posterior analytics-第7章

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well　as　where　one's　belief　is　acquired　by　inference。　The　error；



however；　that　consists　in　a　direct　belief　is　without　complication；　but



the　error　resulting　from　inference…which　here　concerns　us…takes　many



forms。　Thus；　let　A　be　atomically　disconnected　from　all　B：　then　the



conclusion　inferred　through　a　middle　term　C；　that　all　B　is　A；　will



be　a　case　of　error　produced　by　syllogism。　Now；　two　cases　are　possible。



Either　（a）　both　premisses；　or　（b）　one　premiss　only；　may　be　false。



（a）　If　neither　A　is　an　attribute　of　any　C　nor　C　of　any　B；　whereas



the　contrary　was　posited　in　both　cases；　both　premisses　will　be



false。　（C　may　quite　well　be　so　related　to　A　and　B　that　C　is　neither



subordinate　to　A　nor　a　universal　attribute　of　B：　for　B；　since　A　was



said　to　be　primarily　disconnected　from　B；　cannot　have　a　genus；　and　A



need　not　necessarily　be　a　universal　attribute　of　all　things。



Consequently　both　premisses　may　be　false。）　On　the　other　hand；　（b）



one　of　the　premisses　may　be　true；　though　not　either　indifferently



but　only　the　major　A…C　since；　B　having　no　genus；　the　premiss　C…B



will　always　be　false；　while　A…C　may　be　true。　This　is　the　case　if；



for　example；　A　is　related　atomically　to　both　C　and　B；　because　when　the



same　term　is　related　atomically　to　more　terms　than　one；　neither　of



those　terms　will　belong　to　the　other。　It　is；　of　course；　equally　the



case　if　A…C　is　not　atomic。



　　Error　of　attribution；　then；　occurs　through　these　causes　and　in



this　form　only…for　we　found　that　no　syllogism　of　universal　attribution



was　possible　in　any　figure　but　the　first。　On　the　other　hand；　an



error　of　non…attribution　may　occur　either　in　the　first　or　in　the



second　figure。　Let　us　therefore　first　explain　the　various　forms　it



takes　in　the　first　figure　and　the　character　of　the　premisses　in　each



case。



　　（c）　It　may　occur　when　both　premisses　are　false；　e。g。　supposing　A



atomically　connected　with　both　C　and　B；　if　it　be　then　assumed　that



no　C　is　and　all　B　is　C；　both　premisses　are　false。



　　（d）　It　is　also　possible　when　one　is　false。　This　may　be　either



premiss　indifferently。　A…C　may　be　true；　C…B　false…A…C　true　because　A



is　not　an　attribute　of　all　things；　C…B　false　because　C；　which　never



has　the　attribute　A；　cannot　be　an　attribute　of　B；　for　if　C…B　were



true；　the　premiss　A…C　would　no　longer　be　true；　and　besides　if　both



premisses　were　true；　the　conclusion　would　be　true。　Or　again；　C…B　may



be　true　and　A…C　false；　e。g。　if　both　C　and　A　contain　B　as　genera；　one



of　them　must　be　subordinate　to　the　other；　so　that　if　the　premiss　takes



the　form　No　C　is　A；　it　will　be　false。　This　makes　it　clear　that　whether



either　or　both　premisses　are　false；　the　conclusion　will　equally　be



false。



　　In　the　second　figure　the　premisses　cannot　both　be　wholly　false；



for　if　all　B　is　A；　no　middle　term　can　be　with　truth　universally



affirmed　of　one　extreme　and　universally　denied　of　the　other：　but



premisses　in　which　the　middle　is　affirmed　of　one　extreme　and　denied　of



the　other　are　the　necessary　condition　if　one　is　to　get　a　valid



inference　at　all。　Therefore　if；　taken　in　this　way；　they　are　wholly



false；　their　contraries　conversely　should　be　wholly　true。　But　this



is　impossible。　On　the　other　hand；　there　is　nothing　to　prevent　both



premisses　being　partially　false；　e。g。　if　actually　some　A　is　C　and　some



B　is　C；　then　if　it　is　premised　that　all　A　is　C　and　no　B　is　C；　both



premisses　are　false；　yet　partially；　not　wholly；　false。　The　same　is



true　if　the　major　is　made　negative　instead　of　the　minor。　Or　one



premiss　may　be　wholly　false；　and　it　may　be　either　of　them。　Thus；



supposing　that　actually　an　attribute　of　all　A　must　also　be　an



attribute　of　all　B；　then　if　C　is　yet　taken　to　be　a　universal　attribute



of　all　but　universally　non…attributable　to　B；　C…A　will　be　true　but　C…B



false。　Again；　actually　that　which　is　an　attribute　of　no　B　will　not



be　an　attribute　of　all　A　either；　for　if　it　be　an　attribute　of　all　A；



it　will　also　be　an　attribute　of　all　B；　which　is　contrary　to



supposition；　but　if　C　be　nevertheless　assumed　to　be　a　universal



attribute　of　A；　but　an　attribute　of　no　B；　then　the　premiss　C…B　is　true



but　the　major　is　false。　The　case　is　similar　if　the　major　is　made　the



negative　premiss。　For　in　fact　what　is　an　attribute　of　no　A　will　not　be



an　attribute　of　any　B　either；　and　if　it　be　yet　assumed　that　C　is



universally　non…attributable　to　A；　but　a　universal　attribute　of　B；　the



premiss　C…A　is　true　but　the　minor　wholly　false。　Again；　in　fact　it　is



false　to　assume　that　that　which　is　an　attribute　of　all　B　is　an



attribute　of　no　A；　for　if　it　be　an　attribute　of　all　B；　it　must　be　an



attribute　of　some　A。　If　then　C　is　nevertheless　assumed　to　be　an



attribute　of　all　B　but　of　no　A；　C…B　will　be　true　but　C…A　false。



　　It　is　thus　clear　that　in　the　case　of　atomic　propositions　erroneous



inference　will　be　possible　not　only　when　both　premisses　are　false



but　also　when　only　one　is　false。







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　　In　the　case　of　attributes　not　atomically　connected　with　or



