posterior analytics-第14部分

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them；　and　'no　C　is　A'　is　the　conclusion；　'no　B　is　A'　one　of　its



premisses。　For　the　destructive　result　of　reductio　ad　impossibile　is



not　a　proper　conclusion；　nor　are　its　antecedents　proper　premisses。



On　the　contrary：　the　constituents　of　syllogism　are　premisses　related



to　one　another　as　whole　to　part　or　part　to　whole；　whereas　the



premisses　A…C　and　A…B　are　not　thus　related　to　one　another。　Now　the



superior　demonstration　is　that　which　proceeds　from　better　known　and



prior　premisses；　and　while　both　these　forms　depend　for　credence　on　the



not…being　of　something；　yet　the　source　of　the　one　is　prior　to　that



of　the　other。　Therefore　negative　demonstration　will　have　an



unqualified　superiority　to　reductio　ad　impossibile；　and　affirmative



demonstration；　being　superior　to　negative；　will　consequently　be



superior　also　to　reductio　ad　impossibile。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　27







　　The　science　which　is　knowledge　at　once　of　the　fact　and　of　the



reasoned　fact；　not　of　the　fact　by　itself　without　the　reasoned　fact；　is



the　more　exact　and　the　prior　science。



　　A　science　such　as　arithmetic；　which　is　not　a　science　of　properties



qua　inhering　in　a　substratum；　is　more　exact　than　and　prior　to　a



science　like　harmonics；　which　is　a　science　of　pr；operties　inhering



in　a　substratum；　and　similarly　a　science　like　arithmetic；　which　is



constituted　of　fewer　basic　elements；　is　more　exact　than　and　prior　to



geometry；　which　requires　additional　elements。　What　I　mean　by



'additional　elements'　is　this：　a　unit　is　substance　without　position；



while　a　point　is　substance　with　position；　the　latter　contains　an



additional　element。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　28







　　A　single　science　is　one　whose　domain　is　a　single　genus；　viz。　all　the



subjects　constituted　out　of　the　primary　entities　of　the　genus…i。e。　the



parts　of　this　total　subject…and　their　essential　properties。



　　One　science　differs　from　another　when　their　basic　truths　have



neither　a　common　source　nor　are　derived　those　of　the　one　science



from　those　the　other。　This　is　verified　when　we　reach　the



indemonstrable　premisses　of　a　science；　for　they　must　be　within　one



genus　with　its　conclusions：　and　this　again　is　verified　if　the



conclusions　proved　by　means　of　them　fall　within　one　genus…i。e。　are



homogeneous。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　29







　　One　can　have　several　demonstrations　of　the　same　connexion　not　only



by　taking　from　the　same　series　of　predication　middles　which　are



other　than　the　immediately　cohering　term　e。g。　by　taking　C；　D；　and　F



severally　to　prove　A…Bbut　also　by　taking　a　middle　from　another



series。　Thus　let　A　be　change；　D　alteration　of　a　property；　B　feeling



pleasure；　and　G　relaxation。　We　can　then　without　falsehood　predicate



D　of　B　and　A　of　D；　for　he　who　is　pleased　suffers　alteration　of　a



property；　and　that　which　alters　a　property　changes。　Again；　we　can



predicate　A　of　G　without　falsehood；　and　G　of　B；　for　to　feel　pleasure



is　to　relax；　and　to　relax　is　to　change。　So　the　conclusion　can　be　drawn



through　middles　which　are　different；　i。e。　not　in　the　same　series…yet



not　so　that　neither　of　these　middles　is　predicable　of　the　other；　for



they　must　both　be　attributable　to　some　one　subject。



　　A　further　point　worth　investigating　is　how　many　ways　of　proving



the　same　conclusion　can　be　obtained　by　varying　the　figure；







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　30







　　There　is　no　knowledge　by　demonstration　of　chance　conjunctions；　for



chance　conjunctions　exist　neither　by　necessity　nor　as　general



connexions　but　comprise　what　comes　to　be　as　something　distinct　from



these。　Now　demonstration　is　concerned　only　with　one　or　other　of



these　two；　for　all　reasoning　proceeds　from　necessary　or　general



premisses；　the　conclusion　being　necessary　if　the　premisses　are



necessary　and　general　if　the　premisses　are　general。　Consequently；　if



chance　conjunctions　are　neither　general　nor　necessary；　they　are　not



demonstrable。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　31







　　Scientific　knowledge　is　not　possible　through　the　act　of



perception。　Even　if　perception　as　a　faculty　is　of　'the　such'　and　not



merely　of　a　'this　somewhat'；　yet　one　must　at　any　rate　actually



