posterior analytics- 第15部分

　　Thus；　as　we　maintain；　to　know　a　thing's　nature　is　to　know　the　reason



why　it　is；　and　this　is　equally　true　of　things　in　so　far　as　they　are



said　without　qualification　to　he　as　opposed　to　being　possessed　of　some



attribute；　and　in　so　far　as　they　are　said　to　be　possessed　of　some



attribute　such　as　equal　to　right　angles；　or　greater　or　less。







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　　It　is　clear；　then；　that　all　questions　are　a　search　for　a　'middle'。



Let　us　now　state　how　essential　nature　is　revealed　and　in　what　way　it



can　be　reduced　to　demonstration；　what　definition　is；　and　what　things



are　definable。　And　let　us　first　discuss　certain　difficulties　which



these　questions　raise；　beginning　what　we　have　to　say　with　a　point　most



intimately　connected　with　our　immediately　preceding　remarks；　namely



the　doubt　that　might　be　felt　as　to　whether　or　not　it　is　possible　to



know　the　same　thing　in　the　same　relation；　both　by　definition　and　by



demonstration。　It　might；　I　mean；　be　urged　that　definition　is　held　to



concern　essential　nature　and　is　in　every　case　universal　and



affirmative；　whereas；　on　the　other　hand；　some　conclusions　are　negative



and　some　are　not　universal；　e。g。　all　in　the　second　figure　are



negative；　none　in　the　third　are　universal。　And　again；　not　even　all



affirmative　conclusions　in　the　first　figure　are　definable；　e。g。　'every



triangle　has　its　angles　equal　to　two　right　angles'。　An　argument



proving　this　difference　between　demonstration　and　definition　is　that



to　have　scientific　knowledge　of　the　demonstrable　is　identical　with



possessing　a　demonstration　of　it：　hence　if　demonstration　of　such



conclusions　as　these　is　possible；　there　clearly　cannot　also　be



definition　of　them。　If　there　could；　one　might　know　such　a　conclusion



also　in　virtue　of　its　definition　without　possessing　the



demonstration　of　it；　for　there　is　nothing　to　stop　our　having　the　one



without　the　other。



　　Induction　too　will　sufficiently　convince　us　of　this　difference；



for　never　yet　by　defining　anything…essential　attribute　or　accident…did



we　get　knowledge　of　it。　Again；　if　to　define　is　to　acquire　knowledge　of



a　substance；　at　any　rate　such　attributes　are　not　substances。



　　It　is　evident；　then；　that　not　everything　demonstrable　can　be





defined。　What　then？　Can　everything　definable　be　demonstrated；　or



not？　There　is　one　of　our　previous　arguments　which　covers　this　too。



Of　a　single　thing　qua　single　there　is　a　single　scientific　knowledge。



Hence；　since　to　know　the　demonstrable　scientifically　is　to　possess　the



demonstration　of　it；　an　impossible　consequence　will　follow：…possession



of　its　definition　without　its　demonstration　will　give　knowledge　of　the



demonstrable。



　　Moreover；　the　basic　premisses　of　demonstrations　are　definitions；　and



it　has　already　been　shown　that　these　will　be　found　indemonstrable；



either　the　basic　premisses　will　be　demonstrable　and　will　depend　on



prior　premisses；　and　the　regress　will　be　endless；　or　the　primary



truths　will　be　indemonstrable　definitions。



　　But　if　the　definable　and　the　demonstrable　are　not　wholly　the　same；



may　they　yet　be　partially　the　same？　Or　is　that　impossible；　because



there　can　be　no　demonstration　of　the　definable？　There　can　be　none；



because　definition　is　of　the　essential　nature　or　being　of　something；



and　all　demonstrations　evidently　posit　and　assume　the　essential



nature…mathematical　demonstrations；　for　example；　the　nature　of　unity



and　the　odd；　and　all　the　other　sciences　likewise。　Moreover；　every



demonstration　proves　a　predicate　of　a　subject　as　attaching　or　as　not



attaching　to　it；　but　in　definition　one　thing　is　not　predicated　of



another；　we　do　not；　e。g。　predicate　animal　of　biped　nor　biped　of



animal；　nor　yet　figure　of　plane…plane　not　being　figure　nor　figure



plane。　Again；　to　prove　essential　nature　is　not　the　same　as　to　prove



the　fact　of　a　connexion。　Now　definition　reveals　essential　nature；



demonstration　reveals　that　a　given　attribute　attaches　or　does　not



attach　to　a　given　subject；　but　different　things　require　different



demonstrations…unless　the　one　demonstration　is　related　to　the　other　as



part　to　whole。　I　add　this　because　if　all　triangles　have　been　proved　to



possess　angles　equal　to　two　right　angles；　then　this　attribute　has　been



proved　to　attach　to　isosceles；　for　isosceles　is　a　part　of　which　all



triangles　constitute　the　whole。　But　in　the　case　before　us　the　fact　and



the　essential　nature　are　not　so　related　to　one　another；　since　the



one　is　not　a　part　of　the　other。



　　So　it　emerges　that　not　all　the　definable　is　demonstrable　nor　all　the



demonstrable　definable；　and　we　may　draw　the　general　conclusion　that



there　is　no　identical　object　of　which　it　is　possible　to　possess　both　a



definition　and　a　demonstration。　It　follows　obviously　that　definition



and　demonstration　are　neither　identical　nor　contained　either　within



the　other：　if　they　were；　their　objects　would　be　related　either　as



identical　or　as　whole　and　part。







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　　So　much；　then；　for　the　first　stage　of　our　problem。　The　next　step



