posterior analytics-第2部分

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or　a　'laying　something　down'；　since　the　arithmetician　lays　it　down



that　to　be　a　unit　is　to　be　quantitatively　indivisible；　but　it　is　not　a



hypothesis；　for　to　define　what　a　unit　is　is　not　the　same　as　to



affirm　its　existence。



　　Now　since　the　required　ground　of　our　knowledge…i。e。　of　our



conviction…of　a　fact　is　the　possession　of　such　a　syllogism　as　we



call　demonstration；　and　the　ground　of　the　syllogism　is　the　facts



constituting　its　premisses；　we　must　not　only　know　the　primary



premisses…some　if　not　all　of　them…beforehand；　but　know　them　better



than　the　conclusion：　for　the　cause　of　an　attribute's　inherence　in　a



subject　always　itself　inheres　in　the　subject　more　firmly　than　that



attribute；　e。g。　the　cause　of　our　loving　anything　is　dearer　to　us



than　the　object　of　our　love。　So　since　the　primary　premisses　are　the



cause　of　our　knowledge…i。e。　of　our　conviction…it　follows　that　we



know　them　better…that　is；　are　more　convinced　of　them…than　their



consequences；　precisely　because　of　our　knowledge　of　the　latter　is



the　effect　of　our　knowledge　of　the　premisses。　Now　a　man　cannot　believe



in　anything　more　than　in　the　things　he　knows；　unless　he　has　either



actual　knowledge　of　it　or　something　better　than　actual　knowledge。



But　we　are　faced　with　this　paradox　if　a　student　whose　belief　rests



on　demonstration　has　not　prior　knowledge；　a　man　must　believe　in



some；　if　not　in　all；　of　the　basic　truths　more　than　in　the



conclusion。　Moreover；　if　a　man　sets　out　to　acquire　the　scientific



knowledge　that　comes　through　demonstration；　he　must　not　only　have　a



better　knowledge　of　the　basic　truths　and　a　firmer　conviction　of　them



than　of　the　connexion　which　is　being　demonstrated：　more　than　this；



nothing　must　be　more　certain　or　better　known　to　him　than　these　basic



truths　in　their　character　as　contradicting　the　fundamental　premisses



which　lead　to　the　opposed　and　erroneous　conclusion。　For　indeed　the



conviction　of　pure　science　must　be　unshakable。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　3







