posterior analytics-第14章

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to　the　definition　of　some　entity　which　is　neither　line；　number；　solid；



nor　plane；　but　a　proportionate　apart　from　all　these。　Since；　then；　such



a　proof　is　characteristically　commensurate　and　universal；　and　less



touches　reality　than　does　particular　demonstration；　and　creates　a



false　opinion；　it　will　follow　that　commensurate　and　universal　is



inferior　to　particular　demonstration。



　　We　may　retort　thus。　（1）　The　first　argument　applies　no　more　to



commensurate　and　universal　than　to　particular　demonstration。　If



equality　to　two　right　angles　is　attributable　to　its　subject　not　qua



isosceles　but　qua　triangle；　he　who　knows　that　isosceles　possesses　that



attribute　knows　the　subject　as　qua　itself　possessing　the　attribute；　to



a　less　degree　than　he　who　knows　that　triangle　has　that　attribute。　To



sum　up　the　whole　matter：　if　a　subject　is　proved　to　possess　qua



triangle　an　attribute　which　it　does　not　in　fact　possess　qua



triangle；　that　is　not　demonstration：　but　if　it　does　possess　it　qua



triangle　the　rule　applies　that　the　greater　knowledge　is　his　who



knows　the　subject　as　possessing　its　attribute　qua　that　in　virtue　of



which　it　actually　does　possess　it。　Since；　then；　triangle　is　the



wider　term；　and　there　is　one　identical　definition　of　triangle…i。e。　the



term　is　not　equivocal…and　since　equality　to　two　right　angles　belongs



to　all　triangles；　it　is　isosceles　qua　triangle　and　not　triangle　qua



isosceles　which　has　its　angles　so　related。　It　follows　that　he　who



knows　a　connexion　universally　has　greater　knowledge　of　it　as　it　in



fact　is　than　he　who　knows　the　particular；　and　the　inference　is　that



commensurate　and　universal　is　superior　to　particular　demonstration。



　　（2）　If　there　is　a　single　identical　definition　i。e。　if　the



commensurate　universal　is　unequivocal…then　the　universal　will



possess　being　not　less　but　more　than　some　of　the　particulars；　inasmuch



as　it　is　universals　which　comprise　the　imperishable；　particulars



that　tend　to　perish。



　　（3）　Because　the　universal　has　a　single　meaning；　we　are　not　therefore



compelled　to　suppose　that　in　these　examples　it　has　being　as　a



substance　apart　from　its　particulars…any　more　than　we　need　make　a



similar　supposition　in　the　other　cases　of　unequivocal　universal



predication；　viz。　where　the　predicate　signifies　not　substance　but



quality；　essential　relatedness；　or　action。　If　such　a　supposition　is



entertained；　the　blame　rests　not　with　the　demonstration　but　with　the



hearer。



　　（4）　Demonstration　is　syllogism　that　proves　the　cause；　i。e。　the



reasoned　fact；　and　it　is　rather　the　commensurate　universal　than　the



particular　which　is　causative　（as　may　be　shown　thus：　that　which



possesses　an　attribute　through　its　own　essential　nature　is　itself



the　cause　of　the　inherence；　and　the　commensurate　universal　is　primary；



hence　the　commensurate　universal　is　the　cause）。　Consequently



commensurately　universal　demonstration　is　superior　as　more



especially　proving　the　cause；　that　is　the　reasoned　fact。



　　（5）　Our　search　for　the　reason　ceases；　and　we　think　that　we　know；



when　the　coming　to　be　or　existence　of　the　fact　before　us　is　not　due　to



the　coming　to　be　or　existence　of　some　other　fact；　for　the　last　step　of



a　search　thus　conducted　is　eo　ipso　the　end　and　limit　of　the　problem。



Thus：　'Why　did　he　come？'　'To　get　the　money…wherewith　to　pay　a



debt…that　he　might　thereby　do　what　was　right。'　When　in　this　regress　we



can　no　longer　find　an　efficient　or　final　cause；　we　regard　the　last



step　of　it　as　the　end　of　the　coming…or　being　or　coming　to　be…and　we



regard　ourselves　as　then　only　having　full　knowledge　of　the　reason



why　he　came。



　　If；　then；　all　causes　and　reasons　are　alike　in　this　respect；　and　if



this　is　the　means　to　full　knowledge　in　the　case　of　final　causes　such



as　we　have　exemplified；　it　follows　that　in　the　case　of　the　other



causes　also　full　knowledge　is　attained　when　an　attribute　no　longer



inheres　because　of　something　else。　Thus；　when　we　learn　that　exterior



angles　are　equal　to　four　right　angles　because　they　are　the　exterior



angles　of　an　isosceles；　there　still　remains　the　question　'Why　has



isosceles　this　attribute？'　and　its　answer　'Because　it　is　a　triangle；



and　a　triangle　has　it　because　a　triangle　is　a　rectilinear　figure。'



