posterior analytics- 第6部分

peculiar　propositions　from　which　its　peculiar　conclusion　is　developed；



then　there　is　such　a　thing　as　a　distinctively　scientific　question；　and



it　is　the　interrogative　form　of　the　premisses　from　which　the



'appropriate'　conclusion　of　each　science　is　developed。　Hence　it　is



clear　that　not　every　question　will　be　relevant　to　geometry；　nor　to



medicine；　nor　to　any　other　science：　only　those　questions　will　be



geometrical　which　form　premisses　for　the　proof　of　the　theorems　of



geometry　or　of　any　other　science；　such　as　optics；　which　uses　the



same　basic　truths　as　geometry。　Of　the　other　sciences　the　like　is　true。



Of　these　questions　the　geometer　is　bound　to　give　his　account；　using



the　basic　truths　of　geometry　in　conjunction　with　his　previous



conclusions；　of　the　basic　truths　the　geometer；　as　such；　is　not　bound





to　give　any　account。　The　like　is　true　of　the　other　sciences。　There



is　a　limit；　then；　to　the　questions　which　we　may　put　to　each　man　of



science；　nor　is　each　man　of　science　bound　to　answer　all　inquiries　on



each　several　subject；　but　only　such　as　fall　within　the　defined　field



of　his　own　science。　If；　then；　in　controversy　with　a　geometer　qua



geometer　the　disputant　confines　himself　to　geometry　and　proves



anything　from　geometrical　premisses；　he　is　clearly　to　be　applauded；　if



he　goes　outside　these　he　will　be　at　fault；　and　obviously　cannot　even



refute　the　geometer　except　accidentally。　One　should　therefore　not



discuss　geometry　among　those　who　are　not　geometers；　for　in　such　a



company　an　unsound　argument　will　pass　unnoticed。　This　is



correspondingly　true　in　the　other　sciences。



　　Since　there　are　'geometrical'　questions；　does　it　follow　that　there



are　also　distinctively　'ungeometrical'　questions？　Further；　in　each



special　science…geometry　for　instance…what　kind　of　error　is　it　that



may　vitiate　questions；　and　yet　not　exclude　them　from　that　science？



Again；　is　the　erroneous　conclusion　one　constructed　from　premisses



opposite　to　the　true　premisses；　or　is　it　formal　fallacy　though　drawn



from　geometrical　premisses？　Or；　perhaps；　the　erroneous　conclusion　is



due　to　the　drawing　of　premisses　from　another　science；　e。g。　in　a



geometrical　controversy　a　musical　question　is　distinctively



ungeometrical；　whereas　the　notion　that　parallels　meet　is　in　one



sense　geometrical；　being　ungeometrical　in　a　different　fashion：　the



reason　being　that　'ungeometrical'；　like　'unrhythmical'；　is



equivocal；　meaning　in　the　one　case　not　geometry　at　all；　in　the　other



bad　geometry？　It　is　this　error；　i。e。　error　based　on　premisses　of



this　kind…'of'　the　science　but　false…that　is　the　contrary　of



science。　In　mathematics　the　formal　fallacy　is　not　so　common；　because



it　is　the　middle　term　in　which　the　ambiguity　lies；　since　the　major



is　predicated　of　the　whole　of　the　middle　and　the　middle　of　the　whole



of　the　minor　（the　predicate　of　course　never　has　the　prefix　'all'）；　and



in　mathematics　one　can；　so　to　speak；　see　these　middle　terms　with　an



intellectual　vision；　while　in　dialectic　the　ambiguity　may　escape



detection。　E。g。　'Is　every　circle　a　figure？'　A　diagram　shows　that



this　is　so；　but　the　minor　premiss　'Are　epics　circles？'　is　shown　by　the



diagram　to　be　false。



　　If　a　proof　has　an　inductive　minor　premiss；　one　should　not　bring　an



'objection'　against　it。　For　since　every　premiss　must　be　applicable



to　a　number　of　cases　（otherwise　it　will　not　be　true　in　every　instance；



which；　since　the　syllogism　proceeds　from　universals；　it　must　be）；　then



assuredly　the　same　is　true　of　an　'objection'；　since　premisses　and



'objections'　are　so　far　the　same　that　anything　which　can　be　validly



advanced　as　an　'objection'　must　be　such　that　it　could　take　the　form　of



a　premiss；　either　demonstrative　or　dialectical。　On　the　other　hand；



arguments　formally　illogical　do　sometimes　occur　through　taking　as



middles　mere　attributes　of　the　major　and　minor　terms。　An　instance　of



this　is　Caeneus'　proof　that　fire　increases　in　geometrical



proportion：　'Fire'；　he　argues；　'increases　rapidly；　and　so　does



geometrical　proportion'。　There　is　no　syllogism　so；　but　there　is　a



syllogism　if　the　most　rapidly　increasing　proportion　is　geometrical　and



the　most　rapidly　increasing　proportion　is　attributable　to　fire　in



its　motion。　Sometimes；　no　doubt；　it　is　impossible　to　reason　from



premisses　predicating　mere　attributes：　but　sometimes　it　is　possible；



though　the　possibility　is　overlooked。　If　false　premisses　could　never



give　true　conclusions　'resolution'　would　be　easy；　for　premisses　and



conclusion　would　in　that　case　inevitably　reciprocate。　I　might　then



argue　thus：　let　A　be　an　existing　fact；　let　the　existence　of　A　imply



such　and　such　facts　actually　known　to　me　to　exist；　which　we　may　call



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。







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　　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