prior analytics-第12章

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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



all　A　since　B　belongs　to　A　and　E　to　B　（for　B　was　found　to　be　identical



with　G）：　but　that　A　should　belong　to　all　E　is　not　necessary；　but　it



must　belong　to　some　E　because　it　is　possible　to　convert　the



universal　statement　into　a　particular。



　　It　is　clear　then　that　in　every　proposition　which　requires　proof　we



must　look　to　the　aforesaid　relations　of　the　subject　and　predicate　in



question：　for　all　syllogisms　proceed　through　these。　But　if　we　are



seeking　consequents　and　antecedents　we　must　look　for　those　which　are



primary　and　most　universal；　e。g。　in　reference　to　E　we　must　look　to



KF　rather　than　to　F　alone；　and　in　reference　to　A　we　must　look　to　KC



rather　than　to　C　alone。　For　if　A　belongs　to　KF；　it　belongs　both　to　F



and　to　E：　but　if　it　does　not　follow　KF；　it　may　yet　follow　F。　Similarly



we　must　consider　the　antecedents　of　A　itself：　for　if　a　term　follows



the　primary　antecedents；　it　will　follow　those　also　which　are



subordinate；　but　if　it　does　not　follow　the　former；　it　may　yet　follow



the　latter。



　　It　is　clear　too　that　the　inquiry　proceeds　through　the　three　terms



and　the　two　premisses；　and　that　all　the　syllogisms　proceed　through　the



aforesaid　figures。　For　it　is　proved　that　A　belongs　to　all　E；



whenever　an　identical　term　is　found　among　the　Cs　and　Fs。　This　will



be　the　middle　term；　A　and　E　will　be　the　extremes。　So　the　first



figure　is　formed。　And　A　will　belong　to　some　E；　whenever　C　and　G　are



apprehended　to　be　the　same。　This　is　the　last　figure：　for　G　becomes　the



middle　term。　And　A　will　belong　to　no　E；　when　D　and　F　are　identical。



Thus　we　have　both　the　first　figure　and　the　middle　figure；　the　first；



because　A　belongs　to　no　F；　since　the　negative　statement　is



convertible；　and　F　belongs　to　all　E：　the　middle　figure　because　D



belongs　to　no　A；　and　to　all　E。　And　A　will　not　belong　to　some　E；



whenever　D　and　G　are　identical。　This　is　the　last　figure：　for　A　will



belong　to　no　G；　and　E　will　belong　to　all　G。　Clearly　then　all



syllogisms　proceed　through　the　aforesaid　figures；　and　we　must　not



select　consequents　of　all　the　terms；　because　no　syllogism　is



produced　from　them。　For　（as　we　saw）　it　is　not　possible　at　all　to



establish　a　proposition　from　consequents；　and　it　is　not　possible　to



refute　by　means　of　a　consequent　of　both　the　terms　in　question：　for　the



middle　term　must　belong　to　the　one；　and　not　belong　to　the　other。



　　It　is　clear　too　that　other　methods　of　inquiry　by　selection　of　middle



terms　are　useless　to　produce　a　syllogism；　e。g。　if　the　consequents　of



the　terms　in　question　are　identical；　or　if　the　antecedents　of　A　are



identical　with　those　attributes　which　cannot　possibly　belong　to　E；



or　if　those　attributes　are　identical　which　cannot　belong　to　either



term：　for　no　syllogism　is　produced　by　means　of　these。　For　if　the



consequents　are　identical；　e。g。　B　and　F；　we　have　the　middle　figure



with　both　premisses　affirmative：　if　the　antecedents　of　A　are　identical



with　attributes　which　cannot　belong　to　E；　e。g。　C　with　H；　we　have　the



first　figure　with　its　minor　premiss　negative。　If　attributes　which



cannot　belong　to　either　term　are　identical；　e。g。　C　and　H；　both



premisses　are　negative；　either　in　the　first　or　in　the　middle　figure。



But　no　syllogism　is　possible　in　this　way。



　　It　is　evident　too　that　we　must　find　out　which　terms　in　this



inquiry　are　identical；　not　which　are　different　or　contrary；　first



because　the　object　of　our　investigation　is　the　middle　term；　and　the



middle　term　must　be　not　diverse　but　identical。　Secondly；　wherever　it



happens　that　a　syllogism　results　from　taking　contraries　or　terms　which



cannot　belong　to　the　same　thing；　all　arguments　can　be　reduced　to　the



aforesaid　moods；　e。g。　if　B　and　F　are　contraries　or　cannot　belong　to



the　same　thing。　For　if　these　are　taken；　a　syllogism　will　be　formed



to　prove　that　A　belongs　to　none　of　the　Es；　not　however　from　the



premisses　taken　but　in　the　aforesaid　mood。　For　B　will　belong　to　all



A　and　to　no　E。　Consequently　B　must　be　identical　with　one　of　the　Hs。



Again；　if　B　and　G　cannot　belong　to　the　same　thing；　it　follows　that　A



will　not　belong　to　some　of　the　Es：　for　then　too　we　shall　have　the



middle　figure：　for　B　will　belong　to　all　A　and　to　no　G。　Consequently



B　must　be　identical　with　some　of　the　Hs。　For　the　fact　that　B　and　G



cannot　belong　to　the　same　thing　differs　in　no　way　from　the　fact　that　B



is　identical　with　some　of　the　Hs：　for　that　includes　everything　which



cannot　belong　to　E。



　　It　is　clear　then　that　from　the　inquiries　taken　by　themselves　no



syllogism　results；　but　if　B　and　F　are　contraries　B　must　be　identical



with　one　of　the　Hs；　and　the　syllogism　results　through　these　terms。



It　turns　out　then　that　those　who　inquire　in　this　manner　are　looking



gratuitously　for　some　other　way　than　the　necessary　way　because　they



have　failed　to　observe　the　identity　of　the　Bs　with　the　Hs。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　29







