posterior analytics-第6章

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B。　I　can　now；　since　they　reciprocate；　infer　A　from　B。



　　Reciprocation　of　premisses　and　conclusion　is　more　frequent　in



mathematics；　because　mathematics　takes　definitions；　but　never　an



accident；　for　its　premisses…a　second　characteristic　distinguishing



mathematical　reasoning　from　dialectical　disputations。



　　A　science　expands　not　by　the　interposition　of　fresh　middle　terms；



but　by　the　apposition　of　fresh　extreme　terms。　E。g。　A　is　predicated



of　B；　B　of　C；　C　of　D；　and　so　indefinitely。　Or　the　expansion　may　be



lateral：　e。g。　one　major　A；　may　be　proved　of　two　minors；　C　and　E。



Thus　let　A　represent　number…a　number　or　number　taken



indeterminately；　B　determinate　odd　number；　C　any　particular　odd



number。　We　can　then　predicate　A　of　C。　Next　let　D　represent　determinate



even　number；　and　E　even　number。　Then　A　is　predicable　of　E。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　13







　　Knowledge　of　the　fact　differs　from　knowledge　of　the　reasoned　fact。



To　begin　with；　they　differ　within　the　same　science　and　in　two　ways：



（1）　when　the　premisses　of　the　syllogism　are　not　immediate　（for　then



the　proximate　cause　is　not　contained　in　them…a　necessary　condition



of　knowledge　of　the　reasoned　fact）：　（2）　when　the　premisses　are



immediate；　but　instead　of　the　cause　the　better　known　of　the　two



reciprocals　is　taken　as　the　middle；　for　of　two　reciprocally　predicable



terms　the　one　which　is　not　the　cause　may　quite　easily　be　the　better



known　and　so　become　the　middle　term　of　the　demonstration。　Thus　（2）　（a）



you　might　prove　as　follows　that　the　planets　are　near　because　they　do



not　twinkle：　let　C　be　the　planets；　B　not　twinkling；　A　proximity。



Then　B　is　predicable　of　C；　for　the　planets　do　not　twinkle。　But　A　is



also　predicable　of　B；　since　that　which　does　not　twinkle　is　nearwe



must　take　this　truth　as　having　been　reached　by　induction　or



sense…perception。　Therefore　A　is　a　necessary　predicate　of　C；　so　that



we　have　demonstrated　that　the　planets　are　near。　This　syllogism；



then；　proves　not　the　reasoned　fact　but　only　the　fact；　since　they　are



not　near　because　they　do　not　twinkle；　but；　because　they　are　near；　do



not　twinkle。　The　major　and　middle　of　the　proof；　however；　may　be



reversed；　and　then　the　demonstration　will　be　of　the　reasoned　fact。



Thus：　let　C　be　the　planets；　B　proximity；　A　not　twinkling。　Then　B　is　an



attribute　of　C；　and　A…not　twinkling…of　B。　Consequently　A　is　predicable



of　C；　and　the　syllogism　proves　the　reasoned　fact；　since　its　middle



term　is　the　proximate　cause。　Another　example　is　the　inference　that　the



moon　is　spherical　from　its　manner　of　waxing。　Thus：　since　that　which　so



waxes　is　spherical；　and　since　the　moon　so　waxes；　clearly　the　moon　is



spherical。　Put　in　this　form；　the　syllogism　turns　out　to　be　proof　of



the　fact；　but　if　the　middle　and　major　be　reversed　it　is　proof　of　the



reasoned　fact；　since　the　moon　is　not　spherical　because　it　waxes　in　a



certain　manner；　but　waxes　in　such　a　manner　because　it　is　spherical。



（Let　C　be　the　moon；　B　spherical；　and　A　waxing。）　Again　（b）；　in　cases



where　the　cause　and　the　effect　are　not　reciprocal　and　the　effect　is



the　better　known；　the　fact　is　demonstrated　but　not　the　reasoned



fact。　This　also　occurs　（1）　when　the　middle　falls　outside　the　major　and



minor；　for　here　too　the　strict　cause　is　not　given；　and　so　the



demonstration　is　of　the　fact；　not　of　the　reasoned　fact。　For　example；



the　question　'Why　does　not　a　wall　breathe？'　might　be　answered；



'Because　it　is　not　an　animal'；　but　that　answer　would　not　give　the



strict　cause；　because　if　not　being　an　animal　causes　the　absence　of



respiration；　then　being　an　animal　should　be　the　cause　of



respiration；　according　to　the　rule　that　if　the　negation　of　causes



the　non…inherence　of　y；　the　affirmation　of　x　causes　the　inherence　of



y；　e。g。　if　the　disproportion　of　the　hot　and　cold　elements　is　the　cause



of　ill　health；　their　proportion　is　the　cause　of　health；　and



conversely；　if　the　assertion　of　x　causes　the　inherence　of　y；　the



negation　of　x　must　cause　y's　non…inherence。　But　in　the　case　given　this



consequence　does　not　result；　for　not　every　animal　breathes。　A



syllogism　with　this　kind　of　cause　takes　place　in　the　second　figure。



Thus：　let　A　be　animal；　B　respiration；　C　wall。　Then　A　is　predicable



of　all　B　（for　all　that　breathes　is　animal）；　but　of　no　C；　and



consequently　B　is　predicable　of　no　C；　that　is；　the　wall　does　not



breathe。　Such　causes　are　like　far…fetched　explanations；　which



precisely　consist　in　making　the　cause　too　remote；　as　in　Anacharsis'



