prior analytics-第32章

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described　and　effecting　a　reciprocal　proof　with　three　propositions。



　　Similarly　if　he　should　assume　that　B　belongs　to　C；　this　being　as



uncertain　as　the　question　whether　A　belongs　to　C；　the　question　is



not　yet　begged；　but　no　demonstration　is　made。　If　however　A　and　B　are



identical　either　because　they　are　convertible　or　because　A　follows



B；　then　the　question　is　begged　for　the　same　reason　as　before。　For　we



have　explained　the　meaning　of　begging　the　question；　viz。　proving



that　which　is　not　self…evident　by　means　of　itself。



　　If　then　begging　the　question　is　proving　what　is　not　self…evident



by　means　of　itself；　in　other　words　failing　to　prove　when　the　failure



is　due　to　the　thesis　to　be　proved　and　the　premiss　through　which　it



is　proved　being　equally　uncertain；　either　because　predicates　which　are



identical　belong　to　the　same　subject；　or　because　the　same　predicate



belongs　to　subjects　which　are　identical；　the　question　may　be　begged　in



the　middle　and　third　figures　in　both　ways；　though；　if　the　syllogism　is



affirmative；　only　in　the　third　and　first　figures。　If　the　syllogism



is　negative；　the　question　is　begged　when　identical　predicates　are



denied　of　the　same　subject；　and　both　premisses　do　not　beg　the　question



indifferently　（in　a　similar　way　the　question　may　be　begged　in　the



middle　figure）；　because　the　terms　in　negative　syllogisms　are　not



convertible。　In　scientific　demonstrations　the　question　is　begged



when　the　terms　are　really　related　in　the　manner　described；　in



dialectical　arguments　when　they　are　according　to　common　opinion　so



related。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　17







　　The　objection　that　'this　is　not　the　reason　why　the　result　is　false'；



which　we　frequently　make　in　argument；　is　made　primarily　in　the　case　of



a　reductio　ad　impossibile；　to　rebut　the　proposition　which　was　being



proved　by　the　reduction。　For　unless　a　man　has　contradicted　this



proposition　he　will　not　say；　'False　cause'；　but　urge　that　something



false　has　been　assumed　in　the　earlier　parts　of　the　argument；　nor



will　he　use　the　formula　in　the　case　of　an　ostensive　proof；　for　here



what　one　denies　is　not　assumed　as　a　premiss。　Further　when　anything



is　refuted　ostensively　by　the　terms　ABC；　it　cannot　be　objected　that



the　syllogism　does　not　depend　on　the　assumption　laid　down。　For　we



use　the　expression　'false　cause'；　when　the　syllogism　is　concluded　in



spite　of　the　refutation　of　this　position；　but　that　is　not　possible



in　ostensive　proofs：　since　if　an　assumption　is　refuted；　a　syllogism



can　no　longer　be　drawn　in　reference　to　it。　It　is　clear　then　that　the



expression　'false　cause'　can　only　be　used　in　the　case　of　a　reductio　ad



impossibile；　and　when　the　original　hypothesis　is　so　related　to　the



impossible　conclusion；　that　the　conclusion　results　indifferently



whether　the　hypothesis　is　made　or　not。　The　most　obvious　case　of　the



irrelevance　of　an　assumption　to　a　conclusion　which　is　false　is　when



a　syllogism　drawn　from　middle　terms　to　an　impossible　conclusion　is



independent　of　the　hypothesis；　as　we　have　explained　in　the　Topics。　For



to　put　that　which　is　not　the　cause　as　the　cause；　is　just　this：　e。g。　if



a　man；　wishing　to　prove　that　the　diagonal　of　the　square　is



incommensurate　with　the　side；　should　try　to　prove　Zeno's　theorem



that　motion　is　impossible；　and　so　establish　a　reductio　ad　impossibile：



for　Zeno's　false　theorem　has　no　connexion　at　all　with　the　original



assumption。　Another　case　is　where　the　impossible　conclusion　is



connected　with　the　hypothesis；　but　does　not　result　from　it。　This　may



happen　whether　one　traces　the　connexion　upwards　or　downwards；　e。g。



if　it　is　laid　down　that　A　belongs　to　B；　B　to　C；　and　C　to　D；　and　it



should　be　false　that　B　belongs　to　D：　for　if　we　eliminated　A　and



