posterior analytics-第16章

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exhibit　through　demonstration　the　essential　nature　of　things　which



have　a　'middle'；　i。e。　a　cause　of　their　substantial　being　other　than



that　being　itself；　but　we　do　not　thereby　demonstrate　it。







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　　Since　definition　is　said　to　be　the　statement　of　a　thing's　nature；



obviously　one　kind　of　definition　will　be　a　statement　of　the　meaning　of



the　name；　or　of　an　equivalent　nominal　formula。　A　definition　in　this



sense　tells　you；　e。g。　the　meaning　of　the　phrase　'triangular



character'。　When　we　are　aware　that　triangle　exists；　we　inquire　the



reason　why　it　exists。　But　it　is　difficult　thus　to　learn　the　definition



of　things　the　existence　of　which　we　do　not　genuinely　know…the　cause　of



this　difficulty　being；　as　we　said　before；　that　we　only　know



accidentally　whether　or　not　the　thing　exists。　Moreover；　a　statement



may　be　a　unity　in　either　of　two　ways；　by　conjunction；　like　the



Iliad；　or　because　it　exhibits　a　single　predicate　as　inhering　not



accidentally　in　a　single　subject。



　　That　then　is　one　way　of　defining　definition。　Another　kind　of



definition　is　a　formula　exhibiting　the　cause　of　a　thing's　existence。



Thus　the　former　signifies　without　proving；　but　the　latter　will　clearly



be　a　quasi…demonstration　of　essential　nature；　differing　from



demonstration　in　the　arrangement　of　its　terms。　For　there　is　a



difference　between　stating　why　it　thunders；　and　stating　what　is　the



essential　nature　of　thunder；　since　the　first　statement　will　be



'Because　fire　is　quenched　in　the　clouds'；　while　the　statement　of



what　the　nature　of　thunder　is　will　be　'The　noise　of　fire　being



quenched　in　the　clouds'。　Thus　the　same　statement　takes　a　different



form：　in　one　form　it　is　continuous　demonstration；　in　the　other



definition。　Again；　thunder　can　be　defined　as　noise　in　the　clouds；



which　is　the　conclusion　of　the　demonstration　embodying　essential



nature。　On　the　other　hand　the　definition　of　immediates　is　an



indemonstrable　positing　of　essential　nature。



　　We　conclude　then　that　definition　is　（a）　an　indemonstrable



statement　of　essential　nature；　or　（b）　a　syllogism　of　essential



nature　differing　from　demonstration　in　grammatical　form；　or　（c）　the



conclusion　of　a　demonstration　giving　essential　nature。



　　Our　discussion　has　therefore　made　plain　（1）　in　what　sense　and　of



what　things　the　essential　nature　is　demonstrable；　and　in　what　sense



and　of　what　things　it　is　not；　（2）　what　are　the　various　meanings　of　the



term　definition；　and　in　what　sense　and　of　what　things　it　proves　the



essential　nature；　and　in　what　sense　and　of　what　things　it　does　not；



（3）　what　is　the　relation　of　definition　to　demonstration；　and　how　far



the　same　thing　is　both　definable　and　demonstrable　and　how　far　it　is



not。







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　　We　think　we　have　scientific　knowledge　when　we　know　the　cause；　and