disconnected　from　their　subjects；　（a）　（i）　as　long　as　the　false



conclusion　is　inferred　through　the　'appropriate'　middle；　only　the



major　and　not　both　premisses　can　be　false。　By　'appropriate　middle'　I



mean　the　middle　term　through　which　the　contradictory…i。e。　the



true…conclusion　is　inferrible。　Thus；　let　A　be　attributable　to　B



through　a　middle　term　C：　then；　since　to　produce　a　conclusion　the



premiss　C…B　must　be　taken　affirmatively；　it　is　clear　that　this　premiss



must　always　be　true；　for　its　quality　is　not　changed。　But　the　major　A…C



is　false；　for　it　is　by　a　change　in　the　quality　of　A…C　that　the



conclusion　becomes　its　contradictory…i。e。　true。　Similarly　（ii）　if



the　middle　is　taken　from　another　series　of　predication；　e。g。　suppose　D



to　be　not　only　contained　within　A　as　a　part　within　its　whole　but



also　predicable　of　all　B。　Then　the　premiss　D…B　must　remain



unchanged；　but　the　quality　of　A…D　must　be　changed；　so　that　D…B　is



always　true；　A…D　always　false。　Such　error　is　practically　identical



with　that　which　is　inferred　through　the　'appropriate'　middle。　On　the



other　hand；　（b）　if　the　conclusion　is　not　inferred　through　the



'appropriate'　middle…（i）　when　the　middle　is　subordinate　to　A　but　is



predicable　of　no　B；　both　premisses　must　be　false；　because　if　there



is　to　be　a　conclusion　both　must　be　posited　as　asserting　the　contrary



of　what　is　actually　the　fact；　and　so　posited　both　become　false：　e。g。



suppose　that　actually　all　D　is　A　but　no　B　is　D；　then　if　these



premisses　are　changed　in　quality；　a　conclusion　will　follow　and　both　of



the　new　premisses　will　be　false。　When；　however；　（ii）　the　middle　D　is



not　subordinate　to　A；　A…D　will　be　true；　D…B　false…A…D　true　because　A



was　not　subordinate　to　D；　D…B　false　because　if　it　had　been　true；　the



conclusion　too　would　have　been　true；　but　it　is　ex　hypothesi　false。



　　When　the　erroneous　inference　is　in　the　second　figure；　both　premisses



cannot　be　entirely　false；　since　if　B　is　subordinate　to　A；　there　can　be



no　middle　predicable　of　all　of　one　extreme　and　of　none　of　the　other；



as　was　stated　before。　One　premiss；　however；　may　be　false；　and　it　may



be　either　of　them。　Thus；　if　C　is　actually　an　attribute　of　both　A　and



B；　but　is　assumed　to　be　an　attribute　of　A　only　and　not　of　B；　C…A



will　be　true；　C…B　false：　or　again　if　C　be　assumed　to　be　attributable



to　B　but　to　no　A；　C…B　will　be　true；　C…A　false。



　　We　have　stated　when　and　through　what　kinds　of　premisses　error　will



result　in　cases　where　the　erroneous　conclusion　is　negative。　If　the



conclusion　is　affirmative；　（a）　（i）　it　may　be　inferred　through　the



'appropriate'　middle　term。　In　this　case　both　premisses　cannot　be　false



since；　as　we　said　before；　C…B　must　remain　unchanged　if　there　is　to



