posterior analytics-第19部分

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was　bound　to　rise；　and　when　an　exhalation　had　risen　cloud　was　bound　to



form；　and　from　the　formation　of　cloud　rain　necessarily　resulted　and　by



the　fall　of　rain　the　earth　was　necessarily　moistened：　but　this　was　the



starting…point；　so　that　a　circle　is　completed；　for　posit　any　one　of



the　terms　and　another　follows　from　it；　and　from　that　another；　and　from



that　again　the　first。



　　Some　occurrences　are　universal　（for　they　are；　or　come…to…be　what



they　are；　always　and　in　ever　case）；　others　again　are　not　always　what



they　are　but　only　as　a　general　rule：　for　instance；　not　every　man　can



grow　a　beard；　but　it　is　the　general　rule。　In　the　case　of　such



connexions　the　middle　term　too　must　be　a　general　rule。　For　if　A　is



predicated　universally　of　B　and　B　of　C；　A　too　must　be　predicated



always　and　in　every　instance　of　C；　since　to　hold　in　every　instance　and



always　is　of　the　nature　of　the　universal。　But　we　have　assumed　a



connexion　which　is　a　general　rule；　consequently　the　middle　term　B　must



also　be　a　general　rule。　So　connexions　which　embody　a　general　rule…i。e。



which　exist　or　come　to　be　as　a　general　rule…will　also　derive　from



immediate　basic　premisses。



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　　We　have　already　explained　how　essential　nature　is　set　out　in　the



terms　of　a　demonstration；　and　the　sense　in　which　it　is　or　is　not



demonstrable　or　definable；　so　let　us　now　discuss　the　method　to　be



adopted　in　tracing　the　elements　predicated　as　constituting　the



definable　form。



　　Now　of　the　attributes　which　inhere　always　in　each　several　thing



there　are　some　which　are　wider　in　extent　than　it　but　not　wider　than



its　genus　（by　attributes　of　wider　extent　mean　all　such　as　are



universal　attributes　of　each　several　subject；　but　in　their　application



are　not　confined　to　that　subject）。　while　an　attribute　may　inhere　in



every　triad；　yet　also　in　a　subject　not　a　triad…as　being　inheres　in



triad　but　also　in　subjects　not　numbers　at　all…odd　on　the　other　hand　is



an　attribute　inhering　in　every　triad　and　of　wider　application



（inhering　as　it　does　also　in　pentad）；　but　which　does　not　extend　beyond



the　genus　of　triad；　for　pentad　is　a　number；　but　nothing　outside　number



is　odd。　It　is　such　attributes　which　we　have　to　select；　up　to　the　exact



point　at　which　they　are　severally　of　wider　extent　than　the　subject　but



collectively　coextensive　with　it；　for　this　synthesis　must　be　the



substance　of　the　thing。　For　example　every　triad　possesses　the



attributes　number；　odd；　and　prime　in　both　senses；　i。e。　not　only　as



possessing　no　divisors；　but　also　as　not　being　a　sum　of　numbers。



This；　then；　is　precisely　what　triad　is；　viz。　a　number；　odd；　and



prime　in　the　former　and　also　the　latter　sense　of　the　term：　for　these



attributes　taken　severally　apply；　the　first　two　to　all　odd　numbers；



the　last　to　the　dyad　also　as　well　as　to　the　triad；　but；　taken



collectively；　to　no　other　subject。　Now　since　we　have　shown　above'　that



attributes　predicated　as　belonging　to　the　essential　nature　are



necessary　and　that　universals　are　necessary；　and　since　the



attributes　which　we　select　as　inhering　in　triad；　or　in　any　other



subject　whose　attributes　we　select　in　this　way；　are　predicated　as



belonging　to　its　essential　nature；　triad　will　thus　possess　these



attributes　necessarily。　Further；　that　the　synthesis　of　them



constitutes　the　substance　of　triad　is　shown　by　the　following　argument。



If　it　is　not　identical　with　the　being　of　triad；　it　must　be　related



to　triad　as　a　genus　named　or　nameless。　It　will　then　be　of　wider　extent



than　triad…assuming　that　wider　potential　extent　is　the　character　of



a　genus。　If　on　the　other　hand　this　synthesis　is　applicable　to　no



subject　other　than　the　individual　triads；　it　will　be　identical　with



the　being　of　triad；　because　we　make　the　further　assumption　that　the



substance　of　each　subject　is　the　predication　of　elements　in　its



essential　nature　down　to　the　last　differentia　characterizing　the



individuals。　It　follows　that　any　other　synthesis　thus　exhibited　will



likewise　be　identical　with　the　being　of　the　subject。



　　The　author　of　a　hand…book　on　a　subject　that　is　a　generic　whole



should　divide　the　genus　into　its　first　infimae　species…number　e。g。



into　triad　and　dyad…and　then　endeavour　to　seize　their　definitions　by



the　method　we　have　described…the　definition；　for　example；　of



straight　line　or　circle　or　right　angle。　After　that；　having　established



what　the　category　is　to　which　the　subaltern　genus　belongs…quantity



or　quality；　for　instance…he　should　examine　the　properties　'peculiar'



