prior analytics-第12章

按键盘上方向键 ← 或 → 可快速上下翻页，按键盘上的 Enter 键可回到本书目录页，按键盘上方向键 ↑ 可回到本页顶部！
————未阅读完？加入书签已便下次继续阅读！





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　uni