　　Syllogisms　which　lead　to　impossible　conclusions　are　similar　to



ostensive　syllogisms；　they　also　are　formed　by　means　of　the　consequents



and　antecedents　of　the　terms　in　question。　In　both　cases　the　same



inquiry　is　involved。　For　what　is　proved　ostensively　may　also　be



concluded　syllogistically　per　impossibile　by　means　of　the　same



terms；　and　what　is　proved　per　impossibile　may　also　be　proved



ostensively；　e。g。　that　A　belongs　to　none　of　the　Es。　For　suppose　A　to



belong　to　some　E：　then　since　B　belongs　to　all　A　and　A　to　some　of　the



Es；　B　will　belong　to　some　of　the　Es：　but　it　was　assumed　that　it



belongs　to　none。　Again　we　may　prove　that　A　belongs　to　some　E：　for　if　A



belonged　to　none　of　the　Es；　and　E　belongs　to　all　G；　A　will　belong　to



none　of　the　Gs：　but　it　was　assumed　to　belong　to　all。　Similarly　with



the　other　propositions　requiring　proof。　The　proof　per　impossibile　will



always　and　in　all　cases　be　from　the　consequents　and　antecedents　of　the



terms　in　question。　Whatever　the　problem　the　same　inquiry　is



necessary　whether　one　wishes　to　use　an　ostensive　syllogism　or　a



reduction　to　impossibility。　For　both　the　demonstrations　start　from　the



same　terms；　e。g。　suppose　it　has　been　proved　that　A　belongs　to　no　E；



because　it　turns　out　that　otherwise　B　belongs　to　some　of　the　Es　and



this　is　impossible…if　now　it　is　assumed　that　B　belongs　to　no　E　and



to　all　A；　it　is　clear　that　A　will　belong　to　no　E。　Again　if　it　has　been



proved　by　an　ostensive　syllogism　that　A　belongs　to　no　E；　assume　that　A



belongs　to　some　E　and　it　will　be　proved　per　impossibile　to　belong　to



no　E。　Similarly　with　the　rest。　In　all　cases　it　is　necessary　to　find



some　common　term　other　than　the　subjects　of　inquiry；　to　which　the



syllogism　establishing　the　false　conclusion　may　relate；　so　that　if



this　premiss　is　converted；　and　the　other　remains　as　it　is；　the



syllogism　will　be　ostensive　by　means　of　the　same　terms。　For　the



ostensive　syllogism　differs　from　the　reductio　ad　impossibile　in



this：　in　the　ostensive　syllogism　both　remisses　are　laid　down　in



accordance　with　the　truth；　in　the　reductio　ad　impossibile　one　of　the



premisses　is　assumed　falsely。



　　These　points　will　be　made　clearer　by　the　sequel；　when　we　discuss　the



reduction　to　impossibility：　at　present　this　much　must　be　clear；　that



we　must　look　to　terms　of　the　kinds　mentioned　whether　we　wish　to　use　an



ostensive　syllogism　or　a　reduction　to　impossibility。　In　the　other



hypothetical　syllogisms；　I　mean　those　which　proceed　by　substitution；



or　by　positing　a　certain　quality；　the　inquiry　will　be　directed　to



the　terms　of　the　problem　to　be　proved…not　the　terms　of　the　original



problem；　but　the　new　terms　introduced；　and　the　method　of　the　inquiry