there　are　four　causes：　（1）　the　definable　form；　（2）　an　antecedent　which



necessitates　a　consequent；　（3）　the　efficient　cause；　（4）　the　final



cause。　Hence　each　of　these　can　be　the　middle　term　of　a　proof；　for



（a）　though　the　inference　from　antecedent　to　necessary　consequent



does　not　hold　if　only　one　premiss　is　assumed…two　is　the



minimum…still　when　there　are　two　it　holds　on　condition　that　they



have　a　single　common　middle　term。　So　it　is　from　the　assumption　of　this



single　middle　term　that　the　conclusion　follows　necessarily。　The



following　example　will　also　show　this。　Why　is　the　angle　in　a



semicircle　a　right　angle？…or　from　what　assumption　does　it　follow



that　it　is　a　right　angle？　Thus；　let　A　be　right　angle；　B　the　half　of



two　right　angles；　C　the　angle　in　a　semicircle。　Then　B　is　the　cause



in　virtue　of　which　A；　right　angle；　is　attributable　to　C；　the　angle



in　a　semicircle；　since　B=A　and　the　other；　viz。　C；=B；　for　C　is　half



of　two　right　angles。　Therefore　it　is　the　assumption　of　B；　the　half



of　two　right　angles；　from　which　it　follows　that　A　is　attributable　to



C；　i。e。　that　the　angle　in　a　semicircle　is　a　right　angle。　Moreover；　B



is　identical　with　（b）　the　defining　form　of　A；　since　it　is　what　A's



definition　signifies。　Moreover；　the　formal　cause　has　already　been



shown　to　be　the　middle。　（c）　'Why　did　the　Athenians　become　involved



in　the　Persian　war？'　means　'What　cause　originated　the　waging　of　war



against　the　Athenians？'　and　the　answer　is；　'Because　they　raided　Sardis



with　the　Eretrians'；　since　this　originated　the　war。　Let　A　be　war；　B



unprovoked　raiding；　C　the　Athenians。　Then　B；　unprovoked　raiding；　is



true　of　C；　the　Athenians；　and　A　is　true　of　B；　since　men　make　war　on



the　unjust　aggressor。　So　A；　having　war　waged　upon　them；　is　true　of



B；　the　initial　aggressors；　and　B　is　true　of　C；　the　Athenians；　who　were



the　aggressors。　Hence　here　too　the　cause…in　this　case　the　efficient



cause…is　the　middle　term。　（d）　This　is　no　less　true　where　the　cause



is　the　final　cause。　E。g。　why　does　one　take　a　walk　after　supper？　For



the　sake　of　one's　health。　Why　does　a　house　exist？　For　the　preservation



of　one's　goods。　The　end　in　view　is　in　the　one　case　health；　in　the



other　preservation。　To　ask　the　reason　why　one　must　walk　after　supper



is　precisely　to　ask　to　what　end　one　must　do　it。　Let　C　be　walking　after



supper；　B　the　non…regurgitation　of　food；　A　health。　Then　let　walking



after　supper　possess　the　property　of　preventing　food　from　rising　to



the　orifice　of　the　stomach；　and　let　this　condition　be　healthy；　since



it　seems　that　B；　the　non…regurgitation　of　food；　is　attributable　to



C；　taking　a　walk；　and　that　A；　health；　is　attributable　to　B。　What；



then；　is　the　cause　through　which　A；　the　final　cause；　inheres　in　C？



It　is　B；　the　non…regurgitation　of　food；　but　B　is　a　kind　of



definition　of　A；　for　A　will　be　explained　by　it。　Why　is　B　the　cause



of　A's　belonging　to　C？　Because　to　be　in　a　condition　such　as　B　is　to　be



in　health。　The　definitions　must　be　transposed；　and　then　the　detail



will　become　clearer。　Incidentally；　here　the　order　of　coming　to　be　is



the　reverse　of　what　it　is　in　proof　through　the　efficient　cause：　in　the



efficient　order　the　middle　term　must　come　to　be　first；　whereas　in



the　teleological　order　the　minor；　C；　must　first　take　place；　and　the



end　in　view　comes　last　in　time。



　　The　same　thing　may　exist　for　an　end　and　be　necessitated　as　well。　For



example；　light　shines　through　a　lantern　（1）　because　that　which　consists



of　relatively　small　particles　necessarily　passes　through　pores　larger



than　those　particles…assuming　that　light　does　issue　by　penetration…



and　（2）　for　an　end；　namely　to　save　us　from　stumbling。　If　then；　a



thing　can　exist　through　two　causes；　can　it　come　to　be　through　two



causes…as　for　instance　if　thunder　be　a　hiss　and　a　roar　necessarily



