posterior analytics-第11章

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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　in　one　relation　and　natural



predication　in　the　other。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　20







　　Now；　it　is　clear　that　if　the　predications　terminate　in　both　the



upward　and　the　downward　direction　（by　'upward'　I　mean　the　ascent　to



the　more　universal；　by　'downward'　the　descent　to　the　more　particular）；



the　middle　terms　cannot　be　infinite　in　number。　For　suppose　that　A　is



predicated　of　F；　and　that　the　intermediates…call　them　BB'B〃。。。…are



infinite；　then　clearly　you　might　descend　from　and　find　one　term



predicated　of　another　ad　infinitum；　since　you　have　an　infinity　of



terms　between　you　and　F；　and　equally；　if　you　ascend　from　F；　there



are　infinite　terms　between　you　and　A。　It　follows　that　if　these



processes　are　impossible　there　cannot　be　an　infinity　of



intermediates　between　A　and　F。　Nor　is　it　of　any　effect　to　urge　that



some　terms　of　the　series　AB。。。F　are　contiguous　so　as　to　exclude



intermediates；　while　others　cannot　be　taken　into　the　argument　at



all：　whichever　terms　of　the　series　B。。。I　take；　the　number　of



intermediates　in　the　direction　either　of　A　or　of　F　must　be　finite　or



infinite：　where　the　infinite　series　starts；　whether　from　the　first



term　or　from　a　later　one；　is　of　no　moment；　for　the　succeeding　terms　in



any　case　are　infinite　in　number。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　21







　　Further；　if　in　affirmative　demonstration　the　series　terminates　in



both　directions；　clearly　it　will　terminate　too　in　negative



demonstration。　Let　us　assume　that　we　cannot　proceed　to　infinity　either



by　ascending　from　the　ultimate　term　（by　'ultimate　term'　I　mean　a



term　such　as　was；　not　itself　attributable　to　a　subject　but　itself



the　subject　of　attributes）；　or　by　descending　towards　an　ultimate



from　the　primary　term　（by　'primary　term'　I　mean　a　term　predicable　of　a



subject　but　not　itself　a　subject）。　If　this　assumption　is　justified；



the　series　will　also　terminate　in　the　case　of　negation。　For　a　negative



conclusion　can　be　proved　in　all　three　figures。　In　the　first　figure



it　is　proved　thus：　no　B　is　A；　all　C　is　B。　In　packing　the　interval



B…C　we　must　reach　immediate　propositionsas　is　always　the　case　with



the　minor　premisssince　B…C　is　affirmative。　As　regards　the　other



premiss　it　is　plain　that　if　the　major　term　is　denied　of　a　term　D　prior



to　B；　D　will　have　to　be　predicable　of　all　B；　and　if　the　major　is



denied　of　yet　another　term　prior　to　D；　this　term　must　be　predicable　of



all　D。　Consequently；　since　the　ascending　series　is　finite；　the　descent



will　also　terminate　and　there　will　be　a　subject　of　which　A　is



primarily　non…predicable。　In　the　second　figure　the　syllogism　is；　all　A



is　B；　no　C　is　B；。。no　C　is　A。　If　proof　of　this　is　required；　plainly



it　may　be　shown　either　in　the　first　figure　as　above；　in　the　second



as　here；　or　in　the　third。　The　first　figure　has　been　discussed；　and



we　will　proceed　to　display　the　second；　proof　by　which　will　be　as



follows：　all　B　is　D；　no　C　is　D。。。；　since　it　is　required　that　B



should　be　a　subject　of　which　a　predicate　is　affirmed。　Next；　since　D　is



to　be　proved　not　to　belong　to　C；　then　D　has　a　further　predicate



which　is　denied　of　C。　Therefore；　since　the　succession　of　predicates



affirmed　of　an　ever　higher　universal　terminates；　the　succession　of



predicates　denied　terminates　too。



　　The　third　figure　shows　it　as　follows：　all　B　is　A；　some　B　is　not　C。



Therefore　some　A　is　not　C。　This　premiss；　i。e。　C…B；　will　be　proved



either　in　the　same　figure　or　in　one　of　the　two　figures　discussed



above。　In　the　first　and　second　figures　the　series　terminates。　If　we



use　the　third　figure；　we　shall　take　as　premisses；　all　E　is　B；　some　E



is　not　C；　and　this　premiss　again　will　be　proved　by　a　similar



prosyllogism。　But　since　it　is　assumed　that　the　series　of　descending



subjects　also　terminates；　plainly　the　series　of　more　universal



non…predicables　will　terminate　also。　Even　supposing　that　the　proof



is　not　confined　to　one　method；　but　employs　them　all　and　is　now　in



the　first　figure；　now　in　the　second　or　third…even　so　the　regress



will　terminate；　for　the　methods　are　finite　in　number；　and　if　finite



things　are　combined　in　a　finite　number　of　ways；　the　result　must　be



finite。



　　Thus　it　is　plain　that　the　regress　of　middles　terminates　in　the



case　of　negative　demonstration；　if　it　does　so　also　in　the　case　of



affirmative　demonstration。　That　in　fact　the　regress　terminates　in　both



these　cases　may　be　made　clear　by　the　following　dialectical



considerations。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　22







　　In　the　case　of　predicates　constituting　the　essential　nature　of　a



thing；　it　clearly　terminates；　seeing　that　if　definition　is　possible；



or　in　other　words；　if　essential　form　is　knowable；　and　an　infinite



series　cannot　be　traversed；　predicates　constituting　a　thing's



essential　nature　must　be　finite　in　number。　But　as　regards　predicates



generally　we　have　the　following　prefatory　remarks　to　make。　（1）　We



can　affirm　without　falsehood　'the　white　（thing）　is　walking'；　and



that　big　（thing）　is　a　log'；　or　again；　'the　log　is　big'；　and　'the　man



walks'。　But　the　affirmation　differs　in　the　two　cases。　When　I　affirm



'the　white　is　a　log'；　I　mean　that　something　which　happens　to　be



white　is　a　log…not　that　white　is　the　substratum　in　which　log



inheres；　for　it　was　not　qua　white　or　qua　a　species　of　white　that　the



white　（thing）　came　to　be　a　log；　and　the　white　（thing）　is



consequently　not　a　log　except　incidentally。　On　the　other　hand；　when



I　affirm　'the　log　is　white'；　I　do　not　mean　that　something　else；



which　happens　also　to　be　a　log；　is　white　（as　I　should　if　I　said　'the



musician　is　white；'　which　would　mean　'the　man　who　happens　also　to　be　a



musician　is　white'）；　on　the　contrary；　log　is　here　the　substratum…the



substratum　which　actually　came　to　be　white；　and　did　so　qua　wood　or　qua



a　species　of　wood　and　qua　nothing　else。



　　If　we　must　lay　down　a　rule；　let　us　entitle　the　latter　kind　of



statement　predication；　and　the　former　not　predication　at　all；　or　not



strict　but　accidental　predication。　'White'　and　'log'　will　thus　serve



as　types　respectively　of　predicate　and　subject。



　　We　shall　assume；　then；　that　the　predicate　is　invariably　predicated



strictly　and　not　accidentally　of　the　subject；　for　on　such



predication　demonstrations　depend　for　their　force。　It　follows　from



this　that　when　a　single　attribute　is　predicated　of　a　single　subject；



the　predicate　must　affirm　of　the　subject　either　some　element



constituting　its　essential　nature；　or　that　it　is　in　some　way



qualified；　quantified；　essentially　related；　active；　passive；　placed；



or　dated。