　the　terms



or　the　premisses。







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　　Since　we　understand　the　subjects　with　which　syllogisms　are



concerned；　what　sort　of　conclusion　is　established　in　each　figure；



and　in　how　many　moods　this　is　done；　it　is　evident　to　us　both　what　sort



of　problem　is　difficult　and　what　sort　is　easy　to　prove。　For　that　which



is　concluded　in　many　figures　and　through　many　moods　is　easier；　that



which　is　concluded　in　few　figures　and　through　few　moods　is　more



difficult　to　attempt。　The　universal　affirmative　is　proved　by　means



of　the　first　figure　only　and　by　this　in　only　one　mood；　the　universal



negative　is　proved　both　through　the　first　figure　and　through　the



second；　through　the　first　in　one　mood；　through　the　second　in　two。



The　particular　affirmative　is　proved　through　the　first　and　through　the



last　figure；　in　one　mood　through　the　first；　in　three　moods　through　the



last。　The　particular　negative　is　proved　in　all　the　figures；　but　once



in　the　first；　in　two　moods　in　the　second；　in　three　moods　in　the　third。



It　is　clear　then　that　the　universal　affirmative　is　most　difficult　to



establish；　most　easy　to　overthrow。　In　general；　universals　are　easier



game　for　the　destroyer　than　particulars：　for　whether　the　predicate



belongs　to　none　or　not　to　some；　they　are　destroyed：　and　the　particular



negative　is　proved　in　all　the　figures；　the　universal　negative　in



two。　Similarly　with　universal　negatives：　the　original　statement　is



destroyed；　whether　the　predicate　belongs　to　all　or　to　some：　and　this



we　found　possible　in　two　figures。　But　particular　statements　can　be



refuted　in　one　way　only…by　proving　that　the　predicate　belongs　either



to　all　or　to　none。　But　particular　statements　are　easier　to



establish：　for　proof　is　possible　in　more　figures　and　through　more



moods。　And　in　general　we　must　not　forget　that　it　is　possible　to　refute



statements　by　means　of　one　another；　I　mean；　universal　s