posterior analytics-第9节

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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。







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　　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　are　the　fundamentals　and



so…called　hypotheses　of　syllogism。　Assume　them　as　they　have　been



stated；　and　proof　is　bound　to　follow…proof　that　A　inheres　in　C　through



B；　and　again　that　A　inheres　in　B　through　some　other　middle　term；　and



similarly　that　B　inheres　in　C。　If　our　reasoning　aims　at　gaining



credence　and　so　is　merely　dialectical；　it　is　obvious　that　we　have　only



to　see　that　our　inference　is　based　on　premisses　as　credible　as



possible：　so　that　if　a　middle　term　between　A　and　B　is　credible



though　not　real；　one　can　reason　through　it　and　complete　a



dialectical　syllogism。　If；　however；　one　is　aiming　at　truth；　one　must



be　guided　by　the　real　connexions　of　subjects　and　attributes。　Thus：



since　there　are　attributes　which　are　predicated　of　a　subject



essentially　or　naturally　and　not　coincidentally…not；　that　is；　in　the



sense　in　which　we　say　'That　white　（thing）　is　a　man'；　which　is　not



the　same　mode　of　predication　as　when　we　say　'The　man　is　white'：　the



man　is　white　not　because　he　is　something　else　but　because　he　is　man；



but　the　white　is　man　because　'being　white'　coincides　with　'humanity'



within　one　substratum…therefore　there　are　terms　such　as　are



naturally　subjects　of　predicates。　Suppose；　then；　C　such　a　term　not



itself　attributable　to　anything　else　as　to　a　subject；　but　the



proximate　subject　of　the　attribute　Bi。e。　so　that　B…C　is　immediate；



suppose　further　E　related　immediately　to　F；　and　F　to　B。　The　first



question　is；　must　this　series　terminate；　or　can　it　proceed　to



infinity？　The　second　question　is　as　follows：　Suppose　nothing　is



essentially　predicated　of　A；　but　A　is　predicated　primarily　of　H　and　of



no　intermediate　prior　term；　and　suppose　H　similarly　related　to　G　and　G



to　B；　then　must　this　series　also　terminate；　or　can　it　too　proceed　to



infinity？　There　is　this　much　difference　between　the　questions：　the



first　is；　is　it　possible　to　start　from　that　which　is　not　itself



attributable　to　anything　else　but　is　the　subject　of　attributes；　and



ascend　to　infinity？　The　second　is　the　problem　whether　one　can　start



from　that　which　is　a　predicate　but　not　itself　a　subject　of　predicates；



and　descend　to　infinity？　A　third　question　is；　if　the　extreme　terms　are



fixed；　can　there　be　an　infinity　of　middles？　I　mean　this：　suppose　for



example　that　A　inheres　in　C　and　B　is　intermediate　between　them；　but



between　B　and　A　there　are　other　middles；　and　between　these　again　fresh



middles；　can　these　proceed　to　infinity　or　can　they　not？　This　is　the



equivalent　of　inquiring；　do　demonstrations　proceed　to　infinity；　i。e。



is　everything　demonstrable？　Or　do　ultimate　subject　and　primary



attribute　limit　one　another？



　　I　hold　that　the　same　questions　arise　with　regard　to　negative



conclusions　and　premisses：　viz。　if　A　is　attributable　to　no　B；　then



either　this　predication　will　be　primary；　or　there　will　be　an



intermediate　term　prior　to　B　to　which　a　is　not　attributable…G；　let



us　say；　which　is　attributable　to　all　B…and　there　may　still　be



another　term　H　prior　to　G；　which　is　attributable　to　all　G。　The　same



questions　arise；　I　say；　because　in　these　cases　too　either　the　series



of　prior　terms　to　which　a　is　not　attributable　is　infinite　or　it



terminates。



　　One　cannot　ask　the　same　questions　in　the　case　of　reciprocating



terms；　since　when　subject　and　predicate　are　convertible　there　is





neither　primary　nor　ultimate　subject；　seeing　that　all　the



reciprocals　qua　subjects　stand　in　the　same　relation　to　one　another；



whether　we　say　that　the　subject　has　an　infinity　of　attributes　or



that　both　subjects　and　attributes…and　we　raised　the　question　in　both



cases…are　infinite　in　number。　These　questions　then　cannot　be



asked…unless；　indeed；　the　terms　can　reciprocate　by　two　different



modes；　by　accidental　predication　i