be　a　conclusion；　and　consequently　A…C；　the　quality　of　which　is



changed；　will　always　be　false。　This　is　equally　true　if　（ii）　the　middle



is　taken　from　another　series　of　predication；　as　was　stated　to　be　the



case　also　with　regard　to　negative　error；　for　D…B　must　remain



unchanged；　while　the　quality　of　A…D　must　be　converted；　and　the　type　of



error　is　the　same　as　before。



　　（b）　The　middle　may　be　inappropriate。　Then　（i）　if　D　is　subordinate　to



A；　A…D　will　be　true；　but　D…B　false；　since　A　may　quite　well　be



predicable　of　several　terms　no　one　of　which　can　be　subordinated　to



another。　If；　however；　（ii）　D　is　not　subordinate　to　A；　obviously　A…D；



since　it　is　affirmed；　will　always　be　false；　while　D…B　may　be　either



true　or　false；　for　A　may　very　well　be　an　attribute　of　no　D；　whereas



all　B　is　D；　e。g。　no　science　is　animal；　all　music　is　science。　Equally



well　A　may　be　an　attribute　of　no　D；　and　D　of　no　B。　It　emerges；　then；



that　if　the　middle　term　is　not　subordinate　to　the　major；　not　only　both



premisses　but　either　singly　may　be　false。



　　Thus　we　have　made　it　clear　how　many　varieties　of　erroneous　inference



are　liable　to　happen　and　through　what　kinds　of　premisses　they　occur；



in　the　case　both　of　immediate　and　of　demonstrable　truths。







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　　It　is　also　clear　that　the　loss　of　any　one　of　the　senses　entails



the　loss　of　a　corresponding　portion　of　knowledge；　and　that；　since　we



learn　either　by　induction　or　by　demonstration；　this　knowledge　cannot



be　acquired。　Thus　demonstration　develops　from　universals；　induction



from　particulars；　but　since　it　is　possible　to　familiarize　the　pupil



with　even　the　so…called　mathematical　abstractions　only　through



induction…i。e。　only　because　each　subject　genus　possesses；　in　virtue　of



a　determinate　mathematical　character；　certain　properties　which　can



be　treated　as　separate　even　though　they　do　not　exist　in　isolation…it



is　consequently　impossible　to　come　to　grasp　universals　except



through　induction。　But　induction　is　impossible　for　those　who　have



not　sense…perception。　For　it　is　sense…perception　alone　which　is



adequate　for　grasping　the　particulars：　they　cannot　be　objects　of



scientific　knowledge；　because　neither　can　universals　give　us　knowledge



of　them　without　induction；　nor　can　we　get　it　through　induction　without



sense…perception。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　19







　　Every　syllogism　is　effected　by　means　of　three　terms。　One　kind　of



syllogism　serves　to　prove　that　A　inheres　in　C　by　showing　that　A



inheres　in　B　and　B　in　C；　the　other　is　negative　and　one　of　its



premisses　asserts　one　term　of　another；　while　the　other　denies　one　term



of　another。　It　is　clear；　then；　that　these　a