posterior analytics- 第4部分

necessary　premisses　is　as　follows。　Where　demonstration　is　possible；



one　who　can　give　no　account　which　includes　the　cause　has　no　scientific



knowledge。　If；　then；　we　suppose　a　syllogism　in　which；　though　A



necessarily　inheres　in　C；　yet　B；　the　middle　term　of　the　demonstration；



is　not　necessarily　connected　with　A　and　C；　then　the　man　who　argues



thus　has　no　reasoned　knowledge　of　the　conclusion；　since　this



conclusion　does　not　owe　its　necessity　to　the　middle　term；　for　though



the　conclusion　is　necessary；　the　mediating　link　is　a　contingent



fact。　Or　again；　if　a　man　is　without　knowledge　now；　though　he　still



retains　the　steps　of　the　argument；　though　there　is　no　change　in



himself　or　in　the　fact　and　no　lapse　of　memory　on　his　part；　then



neither　had　he　knowledge　previously。　But　the　mediating　link；　not　being



necessary；　may　have　perished　in　the　interval；　and　if　so；　though



there　be　no　change　in　him　nor　in　the　fact；　and　though　he　will　still



retain　the　steps　of　the　argument；　yet　he　has　not　knowledge；　and



therefore　had　not　knowledge　before。　Even　if　the　link　has　not



actually　perished　but　is　liable　to　perish；　this　situation　is



possible　and　might　occur。　But　such　a　condition　cannot　be　knowledge。



　　When　the　conclusion　is　necessary；　the　middle　through　which　it　was



proved　may　yet　quite　easily　be　non…necessary。　You　can　in　fact　infer



the　necessary　even　from　a　non…necessary　premiss；　just　as　you　can　infer



the　true　from　the　not　true。　On　the　other　hand；　when　the　middle　is



necessary　the　conclusion　must　be　necessary；　just　as　true　premisses



always　give　a　true　conclusion。　Thus；　if　A　is　necessarily　predicated　of



B　and　B　of　C；　then　A　is　necessarily　predicated　of　C。　But　when　the



conclusion　is　nonnecessary　the　middle　cannot　be　necessary　either。



Thus：　let　A　be　predicated　non…necessarily　of　C　but　necessarily　of　B；



and　let　B　be　a　necessary　predicate　of　C；　then　A　too　will　be　a



necessary　predicate　of　C；　which　by　hypothesis　it　is　not。



　　To　sum　up；　then：　demonstrative　knowledge　must　be　knowledge　of　a



necessary　nexus；　and　therefore　must　clearly　be　obtained　through　a



necessary　middle　term；　otherwise　its　possessor　will　know　neither　the



cause　nor　the　fact　that　his　conclusion　is　a　necessary　connexion。



Either　he　will　mistake　the　non…necessary　for　the　necessary　and　believe



the　necessity　of　the　conclusion　without　knowing　it；　or　else　he　will



not　even　believe　it…in　which　case　he　will　be　equally　ignorant；　whether



he　actually　infers　the　mere　fact　through　middle　terms　or　the



reasoned　fact　and　from　immediate　premisses。



　　Of　accidents　that　are　not　essential　according　to　our　definition　of



essential　there　is　no　demonstrative　knowledge；　for　since　an



accident；　in　the　sense　in　which　I　here　speak　of　it；　may　also　not



inhere；　it　is　impossible　to　prove　its　inherence　as　a　necessary



conclusion。　A　difficulty；　however；　might　be　raised　as　to　why　in



dialectic；　if　the　conclusion　is　not　a　necessary　connexion；　such　and



such　determinate　premisses　should　be　proposed　in　order　to　deal　with



such　and　such　determinate　problems。　Would　not　the　result　be　the　same



if　one　asked　any　questions　whatever　and　then　merely　stated　one's



conclusion？　The　solution　is　that　determinate　questions　have　to　be　put；



not　because　the　replies　to　them　affirm　facts　which　necessitate　facts



affirmed　by　the　conclusion；　but　because　these　answers　are　propositions



which　if　the　answerer　affirm；　he　must　affirm　the　conclusion　and　affirm



it　with　truth　if　they　are　true。



　　Since　it　is　just　those　attributes　within　every　genus　which　are



essential　and　possessed　by　their　respective　subjects　as　such　that



are　necessary　it　is　clear　that　both　the　conclusions　and　the



premisses　of　demonstrations　which　produce　scientific　knowledge　are



essential。　For　accidents　are　not　necessary：　and；　further；　since



accidents　are　not　necessary　one　does　not　necessarily　have　reasoned



knowledge　of　a　conclusion　drawn　from　them　（this　is　so　even　if　the



accidental　premisses　are　invariable　but　not　essential；　as　in　proofs



through　signs；　for　though　the　conclusion　be　actually　essential；　one



will　not　know　it　as　essential　nor　know　its　reason）；　but　to　have



reasoned　knowledge　of　a　conclusion　is　to　know　it　through　its　cause。　We



may　conclude　that　the　middle　must　be　consequentially　connected　with



the　minor；　and　the　major　with　the　middle。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　7







