posterior analytics-第12章

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



or　dated。



　　（2）　Predicates　which　signify　substance　signify　that　the　subject　is



identical　with　the　predicate　or　with　a　species　of　the　predicate。



Predicates　not　signifying　substance　which　are　predicated　of　a



subject　not　identical　with　themselves　or　with　a　species　of



themselves　are　accidental　or　coincidental；　e。g。　white　is　a



coincident　of　man；　seeing　that　man　is　not　identical　with　white　or　a



species　of　white；　but　rather　with　animal；　since　man　is　identical



with　a　species　of　animal。　These　predicates　which　do　not　signify



substance　must　be　predicates　of　some　other　subject；　and　nothing　can　be



white　which　is　not　also　other　than　white。　The　Forms　we　can　dispense



with；　for　they　are　mere　sound　without　sense；　and　even　if　there　are



such　things；　they　are　not　relevant　to　our　discussion；　since



demonstrations　are　concerned　with　predicates　such　as　we　have　defined。



　　（3）　If　A　is　a　quality　of　B；　B　cannot　be　a　quality　of　A…a　quality



of　a　quality。　Therefore　A　and　B　cannot　be　predicated　reciprocally　of





one　another　in　strict　predication：　they　can　be　affirmed　without



falsehood　of　one　another；　but　not　genuinely　predicated　of　each



other。　For　one　alternative　is　that　they　should　be　substantially



predicated　of　one　another；　i。e。　B　would　become　the　genus　or



differentia　of　A…the　predicate　now　become　subject。　But　it　has　been



shown　that　in　these　substantial　predications　neither　the　ascending



predicates　nor　the　descending　subjects　form　an　infinite　series；　e。g。



neither　the　series；　man　is　biped；　biped　is　animal；　&c。；　nor　the　series



predicating　animal　of　man；　man　of　Callias；　Callias　of　a　further。



subject　as　an　element　of　its　essential　nature；　is　infinite。　For　all



such　substance　is　definable；　and　an　infinite　series　cannot　be



traversed　in　thought：　consequently　neither　the　ascent　nor　the



descent　is　infinite；　since　a　substance　whose　predicates　were



infinite　would　not　be　definable。　Hence　they　will　not　be　predicated



each　as　the　genus　of　the　other；　for　this　would　equate　a　genus　with　one



of　its　own　species。　Nor　（the　other　alternative）　can　a　quale　be



reciprocally　predicated　of　a　quale；　nor　any　term　belonging　to　an



adjectival　category　of　another　such　term；　except　by　accidental



predication；　for　all　such　predicates　are　coincidents　and　are



predicated　of　substances。　On　the　other　hand…in　proof　of　the



impossibility　of　an　infinite　ascending　series…every　predication



displays　the　subject　as　somehow　qualified　or　quantified　or　as



characterized　under　one　of　the　other　adjectival　categories；　or　else　is



an　element　in　its　substantial　nature：　these　latter　are　limited　in



number；　and　the　number　of　the　widest　kinds　under　which　predications



fall　is　also　limited；　for　every　predication　must　exhibit　its　subject



as　somehow　qualified；　quantified；　essentially　related；　acting　or



suffering；　or　in　some　place　or　at　some　time。



　　I　assume　first　that　predication　implies　a　single　subject　and　a



single　attribute；　and　secondly　that　predicates　which　are　not



substantial　are　not　predicated　of　one　another。　We　assume　this



because　such　predicates　are　all　coincidents；　and　though　some　are



essential　coincidents；　others　of　a　different　type；　yet　we　maintain



that　all　of　them　alike　are　predicated　of　some　substratum　and　that　a



coincident　is　never　a　substratum…since　we　do　not　class　as　a　coincident



anything　which　does　not　owe　its　designation　to　its　being　something



other　than　itself；　but　always　hold　that　any　coincident　is　predicated



of　some　substratum　other　than　itself；　and　that　another　group　of



coincidents　may　have　a　different　substratum。　Subject　to　these



assumptions　then；　neither　the　ascending　nor　the　descending　series　of



predication　in　which　a　single　attribute　is　predicated　of　a　single



