prior analytics-第22章

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and　let　D　stand　for　not　to　be　not…good'　and　be　placed　under　A。　Then



either　A　or　B　will　belong　to　everything；　but　they　will　never　belong　to



the　same　thing；　and　either　C　or　D　will　belong　to　everything；　but



they　will　never　belong　to　the　same　thing。　And　B　must　belong　to



everything　to　which　C　belongs。　For　if　it　is　true　to　say　'it　is　a



not…white'；　it　is　true　also　to　say　'it　is　not　white'：　for　it　is



impossible　that　a　thing　should　simultaneously　be　white　and　be



not…white；　or　be　a　not…white　log　and　be　a　white　log；　consequently　if



the　affirmation　does　not　belong；　the　denial　must　belong。　But　C　does



not　always　belong　to　B：　for　what　is　not　a　log　at　all；　cannot　be　a



not…white　log　either。　On　the　other　hand　D　belongs　to　everything　to



which　A　belongs。　For　either　C　or　D　belongs　to　everything　to　which　A



belongs。　But　since　a　thing　cannot　be　simultaneously　not…white　and



white；　D　must　belong　to　everything　to　which　A　belongs。　For　of　that



which　is　white　it　is　true　to　say　that　it　is　not　not…white。　But　A　is



not　true　of　all　D。　For　of　that　which　is　not　a　log　at　all　it　is　not



true　to　say　A；　viz。　that　it　is　a　white　log。　Consequently　D　is　true；



but　A　is　not　true；　i。e。　that　it　is　a　white　log。　It　is　clear　also



that　A　and　C　cannot　together　belong　to　the　same　thing；　and　that　B



and　D　may　possibly　belong　to　the　same　thing。



　　Privative　terms　are　similarly　related　positive　ter　terms　respect



of　this　arrangement。　Let　A　stand　for　'equal'；　B　for　'not　equal'；　C　for



'unequal'；　D　for　'not　unequal'。



　　In　many　things　also；　to　some　of　which　something　belongs　which　does



not　belong　to　others；　the　negation　may　be　true　in　a　similar　way；



viz。　that　all　are　not　white　or　that　each　is　not　white；　while　that　each



is　not…white　or　all　are　not…white　is　false。　Similarly　also　'every



animal　is　not…white'　is　not　the　negation　of　'every　animal　is　white'



（for　both　are　false）：　the　proper　negation　is　'every　animal　is　not



white'。　Since　it　is　clear　that　'it　is　not…white'　and　'it　is　not　white'



