prior analytics-第11章

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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　attributes　peculiar　to



each。　Nor　must　we　take　as　things　which　the　superior　term　follows；



those　things　which　the　inferior　term　follows；　e。g。　take　as　subjects　of



the　predicate　'animal'　what　are　really　subjects　of　the　predicate



'man'。　It　is　necessary　indeed；　if　animal　follows　man；　that　it　should



follow　all　these　also。　But　these　belong　more　properly　to　the　choice　of



what　concerns　man。　One　must　apprehend　also　normal　consequents　and



normal　antecedents…；　for　propositions　which　obtain　normally　are



established　syllogistically　from　premisses　which　obtain　normally；　some



if　not　all　of　them　having　this　character　of　normality。　For　the



conclusion　of　each　syllogism　resembles　its　principles。　We　must　not



however　choose　attributes　which　are　consequent　upon　all　the　terms：　for



no　syllogism　can　be　made　out　of　such　premisses。　The　reason　why　this　is



so　will　be　clear　in　the　sequel。







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　　If　men　wish　to　establish　something　about　some　whole；　they　must



look　to　the　subjects　of　that　which　is　being　established　（the



subjects　of　which　it　happens　to　be　asserted）；　and　the　attributes　which



follow　that　of　which　it　is　to　be　predicated。　For　if　any　of　these



subjects　is　the　same　as　any　of　these　attributes；　the　attribute



originally　in　question　must　belong　to　the　subject　originally　in



question。　But　if　the　purpose　is　to　establish　not　a　universal　but　a



particular　proposition；　they　must　look　for　the　terms　of　which　the



terms　in　question　are　predicable：　for　if　any　of　these　are　identical；



the　attribute　in　question　must　belong　to　some　of　the　subject　in



question。　Whenever　the　one　term　has　to　belong　to　none　of　the　other；



one　must　look　to　the　consequents　of　the　subject；　and　to　those



attributes　which　cannot　possibly　be　present　in　the　predicate　in



question：　or　conversely　to　the　attributes　which　cannot　possibly　be



present　in　the　subject；　and　to　the　consequents　of　the　predicate。　If



any　members　of　these　groups　are　identical；　one　of　the　terms　in



question　cannot　possibly　belong　to　any　of　the　other。　For　sometimes　a



syllogism　in　the　first　figure　results；　sometimes　a　syllogism　in　the



second。　But　if　the　object　is　to　establish　a　particular　negative



proposition；　we　must　find　antecedents　of　the　subject　in　question　and



attributes　which　cannot　possibly　belong　to　the　predicate　in



question。　If　any　members　of　these　two　groups　are　identical；　it　follows



that　one　of　the　terms　in　question　does　not　belong　to　some　of　the



other。　Perhaps　each　of　these　statements　will　become　clearer　in　the



following　way。　Suppose　the　consequents　of　A　are　designated　by　B；　the



antecedents　of　A　by　C；　attributes　which　cannot　possibly　belong　to　A　by



D。　Suppose　again　that　the　attributes　of　E　are　designated　by　F；　the



antecedents　of　E　by　G；　and　attributes　which　cannot　belong　to　E　by　H。



If　then　one　of　the　Cs　should　be　identical　with　one　of　the　Fs；　A　must



belong　to　all　E：　for　F　belongs　to　all　E；　and　A　to　all　C；



consequently　A　belongs　to　all　E。　If　C　and　G　are　identical；　A　must



belong　to　some　of　the　Es：　for　A　follows　C；　and　E　follows　all　G。　If　F



and　D　are　identical；　A　will　belong　to　none　of　the　Es　by　a



prosyllogism：　for　since　the　negative　proposition　is　convertible；　and　F



is　identical　with　D；　A　will　belong　to　none　of　the　Fs；　but　F　belongs　to



all　E。　Again；　if　B　and　H　are　identical；　A　will　belong　to　none　of　the



Es：　for　B　will　belong　to　all　A；　but　to　no　E：　for　it　was　assumed　to



be　identical　with　H；　and　H　belonged　to　none　of　the　Es。　If　D　and　G



are　identical；　A　will　not　belong　to　some　of　the　Es：　for　it　will　not



belong　to　G；　because　it　does　not　belong　to　D：　but　G　falls　under　E：



consequently　A　will　not　belong　to　some　of　the　Es。　If　B　is　identical



with　G；　there　will　be　a　converted　syllogism：　for　E　will　belong　to