prior analytics-第9章

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premiss　is　necessary；　if　it　is　affirmative　the　conclusion　will　be



neither　necessary　or　assertoric；　but　if　it　is　negative　the　syllogism



will　result　in　a　negative　assertoric　proposition；　as　above。　In　these



also　we　must　understand　the　expression　'possible'　in　the　conclusion　in



the　same　way　as　before。



　　First　let　the　premisses　be　problematic　and　suppose　that　both　A　and　B



may　possibly　belong　to　every　C。　Since　then　the　affirmative　proposition



is　convertible　into　a　particular；　and　B　may　possibly　belong　to　every



C；　it　follows　that　C　may　possibly　belong　to　some　B。　So；　if　A　is



possible　for　every　C；　and　C　is　possible　for　some　of　the　Bs；　then　A



is　possible　for　some　of　the　Bs。　For　we　have　got　the　first　figure。



And　A　if　may　possibly　belong　to　no　C；　but　B　may　possibly　belong　to　all



C；　it　follows　that　A　may　possibly　not　belong　to　some　B：　for　we　shall



have　the　first　figure　again　by　conversion。　But　if　both　premisses



should　be　negative　no　necessary　consequence　will　follow　from　them　as



they　are　stated；　but　if　the　premisses　are　converted　into　their



corresponding　affirmatives　there　will　be　a　syllogism　as　before。　For　if



A　and　B　may　possibly　not　belong　to　C；　if　'may　possibly　belong'　is



substituted　we　shall　again　have　the　first　figure　by　means　of



conversion。　But　if　one　of　the　premisses　is　universal；　the　other



particular；　a　syllogism　will　be　possible；　or　not；　under　the



arrangement　of　the　terms　as　in　the　case　of　assertoric　propositions。



Suppose　that　A　may　possibly　belong　to　all　C；　and　B　to　some　C。　We　shall



have　the　first　figure　again　if　the　particular　premiss　is　converted。



For　if　A　is　possible　for　all　C；　and　C　for　some　of　the　Bs；　then　A　is



possible　for　some　of　the　Bs。　Similarly　if　the　proposition　BC　is



universal。　Likewise　also　if　the　proposition　AC　is　negative；　and　the



proposition　BC　affirmative：　for　we　shall　again　have　the　first　figure



by　conversion。　But　if　both　premisses　should　be　negative…the　one



universal　and　the　other　particular…although　no　syllogistic



conclusion　will　follow　from　the　premisses　as　they　are　put；　it　will



follow　if　they　are　converted；　as　above。　But　when　both　premisses　are



indefinite　or　particular；　no　syllogism　can　be　formed：　for　A　must



belong　sometimes　to　all　B　and　sometimes　to　no　B。　To　illustrate　the



affirmative　relation　take　the　terms　animal…man…white；　to　illustrate



the　negative；　take　the　terms　horse…man…whitewhite　being　the　middle



term。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　21







　　If　one　premiss　is　pure；　the　other　problematic；　the　conclusion　will



be　problematic；　not　pure；　and　a　syllogism　will　be　possible　under　the



same　arrangement　of　the　terms　as　before。　First　let　the　premisses　be



affirmative：　suppose　that　A　belongs　to　all　C；　and　B　may　possibly



belong　to　all　C。　If　the　proposition　BC　is　converted；　we　shall　have　the



first　figure；　and　the　conclusion　that　A　may　possibly　belong　to　some　of



the　Bs。　For　when　one　of　the　premisses　in　the　first　figure　is



problematic；　the　conclusion　also　（as　we　saw）　is　problematic。　Similarly



if　the　proposition　BC　is　pure；　AC　problematic；　or　if　AC　is　negative；



BC　affirmative；　no　matter　which　of　the　two　is　pure；　in　both　cases



the　conclusion　will　be　problematic：　for　the　first　figure　is　obtained



once　more；　and　it　has　been　proved　that　if　one　premiss　is　problematic



in　that　figure　the　conclusion　also　will　be　problematic。　But　if　the



minor　premiss　BC　is　negative；　or　if　both　premisses　are　negative；　no



syllogistic　conclusion　can　be　drawn　from　the　premisses　as　they



stand；　but　if　they　are　converted　a　syllogism　is　obtained　as　before。



　　If　one　of　the　premisses　is　universal；　the　other　particular；　then



when　both　are　affirmative；　or　when　the　universal　is　negative；　the



particular　affirmative；　we　shall　have　the　same　sort　of　syllogisms：　for



all　are　completed　by　means　of　the　first　figure。　So　it　is　clear　that　we



shall　have　not　a　pure　but　a　problematic　syllogistic　conclusion。　But　if



the　affirmative　premiss　is　universal；　the　negative　particular；　the



proof　will　proceed　by　a　reductio　ad　impossibile。　Suppose　that　B



belongs　to　all　C；　and　A　may　possibly　not　belong　to　some　C：　it



follows　that　may　possibly　not　belong　to　some　B。　For　if　A　necessarily



belongs　to　all　B；　and　B　（as　has　been　assumed）　belongs　to　all　C；　A　will



necessarily　belong　to　all　C：　for　this　has　been　proved　before。　But　it



was　assumed　at　the　outset　that　A　may　possibly　not　belong　to　some　C。



　　Whenever　both　premisses　are　indefinite　or　particular；　no　syllogism



will　be　possible。　The　demonstration　is　the　same　as　was　given　in　the



case　of　universal　premisses；　and　proceeds　by　means　of　the　same　terms。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　22







