prior analytics-第26部分

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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　as　far　as　possible　those　that　are　not



connected　by　middle　terms。　For　example　suppose　that　A　is　to　be



inferred　to　be　true　of　F；　B；　C；　D；　and　E　being　middle　terms。　One　ought



then　to　ask　whether　A　belongs　to　B；　and　next　whether　D　belongs　to　E；



instead　of　asking　whether　B　belongs　to　C；　after　that　he　may　ask



whether　B　belongs　to　C；　and　so　on。　If　the　syllogism　is　drawn　through



one　middle　term；　he　ought　to　begin　with　that：　in　this　way　he　will　most



likely　deceive　his　opponent。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　20







　　Since　we　know　when　a　syllogism　can　be　formed　and　how　its　terms



must　be　related；　it　is　clear　when　refutation　will　be　possible　and　when



impossible。　A　refutation　is　possible　whether　everything　is　conceded；



or　the　answers　alternate　（one；　I　mean；　being　affirmative；　the　other



negative）。　For　as　has　been　shown　a　syllogism　is　possible　whether　the



terms　are　related　in　affirmative　propositions　or　one　proposition　is



affirmative；　the　other　negative：　consequently；　if　what　is　laid　down　is



contrary　to　the　conclusion；　a　refutation　must　take　place：　for　a



refutation　is　a　syllogism　which　establishes　the　contradictory。　But



if　nothing　is　conceded；　a　refutation　is　impossible：　for　no　syllogism



is　possible　（as　we　saw）　when　all　the　terms　are　negative：　therefore



no　refutation　is　possible。　For　if　a　refutation　were　possible；　a



syllogism　must　be　possible；　although　if　a　syllogism　is　possible　it



does　not　follow　that　a　refutation　is　possible。　Similarly　refutation　is



not　possible　if　nothing　is　conceded　universally：　since　the　fields　of



refutation　and　syllogism　are　defined　in　the　same　way。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　21







　　It　sometimes　happens　that　just　as　we　are　deceived　in　the　arrangement



of　the　terms；　so　error　may　arise　in　our　thought　about　them；　e。g。　if　it



is　possible　that　the　same　predicate　should　belong　to　more　than　one



subject　immediately；　but　although　knowing　the　one；　a　man　may　forget



the　other　and　think　the　opposite　true。　Suppose　that　A　belongs　to　B　and



to　C　in　virtue　of　their　nature；　and　that　B　and　C　belong　to　all　D　in



the　same　way。　If　then　a　man　thinks　that　A　belongs　to　all　B；　and　B　to



D；　but　A　to　no　C；　and　C　to　all　D；　he　will　both　know　and　not　know　the



same　thing　in　respect　of　the　same　thing。　Again　if　a　man　were　to　make　a



mistake　about　the　members　of　a　single　series；　e。g。　suppose　A　belongs



to　B；　B　to　C；　and　C　to　D；　but　some　one　thinks　that　A　belongs　to　all　B；



but　to　no　C：　he　will　both　know　that　A　belongs　to　D；　and　think　that



it　does　not。　Does　he　then　maintain　after　this　simply　that　what　he



knows；　he　does　not　think？　For　he　knows　in　a　way　that　A　belongs　to　C



through　B；　since　the　part　is　included　in　the　whole；　so　that　what　he



knows　in　a　way；　this　he　maintains　he　does　not　think　at　all：　but　that



is　impossible。



　　In　the　former　case；　where　the　middle　term　does　not　belong　to　the



same　series；　it　is　not　possible　to　think　both　the　premisses　with



reference　to　each　of　the　two　middle　terms：　e。g。　that　A　belongs　to



all　B；　but　to　no　C；　and　both　B　and　C　belong　to　all　D。　For　it　turns　out



that　the　first　premiss　of　the　one　syllogism　is　either　wholly　or



partially　contrary　to　the　first　premiss　of　the　other。　For　if　he　thinks



that　A　belongs　to　everything　to　which　B　belongs；　and　he　knows　that　B



belongs　to　D；　then　he　knows　that　A　belongs　to　D。　Consequently　if　again



he　thinks　that　A　belongs　to　nothing　to　which　C　belongs；　he　thinks　that



A　does　not　belong　to　some　of　that　to　which　B　belongs；　but　if　he　thinks



that　A　belongs　to　everything　to　which　B　belongs；　and　again　thinks　that



A　does　not　belong　to　some　of　that　to　which　B　belongs；　these　beliefs



are　wholly　or　partially　contrary。　In　this　way　then　it　is　not



possible　to　think；　but　nothing　prevents　a　man　thinking　one　premiss



o