　　It　follows　that　we　cannot　in　demonstrating　pass　from　one　genus　to



another。　We　cannot；　for　instance；　prove　geometrical　truths　by



arithmetic。　For　there　are　three　elements　in　demonstration：　（1）　what　is



proved；　the　conclusion…an　attribute　inhering　essentially　in　a　genus；



（2）　the　axioms；　i。e。　axioms　which　are　premisses　of　demonstration；



（3）　the　subject…genus　whose　attributes；　i。e。　essential　properties；　are



revealed　by　the　demonstration。　The　axioms　which　are　premisses　of



demonstration　may　be　identical　in　two　or　more　sciences：　but　in　the



case　of　two　different　genera　such　as　arithmetic　and　geometry　you



cannot　apply　arithmetical　demonstration　to　the　properties　of



magnitudes　unless　the　magnitudes　in　question　are　numbers。　How　in



certain　cases　transference　is　possible　I　will　explain　later。



　　Arithmetical　demonstration　and　the　other　sciences　likewise



possess；　each　of　them；　their　own　genera；　so　that　if　the



demonstration　is　to　pass　from　one　sphere　to　another；　the　genus　must　be



either　absolutely　or　to　some　extent　the　same。　If　this　is　not　so；



transference　is　clearly　impossible；　because　the　extreme　and　the　middle



terms　must　be　drawn　from　the　same　genus：　otherwise；　as　predicated；



they　will　not　be　essential　and　will　thus　be　accidents。　That　is　why



it　cannot　be　proved　by　geometry　that　opposites　fall　under　one　science；



nor　even　that　the　product　of　two　cubes　is　a　cube。　Nor　can　the



theorem　of　any　one　science　be　demonstrated　by　means　of　another



science；　unless　these　theorems　are　related　as　subordinate　to



superior　（e。g。　as　optical　theorems　to　geometry　or　harmonic　theorems　to



arithmetic）。　Geometry　again　cannot　prove　of　lines　any　property　which



they　do　not　possess　qua　lines；　i。e。　in　virtue　of　the　fundamental



truths　of　their　peculiar　genus：　it　cannot　show；　for　example；　that



the　straight　line　is　the　most　beautiful　of　lines　or　the　contrary　of



the　circle；　for　these　qualities　do　not　belong　to　lines　in　virtue　of



their　peculiar　genus；　but　through　some　property　which　it　shares　with



other　genera。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　8







　　It　is　also　clear　that　if　the　premisses　from　which　the　syllogism



proceeds　are　commensurately　universal；　the　conclusion　of　such　i。e。



in　the　unqualified　sense…must　also　be　eternal。　Therefore　no



attribute　can　be　demonstrated　nor　known　by　strictly　scientific



knowledge　to　inhere　in　perishable　things。　The　proof　can　only　be



accidental；　because　the　attribute's　connexion　with　its　perishable



subject　is　not　commensurately　universal　but　temporary　and　special。



If　such　a　demonstration　is　made；　one　premiss　must　be　perishable　and



not　commensurately　universal　（perishable　because　only　if　it　is



perishable　will　the　conclusion　be　perishable；　not　commensurately



universal；　because　the　predicate　will　be　predicable　of　some



instances　of　the　subject　and　not　of　others）；　so　that　the　conclusion



can　only　be　that　a　fact　is　true　at　the　moment…not　commensurately　and



universally。　The　same　is　true　of　definitions；　since　a　definition　is



either　a　primary　premiss　or　a　conclusion　of　a　demonstration；　or　else



only　differs　from　a　demonstration　in　the　order　of　its　terms。



Demonstration　and　science　of　merely　frequent　occurrences…e。g。　of



eclipse　as　happening　to　the　moon…are；　as　such；　clearly　eternal：



whereas　so　far　as　they　are　not　eternal　they　are　not　fully



commensurate。　Other　subjects　too　have　properties　attaching　to　them



in　the　same　way　as　eclipse　attaches　to　the　moon。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　9







　　It　is　clear　that　if　the　conclusion　is　to　show　an　attribute



inhering　as　such；　nothing　can　be　demonstrated　except　from　its



'appropriate'　basic　truths。　Consequently　a　proof　even　from　true；



indemonstrable；　and　immediate　premisses　does　not　constitute　knowledge。



Such　proofs　are　like　Bryson's　method　of　squaring　the　circle；　for



they　operate　by　taking　as　their　middle　a　common　character…a　character；



therefore；　which　the　subject　may　share　with　another…and　consequently



they　apply　equally　to　subjects　different　in　kind。　They　therefore



afford　knowledge　of　an　attribute　only　as　inhering　accidentally；　not　as



belonging　to　its　subject　as　such：　otherwise　they　would　not　have　been



applicable　to　another　genus。



　　Our　knowledge　of　any　attribute's　connexion　with　a　subject　is



accidental　unless　we　know　that　connexion　through　the　middle　term　in



virtue　of　which　it　inheres；　and　as　an　inference　from　basic　premisses



essential　and　'appropriate'　to　the　subject…unless　we　know；　e。g。　the



property　of　possessing　angles　equal　to　two　right　angles　as　belonging



to　that　subject　in　which　it　inheres　essentially；　and　as　inferred



from　basic　premisses　essential　and　'appropriate'　to　that　subject：　so



that　if　that　middle　term　also　belongs　essentially　to　the　minor；　the



middle　must　belong　to　the　same　kind　as　the　major　and　minor　terms。



The　only　exceptions　to　this　rule　are　such　cases　as　theorems　in



harmonics　which　are　demonstrable　by　arithmetic。　Such　theorems　are



proved　by　the　same　middle　terms　as　arithmetical　properties；　but　with　a



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



genus　is　separate