　　If　one　of　the　premisses　is　necessary；　the　other　problematic；　when



the　premisses　are　affirmative　a　problematic　affirmative　conclusion　can



always　be　drawn；　when　one　proposition　is　affirmative；　the　other



negative；　if　the　affirmative　is　necessary　a　problematic　negative　can



be　inferred；　but　if　the　negative　proposition　is　necessary　both　a



problematic　and　a　pure　negative　conclusion　are　possible。　But　a



necessary　negative　conclusion　will　not　be　possible；　any　more　than　in



the　other　figures。　Suppose　first　that　the　premisses　are　affirmative；



i。e。　that　A　necessarily　belongs　to　all　C；　and　B　may　possibly　belong　to



all　C。　Since　then　A　must　belong　to　all　C；　and　C　may　belong　to　some



B；　it　follows　that　A　may　（not　does）　belong　to　some　B：　for　so　it



resulted　in　the　first　figure。　A　similar　proof　may　be　given　if　the



proposition　BC　is　necessary；　and　AC　is　problematic。　Again　suppose



one　proposition　is　affirmative；　the　other　negative；　the　affirmative



being　necessary：　i。e。　suppose　A　may　possibly　belong　to　no　C；　but　B



necessarily　belongs　to　all　C。　We　shall　have　the　first　figure　once



more：　and…since　the　negative　premiss　is　problematic…it　is　clear　that



the　conclusion　will　be　problematic：　for　when　the　premisses　stand



thus　in　the　first　figure；　the　conclusion　（as　we　found）　is　problematic。



But　if　the　negative　premiss　is　necessary；　the　conclusion　will　be　not



only　that　A　may　possibly　not　belong　to　some　B　but　also　that　it　does



not　belong　to　some　B。　For　suppose　that　A　necessarily　does　not　belong



to　C；　but　B　may　belong　to　all　C。　If　the　affirmative　proposition　BC



is　converted；　we　shall　have　the　first　figure；　and　the　negative　premiss



is　necessary。　But　when　the　premisses　stood　thus；　it　resulted　that　A



might　possibly　not　belong　to　some　C；　and　that　it　did　not　belong　to



some　C；　consequently　here　it　follows　that　A　does　not　belong　to　some　B。



But　when　the　minor　premiss　is　negative；　if　it　is　problematic　we



shall　have　a　syllogism　by　altering　the　premiss　into　its



complementary　affirmative；　as　before；　but　if　it　is　necessary　no



syllogism　can　be　formed。　For　A　sometimes　necessarily　belongs　to　all　B；



and　sometimes　cannot　possibly　belong　to　any　B。　To　illustrate　the



former　take　the　terms　sleep…sleeping　horse…man；　to　illustrate　the



latter　take　the　terms　sleep…waking　horse…man。



　　Similar　results　will　obtain　if　one　of　the　terms　is　related



universally　to　the　middle；　the　other　in　part。　If　both　premisses　are



affirmative；　the　conclusion　will　be　problematic；　not　pure；　and　also



when　one　premiss　is　negative；　the　other　affirmative；　the　latter



being　necessary。　But　when　the　negative　premiss　is　necessary；　the



conclusion　also　will　be　a　pure　negative　proposition；　for　the　same　kind



of　proof　can　be　given　whether　the　terms　are　universal　or　not。　For



the　syllogisms　must　be　made　perfect　by　means　of　the　first　figure；　so



that　a　result　which　follows　in　the　first　figure　follows　also　in　the