is　to　raise　the　question　whether　syllogism…i。e。　demonstration…of　the



definable　nature　is　possible　or；　as　our　recent　argument　assumed；



impossible。



　　We　might　argue　it　impossible　on　the　following　grounds：…（a）　syllogism



proves　an　attribute　of　a　subject　through　the　middle　term；　on　the　other



hand　（b）　its　definable　nature　is　both　'peculiar'　to　a　subject　and



predicated　of　it　as　belonging　to　its　essence。　But　in　that　case　（1）　the



subject；　its　definition；　and　the　middle　term　connecting　them　must　be



reciprocally　predicable　of　one　another；　for　if　A　is　to　C；　obviously



A　is　'peculiar'　to　B　and　B　to　C…in　fact　all　three　terms　are　'peculiar'



to　one　another：　and　further　（2）　if　A　inheres　in　the　essence　of　all　B



and　B　is　predicated　universally　of　all　C　as　belonging　to　C's



essence；　A　also　must　be　predicated　of　C　as　belonging　to　its　essence。



　　If　one　does　not　take　this　relation　as　thus　duplicated…if；　that　is；　A



is　predicated　as　being　of　the　essence　of　B；　but　B　is　not　of　the



essence　of　the　subjects　of　which　it　is　predicated…A　will　not



necessarily　be　predicated　of　C　as　belonging　to　its　essence。　So　both



premisses　will　predicate　essence；　and　consequently　B　also　will　be



predicated　of　C　as　its　essence。　Since；　therefore；　both　premisses　do



predicate　essence…i。e。　definable　form…C's　definable　form　will　appear



in　the　middle　term　before　the　conclusion　is　drawn。



　　We　may　generalize　by　supposing　that　it　is　possible　to　prove　the



essential　nature　of　man。　Let　C　be　man；　A　man's　essential



naturetwo…footed　animal；　or　aught　else　it　may　be。　Then；　if　we　are　to



syllogize；　A　must　be　predicated　of　all　B。　But　this　premiss　will　be



mediated　by　a　fresh　definition；　which　consequently　will　also　be　the



essential　nature　of　man。　Therefore　the　argument　assumes　what　it　has　to



prove；　since　B　too　is　the　essential　nature　of　man。　It　is；　however；　the



case　in　which　there　are　only　the　two　premisses…i。e。　in　which　the



premisses　are　primary　and　immediate…which　we　ought　to　investigate；



because　it　best　illustrates　the　point　under　discussion。



　　Thus　they　who　prove　the　essential　nature　of　soul　or　man　or



anything　else　through　reciprocating　terms　beg　the　question。　It　would



be　begging　the　question；　for　example；　to　contend　that　the　soul　is　that



which　causes　its　own　life；　and　that　what　causes　its　own　life　is　a



self…moving　number；　for　one　would　have　to　postulate　that　the　soul　is　a



self…moving　number　in　the　sense　of　being　identical　with　it。　For　if　A



is　predicable　as　a　mere　consequent　of　B　and　B　of　C；　A　will　not　on　that



account　be　the　definable　form　of　C：　A　will　merely　be　what　it　was



true　to　say　of　C。　Even　if　A　is　predicated　of　all　B　inasmuch　as　B　is



identical　with　a　species　of　A；　still　it　will　not　follow：　being　an



animal　is　predicated　of　being　a　man…since　it　is　true　that　in　all



instances　to　be　human　is　to　be　animal；　just　as　it　is　also　true　that



every　man　is　an　animal…but　not　as　identical　with　being　man。



　　We　conclude；　then；　that　unless　one　takes　both　the　premisses　as



predicating　essence；　one　cannot　infer　that　A　is　the　definable　form　and



essence　of　C：　but　if　one　does　so　take　them；　in　assuming　B　one　will



have　assumed；　before　drawing　the　conclusion；　what　the　definable　form



of　C　is；　so　that　there　has　been　no　inference；　for　one　has　begged　the



question。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　5







　　Nor；　as　was　said　in　my　formal　logic；　is　the　method　of　division　a



process　of　inference　at　all；　since　at　no　point　does　the



characterization　of　the　subject　follow　necessarily　from　the



premising　of　certain　other　facts：　division　demonstrates　as　little　as



does　induction。　For　in　a　genuine　demonstration　the　conclusion　must　not



be　put　as　a　question　nor　depend　on　a　concession；　but　must　follow



necessarily　from　its　premisses；　even　if　the　respondent　deny　it。　The



definer　asks　'Is　man　animal　or　inanimate？'　and　then　assumes…he　has　not



inferred…that　man　is　animal。　Next；　when　presented　with　an　exhaustive



division　of　animal　into　terrestrial　and　aquatic；　he　assumes　that　man



is　terrestrial。　Moreover；　that　man　is　the　complete　formula；



terrestrial…animal；　does　not　follow　necessarily　from　the　premisses：



this　too　is　an　assumption；　and　equally　an　assumption　whether　the



division　comprises　many　differentiae　or　few。　（Indeed　as　this　method　of



division　is　used　by　those　who　proceed　by　it；　even　truths　that　can　be



inferred　actually　fail　to　appear　as　such。）　For　why　should　not　the



whole　of　this　f