prior analytics-第31章

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be　made　out　of　opposed　premisses：　no　affirmative　syllogism　is　possible



because　both　premisses　must　be　affirmative；　but　opposites　are；　the　one



affirmative；　the　other　negative：　no　negative　syllogism　is　possible



because　opposites　affirm　and　deny　the　same　predicate　of　the　same



subject；　and　the　middle　term　in　the　first　figure　is　not　predicated



of　both　extremes；　but　one　thing　is　denied　of　it；　and　it　is　affirmed　of



something　else：　but　such　premisses　are　not　opposed。



　　In　the　middle　figure　a　syllogism　can　be　made　both



oLcontradictories　and　of　contraries。　Let　A　stand　for　good；　let　B　and　C



stand　for　science。　If　then　one　assumes　that　every　science　is　good；　and



no　science　is　good；　A　belongs　to　all　B　and　to　no　C；　so　that　B



belongs　to　no　C：　no　science　then　is　a　science。　Similarly　if　after



taking　'every　science　is　good'　one　took　'the　science　of　medicine　is



not　good'；　for　A　belongs　to　all　B　but　to　no　C；　so　that　a　particular



science　will　not　be　a　science。　Again；　a　particular　science　will　not　be



a　science　if　A　belongs　to　all　C　but　to　no　B；　and　B　is　science；　C



medicine；　and　A　supposition：　for　after　taking　'no　science　is



supposition'；　one　has　assumed　that　a　particular　science　is



supposition。　This　syllogism　differs　from　the　preceding　because　the



relations　between　the　terms　are　reversed：　before；　the　affirmative



statement　concerned　B；　now　it　concerns　C。　Similarly　if　one　premiss



is　not　universal：　for　the　middle　term　is　always　that　which　is　stated



negatively　of　one　extreme；　and　affirmatively　of　the　other。



Consequently　it　is　possible　that　contradictories　may　lead　to　a



conclusion；　though　not　always　or　in　every　mood；　but　only　if　the



terms　subordinate　to　the　middle　are　such　that　they　are　either



identical　or　related　as　whole　to　part。　Otherwise　it　is　impossible：　for



the　premisses　cannot　anyhow　be　either　contraries　or　contradictories。



　　In　the　third　figure　an　affirmative　syllogism　can　never　be　made　out



of　opposite　premisses；　for　the　reason　given　in　reference　to　the



first　figure；　but　a　negative　syllogism　is　possible　whether　the　terms



are　universal　or　not。　Let　B　and　C　stand　for　science；　A　for　medicine。



If　then　one　should　assume　that　all　medicine　is　science　and　that　no



medicine　is　science；　he　has　assumed　that　B　belongs　to　all　A　and　C　to



no　A；　so　that　a　particular　science　will　not　be　a　science。　Similarly　if



the　premiss　BA　is　not　assumed　universally。　For　if　some　medicine　is



science　and　again　no　medicine　is　science；　it　results　that　some　science



is　not　science；　The　premisses　are　contrary　if　the　terms　are　taken



universally；　if　one　is　particular；　they　are　contradictory。



　　We　must　recognize　that　it　is　possible　to　take　opposites　in　the　way



we　said；　viz。　'all　science　is　good'　and　'no　science　is　good'　or



'some　science　is　not　good'。　This　does　not　usually　escape　notice。　But



it　is　possible　to　establish　one　part　of　a　contradiction　through



other　premisses；　or　to　assume　it　in　the　way　suggested　in　the　Topics。



Since　there　are　three　oppositions　to　affirmative　statements；　it



follows　that　opposite　statements　may　be　assumed　as　premisses　in　six



ways；　we　may　have　either　universal　affirmative　and　negative；　or



universal　affirmative　and　particular　negative；　or　particular



affirmative　and　universal　negative；　and　the　relations　between　the



terms　may　be　reversed；　e。g。　A　may　belong　to　all　B　and　to　no　C；　or　to



all　C　and　to　no　B；　or　to　all　of　the　one；　not　to　all　of　the　other；　here



too　the　relation　between　the　terms　may　be　reversed。　Similarly　in　the



third　figure。　So　it　is　clear　in　how　many　ways　and　in　what　figures　a



syllogism　can　be　made　by　means　of　premisses　which　are　opposed。



　　It　is　clear　too　that　from　false　premisses　it　is　possible　to　draw　a



true　conclusion；　as　has　been　said　before；　but　it　is　not　possible　if