account　of　why　the　Scythians　have　no　flute…players；　namely　because



they　have　no　vines。



　　Thus；　then；　do　the　syllogism　of　the　fact　and　the　syllogism　of　the



reasoned　fact　differ　within　one　science　and　according　to　the



position　of　the　middle　terms。　But　there　is　another　way　too　in　which



the　fact　and　the　reasoned　fact　differ；　and　that　is　when　they　are



investigated　respectively　by　different　sciences。　This　occurs　in　the



case　of　problems　related　to　one　another　as　subordinate　and　superior；



as　when　optical　problems　are　subordinated　to　geometry；　mechanical



problems　to　stereometry；　harmonic　problems　to　arithmetic；　the　data



of　observation　to　astronomy。　（Some　of　these　sciences　bear　almost　the



same　name；　e。g。　mathematical　and　nautical　astronomy；　mathematical



and　acoustical　harmonics。）　Here　it　is　the　business　of　the　empirical



observers　to　know　the　fact；　of　the　mathematicians　to　know　the　reasoned



fact；　for　the　latter　are　in　possession　of　the　demonstrations　giving



the　causes；　and　are　often　ignorant　of　the　fact：　just　as　we　have



often　a　clear　insight　into　a　universal；　but　through　lack　of



observation　are　ignorant　of　some　of　its　particular　instances。　These



connexions　have　a　perceptible　existence　though　they　are　manifestations



of　forms。　For　the　mathematical　sciences　concern　forms：　they　do　not



demonstrate　properties　of　a　substratum；　since；　even　though　the



geometrical　subjects　are　predicable　as　properties　of　a　perceptible



substratum；　it　is　not　as　thus　predicable　that　the　mathematician



demonstrates　properties　of　them。　As　optics　is　related　to　geometry；



so　another　science　is　related　to　optics；　namely　the　theory　of　the



rainbow。　Here　knowledge　of　the　fact　is　within　the　province　of　the



natural　philosopher；　knowledge　of　the　reasoned　fact　within　that　of　the



optician；　either　qua　optician　or　qua　mathematical　optician。　Many



sciences　not　standing　in　this　mutual　relation　enter　into　it　at　points；



e。g。　medicine　and　geometry：　it　is　the　physician's　business　to　know



that　circular　wounds　heal　more　slowly；　the　geometer's　to　know　the



reason　why。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　14







　　Of　all　the　figures　the　most　scientific　is　the　first。　Thus；　it　is　the



vehicle　of　the　demonstrations　of　all　the　mathematical　sciences；　such



as　arithmetic；　geometry；　and　optics；　and　practically　all　of　all



sciences　that　investigate　causes：　for　the　syllogism　of　the　reasoned



fact　is　either　exclusively　or　generally　speaking　and　in　most　cases



in　this　figure…a　second　proof　that　this　figure　is　the　most　scientific；



for　grasp　of　a　reasoned　conclusion　is　the　primary　condition　of



knowledge。　Thirdly；　the　first　is　the　only　figure　which　enables　us　to



pursue　knowledge　of　the　essence　of　a　thing。　In　the　second　figure　no



affirmative　conclusion　is　possible；　and　knowledge　of　a　thing's　essence



must　be　affirmative；　while　in　the　third　figure　the　conclusion　can　be



affirmative；　but　cannot　be　universal；　and　essence　must　have　a



