posterior analytics- 第5部分

qualification…the　fact　falls　under　a　separate　science　（for　the　subject



genus　is　separate）；　but　the　reasoned　fact　concerns　the　superior



science；　to　which　the　attributes　essentially　belong。　Thus；　even



these　apparent　exceptions　show　that　no　attribute　is　strictly



demonstrable　except　from　its　'appropriate'　basic　truths；　which；



however；　in　the　case　of　these　sciences　have　the　requisite　identity



of　character。



　　It　is　no　less　evident　that　the　peculiar　basic　truths　of　each



inhering　attribute　are　indemonstrable；　for　basic　truths　from　which



they　might　be　deduced　would　be　basic　truths　of　all　that　is；　and　the



science　to　which　they　belonged　would　possess　universal　sovereignty。



This　is　so　because　he　knows　better　whose　knowledge　is　deduced　from



higher　causes；　for　his　knowledge　is　from　prior　premisses　when　it



derives　from　causes　themselves　uncaused：　hence；　if　he　knows　better



than　others　or　best　of　all；　his　knowledge　would　be　science　in　a　higher



or　the　highest　degree。　But；　as　things　are；　demonstration　is　not



transferable　to　another　genus；　with　such　exceptions　as　we　have



mentioned　of　the　application　of　geometrical　demonstrations　to　theorems



in　mechanics　or　optics；　or　of　arithmetical　demonstrations　to　those



of　harmonics。



　　It　is　hard　to　be　sure　whether　one　knows　or　not；　for　it　is　hard　to　be



sure　whether　one's　knowledge　is　based　on　the　basic　truths



appropriate　to　each　attribute…the　differentia　of　true　knowledge。　We



think　we　have　scientific　knowledge　if　we　have　reasoned　from　true　and



primary　premisses。　But　that　is　not　so：　the　conclusion　must　be



homogeneous　with　the　basic　facts　of　the　science。







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　　I　call　the　basic　truths　of　every　genus　those　clements　in　it　the



