posterior analytics-第11部分

快捷操作: 按键盘上方向键 ← 或 → 可快速上下翻页 按键盘上的 Enter 键可回到本书目录页 按键盘上方向键 ↑ 可回到本页顶部! 如果本书没有阅读完，想下次继续接着阅读，可使用上方 "收藏到我的浏览器" 功能 和 "加入书签" 功能！




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　descending　series　too。



　　If　this　is　so；　it　follows　that　the　intermediates　between　any　two



terms　are　also　always　limited　in　number。　An　immediately　obvious



consequence　of　this　is　that　demonstrations　necessarily　involve　basic



truths；　and　that　the　contention　of　some…referred　to　at　the　outset…that



all　truths　are　demonstrable　is　mistaken。　For　if　there　are　basic



truths；　（a）　not　all　truths　are　demonstrable；　and　（b）　an　infinite



regress　is　impossible；　since　if　either　（a）　or　（b）　were　not　a　fact；



it　would　mean　that　no　interval　was　immediate　and　indivisible；　but　that



all　intervals　were　divisible。　This　is　true　because　a　conclusion　is



demonstrated　by　the　interposition；　not　the　apposition；　of　a　fresh



term。　If　such　interposition　could　continue　to　infinity　there　might



be　an　infinite　number　of　terms　between　any　two　terms；　but　this　is



impossible　if　both　the　ascending　and　descending　series　of



predication　terminate；　and　of　this　fact；　which　before　was　shown



dialectically；　analytic　proof　has　now　been　given。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　23







　　It　is　an　evident　corollary　of　these　conclusions　that　if　the　same



attribute　A　inheres　in　two　terms　C　and　D　predicable　either　not　at　all；



or　not　of　all　instances；　of　one　another；　it　does　not　always　belong



to　them　in　virtue　of　a　common　middle　term。　Isosceles　and　scalene



possess　the　attribute　of　having　their　angles　equal　to　two　right　angles



in　virtue　of　a　common　middle；　for　they　possess　it　in　so　far　as　they



are　both　a　certain　kind　of　figure；　and　not　in　so　far　as　they　differ



from　one　another。　But　this　is　not　always　the　case：　for；　were　it　so；　if



we　take　B　as　the　common　middle　in　virtue　of　which　A　inheres　in　C　and



D；　clearly　B　would　inhere　in　C　and　D　through　a　second　common　middle；



and　this　in　turn　would　inhere　in　C　and　D　through　a　third；　so　that



between　two　terms　an　infinity　of　intermediates　would　fall…an



impossibility。　Thus　it　need　not　always　be　in　virtue　of　a　common　middle



term　that　a　single　attribute　inheres　in　several　subjects；　since



there　must　be　immediate　intervals。　Yet　if　the　attribute　to　be　proved



common　to　two　subjects　is　to　be　one　of　their　essential　attributes；　the



middle　terms　involved　must　be　within　one　subject　genus　and　be



derived　from　the　same　group　of　immediate　premisses；　for　we　have　seen



that　processes　of　proof　cannot　pass　from　one　genus　to　another。



　　It　is　also　clear　that　when　A　inheres　in　B；　this　can　be



demonstrated　if　there　is　a　middle　term。　Further；　the　'elements'　of



such　a　conclusion　are　the　premisses　containing　the　middle　in　question；



and　they　are　identical　in　number　with　the　middle　terms；　seeing　that



the　immediate　propositions…or　at　least　such　immediate　propositions



as　are　universal…are　the　'elements'。　If；　on　the　other　hand；　there　is



no　middle　term；　demonstration　ceases　to　be　possib