universal　character：　e。g。　man　is　not　two…footed　animal　in　any



qualified　sense；　but　universally。　Finally；　the　first　figure　has　no



need　of　the　others；　while　it　is　by　means　of　the　first　that　the　other



two　figures　are　developed；　and　have　their　intervals　closepacked



until　immediate　premisses　are　reached。



　　Clearly；　therefore；　the　first　figure　is　the　primary　condition　of



knowledge。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　15







　　Just　as　an　attribute　A　may　（as　we　saw）　be　atomically　connected



with　a　subject　B；　so　its　disconnexion　may　be　atomic。　I　call　'atomic'



connexions　or　disconnexions　which　involve　no　intermediate　term；



since　in　that　case　the　connexion　or　disconnexion　will　not　be



mediated　by　something　other　than　the　terms　themselves。　It　follows　that



if　either　A　or　B；　or　both　A　and　B；　have　a　genus；　their　disconnexion



cannot　be　primary。　Thus：　let　C　be　the　genus　of　A。　Then；　if　C　is　not



the　genus　of　B…for　A　may　well　have　a　genus　which　is　not　the　genus　of



B…there　will　be　a　syllogism　proving　A's　disconnexion　from　B　thus：







　　　　　　　　all　A　is　C；



　　　　　　　　no　B　is　C；



　　　　　　　　therefore　no　B　is　A。







Or　if　it　is　B　which　has　a　genus　D；　we　have











　　　　　　　　all　B　is　D；



　　　　　　　　no　D　is　A；



　　　　　　　　therefore　no　B　is　A；　by　syllogism；







and　the　proof　will　be　similar　if　both　A　and　B　have　a　genus。　That　the



genus　of　A　need　not　be　the　genus　of　B　and　vice　versa；　is　shown　by



the　existence　of　mutually　exclusive　coordinate　series　of



predication。　If　no　term　in　the　series　ACD。。。is　predicable　of　any



term　in　the　series　BEF。。。；and　if　G…a　term　in　the　former　series…is



the　genus　of　A；　clearly　G　will　not　be　the　genus　of　B；　since；　if　it



were；　the　series　would　not　be　mutually　exclusive。　So　also　if　B　has　a



genus；　it　will　not　be　the　genus　of　A。　If；　on　the　other　hand；　neither　A



nor　B　has　a　genus　and　A　does　not　inhere　in　B；　this　disconnexion　must



be　atomic。　If　there　be　a　middle　term；　one　or　other　of　them　is　bound　to



have　a　genus；　for　the　syllogism　will　be　either　in　the　first　or　the



second　figure。　If　it　is　in　the　first；　B　will　have　a　genus…for　the



premiss　containing　it　must　be　affirmative：　if　in　the　second；　either



A　or　B　indifferently；　since　syllogism　is　possible　if　either　is



contained　in　a　negative　premiss；　but　not　if　both　premisses　are



negative。



　　Hence　it　is　clear　that　one　thing　may　be　atomically　disconnected　from



another；　and　we　have　stated　when　and　how　this　is　possible。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　16







　　Ignorance…defined　not　as　the　negation　of　knowledge　but　as　a　positive



state　of　mind…is　error　produced　by　inference。



　　（1）　Let　us　first　consider　propositions　asserting　a　predicate's



immediate　connexion　with　or　disconnexion　from　a　subject。　Here；　it　is



true；　positive　error　may　befall　one　in　alternative　ways；　for　it　may



arise　where　one　directly　believes　a　connexion　or　disconnexion　as



well　as　where　one's　belief　is　acquired　by　inference。　The　error；



however；　that