perceive　a　'this　somewhat'；　and　at　a　definite　present　place　and



time：　but　that　which　is　commensurately　universal　and　true　in　all　cases



one　cannot　perceive；　since　it　is　not　'this'　and　it　is　not　'now'；　if　it



were；　it　would　not　be　commensurately　universal…the　term　we　apply　to



what　is　always　and　everywhere。　Seeing；　therefore；　that



demonstrations　are　commensurately　universal　and　universals



imperceptible；　we　clearly　cannot　obtain　scientific　knowledge　by　the



act　of　perception：　nay；　it　is　obvious　that　even　if　it　were　possible　to



perceive　that　a　triangle　has　its　angles　equal　to　two　right　angles；



we　should　still　be　looking　for　a　demonstration…we　should　not　（as



some　say）　possess　knowledge　of　it；　for　perception　must　be　of　a



particular；　whereas　scientific　knowledge　involves　the　recognition　of



the　commensurate　universal。　So　if　we　were　on　the　moon；　and　saw　the



earth　shutting　out　the　sun's　light；　we　should　not　know　the　cause　of



the　eclipse：　we　should　perceive　the　present　fact　of　the　eclipse；　but



not　the　reasoned　fact　at　all；　since　the　act　of　perception　is　not　of



the　commensurate　universal。　I　do　not；　of　course；　deny　that　by　watching



the　frequent　recurrence　of　this　event　we　might；　after　tracking　the



commensurate　universal；　possess　a　demonstration；　for　the



commensurate　universal　is　elicited　from　the　several　groups　of



singulars。



　　The　commensurate　universal　is　precious　because　it　makes　clear　the



cause；　so　that　in　the　case　of　facts　like　these　which　have　a　cause



other　than　themselves　universal　knowledge　is　more　precious　than



sense…perceptions　and　than　intuition。　（As　regards　primary　truths　there



is　of　course　a　different　account　to　be　given。）　Hence　it　is　clear



that　knowledge　of　things　demonstrable　cannot　be　acquired　by



perception；　unless　the　term　perception　is　applied　to　the　possession　of



scientific　knowledge　through　demonstration。　Nevertheless　certain



points　do　arise　with　regard　to　connexions　to　be　proved　which　are



referred　for　their　explanation　to　a　failure　in　sense…perception：　there



are　cases　when　an　act　of　vision　would　terminate　our　inquiry；　not



because　in　seeing　we　should　be　knowing；　but　because　we　should　have



elicited　the　universal　from　seeing；　if；　for　example；　we　saw　the



pores　in　the　glass　and　the　light　passing　through；　the　reason　of　the



kindling　would　be　clear　to　us　because　we　should　at　the　same　time　see



it　in　each　instance　and　intuit　that　it　must　be　so　in　all　instances。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　32







　　All　syllogisms　cannot　have　the　same　basic　truths。　This　may　be



shown　first　of　all　by　the　following　dialectical　considerations。　（1）



Some　syllogisms　are　true　and　some　false：　for　though　a　true　inference



is　possible　from　false　premisses；　yet　this　occurs　once　only…I　mean



if　A　for　instance；　is　truly　predicable　of　C；　but　B；　the　middle；　is



false；　both　A…B　and　B…C　being　false；　nevertheless；　if　middles　are



taken　to　prove　these　premisses；　they　will　be　false　because　every



conclusion　which　is　a　falsehood　has　false　premisses；　while　true



conclusions　have　true　premisses；　and　false　and　true　differ　in　kind。



Then　again；　（2）　falsehoods　are　not　all　derived　from　a　single　identical



set　of　principles：　there　are　falsehoods　which　are　the　contraries　of



one　another　and　cannot　coexist；　e。g。　'justice　is　injustice'；　and



'justice　is　cowardice'；　'man　is　horse'；　and　'man　is　ox'；　'the　equal　is



greater'；　and　'the　equal　is　less。'　From　established　principles　we



may　argue　the　case　as　follows；　confining…ourselves　therefore　to　true



conclusions。　Not　even　all　these　are　inferred　from　the　same　basic



truths；　many　of　them　in　fact　have　basic　truths　which　differ



generically　and　are　not　transferable；　units；　for　instance；　which　are



without　position；　cannot　take　the　place　of　points；　which　have



position。　The　transferred　terms　could　only　fit　in　as　middle　terms　or



as　major　or　minor　terms；　or　else　have　some　of　the　other　terms



between　them；　others　outside　them。



　　Nor　can　any　of　the　common　axioms…such；　I　mean；　as　the　law　of



excluded　middle…serve　as　premisses　for　the　proof　of　all　conclusions。



For　the　kinds　of　being　are　different；　and　some　attributes　attach　to



quanta　and　some　to　qualia　only；　and　proof　is　achieved　by　means　of



the　common　axioms　taken　in　conjunction　with　these　several　kinds　and



their　attributes。



　　Again；　it　is　not