If　rectilinear　figure　possesses　the　property　for　no　further　reason；　at



this　point　we　have　full　knowledge…but　at　this　point　our　knowledge



has　become　commensurately　universal；　and　so　we　conclude　that



commensurately　universal　demonstration　is　superior。



　　（6）　The　more　demonstration　becomes　particular　the　more　it　sinks　into



an　indeterminate　manifold；　while　universal　demonstration　tends　to



the　simple　and　determinate。　But　objects　so　far　as　they　are　an



indeterminate　manifold　are　unintelligible；　so　far　as　they　are



determinate；　intelligible：　they　are　therefore　intelligible　rather　in



so　far　as　they　are　universal　than　in　so　far　as　they　are　particular。



From　this　it　follows　that　universals　are　more　demonstrable：　but



since　relative　and　correlative　increase　concomitantly；　of　the　more



demonstrable　there　will　be　fuller　demonstration。　Hence　the



commensurate　and　universal　form；　being　more　truly　demonstration；　is



the　superior。



　　（7）　Demonstration　which　teaches　two　things　is　preferable　to



demonstration　which　teaches　only　one。　He　who　possesses



commensurately　universal　demonstration　knows　the　particular　as　well；



but　he　who　possesses　particular　demonstration　does　not　know　the



universal。　So　that　this　is　an　additional　reason　for　preferring



commensurately　universal　demonstration。　And　there　is　yet　this



further　argument：



　　（8）　Proof　becomes　more　and　more　proof　of　the　commensurate



universal　as　its　middle　term　approaches　nearer　to　the　basic　truth；　and



nothing　is　so　near　as　the　immediate　premiss　which　is　itself　the



basic　truth。　If；　then；　proof　from　the　basic　truth　is　more　accurate



than　proof　not　so　derived；　demonstration　which　depends　more　closely　on



it　is　more　accurate　than　demonstration　which　is　less　closely



dependent。　But　commensurately　universal　demonstration　is　characterized



by　this　closer　dependence；　and　is　therefore　superior。　Thus；　if　A　had



to　be　proved　to　inhere　in　D；　and　the　middles　were　B　and　C；　B　being　the



higher　term　would　render　the　demonstration　which　it　mediated　the



more　universal。



　　Some　of　these　arguments；　however；　are　dialectical。　The　clearest



indication　of　the　precedence　of　commensurately　universal　demonstration



is　as　follows：　if　of　two　propositions；　a　prior　and　a　posterior；　we



have　a　grasp　of　the　prior；　we　have　a　kind　of　knowledge…a　potential



grasp…of　the　posterior　as　well。　For　example；　if　one　knows　that　the



angles　of　all　triangles　are　equal　to　two　right　angles；　one　knows　in



a　sense…potentially…that　the　isosceles'　angles　also　are　equal　to　two



right　angles；　even　if　one　does　not　know　that　the　isosceles　is　a



triangle；　but　to　grasp　this　posterior　proposition　is　by　no　means　to



know　the　commensurate　universal　either　potentially　or　actually。



Moreover；　commensurately　universal　demonstration　is　through　and



through　intelligible；　particular　demonstration　issues　in



sense…perception。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　25







　　The　preceding　arguments　constitute　our　defence　of　the　superiority　of



commensurately　universal　to　particular　demonstration。　That　affirmative



demonstration　excels　negative　may　be　shown　as　follows。



　　（1）　We　may　assume　the　superiority　ceteris　paribus　of　the



demonstration　which　derives　from　fewer　postulates　or　hypotheses…in



short　from　fewer　premisses；　for；　given　that　all　these　are　equally　well



known；　where　they　are　fewer　knowledge　will　be　more　speedily