the　premisses　are　opposed。　For　the　syllogism　is　always　contrary　to　the



fact；　e。g。　if　a　thing　is　good；　it　is　proved　that　it　is　not　good；　if　an



animal；　that　it　is　not　an　animal　because　the　syllogism　springs　out



of　a　contradiction　and　the　terms　presupposed　are　either　identical　or



related　as　whole　and　part。　It　is　evident　also　that　in　fallacious



reasonings　nothing　prevents　a　contradiction　to　the　hypothesis　from



resulting；　e。g。　if　something　is　odd；　it　is　not　odd。　For　the



syllogism　owed　its　contrariety　to　its　contradictory　premisses；　if　we



assume　such　premisses　we　shall　get　a　result　that　contradicts　our



hypothesis。　But　we　must　recognize　that　contraries　cannot　be　inferred



from　a　single　syllogism　in　such　a　way　that　we　conclude　that　what　is



not　good　is　good；　or　anything　of　that　sort　unless　a　self…contradictory



premiss　is　at　once　assumed；　e。g。　'every　animal　is　white　and　not



white'；　and　we　proceed　'man　is　an　animal'。　Either　we　must　introduce



the　contradiction　by　an　additional　assumption；　assuming；　e。g。；　that



every　science　is　supposition；　and　then　assuming　'Medicine　is　a



science；　but　none　of　it　is　supposition'　（which　is　the　mode　in　which



refutations　are　made）；　or　we　must　argue　from　two　syllogisms。　In　no



other　way　than　this；　as　was　said　before；　is　it　possible　that　the



premisses　should　be　really　contrary。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　16







　　To　beg　and　assume　the　original　question　is　a　species　of　failure　to



demonstrate　the　problem　proposed；　but　this　happens　in　many　ways。　A　man



may　not　reason　syllogistically　at　all；　or　he　may　argue　from



premisses　which　are　less　known　or　equally　unknown；　or　he　may　establish



the　antecedent　by　means　of　its　consequents；　for　demonstration　proceeds



from　what　is　more　certain　and　is　prior。　Now　begging　the　question　is



none　of　these：　but　since　we　get　to　know　some　things　naturally



through　themselves；　and　other　things　by　means　of　something　else　（the



first　principles　through　themselves；　what　is　subordinate　to　them



through　something　else）；　whenever　a　man　tries　to　prove　what　is　not



self…evident　by　means　of　itself；　then　he　begs　the　original　question。



This　may　be　done　by　assuming　what　is　in　question　at　once；　it　is　also



possible　to　make　a　transition　to　other　things　which　would　naturally　be



proved　through　the　thesis　proposed；　and　demonstrate　it　through　them；



e。g。　if　A　should　be　proved　through　B；　and　B　through　C；　though　it　was



natural　that　C　should　be　proved　through　A：　for　it　turns　out　that　those



who　reason　thus　are　proving　A　by　means　of　itself。　This　is　what　those



persons　do　who　suppose　that　they　are　constructing　parallel　straight



lines：　for　they　fail　to　see　that　they　are　assuming　facts　which　it　is



impossible　to　demonstrate　unless　the　parallels　exist。　So　it　turns



out　that　those　who　reason　thus　merely　say　a　particular　thing　is；　if　it



is：　in　this　way　everything　will　be　self…evident。　But　that　is



impossible。



　　If　then　it　is　uncertain　whether　A　belongs　to　C；　and　also　whether　A



belongs　to　B；　and　if　one　should　assume　that　A　does　belong　to　B；　it



is　not　yet　clear　whether　he　begs　the　original　question；　but　it　is



evident　that　he　is　not　demonstrating：　for　what　is　as　uncertain　as



the　question　to　be　answered　cannot　be　a　principle　of　a



demonstration。　If　however　B　is　so　related　to　C　that　they　are



identical；　or　if　they　are　plainly　convertible；　or　the　one　belongs　to



the　other；　the　original　question　is　begged。　For　one　might　equally　well



prove　that　A　belongs　to　B　through　those　terms　if　they　are　convertible。



But　if　they　are　not　convertible；　it　is　the　fact　that　they　are　not　that



prevents　such　a　demonstration；　not　the　method　of　demonstrating。　But　if



one　were　to　make　the　conversion；　then　he　would　be　doing　what　we　have



described　and　effecting　a　reciprocal　proof　with　three　propositions。



　　Similarly　if　he　should　assume　that　B　b