posterior analytics- 第13部分

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　true　that　the　basic　truths　are　much　fewer　than



the　conclusions；　for　the　basic　truths　are　the　premisses；　and　the



premisses　are　formed　by　the　apposition　of　a　fresh　extreme　term　or



the　interposition　of　a　fresh　middle。　Moreover；　the　number　of



conclusions　is　indefinite；　though　the　number　of　middle　terms　is



finite；　and　lastly　some　of　the　basic　truths　are　necessary；　others



variable。



　　Looking　at　it　in　this　way　we　see　that；　since　the　number　of



conclusions　is　indefinite；　the　basic　truths　cannot　be　identical　or



limited　in　number。　If；　on　the　other　hand；　identity　is　used　in



another　sense；　and　it　is　said；　e。g。　'these　and　no　other　are　the



fundamental　truths　of　geometry；　these　the　fundamentals　of　calculation；



these　again　of　medicine'；　would　the　statement　mean　anything　except



that　the　sciences　have　basic　truths？　To　call　them　identical　because



they　are　self…identical　is　absurd；　since　everything　can　be



identified　with　everything　in　that　sense　of　identity。　Nor　again　can



the　contention　that　all　conclusions　have　the　same　basic　truths　mean



that　from　the　mass　of　all　possible　premisses　any　conclusion　may　be



drawn。　That　would　be　exceedingly　naive；　for　it　is　not　the　case　in



the　clearly　evident　mathematical　sciences；　nor　is　it　possible　in



analysis；　since　it　is　the　immediate　premisses　which　are　the　basic



truths；　and　a　fresh　conclusion　is　only　formed　by　the　addition　of　a　new



immediate　premiss：　but　if　it　be　admitted　that　it　is　these　primary



immediate　premisses　which　are　basic　truths；　each　subject…genus　will



provide　one　basic　truth。　If；　however；　it　is　not　argued　that　from　the



mass　of　all　possible　premisses　any　conclusion　may　be　proved；　nor　yet



admitted　that　basic　truths　differ　so　as　to　be　generically　different



for　each　science；　it　remains　to　consider　the　possibility　that；　while



the　basic　truths　of　all　knowledge　are　within　one　genus；　special



premisses　are　required　to　prove　special　conclusions。　But　that　this



cannot　be　the　case　has　been　shown　by　our　proof　that　the　basic　truths



of　things　generically　different　themselves　differ　generically。　For



fundamental　truths　are　of　two　kinds；　those　which　are　premisses　of



demonstration　and　the　subject…genus；　and　though　the　former　are　common；



the　latter…number；　for　instance；　and　magnitude…are　peculiar。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　33







　　Scientific　knowledge　and　its　object　differ　from　opinion　and　the



object　of　opinion　in　that　scientific　knowledge　is　commensurately



universal　and　proceeds　by　necessary　connexions；　and　that　which　is



necessary　cannot　be　otherwise。　So　though　there　are　things　which　are



true　and　real　and　yet　can　be　otherwise；　scientific　knowledge　clearly



does　not　concern　them：　if　it　did；　things　which　can　be　otherwise



would　be　incapable　of　being　otherwise。　Nor　are　they　any　concern　of



rational　intuition…by　rational　intuition　I　mean　an　originative



source　of　scientific　knowledge…nor　of　indemonstrable　knowledge；



which　is　the　grasping　of　the　immediate　premiss。　Since　then　rational



intuition；　science；　and　opinion；　and　what　is　revealed　by　these



terms；　are　the　only　things　that　can　be　'true'；　it　follows　that　it　is



opinion　that　is　concerned　with　that　which　may　be　true　or　false；　and



can　be　otherwise：　opinion　in　fact　is　the　grasp　of　a　premiss　which　is



immediate　but　not　necessary。　This　view　also　fits　the　observed　facts；



for　opinion　is　unstable；　and　so　is　the　kind　of　being　we　have　described



as　its　object。　Besides；　when　a　man　thinks　a　truth　incapable　of　being



otherwise　he　always　thinks　that　he　knows　it；　never　that　he　opines



it。　He　thinks　that　he　opines　when　he　thinks　that　a　connexion；　though



actually　so；　may　quite　easily　be　otherwise；　for　he　believes　that



such　is　the　proper　object　of　opinion；　while　the　necessary　is　the



object　of　knowledg