posterior analytics- 第16部分

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



whole　of　this　formula　be　true　of　man；　and　yet　not　exhibit　his



essential　nature　or　definable　form？　Again；　what　guarantee　is　there



against　an　unessential　addition；　or　against　the　omission　of　the



final　or　of　an　intermediate　determinant　of　the　substantial　being？



　　The　champion　of　division　might　here　urge　that　though　these　lapses　do



occur；　yet　we　can　solve　that　difficulty　if　all　the　attributes　we



assume　are　constituents　of　the　definable　form；　and　if；　postulating　the



genus；　we　produce　by　division　the　requisite　uninterrupted　sequence



of　terms；　and　omit　nothing；　and　that　indeed　we　cannot　fail　to　fulfil



these　conditions　if　what　is　to　be　divided　falls　whole　into　the



division　at　each　stage；　and　none　of　it　is　omitted；　and　that　this…the



dividendum…must　without　further　question　be　（ultimately）　incapable



of　fresh　specific　division。　Nevertheless；　we　reply；　division　does



not　involve　inference；　if　it　gives　knowledge；　it　gives　it　in　another



way。　Nor　is　there　any　absurdity　in　this：　induction；　perhaps；　is　not



demonstration　any　more　than　is　division；　et　it　does　make　evident



some　truth。　Yet　to　state　a　definition　reached　by　division　is　not　to



state　a　conclusion：　as；　when　conclusions　are　drawn　without　their



appropriate　middles；　the　alleged　necessity　by　which　the　inference



follows　from　the　premisses　is　open　to　a　question　as　to　the　reason



for　it；　so　definitions　reached　by　division　invite　the　same　question。



　　Thus　to　the　question　'What　is　the　essential　nature　of　man？'　the



divider　replies　'Animal；　mortal；　footed；　biped；　wingless'；　and　when　at



each　step　he　is　asked　'Why？'；　he　will　say；　and；　as　he　thinks；　proves



by　division；　that　all　animal　is　mortal　or　immortal：　but　such　a　formula



taken　in　its　entirety　is　not　definition；　so　that　even　if　division　does



demonstrate　its　formula；　definition　at　any　rate　does　not　turn　out　to



be　a　conclusion　of　inference。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　6







　　Can　we　nevertheless　actually　demonstrate　what　a　thing　essentially



and　substantially　is；　but　hypothetically；　i。e。　by　premising　（1）　that



its　definable　form　is　constituted　by　the　'peculiar'　attributes　of



its　essential　nature；　（2）　that　such　and　such　are　the　only　attributes



of　its　essential　nature；　and　that　the　complete　synthesis　of　them　is



peculiar　to　the　thing；　and　thus…since　in　this　synthesis　consists　the



being　of　the　thing…obtaining　our　conclusion？　Or　is　the　truth　that；



since　proof　must　be　through　the　middle　term；　the　definable　form　is



once　more　assumed　in　this　minor　premiss　too？



　　Further；　just　as　in　syllogizing　we　do　not　premise　what　syllogistic



inference　is　（since　the　premisses　from　which　we　conclude　must　be



related　as　whole　and　part）；　so　the　definable　form　must　not　fall　within



the　syllogism　but　remain　outside　the　premisses　posited。　It　is　only



against　a　doubt　as　to　its　having　been　a　syllogistic　inference　at　all



that　we　have　to　defend　our　argument　as　conforming　to　the　definition　of



syllogism。　It　is　only　when　some　one　doubts　whether　the　conclusion



proved　is　the　definable　form　that　we　have　to　defend　it　as　conforming



to　the　definition　of　definable　form　which　we　assumed。　Hence



syllogistic　inference　must　be　possible　even　without　the　express



statement　of　what　syllogism　is　or　what　definable　form　is。



　　The　following　type　of　hypothetical　proof　also　begs　the　question。



If　evil　is　definable　as　the　divisible；　and　the　definition　of　a　thing's



contrary…if　it　has　one　the　contrary　of　the　thing's　definition；　then；



if　good　is　the　contrary　of　evil　and　the　indivisible　of　the



divisible；　we　conclude　that　to　be　good　is　essentially　to　be



indivisible。　The　question　is　begged　because　definable　form　is



assumed　as　a　premiss；　and　as　a　premiss　which　is　to　prove　definable



form。　'But　not　the　same　definable　form'；　you　may　object。　That　I　admit；



for　in　demonstrations　also　we　premise　that　'this'　is　predicable　of



'that'；　but　in　this　premiss　the　term　we　assert　of　the　minor　is　neither



the　major　itself　nor　a　term　identical　in　definition；　or　convertible；



with　the　major。



　　Again；　both　proof　by　division　and　the　syllogism　just　described　are



open　to　the　question　why　man　should　be　animal…biped…terrestrial　and



not　merely　animal　and　terrestrial；　since　what　they　premise　does　not



ensure　that　the　predicates　shall　constitute　a　genuine　unity　and　not



merely　belong　to　a　single　subject　as　do　musical　and　grammatical　when



predicated　of　the　same　man。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　7







