prior analytics-第13节

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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　statements　by



means　of　particular；　and　particular　statements　by　means　of



universal：　but　it　is　not　possible　to　establish　universal　statements　by



means　of　particular；　though　it　is　possible　to　establish　particular



statements　by　means　of　universal。　At　the　same　time　it　is　evident



that　it　is　easier　to　refute　than　to　establish。



　　The　manner　in　which　every　syllogism　is　produced；　the　number　of　the



terms　and　premisses　through　which　it　proceeds；　the　relation　of　the



premisses　to　one　another；　the　character　of　the　problem　proved　in



each　figure；　and　the　number　of　the　figures　appropriate　to　each



problem；　all　these　matters　are　clear　from　what　has　been　said。







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　　We　must　now　state　how　we　may　ourselves　always　have　a　supply　of



syllogisms　in　reference　to　the　problem　proposed　and　by　what　road　we



may　reach　the　principles　relative　to　the　problem：　for　perhaps　we　ought



not　only　to　investigate　the　construction　of　syllogisms；　but　also　to



have　the　power　of　making　them。



　　Of　all　the　things　which　exist　some　are　such　that　they　cannot　be



predicated　of　anything　else　truly　and　universally；　e。g。　Cleon　and



Callias；　i。e。　the　individual　and　sensible；　but　other　things　may　be



predicated　of　them　（for　each　of　these　is　both　man　and　animal）；　and



some　things　are　themselves　predicated　of　others；　but　nothing　prior



is　predicated　of　them；　and　some　are　predicated　of　others；　and　yet



others　of　them；　e。g。　man　of　Callias　and　animal　of　man。　It　is　clear



then　that　some　things　are　naturally　not　stated　of　anything：　for　as　a



rule　each　sensible　thing　is　such　that　it　cannot　be　predicated　of



anything；　save　incidentally：　for　we　sometimes　say　that　that　white



object　is　Socrates；　or　that　that　which　approaches　is　Callias。　We　shall



explain　in　another　place　that　there　is　an　upward　limit　also　to　the



process　of　predicating：　for　the　present　we　must　assume　this。　Of



these　ultimate　predicates　it　is　not　possible　to　demonstrate　another



predicate；　save　as　a　matter　of　opinion；　but　these　may　be　predicated　of



other　things。　Neither　can　individuals　be　predicated　of　other　things；



though　other　things　can　be　predicated　of　them。　Whatever　lies　between



these　limits　can　be　spoken　of　in　both　ways：　they　may　be　stated　of



others；　and　others　stated　of　them。　And　as　a　rule　arguments　and



inquiries　are　concerned　with　these　things。　We　must　select　the



premisses　suitable　to　each　problem　in　this　manner：　first　we　must　lay



down　the　subject　and　the　definitions　and　the　properties　of　the



thing；　next　we　must　lay　down　those　attributes　which　follow　the



thing；　and　again　those　which　the　thing　follows；　and　those　which　cannot



belong　to　it。　But　those　to　which　it　cannot　belong　need　not　be



selected；　because　the　negative　statement　implied　above　is　convertible。



Of　the　attributes　which　follow　we　must　distinguish　those　which　fall



within　the　definition；　those　which　are　predicated　as　properties；　and



those　which　are　predicated　as　accidents；　and　of　the　latter　those　which



apparently　and　those　which　really　belong。　The　larger　the　supply　a



man　has　of　these；　the　more　quickly　will　he　reach　a　conclusion；　and



in　proportion　as　he　apprehends　those　which　are　truer；　the　more



cogently　will　he　demonstrate。　But　he　must　select　not　those　which



follow　some　particular　but　those　which　follow　the　thing　as　a　whole；



e。g。　not　what　follows　a　particular　man　but　what　follows　every　man：　for



the　syllogism　proceeds　through　universal　premisses。　If　the　statement



is　indefinite；　it　is　uncertain　whether　the　premiss　is　universal；　but



if　the　statement　is　definite；　the　matter　is　clear。　Similarly　one



must　select　those　attributes　which　the　subject　follows　as　wholes；



for　the　reason　given。　But　that　which　follows　one　must　not　suppose　to



follow　as　a　whole；　e。g。　that　every　animal　follows　man　or　every　science



music；　but　only　that　it　follows；　without　qualification；　and　indeed



we　state　it　in　a　proposition：　for　the　other　statement　is　useless　and



impossible；　e。g。　that　every　man　is　every　animal　or　justice　is　all



good。　But　that　which　something　follows　receives　the　mark　'every'。



Whenever　the　subject；　for　which　we　must　obtain　the　attributes　that



follow；　is　contained　by　something　else；　what　follows　or　does　not



follow　the　highest　term　universally　must　not　be　selected　in　dealing



with　the　subordinate　term　（for　these　attributes　have　been　taken　in



dealing　with　the　superior　term；　for　what　follows　animal　also　follows



man；　and　what　does　not　belong　to　animal　does　not　belong　to　man）；　but



we　must　choose　those　attributes　which　are　peculiar　to　each　subject。



For　some　things　are　peculiar　to　the　species　as　distinct　from　the



genus；　for　species　being　distinct　there　must　be　attr