subject　is　infinite。　For　the　subjects　of　which　coincidents　are



predicated　are　as　many　as　the　constitutive　elements　of　each　individual



substance；　and　these　we　have　seen　are　not　infinite　in　number；　while　in



the　ascending　series　are　contained　those　constitutive　elements　with



their　coincidents…both　of　which　are　finite。　We　conclude　that　there



is　a　given　subject　（D）　of　which　some　attribute　（C）　is　primarily



predicable；　that　there　must　be　an　attribute　（B）　primarily　predicable



of　the　first　attribute；　and　that　the　series　must　end　with　a　term　（A）



not　predicable　of　any　term　prior　to　the　last　subject　of　which　it　was



predicated　（B）；　and　of　which　no　term　prior　to　it　is　predicable。



　　The　argument　we　have　given　is　one　of　the　so…called　proofs；　an



alternative　proof　follows。　Predicates　so　related　to　their　subjects



that　there　are　other　predicates　prior　to　them　predicable　of　those



subjects　are　demonstrable；　but　of　demonstrable　propositions　one　cannot



have　something　better　than　knowledge；　nor　can　one　know　them　without



demonstration。　Secondly；　if　a　consequent　is　only　known　through　an



antecedent　（viz。　premisses　prior　to　it）　and　we　neither　know　this



antecedent　nor　have　something　better　than　knowledge　of　it；　then　we



shall　not　have　scientific　knowledge　of　the　consequent。　Therefore；　if



it　is　possible　through　demonstration　to　know　anything　without



qualification　and　not　merely　as　dependent　on　the　acceptance　of　certain



premisses…i。e。　hypothetically…the　series　of　intermediate



predications　must　terminate。　If　it　does　not　terminate；　and　beyond



any　predicate　taken　as　higher　than　another　there　remains　another　still



higher；　then　every　predicate　is　demonstrable。　Consequently；　since



these　demonstrable　predicates　are　infinite　in　number　and　therefore



cannot　be　traversed；　we　shall　not　know　them　by　demonstration。　If；



therefore；　we　have　not　something　better　than　knowledge　of　them；　we



cannot　through　demonstration　have　unqualified　but　only　hypothetical



science　of　anything。



　　As　dialectical　proofs　of　our　contention　these　may　carry



conviction；　but　an　analytic　process　will　show　more　briefly　that



neither　the　ascent　nor　the　descent　of　predication　can　be　infinite　in



the　demonstrative　sciences　which　are　the　object　of　our



investigation。　Demonstration　proves　the　inherence　of　essential



attributes　in　things。　Now　attributes　may　be　essential　for　two　reasons：



either　because　they　are　elements　in　the　essential　nature　of　their



subjects；　or　because　their　subjects　are　elements　in　their　essential



nature。　An　example　of　the　latter　is　odd　as　an　attribute　of



number…though　it　is　number's　attribute；　yet　number　itself　is　an



element　in　the　definition　of　odd；　of　the　former；　multiplicity　or　the



indivisible；　which　are　elements　in　the　definition　of　number。　In



neither　kind　of　attribution　can　the　terms　be　infinite。　They　are　not



infinite　where　each　is　related　to　the　term　below　it　as　odd　is　to



number；　for　this　would　mean　the　inherence　in　odd　of　another



attribute　of　odd　in　whose　nature　odd　was　an　essential　element：　but



then　number　will　be　an　ultimate　subject　of　the　whole　infinite　chain　of



attributes；　and　be　an　element　in　the　definition　of　each　of　them。



Hence；　since　an　infinity　of　attributes　such　as　contain　their　subject



in　their　definition　cannot　inhere　in　a　single　thing；　the　ascending



series　is　equally　finite。　Note；　moreover；　that　all　such　attributes



must　so　inhere　in　the　ultimate　subject…e。g。　its　attributes　in　number



and　number　in　them…as　to　be　commensurate　with　the　subject　and　not　of



wider　extent。　Attributes　which　are　essential　elements　in　the　nature　of



their　subjects　are　equally　finite：　otherwise　definition　would　be



impossible。　Hence；　if　all　the　attributes　predicated　are　essential



and　these　cannot　be　infinite；　the　ascending　series　will　terminate；　and



consequently　the