will　be　the　same　as　before。　But　we　must　consider　and　determine　in



how　many　ways　hypothetical　syllogisms　are　possible。



　　Each　of　the　problems　then　can　be　proved　in　the　manner　described；　but



it　is　possible　to　establish　some　of　them　syllogistically　in　another



way；　e。g。　universal　problems　by　the　inquiry　which　leads　up　to　a



particular　conclusion；　with　the　addition　of　an　hypothesis。　For　if



the　Cs　and　the　Gs　should　be　identical；　but　E　should　be　assumed　to



belong　to　the　Gs　only；　then　A　would　belong　to　every　E：　and　again　if



the　Ds　and　the　Gs　should　be　identical；　but　E　should　be　predicated　of



the　Gs　only；　it　follows　that　A　will　belong　to　none　of　the　Es。



Clearly　then　we　must　consider　the　matter　in　this　way　also。　The



method　is　the　same　whether　the　relation　is　necessary　or　possible。



For　the　inquiry　will　be　the　same；　and　the　syllogism　will　proceed



through　terms　arranged　in　the　same　order　whether　a　possible　or　a



pure　proposition　is　proved。　We　must　find　in　the　case　of　possible



relations；　as　well　as　terms　that　belong；　terms　which　can　belong　though



they　actually　do　not：　for　we　have　proved　that　the　syllogism　which



establishes　a　possible　relation　proceeds　through　these　terms　as



well。　Similarly　also　with　the　other　modes　of　predication。



　　It　is　clear　then　from　what　has　been　said　not　only　that　all



syllogisms　can　be　formed　in　this　way；　but　also　that　they　cannot　be



formed　in　any　other。　For　every　syllogism　has　been　proved　to　be



formed　through　one　of　the　aforementioned　figures；　and　these　cannot



be　composed　through　other　terms　than　the　consequents　and　antecedents



of　the　terms　in　question：　for　from　these　we　obtain　the　premisses　and



find　the　middle　term。　Consequently　a　syllogism　cannot　be　formed　by



means　of　other　terms。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　30







　　The　method　is　the　same　in　all　cases；　in　philosophy；　in　any　art　or



study。　We　must　look　for　the　attributes　and　the　subjects　of　both　our



terms；　and　we　must　supply　ourselves　with　as　many　of　these　as　possible；



and　consider　them　by　means　of　the　three　terms；　refuting　statements



in　one　way；　confirming　them　in　another；　in　the　pursuit　of　truth



starting　from　premisses　in　which　the　arrangement　of　the　terms　is　in



accordance　with　truth；　while　if　we　look　for　dialectical　syllogisms



we　must　start　from　probable　premisses。　The　principles　of　syllogisms



have　been　stated　in　general　terms；　both　how　they　are　characterized　and



how　we　must　hunt　for　them；　so　as　not　to　look　to　everything　that　is



said　about　the　terms　of　the　problem　or　to　the　same　points　whether　we



are　confirming　or　refuting；　or　again　whether　we　are　confirming　of



all　or　of　some；　and　whether　we　are　refuting　of　all　or　some。　we　must



look　to　fewer　points　and　they　mus