assumed　all　the　same　that　B　belongs　to　C　and　C　to　D；　the　false



conclusion　would　not　depend　on　the　original　hypothesis。　Or　again　trace



the　connexion　upwards；　e。g。　suppose　that　A　belongs　to　B；　E　to　A　and



F　to　E；　it　being　false　that　F　belongs　to　A。　In　this　way　too　the



impossible　conclusion　would　result；　though　the　original　hypothesis



were　eliminated。　But　the　impossible　conclusion　ought　to　be　connected



with　the　original　terms：　in　this　way　it　will　depend　on　the　hypothesis；



e。g。　when　one　traces　the　connexion　downwards；　the　impossible



conclusion　must　be　connected　with　that　term　which　is　predicate　in



the　hypothesis：　for　if　it　is　impossible　that　A　should　belong　to　D；　the



false　conclusion　will　no　longer　result　after　A　has　been　eliminated。　If



one　traces　the　connexion　upwards；　the　impossible　conclusion　must　be



connected　with　that　term　which　is　subject　in　the　hypothesis：　for　if　it



is　impossible　that　F　should　belong　to　B；　the　impossible　conclusion



will　disappear　if　B　is　eliminated。　Similarly　when　the　syllogisms　are



negative。



　　It　is　clear　then　that　when　the　impossibility　is　not　related　to　the



original　terms；　the　false　conclusion　does　not　result　on　account　of　the



assumption。　Or　perhaps　even　so　it　may　sometimes　be　independent。　For　if



it　were　laid　down　that　A　belongs　not　to　B　but　to　K；　and　that　K　belongs



to　C　and　C　to　D；　the　impossible　conclusion　would　still　stand。



Similarly　if　one　takes　the　terms　in　an　ascending　series。



Consequently　since　the　impossibility　results　whether　the　first



assumption　is　suppressed　or　not；　it　would　appear　to　be　independent



of　that　assumption。　Or　perhaps　we　ought　not　to　understand　the



statement　that　the　false　conclusion　results　independently　of　the



assumption；　in　the　sense　that　if　something　else　were　supposed　the



impossibility　would　result；　but　rather　we　mean　that　when　the　first



assumption　is　eliminated；　the　same　impossibility　results　through　the



remaining　premisses；　since　it　is　not　perhaps　absurd　that　the　same



false　result　should　follow　from　several　hypotheses；　e。g。　that



parallels　meet；　both　on　the　assumption　that　the　interior　angle　is



greater　than　the　exterior　and　on　the　assumption　that　a　triangle



contains　more　than　two　right　angles。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　18







　　A　false　argument　depends　on　the　first　false　statement　in　it。　Every



syllogism　is　made　out　of　two　or　more　premisses。　If　then　the　false



conclusion　is　drawn　from　two　premisses；　one　or　both　of　them　must　be



false：　for　（as　we　proved）　a　false　syllogism　cannot　be　drawn　from　two



premisses。　But　if　the　premisses　are　more　than　two；　e。g。　if　C　is



established　through　A　and　B；　and　these　through　D；　E；　F；　and　G；　one



of　these　higher　propositions　must　be　false；　and　on　this　the　argument



depends：　for　A　and　B　are　inferred　by　means　of　D；　E；　F；　and　G。



Therefore　the　conclusion　and　the　error　results　from　one　of　them。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　19







　　In　order　to　avoid　having　a　syllogism　drawn　against　us　we　must　take



care；　whenever　an　opponent　asks　us　to　admit　the　reason　without　the



conclusions；　not　to　grant　him　the　same　term　twice　over　in　his



premisses；　since　we　know　that　a　syllogism　cannot　be　drawn　without　a



middle　term；　and　that　term　which　is　stated　more　than　once　is　the



middle。　How　we　ought　to　watch　the　middle　in　reference　to　each



conclusion；　is　evident　from　our　knowing　what　kind　of　thesis　is



proved　in　each　figure。　This　will　not　escape　us　since　we　know　how　we



are　maintaining　the　argument。



　　That　which　we　urge　men　to　beware　of　in　their　admissions；　they



ought　in　attack　to　try　to　conceal。　This　will　be　possible　first；　if；



instead　of　drawing　the　conclusions　of　preliminary　syllogisms；　they



take　the　necessary　premisses　and　leave　the　conclusions　in　the　dark；



secondly　if　instead　of　inviting　assent　to　propositions　which　are



closely　connected　they　take