produced　by　the　quenching　of　fire；　and　also　designed；　as　the



Pythagoreans　say；　for　a　threat　to　terrify　those　that　lie　in　Tartarus？



Indeed；　there　are　very　many　such　cases；　mostly　among　the　processes



and　products　of　the　natural　world；　for　nature；　in　different　senses



of　the　term　'nature'；　produces　now　for　an　end；　now　by　necessity。



　　Necessity　too　is　of　two　kinds。　It　may　work　in　accordance　with　a



thing's　natural　tendency；　or　by　constraint　and　in　opposition　to　it；



as；　for　instance；　by　necessity　a　stone　is　borne　both　upwards　and



downwards；　but　not　by　the　same　necessity。



　　Of　the　products　of　man's　intelligence　some　are　never　due　to　chance



or　necessity　but　always　to　an　end；　as　for　example　a　house　or　a　statue；



others；　such　as　health　or　safety；　may　result　from　chance　as　well。



　　It　is　mostly　in　cases　where　the　issue　is　indeterminate　（though



only　where　the　production　does　not　originate　in　chance；　and　the　end　is



consequently　good）；　that　a　result　is　due　to　an　end；　and　this　is　true



alike　in　nature　or　in　art。　By　chance；　on　the　other　hand；　nothing　comes



to　be　for　an　end。



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　The　effect　may　be　still　coming　to　be；　or　its　occurrence　may　be　past



or　future；　yet　the　cause　will　be　the　same　as　when　it　is　actually



existent…for　it　is　the　middle　which　is　the　cause…except　that　if　the



effect　actually　exists　the　cause　is　actually　existent；　if　it　is　coming



to　be　so　is　the　cause；　if　its　occurrence　is　past　the　cause　is　past；　if



future　the　cause　is　future。　For　example；　the　moon　was　eclipsed　because



the　earth　intervened；　is　becoming　eclipsed　because　the　earth　is　in



process　of　intervening；　will　be　eclipsed　because　the　earth　will



intervene；　is　eclipsed　because　the　earth　intervenes。



　　To　take　a　second　example：　assuming　that　the　definition　of　ice　is



solidified　water；　let　C　be　water；　A　solidified；　B　the　middle；　which　is



the　cause；　namely　total　failure　of　heat。　Then　B　is　attributed　to　C；



and　A；　solidification；　to　B：　ice　when　B　is　occurring；　has　formed



when　B　has　occurred；　and　will　form　when　B　shall　occur。



　　This　sort　of　cause；　then；　and　its　effect　come　to　be　simultaneously



when　they　are　in　process　of　becoming；　and　exist　simultaneously　when



they　actually　exist；　and　the　same　holds　good　when　they　are　past　and



when　they　are　future。　But　what　of　cases　where　they　are　not



simultaneous？　Can　causes　and　effects　different　from　one　another



form；　as　they　seem　to　us　to　form；　a　continuous　succession；　a　past



effect　resulting　from　a　past　cause　different　from　itself；　a　future



effect　from　a　future　cause　different　from　it；　and　an　effect　which　is



coming…to…be　from　a　cause　different　from　and　prior　to　it？　Now　on



this　theory　it　is　from　the　posterior　event　that　we　reason　（and　this



though　these　later　events　actually　have　their　source　of　origin　in



previous　eventsa　fact　which　shows　that　also　when　the　effect　is



coming…to…be　we　still　reason　from　the　posterior　event）；　and　from　the



event　we　cannot　reason　（we　cannot　argue　that　because　an　event　A　has



occurred；　therefore　an　event　B　has　occurred　subsequently　to　A　but



still　in　the　past…and　the　same　holds　good　if　the　occurrence　is



future）…cannot　reason　because；　be　the　time　interval　definite　or



indefinite；　it　will　never　be　possible　to　infer　that　because　it　is　true



to　say　that　A　occurred；　therefore　it　is　true　to　say　that　B；　the



subsequent　event；　occurred；　for　in　the　interval　between　the　events；



though　A　has　already　occurred；　the　latter　statement　will　be　false。　And



the　same　argument　applies　also　to　future　events；　i。e。　one　cannot　infer



from　an　event　which　occurred　in　the　past　that　a　future　event　will



occur。　The　reason　of　this　is　that　the　middle　must　be　homogeneous；　past



when　the　extremes　are　past；　future　when　they　are　future；　coming　to