to　the　species；　working　through　the　proximate　common　differentiae。



He　should　proceed　thus　because　the　attributes　of　the　genera　compounded



of　the　infimae　species　will　be　clearly　given　by　the　definitions　of　the



species；　since　the　basic　element　of　them　all　is　the　definition；　i。e。



the　simple　infirma　species；　and　the　attributes　inhere　essentially　in



the　simple　infimae　species；　in　the　genera　only　in　virtue　of　these。



　　Divisions　according　to　differentiae　are　a　useful　accessory　to　this



method。　What　force　they　have　as　proofs　we　did；　indeed；　explain



above；　but　that　merely　towards　collecting　the　essential　nature　they



may　be　of　use　we　will　proceed　to　show。　They　might；　indeed；　seem　to



be　of　no　use　at　all；　but　rather　to　assume　everything　at　the　start



and　to　be　no　better　than　an　initial　assumption　made　without



division。　But；　in　fact；　the　order　in　which　the　attributes　are



predicated　does　make　a　differenceit　matters　whether　we　say



animal…tame…biped；　or　biped…animal…tame。　For　if　every　definable



thing　consists　of　two　elements　and　'animal…tame'　forms　a　unity；　and



again　out　of　this　and　the　further　differentia　man　（or　whatever　else　is



the　unity　under　construction）　is　constituted；　then　the　elements　we



assume　have　necessarily　been　reached　by　division。　Again；　division　is



the　only　possible　method　of　avoiding　the　omission　of　any　element　of



the　essential　nature。　Thus；　if　the　primary　genus　is　assumed　and　we



then　take　one　of　the　lower　divisions；　the　dividendum　will　not　fall



whole　into　this　division：　e。g。　it　is　not　all　animal　which　is　either



whole…winged　or　split…winged　but　all　winged　animal；　for　it　is　winged



animal　to　which　this　differentiation　belongs。　The　primary



differentiation　of　animal　is　that　within　which　all　animal　falls。　The



like　is　true　of　every　other　genus；　whether　outside　animal　or　a



subaltern　genus　of　animal；　e。g。　the　primary　differentiation　of　bird　is



that　within　which　falls　every　bird；　of　fish　that　within　which　falls



every　fish。　So；　if　we　proceed　in　this　way；　we　can　be　sure　that　nothing



has　been　omitted：　by　any　other　method　one　is　bound　to　omit　something



without　knowing　it。



　　To　define　and　divide　one　need　not　know　the　whole　of　existence。　Yet



some　hold　it　impossible　to　know　the　differentiae　distinguishing　each



thing　from　every　single　other　thing　without　knowing　every　single　other



thing；　and　one　cannot；　they　say；　know　each　thing　without　knowing　its



differentiae；　since　everything　is　identical　with　that　from　which　it



does　not　differ；　and　other　than　that　from　which　it　differs。　Now



first　of　all　this　is　a　fallacy：　not　every　differentia　precludes



identity；　since　many　differentiae　inhere　in　things　specifically



identical；　though　not　in　the　substance　of　these　nor　essentially。



Secondly；　when　one　has　taken　one's　differing　pair　of　opposites　and



assumed　that　the　two　sides　exhaust　the　genus；　and　that　the　subject　one



seeks　to　define　is　present　in　one　or　other　of　them；　and　one　has



further　verified　its　presence　in　one　of　them；　then　it　does　not



matter　whether　or　not　one　knows　all　the　other　subjects　of　which　the



differentiae　are　also　predicated。　For　it　is　obvious　that　when　by



this　process　one　reaches　subjects　incapable　of　further　differentiation



one　will　possess　the　formula　defining　the　substance。　Moreover；　to



postulate　that　the　division　exhausts　the　genus　is　not　illegitimate



if　the　opposites　exclude　a　middle；　since　if　it　is　the　differentia　of



that　genus；　anything　contained　in　the　genus　must　lie　on　one　of　the　two



sides。



　　In　establishing　a　definition　by　division　one　should　keep　three



objects　in　view：　（1）　the　admission　only　of　elements　in　the　definable



form；　（2）　the　arrangement　of　these　in　the　right　order；　（3）　the



omission　of　no　such　elements。　The　first　is　feasible　because　one　can



establish　genus　and　differentia　through　the　topic　of　the　genus；　just



as　one　can　conclude　the　inherence　of　an　accident　through　the　topic



of　the　accident。　The　right　order　will　be　achieved　if　the　right　term　is



assumed　as　primary；　and　this　will　be　ensured　if　the　term　selected　is



predicable　of　all　the　others　but　not　all　they　of　it；　since　there



must　be　one　such　term。　Having　assumed　this　we　at　once　proceed　in　the



same　way　with　the　lower　terms；　for　our　second　term　will　be　the　first



of　the　remainder；　our　third　the　first　of　those　which　follow　the　second



in　a　'contiguous'　series；　since　when　the　higher　term　is　excluded；　that



term　of　the　remainder　which　is　'contiguous'　to　it　will　be　primary；　and



so　on。　Our　procedure　makes　it　clear　that　no　elements　in　the



definable　form　have　been　omitted：　we　have　taken　the　differentia　that



comes　first　in　the　order　of　division；　pointing　out　that　animal；　e。g。



is　divisible　exhaustively　into　A　and　B；　and　that　the　subject　accepts



one　of　the　two　as　its　predicate。　Next　we　have　taken　the　differentia　of



the　whole　thus　reached；　and　shown　that　the　whole　we　finally　reach　is



not　further　divisible…i。e。　that　as　soon　as　we　have　taken　the　last



differen