　　Some　hold　that；　owing　to　the　necessity　of　knowing　the　primary



premisses；　there　is　no　scientific　knowledge。　Others　think　there　is；



but　that　all　truths　are　demonstrable。　Neither　doctrine　is　either



true　or　a　necessary　deduction　from　the　premisses。　The　first　school；



assuming　that　there　is　no　way　of　knowing　other　than　by



demonstration；　maintain　that　an　infinite　regress　is　involved；　on　the



ground　that　if　behind　the　prior　stands　no　primary；　we　could　not　know



the　posterior　through　the　prior　（wherein　they　are　right；　for　one



cannot　traverse　an　infinite　series）：　if　on　the　other　hand…they　say…the



series　terminates　and　there　are　primary　premisses；　yet　these　are



unknowable　because　incapable　of　demonstration；　which　according　to　them



is　the　only　form　of　knowledge。　And　since　thus　one　cannot　know　the



primary　premisses；　knowledge　of　the　conclusions　which　follow　from　them



is　not　pure　scientific　knowledge　nor　properly　knowing　at　all；　but



rests　on　the　mere　supposition　that　the　premisses　are　true。　The　other



party　agree　with　them　as　regards　knowing；　holding　that　it　is　only



possible　by　demonstration；　but　they　see　no　difficulty　in　holding



that　all　truths　are　demonstrated；　on　the　ground　that　demonstration　may



be　circular　and　reciprocal。



　　Our　own　doctrine　is　that　not　all　knowledge　is　demonstrative：　on



the　contrary；　knowledge　of　the　immediate　premisses　is　independent　of



demonstration。　（The　necessity　of　this　is　obvious；　for　since　we　must



know　the　prior　premisses　from　which　the　demonstration　is　drawn；　and



since　the　regress　must　end　in　immediate　truths；　those　truths　must　be



indemonstrable。）　Such；　then；　is　our　doctrine；　and　in　addition　we



maintain　that　besides　scientific　knowledge　there　is　its　originative



source　which　enables　us　to　recognize　the　definitions。



　　Now　demonstration　must　be　based　on　premisses　prior　to　and　better



known　than　the　conclusion；　and　the　same　things　cannot　simultaneously



be　both　prior　and　posterior　to　one　another：　so　circular



demonstration　is　clearly　not　possible　in　the　unqualified　sense　of



'demonstration'；　but　only　possible　if　'demonstration'　be　extended　to



include　that　other　method　of　argument　which　rests　on　a　distinction



between　truths　prior　to　us　and　truths　without　qualification　prior；



i。e。　the　method　by　which　induction　produces　knowledge。　But　if　we



accept　this　extension　of　its　meaning；　our　definition　of　unqualified



knowledge　will　prove　faulty；　for　there　seem　to　be　two　kinds　of　it。



Perhaps；　however；　the　second　form　of　demonstration；　that　which



proceeds　from　truths　better　known　to　us；　is　not　demonstration　in　the



unqualified　sense　of　the　term。



　　The　advocates　of　circular　demonstration　are　not　only　faced　with



the　difficulty　we　have　just　stated：　in　addition　their　theory　reduces



to　the　mere　statement　that　if　a　thing　exists；　then　it　does　exist…an



easy　way　of　proving　anything。　That　this　is　so　can　be　clearly　shown



by　taking　three　terms；　for　to　constitute　the　circle　it　makes　no



difference　whether　many　terms　or　few　or　even　only　two　are　taken。



Thus　by　direct　proof；　if　A　is；　B　must　be；　if　B　is；　C　must　be；



therefore　if　A　is；　C　must　be。　Since　then…by　the　circular　proof…if　A



is；　B　must　be；　and　if　B　is；　A　must　be；　A　may　be　substituted　for　C



above。　Then　'if　B　is；　A　must　be'='if　B　is；　C　must　be'；　which　above



gave　the　conclusion　'if　A　is；　C　must　be'：　but　C　and　A　have　been



identified。　Consequently　the　upholders　of　circular　demonstration　are



in　the　position　of　saying　that　if　A　is；　A　must　be…a　simple　way　of



proving　anything。　Moreover；　even　such　circular　demonstration　is



impossible　except　in　the　case　of　attributes　that　imply　one　another；



viz。　'peculiar'　properties。



　　　　Now；　it　has　been　shown　that　the　positing　of　one　thing…be　it　one



term　or　one　premiss…never　involves　a　necessary　consequent：　two



premisses　constitute　the　first　and　smallest　foundation　for　drawing　a



conclusion　at　all　and　therefore　a　fortiori　for　the　demonstrative



syllogism　of　science。　If；　then；　A　is　implied　in　B　and　C；　and　B　and　C



are　reciprocally　implied　in　one　another　and　in　A；　it　is　possible；　as



has　been　shown　in　my　writings　on　the　syllogism；　to　prove　all　the



assumptions　on　which　the　original　conclusion　rested；　by　circular



demonstration　in　the　first　figure。　But　it　has　also　been　shown　that



in　the　other　figures　either　no　conclusion　is　possible；　or　at　least



none　which　proves　both　the　original　premisses。　Propositions　the



terms　of　which　are　not　convertible　cannot　be　circularly　demonstrated



at　all；　and　since　convertible　terms　occur　rarely　in　actual



demonstrations；　it　is　clearly　frivolous　and　impossible　to　say　that



demonstration　is　reciprocal　and　that　therefore　everything　can　be



demonstrated。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　4







　　Since　the　object　of　pure　scientific　knowledge　cannot　be　other　than



it　is；　the　truth　obtained　by　demonstrative　knowledge　will　be



necessary。　And　since　demonstrative　knowledge　is　only　present　when　we



have　a　demonstration；　it　follows　that　demonstration　is　an　inference



from　necessary　premisses。　So　we　must　consider　what　are　the　premisses



of　demonstration…i。e。　what　is　their　character：　and　as　a　preliminary；



let　us　define　what　we　mean　by　an　attribute　'true　in　every　instance



of　its　subject'；　an　'essential'　attribute；　and　a　'commensurate　and



universal'　attribute。　I　call　'true　in　every　instance'　what　is　truly



predicable　of　all　instances…not　of　one　to　the　exclusion　of



others…and　at　all　times；　not　at　this　or　that　time　only；　e。g。　if　animal



is　truly　predicable　of　every　instance　of　man；　then　if　it　be　true　to



say　'this　is　a　man'；　'this　is　an　animal'　is　also　true；　and　if　the



one　be　true　now　the　other　is　true　now。　A　corresponding　account　holds



if　point　is　in　every　instance　predicable　as　contained　in　line。　There



is　evidence　for　this　in　the　fact　that　the　objection　we　raise　against　a



proposition　put　to　us　as　true　in　every　instance　is　either　an



instance　in　which；　or　an　occasion　on　which；　it　is　not　true。



Essential　attributes　are　（1）　such　as　belong　to　their　subject　as



elements　in　its　essential　nature　（e。g。　line　thus　belongs　to



triangle；　point　to　line；　for　the　very　being　or　'substance'　of　triangle



and　line　is　composed　of　these　elements；　which　are　contained　in　the



formulae　defining　triangle　and　line）：　（2）　such　that；　while　they　belong



to　certain　subjects；　the　subjects　to　which　they　belong　are　contained



in　the　attribute's　own　defining　formula。　Thus　straight　and　curved



belong　to　line；　odd　and　even；　prime　and　compound；　square　and　oblong；



to　number；　and　also　the　formul