mean　different　things；　and　one　is　an　affirmation；　the　other　a



denial；　it　is　evident　that　the　method　of　proving　each　cannot　be　the



same；　e。g。　that　whatever　is　an　animal　is　not　white　or　may　not　be



white；　and　that　it　is　true　to　call　it　not…white；　for　this　means　that



it　is　not…white。　But　we　may　prove　that　it　is　true　to　call　it　white



or　not…white　in　the　same　way　for　both　are　proved　constructively　by



means　of　the　first　figure。　For　the　expression　'it　is　true'　stands　on　a



similar　footing　to　'it　is'。　For　the　negation　of　'it　is　true　to　call　it



white'　is　not　'it　is　true　to　call　it　not…white'　but　'it　is　not　true　to



call　it　white'。　If　then　it　is　to　be　true　to　say　that　whatever　is　a　man



is　musical　or　is　not…musical；　we　must　assume　that　whatever　is　an



animal　either　is　musical　or　is　not…musical；　and　the　proof　has　been



made。　That　whatever　is　a　man　is　not　musical　is　proved　destructively　in



the　three　ways　mentioned。



　　In　general　whenever　A　and　B　are　such　that　they　cannot　belong　at



the　same　time　to　the　same　thing；　and　one　of　the　two　necessarily



belongs　to　everything；　and　again　C　and　D　are　related　in　the　same



way；　and　A　follows　C　but　the　relation　cannot　be　reversed；　then　D



must　follow　B　and　the　relation　cannot　be　reversed。　And　A　and　D　may



belong　to　the　same　thing；　but　B　and　C　cannot。　First　it　is　clear　from



the　following　consideration　that　D　follows　B。　For　since　either　C　or



D　necessarily　belongs　to　everything；　and　since　C　cannot　belong　to　that



to　which　B　belongs；　because　it　carries　A　along　with　it　and　A　and　B



cannot　belong　to　the　same　thing；　it　is　clear　that　D　must　follow　B。



Again　since　C　does　not　reciprocate　with　but　A；　but　C　or　D　belongs　to



everything；　it　is　possible　that　A　and　D　should　belong　to　the　same



thing。　But　B　and　C　cannot　belong　to　the　same　thing；　because　A



follows　C；　and　so　something　impossible　results。　It　is　clear　then



that　B　does　not　reciprocate　with　D　either；　since　it　is　possible　that　D



and　A　should　belong　at　the　same　time　to　the　same　thing。



　　It　results　sometimes　even　in　such　an　arrangement　of　terms　that　one



is　deceived　through　not　apprehending　the　opposites　rightly；　one　of



which　must　belong　to　everything；　e。g。　we　may　reason　that　'if　A　and　B



cannot　belong　at　the　same　time　to　the　same　thing；　but　it　is



necessary　that　one　of　them　should　belong　to　whatever　the　other　does



not　belong　to：　and　again　C　and　D　are　related　in　the　same　way；　and



follows　everything　which　C　follows：　it　will　result　that　B　belongs



necessarily　to　everything　to　which　D　belongs'：　but　this　is　false。



'Assume　that　F　stands　for　the　negation　of　A　and　B；　and　again　that　H



stands　for　the　negation　of　C　and　D。　It　is　necessary　then　that　either　A



or　F　should　belong　to　everything：　for　either　the　affirmation　or　the



denial　must　belong。　And　again　either　C　or　H　must　belong　to　everything：



for　they　are　related　as　affirmation　and　denial。　And　ex　hypothesi　A



belongs　to　everything　ever　thing　to　which　C　belongs。　Therefore　H



belongs　to　everything　to　which　F　belongs。　Again　since　either　F　or　B



belongs　to　everything；　and　similarly　either　H　or　D；　and　since　H



follows　F；　B　must　follow　D：　for　we　know　this。　If　then　A　follows　C；　B



must　follow　D'。　But　this　is　false：　for　as　we　proved　the　sequence　is



reversed　in　terms　so　constituted。　The　fallacy　arises　because　perhaps



it　is　not　necessary　that　A　or　F　should　belong　to　everything；　or　that　F



or　B　should　belong　to　everything：　for　F　is　not　the　denial　of　A。　For



not　good　is　the　negation　of　good：　and　not…good　is　not　identical　with



'neither　good　nor　not…good'。　Similarly　also　with　C　and　D。　For　two



negations　have　been　assumed　in　respect　to　one　term。











　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　Book　II



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1







　　WE　have　already　explained　the　number　of　the　figures；　the　character



and　number　of　the　premisses；　when　and　how　a　syllogism　is　formed；



further　what　we　must　look　for　when　a　refuting　and　establishing



propositions；　and　how　we　should　investigate　a　given　problem　in　any



branch　of　inquiry；　also　by　what　means　we　shall　obtain　principles



appropriate　to　each　subject。　Since　some　syllogisms　are　universal；



others　particular；　all　the　universal　syllogisms　give　more　than　one



result；　and　of　particular　syllogisms　the　affirmative　yield　more　than



one；　the　negative　yield　only　the　stated　conclusion。　For　all



propositions　are　convertible　save　only　the　particular　negative：　and



the　conclusion　states　one　definite　thing　about　another　definite　thing。



Consequently　all　syllogisms　save　the　particular　negative　yield　more



than　one　conclusion；　e。g。　if　A　has　been　proved　to　to　all　or　to　some　B；



then　B　must　belong　to　some　A：　and　if　A　has　been　proved　to　belong　to　no



B；　then　B　belongs　to　no　A。　This　is　a　different　conclusion　from　the



former。　But　if　A　does　not　belong　to　some　B；　it　is　not　necessary　that　B



should　not　belong　to　some　A：　for　it　may　possibly　belong　to　all　A。



　　This　then　is　the　reason　common　to　all　syllogisms　whether　universal



or　particular。　But　it　is　possible　to　give　another　reason　concerning



those　which　are　universal。　For　all　the　things　that　are　subordinate



to　the　middle　term　or　to　the　conclusion　may　be　proved　by　the　same



syllogism；　if　the　former　are　placed　in　the　middle；　the　latter　in　the



conclusion；　e。g。　if　the　conclusion　AB　is　proved　through　C；　whatever　is



subordinate　to　B　or　C　must　accept　the　predicate　A：　for　if　D　is



included　in　B　as　in　a　whole；　and　B　is　included　in　A；　then　D　will　be



included　in　A。　Again　if　E　is　included　in　C　as　in　a　whole；　and　C　is



included　in　A；　then　E　will　be　included　in　A。　Similarly　if　the



syllogism　is　negative。　In　the　second　figure　it　will　be　p