posterior analytics-第12节

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as　are　universal…are　the　'elements'。　If；　on　the　other　hand；　there　is



no　middle　term；　demonstration　ceases　to　be　possible：　we　are　on　the　way



to　the　basic　truths。　Similarly　if　A　does　not　inhere　in　B；　this　can



be　demonstrated　if　there　is　a　middle　term　or　a　term　prior　to　B　in



which　A　does　not　inhere：　otherwise　there　is　no　demonstration　and　a



basic　truth　is　reached。　There　are；　moreover；　as　many　'elements'　of　the



demonstrated　conclusion　as　there　are　middle　terms；　since　it　is



propositions　containing　these　middle　terms　that　are　the　basic



premisses　on　which　the　demonstration　rests；　and　as　there　are　some



indemonstrable　basic　truths　asserting　that　'this　is　that'　or　that



'this　inheres　in　that'；　so　there　are　others　denying　that　'this　is



that'　or　that　'this　inheres　in　that'…in　fact　some　basic　truths　will



affirm　and　some　will　deny　being。



　　When　we　are　to　prove　a　conclusion；　we　must　take　a　primary



essential　predicate…suppose　it　C…of　the　subject　B；　and　then　suppose



A　similarly　predicable　of　C。　If　we　proceed　in　this　manner；　no



proposition　or　attribute　which　falls　beyond　A　is　admitted　in　the



proof：　the　interval　is　constantly　condensed　until　subject　and



predicate　become　indivisible；　i。e。　one。　We　have　our　unit　when　the



premiss　becomes　immediate；　since　the　immediate　premiss　alone　is　a



single　premiss　in　the　unqualified　sense　of　'single'。　And　as　in　other



spheres　the　basic　element　is　simple　but　not　identical　in　all…in　a



system　of　weight　it　is　the　mina；　in　music　the　quarter…tone；　and　so



onso　in　syllogism　the　unit　is　an　immediate　premiss；　and　in　the



knowledge　that　demonstration　gives　it　is　an　intuition。　In



syllogisms；　then；　which　prove　the　inherence　of　an　attribute；　nothing



falls　outside　the　major　term。　In　the　case　of　negative　syllogisms　on



the　other　hand；　（1）　in　the　first　figure　nothing　falls　outside　the



major　term　whose　inherence　is　in　question；　e。g。　to　prove　through　a



middle　C　that　A　does　not　inhere　in　B　the　premisses　required　are；　all　B



is　C；　no　C　is　A。　Then　if　it　has　to　be　proved　that　no　C　is　A；　a



middle　must　be　found　between　and　C；　and　this　procedure　will　never



vary。



　　（2）　If　we　have　to　show　that　E　is　not　D　by　means　of　the　premisses；



all　D　is　C；　no　E；　or　not　all　E；　is　C；　then　the　middle　will　never



fall　beyond　E；　and　E　is　the　subject　of　which　D　is　to　be　denied　in



the　conclusion。



　　（3）　In　the　third　figure　the　middle　will　never　fall　beyond　the　limits



of　the　subject　and　the　attribute　denied　of　it。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　24







　　Since　demonstrations　may　be　either　commensurately　universal　or



particular；　and　either　affirmative　or　negative；　the　question　arises；



which　form　is　the　better？　And　the　same　question　may　be　put　in　regard



to　so…called　'direct'　demonstration　and　reductio　ad　impossibile。　Let



us　first　examine　the　commensurately　universal　and　the　particular



forms；　and　when　we　have　cleared　up　this　problem　proceed　to　discuss



'direct'　demonstration　and　reductio　ad　impossibile。



　　The　following　considerations　might　lead　some　minds　to　prefer



particular　demonstration。



　　（1）　The　superior　demonstration　is　the　demonstration　which　gives　us



greater　knowledge　（for　this　is　the　ideal　of　demonstration）；　and　we



have　greater　knowledge　of　a　particular　individual　when　we　know　it　in



itself　than　when　we　know　it　through　something　else；　e。g。　we　know



Coriscus　the　musician　better　when　we　know　that　Coriscus　is　musical



than　when　we　know　only　that　man　is　musical；　and　a　like　argument



holds　in　all　other　cases。　But　commensurately　universal



demonstration；　instead　of　proving　that　the　subject　itself　actually



is　x；　proves　only　that　something　else　is　x…　e。g。　in　attempting　to



prove　that　isosceles　is　x；　it　proves　not　that　isosceles　but　only　that



triangle　is　x…　whereas　particular　demonstration　proves　that　the



subject　itself　is　x。　The　demonstration；　then；　that　a　subject；　as　such；



possesses　an　attribute　is　superior。　If　this　is　so；　and　if　the



particular　rather　than　the　commensurately　universal　forms



demonstrates；　particular　demonstration　is　superior。



　　（2）　The　universal　has　not　a　separate　being　over　against　groups　of



singulars。　Demonstration　nevertheless　creates　the　opinion　that　its



function　is　conditioned　by　something　like　this…some　separate　entity



belonging　to　the　real　world；　that；　for　instance；　of　triangle　or　of



figure　or　number；　over　against　particular　triangles；　figures；　and



numbers。　But　demonstration　which　touches　the　real　and　will　not　mislead



is　superior　to　that　which　moves　among　unrealities　and　is　delusory。　Now



commensurately　universal　demonstration　is　of　the　latter　kind：　if　we



engage　in　it　we　find　ourselves　reasoning　after　a　fashion　well



illustrated　by　the　argument　that　the　proportionate　is　what　answers



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