　　How　then　by　definition　shall　we　prove　substance　or　essential　nature？



We　cannot　show　it　as　a　fresh　fact　necessarily　following　from　the



assumption　of　premisses　admitted　to　be　facts…the　method　of



demonstration：　we　may　not　proceed　as　by　induction　to　establish　a



universal　on　the　evidence　of　groups　of　particulars　which　offer　no



exception；　because　induction　proves　not　what　the　essential　nature　of　a



thing　is　but　that　it　has　or　has　not　some　attribute。　Therefore；　since



presumably　one　cannot　prove　essential　nature　by　an　appeal　to　sense



perception　or　by　pointing　with　the　finger；　what　other　method　remains？



　　To　put　it　another　way：　how　shall　we　by　definition　prove　essential



nature？　He　who　knows　what　human…or　any　other…nature　is；　must　know　also



that　man　exists；　for　no　one　knows　the　nature　of　what　does　not



exist…one　can　know　the　meaning　of　the　phrase　or　name　'goat…stag'　but



not　what　the　essential　nature　of　a　goat…stag　is。　But　further；　if



definition　can　prove　what　is　the　essential　nature　of　a　thing；　can　it



also　prove　that　it　exists？　And　how　will　it　prove　them　both　by　the　same



process；　since　definition　exhibits　one　single　thing　and



demonstration　another　single　thing；　and　what　human　nature　is　and　the



fact　that　man　exists　are　not　the　same　thing？　Then　too　we　hold　that



it　is　by　demonstration　that　the　being　of　everything　must　be



proved…unless　indeed　to　be　were　its　essence；　and；　since　being　is　not　a



genus；　it　is　not　the　essence　of　anything。　Hence　the　being　of



anything　as　fact　is　matter　for　demonstration；　and　this　is　the　actual



procedure　of　the　sciences；　for　the　geometer　assumes　the　meaning　of　the



word　triangle；　but　that　it　is　possessed　of　some　attribute　he　proves。



What　is　it；　then；　that　we　shall　prove　in　defining　essential　nature？



Triangle？　In　that　case　a　man　will　know　by　definition　what　a　thing's



nature　is　without　knowing　whether　it　exists。　But　that　is　impossible。



　　Moreover　it　is　clear；　if　we　consider　the　methods　of　defining



actually　in　use；　that　definition　does　not　prove　that　the　thing　defined



exists：　since　even　if　there　does　actually　exist　something　which　is



equidistant　from　a　centre；　yet　why　should　the　thing　named　in　the



definition　exist？　Why；　in　other　words；　should　this　be　the　formula



defining　circle？　One　might　equally　well　call　it　the　definition　of



mountain　copper。　For　definitions　do　not　carry　a　further　guarantee　that



the　thing　defined　can　exist　or　that　it　is　what　they　claim　to　define：



one　can　always　ask　why。



　　Since；　therefore；　to　define　is　to　prove　either　a　thing's　essential



nature　or　the　meaning　of　its　name；　we　may　conclude　that　definition；　if



it　in　no　sense　proves　essential　nature；　is　a　set　of　words　signifying



precisely　what　a　name　signifies。　But　that　were　a　strange



consequence；　for　（1）　both　what　is　not　substance　and　what　does　not



exist　at　all　would　be　definable；　since　even　non…existents　can　be



signified　by　a　name：　（2）　all　sets　of　words　or　sentences　would　be



definitions；　since　any　kind　of　sentence　could　be　given　a　name；　so　that



we　should　all　be　talking　in　definitions；　and　even　the　Iliad　would　be　a



definition：　（3）　no　demonstration　can　prove　that　any　particular　name



means　any　particular　thing：　neither；　therefore；　do　definitions；　in



addition　to　revealing　the　meaning　of　a　name；　also　reveal　that　the　name



has　this　meaning。　It　appears　then　from　these　considerations　that



neither　definition　and　syllogism　nor　their　objects　are　identical；



and　further　that　definition　neither　demonstrates　nor　proves



anything；　and　that　knowledge　of　essential　nature　is　not　to　be　obtained



either　by　definition　or　by　demonstration。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　8







　　We　must　now　start　afresh　and　consider　which　of　these　conclusions　are



sound　and　which　are　not；　and　what　is　the　nature　of　definition；　and



whether　essential　nature　is　in　any　sense　demonstrable　and　definable　or



in　none。



　　Now　to　know　its　essential　nature　is；　as　we　said；　the　same　as　to　know



the　cause　of　a　thing's　existence；　and　the　proof　of　this　depends　on　the



fact　that　a　thing　must　have　a　cause。　Moreover；　this　cause　is　either



identical　with　the　essential　nature　of　the　thing　or　distinct　from



it；　and　if　its　cause　is　distinct　from　it；　the　essential　nature　of



the　thing　is　either　demonstrable　or　indemonstrable。　Consequently；　if



the　cause　is　distinct　from　the　thing's　essential　nature　and



demonstration　is　possible；　the　cause　must　be　the　middle　term；　and；　the



conclusion　proved　being　universal　and　affirmative；　the　proof　is　in　the



first　figure。　So　the　method　just　examined　of　proving　it　through



another　essential　nature　would　be　one　way　of　proving　essential　nature；



because　a　conclusion　containing　essential　nature　must　be　inferred



through　a　middle　which　is　an　essential　nature　just　as　a　'peculiar'



property　must　be　inferred　through　a　middle　which　is　a　'peculiar'



property；　so　that　of　the　two　definable　natures　of　a　single　thing



this　method　will　prove　one　and　not　the　other。