third。　But　when　the　minor　premiss　is　negative　and　universal；　if　it



is　problematic　a　syllogism　can　be　formed　by　means　of　conversion；　but



if　it　is　necessary　a　syllogism　is　not　possible。　The　proof　will



follow　the　same　course　as　where　the　premisses　are　universal；　and　the



same　terms　may　be　used。



　　It　is　clear　then　in　this　figure　also　when　and　how　a　syllogism　can　be



formed；　and　when　the　conclusion　is　problematic；　and　when　it　is　pure。



It　is　evident　also　that　all　syllogisms　in　this　figure　are　imperfect；



and　that　they　are　made　perfect　by　means　of　the　first　figure。







　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　23







　　It　is　clear　from　what　has　been　said　that　the　syllogisms　in　these



figures　are　made　perfect　by　means　of　universal　syllogisms　in　the　first



figure　and　are　reduced　to　them。　That　every　syllogism　without



qualification　can　be　so　treated；　will　be　clear　presently；　when　it



has　been　proved　that　every　syllogism　is　formed　through　one　or　other　of



these　figures。



　　It　is　necessary　that　every　demonstration　and　every　syllogism



should　prove　either　that　something　belongs　or　that　it　does　not；　and



this　either　universally　or　in　part；　and　further　either　ostensively



or　hypothetically。　One　sort　of　hypothetical　proof　is　the　reductio　ad



impossibile。　Let　us　speak　first　of　ostensive　syllogisms：　for　after



these　have　been　pointed　out　the　truth　of　our　contention　will　be



clear　with　regard　to　those　which　are　proved　per　impossibile；　and　in



general　hypothetically。



　　If　then　one　wants　to　prove　syllogistically　A　of　B；　either　as　an



attribute　of　it　or　as　not　an　attribute　of　it；　one　must　assert



something　of　something　else。　If　now　A　should　be　asserted　of　B；　the



proposition　originally　in　question　will　have　been　assumed。　But　if　A



should　be　asserted　of　C；　but　C　should　not　be　asserted　of　anything；　nor



anything　of　it；　nor　anything　else　of　A；　no　syllogism　will　be　possible。



For　nothing　necessarily　follows　from　the　assertion　of　some　one　thing



concerning　some　other　single　thing。　Thus　we　must　take　another



premiss　as　well。　If　then　A　be　asserted　of　something　else；　or　something



else　of　A；　or　something　different　of　C；　nothing　prevents　a　syllogism



being　formed；　but　it　will　not　be　in　relation　to　B　through　the



premisses　taken。　Nor　when　C　belongs　to　something　else；　and　that　to



something　else　and　so　on；　no　connexion　however　being　made　with　B；　will



a　syllogism　be　possible　concerning　A　in　its　relation　to　B。　For　in



general　we　stated　that　no　syllogism　can　establish　the　attribution　of



one　thing　to　another；　unless　some　middle　term　is　taken；　which　is



somehow　related　to　each　by　way　of　predication。　For　the　syllogism　in



general　is　made　out　of　premisses；　and　a　syllogism　referring　to　this



out　of　premisses　with　the　same　reference；　and　a　syllogism　relating



this　to　that　proceeds　through　premisses　which　relate　this　to　that。　But



it　is　impossi