existence　of　which　cannot　be　proved。　As　regards　both　these　primary



truths　and　the　attributes　dependent　on　them　the　meaning　of　the　name　is



assumed。　The　fact　of　their　existence　as　regards　the　primary　truths



must　be　assumed；　but　it　has　to　be　proved　of　the　remainder；　the



attributes。　Thus　we　assume　the　meaning　alike　of　unity；　straight；　and



triangular；　but　while　as　regards　unity　and　magnitude　we　assume　also



the　fact　of　their　existence；　in　the　case　of　the　remainder　proof　is



required。



　　Of　the　basic　truths　used　in　the　demonstrative　sciences　some　are



peculiar　to　each　science；　and　some　are　common；　but　common　only　in



the　sense　of　analogous；　being　of　use　only　in　so　far　as　they　fall



within　the　genus　constituting　the　province　of　the　science　in　question。



　　Peculiar　truths　are；　e。g。　the　definitions　of　line　and　straight；



common　truths　are　such　as　'take　equals　from　equals　and　equals　remain'。



Only　so　much　of　these　common　truths　is　required　as　falls　within　the



genus　in　question：　for　a　truth　of　this　kind　will　have　the　same　force



even　if　not　used　generally　but　applied　by　the　geometer　only　to



magnitudes；　or　by　the　arithmetician　only　to　numbers。　Also　peculiar



to　a　science　are　the　subjects　the　existence　as　well　as　the　meaning



of　which　it　assumes；　and　the　essential　attributes　of　which　it



investigates；　e。g。　in　arithmetic　units；　in　geometry　points　and



lines。　Both　the　existence　and　the　meaning　of　the　subjects　are



assumed　by　these　sciences；　but　of　their　essential　attributes　only



the　meaning　is　assumed。　For　example　arithmetic　assumes　the　meaning



of　odd　and　even；　square　and　cube；　geometry　that　of　incommensurable；　or



of　deflection　or　verging　of　lines；　whereas　the　existence　of　these



attributes　is　demonstrated　by　means　of　the　axioms　and　from　previous



conclusions　as　premisses。　Astronomy　too　proceeds　in　the　same　way。



For　indeed　every　demonstrative　science　has　three　elements：　（1）　that



which　it　posits；　the　subject　genus　whose　essential　attributes　it



examines；　（2）　the　so…called　axioms；　which　are　primary　premisses　of　its



demonstration；　（3）　the　attributes；　the　meaning　of　which　it　assumes。



Yet　some　sciences　may　very　well　pass　over　some　of　these　elements；　e。g。



we　might　not　expressly　posit　the　existence　of　the　genus　if　its



existence　were　obvious　（for　instance；　the　existence　of　hot　and　cold　is



more　evident　than　that　of　number）；　or　we　might　omit　to　assume



expressly　the　meaning　of　the　attributes　if　it　were　well　understood。　In



the　way　the　meaning　of　axioms；　such　as　'Take　equals　from　equals　and



equals　remain'；　is　well　known　and　so　not　expressly　assumed。



Nevertheless　in　the　nature　of　the　case　the　essential　elements　of



demonstration　are　three：　the　subject；　the　attributes；　and　the　basic



premisses。



　　That　which　expresses　necessary　self…grounded　fact；　and　which　we　must



necessarily　believe；　is　distinct　both　from　the　hypotheses　of　a　science



and　from　illegitimate　postulate…I　say　'must　believe'；　because　all



syllogism；　and　therefore　a　fortiori　demonstration；　is　addressed　not　to



the　spoken　word；　but　to　the　discourse　within　the　soul；　and　though　we



can　always　raise　objections　to　the　spoken　word；　to　the　inward



discourse　we　cannot　always　object。　That　which　is　capable　of　proof



but　assumed　by　the　teacher　without　proof　is；　if　the　pupil　believes　and



accepts　it；　hypothesis；　though　only　in　a　limited　sense　hypothesis…that



is；　relatively　to　the　pupil；　if　the　pupil　has　no　opinion　or　a　contrary



opinion　on　the　matter；　the　same　assumption　is　an　illegitimate



postulate。　Therein　lies　the　distinction　between　hypothesis　and



illegitimate　postulate：　the　latter　is　the　contrary　of　the　pupil's



opinion；　demonstrable；　but　assumed　and　used　without　demonstration。



　　The　definition…viz。　those　which　are　not　expressed　as　statements　that



anything　is　or　is　not…are　not　hypotheses：　but　it　is　in　the　premisses



of　a　science　that　its　hypotheses　are　contained。　Definitions　require



only　to　be　understood；　and　this　is　not　hypothesis…unless　it　be



contended　that　the　pupil's　hearing　is　also　an　hypothesis　required　by



the　teacher。　Hypotheses；　on　the　contrary；　postulate　facts　on　the　being



of　which　depends　the　being　of　the　fact　inferred。　Nor　are　the



geometer's　hypotheses　false；　as　some　have　held；　urging　that　one　must



not　employ　falsehood　and　that　the　geometer　is　uttering　falsehood　in



stating　that　the　line　which　he　draws　is　a　foot　long　or　straight；



when　it　is　actually　neither。　The　truth　is　that　the　geometer　does　not



draw　any　conclusion　from　the　being　of　the　particular　line　of　which



he　speaks；　but　from　what　his　diagrams　symbolize。　A　further　distinction



is　that　all　hypotheses　and　illegitimate　postulates　are　either



universal　or　particular；　whereas　a　definition　is　neither。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　11







　　So　demonstration　does　not　necessarily　imply　the　being　of　Forms　nor　a



One　beside　a　Many；　but　it　does　necessarily　imply　the　possibility　of



truly　predicating　one　of　many；　since　without　this　possibility　we



cannot　save　the　universal；　and　if　the　universal　goes；　the　middle



term　goes　witb。　it；　and　so　demonstration　becomes　impossible。　We



conclude；　then；　that　there　must　be　a　single　identical　term



unequivocally　predicable　of　a　number　of　individuals。



　　The　law　that　it　is　impossible　to　affirm　and　deny　simultaneously



the　same　predicate　of　the　same　subject　is　not　expressly　posited　by　any



demonstration　except　when　the　conclusion　also　has　to　be　expressed　in



that　form；　in　which　case　the　proof　lays　down　as　its　major　premiss　that



the　major　is　truly　affirmed　of　the　middle　but　falsely　denied。　It　makes



no　difference；　however；　if　we　add　to　the　middle；　or　again　to　the　minor



term；　the　corresponding　negative。　For　grant　a　minor　term　of　which　it



is　true　to　predicate　man…even　if　it　be　also　true　to　predicate



not…man　of　itstill　grant　simply　that　man　is　animal　and　not



not…animal；　and　the　conclusion　follows：　for　it　will　still　be　true　to



say　that　Calliaseven　if　it　be　also　true　to　say　that



not…Calliasis　animal　and　not　not…animal。　The　reason　is　that　the



major　term　is　predicable　not　only　of　the　middle；　but　of　something



other　than　the　middle　as　well；　being　of　wider　application；　so　that　the



conclusion　is　not　affected　even　if　the　middle　is　extended　to　cover　the



original　middle　term　and　also　what　is　not　the　original　middle　term。



　　The　law　that　every　predicate　can　be　either　truly　affirmed　or　truly



denied　of　every　subject　is　posited　by　such　demonstration　as　uses



reductio　ad　impossibile；　and　then　not　always　universally；　but　so　far



as　it　is　requisite；　within　the　limits；　that　is；　of　the　genus…the



genus；　I　mean　（as　I　have　already　explained）；　to　which　the　man　of



science　applies　his　demonstrations。　In　virtue　of　the　common　elements



of　demonstration…I　mean　the　common　axioms　which　are　used　as



premisses　of　demonstration；　not　the　subjects　nor　the　attributes



demonstrated　as　belonging　to　them…all　the　sciences　have　communion　with



one　another；　and　in　communion　with　them　all　is　dialectic　and　any



science　which　might　attempt　a　universal　proof　of　axioms　such　as　the



law　of　excluded　middle；　the　law　that　the　subtraction　of　equals　from



equals　leaves　equal　remainders；　or　other　axioms　of　the　same　kind。



Dialectic　has　no　definite　sphere　of　this　kind；　not　being　confined　to　a



single　genus。　Otherwise　its　method　would　not　be　interrogative；　for　the



interrogative　method　is　barred　to　the　demonstrator；　who　cannot　use　the



opposite　facts　to　prove　the　same　nexus。　This　was　shown　in　my　work　on



the　syllogism。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　12







　　If　a　syllogistic　question　is　equivalent　to　a　proposition　embodying



one　of　the　two　sides　of　a　contradiction；　and　if　each　science　has　its



peculiar　propositions　from　which　its　peculiar　conclusi