prior analytics-第22章

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B。　Consequently；　if　this　is　impossible；　A　must　belong　to　some　B。　But



if　it　is　supposed　that　A　does　not　belong　to　some　B；　we　shall　have



the　same　results　as　in　the　first　figure。



　　Again　suppose　that　A　belongs　to　some　B；　and　let　A　belong　to　no　C。　It



is　necessary　then　that　C　should　not　belong　to　some　B。　But　originally



it　belonged　to　all　B；　consequently　the　hypothesis　is　false：　A　then



will　belong　to　no　B。



　　When　A　does　not　belong　to　an　B；　suppose　it　does　belong　to　all　B；　and



to　no　C。　It　is　necessary　then　that　C　should　belong　to　no　B。　But　this



is　impossible：　so　that　it　is　true　that　A　does　not　belong　to　all　B。



It　is　clear　then　that　all　the　syllogisms　can　be　formed　in　the　middle



figure。







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　　Similarly　they　can　all　be　formed　in　the　last　figure。　Suppose　that



A　does　not　belong　to　some　B；　but　C　belongs　to　all　B：　then　A　does　not



belong　to　some　C。　If　then　this　is　impossible；　it　is　false　that　A



does　not　belong　to　some　B；　so　that　it　is　true　that　A　belongs　to　all　B。



But　if　it　is　supposed　that　A　belongs　to　no　B；　we　shall　have　a



syllogism　and　a　conclusion　which　is　impossible：　but　the　problem　in



hand　is　not　proved：　for　if　the　contrary　is　supposed；　we　shall　have　the



same　results　as　before。



　　But　to　prove　that　A　belongs　to　some　B；　this　hypothesis　must　be　made。



If　A　belongs　to　no　B；　and　C　to　some　B；　A　will　belong　not　to　all　C。



If　then　this　is　false；　it　is　true　that　A　belongs　to　some　B。



　　When　A　belongs　to　no　B；　suppose　A　belongs　to　some　B；　and　let　it　have



been　assumed　that　C　belongs　to　all　B。　Then　it　is　necessary　that　A



should　belong　to　some　C。　But　ex　hypothesi　it　belongs　to　no　C；　so



that　it　is　false　that　A　belongs　to　some　B。　But　if　it　is　supposed



that　A　belongs　to　all　B；　the　problem　is　not　proved。



　　But　this　hypothesis　must　be　made　if　we　are　prove　that　A　belongs



not　to　all　B。　For　if　A　belongs　to　all　B　and　C　to　some　B；　then　A



belongs　to　some　C。　But　this　we　assumed　not　to　be　so；　so　it　is　false



that　A　belongs　to　all　B。　But　in　that　case　it　is　true　that　A　belongs



not　to　all　B。　If　however　it　is　assumed　that　A　belongs　to　some　B；　we



shall　have　the　same　result　as　before。



　　It　is　clear　then　that　in　all　the　syllogisms　which　proceed　per



impossibile　the　contradictory　must　be　assumed。　And　it　is　plain　that　in



the　middle　figure　an　affirmative　conclusion；　and　in　the　last　figure



a　universal　conclusion；　are　proved　in　a　way。







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　　Demonstration　per　impossibile　differs　from　ostensive　proof　in　that



it　posits　what　it　wishes　to　refute　by　reduction　to　a　statement



admitted　to　be　false；　whereas　ostensive　proof　starts　from　admitted



positions。　Both；　indeed；　take　two　premisses　that　are　admitted；　but　the



latter　takes　the　premisses　from　which　the　syllogism　starts；　the　former



takes　one　of　these；　along　with　the　contradictory　of　the　original



conclusion。　Also　in　the　ostensive　proof　it　is　not　necessary　that　the



conclusion　should　be　known；　nor　that　one　should　suppose　beforehand



that　it　is　true　or　not：　in　the　other　it　is　necessary　to　suppose



beforehand　that　it　is　not　true。　It　makes　no　difference　whether　the



conclusion　is　affirmative　or　negative；　the　method　is　the　same　in



both　cases。　Everything　which　is　concluded　ostensively　can　be　proved



per　impossibile；　and　that　which　is　proved　per　impossibile　can　be



proved　ostensively；　through　the　same　terms。　Whenever　the　syllogism



is　formed　in　the　first　figure；　the　truth　will　be　found　in　the　middle



or　the　last　figure；　if　negative　in　the　middle；　if　affirmative　in　the



last。　Whenever　the　syllogism　is　formed　in　the　middle　figure；　the　truth



will　be　found　in　the　first；　whatever　the　problem　may　be。　Whenever



the　syllogism　is　formed　in　the　last　figure；　the　truth　will　be　found　in



the　first　and　middle　figures；　if　affirmative　in　first；　if　negative



in　the　middle。　Suppose　that　A　has　been　proved　to　belong　to　no　B；　or



not　to　all　B；　through　the　first　figure。　Then　the　hypothesis　must



have　been　that　A　belongs　to　some　B；　and　the　original　premisses　that



C　belongs　to　all　A　and　to　no　B。　For　thus　the　syllogism　was　made　and



the　impossible　conclusion　reached。　But　this　is　the　middle　figure；　if　C



belongs　to　all　A　and　to　no　B。　And　it　is　clear　from　these　premisses



that　A　belongs　to　no　B。　Similarly　if　has　been　proved　not　to　belong



to　all　B。　For　the　hypothesis　is　that　A　belongs　to　all　B；　and　the



original　premisses　are　that　C　belongs　to　all　A　but　not　to　all　B。



Similarly　too；　if　the　premiss　CA　should　be　negative：　for　thus　also



we　have　the　middle　figure。　Again　suppose　it　has　been　proved　that　A



belongs　to　some　B。　The　hypothesis　here　is　that　is　that　A　belongs　to　no



B；　and　the　original　premisses　that　B　belongs　to　all　C；　and　A　either　to



all　or　to　some　C：　for　in　this　way　we　shall　get　what　is　impossible。　But



if　A　and　B　belong　to　all　C；　we　have　the　last　figure。　And　it　is　clear



from　these　premisses　that　A　must　belong　to　some　B。　Similarly　if　B　or　A



should　be　assumed　to　belong　to　some　C。



　　Again　suppose　it　has　been　proved　in　the　middle　figure　that　A　belongs



to　all　B。　Then　the　hypothesis　must　have　been　that　A　belongs　not　to　all



B；　and　the　original　premisses　that　A　belongs　to　all　C；　and　C　to　all　B：



for　thus　we　shall　get　what　is　impossible。　But　if　A　belongs　to　all　C；



and　C　to　all　B；　we　have　the　first　figure。　Similarly　if　it　has　been



proved　that　A　belongs　to　some　B：　for　the　hypothesis　then　must　have



been　that　A　belongs　to　no　B；　and　the　original　premisses　that　A　belongs



to　all　C；　and　C　to　some　B。　If　the　syllogism　is　negative；　the



hypothesis　must　have　been　that　A　belongs　to　some　B；　and　the　original



premisses　that　A　belongs　to　no　C；　and　C　to　all　B；　so　that　the　first



figure　results。　If　the　syllogism　is　not　universal；　but　proof　has



been　given　that　A　does　not　belong　to　some　B；　we　may　infer　in　the



same　way。　The　hypothesis　is　that　A　belongs　to　all　B；　the　original



premisses　that　A　belongs　to　no　C；　and　C　belongs　to　some　B：　for　thus　we



get　the　first　figure。



　　Again　suppose　it　has　been　proved　in　the　third　figure　that　A



belongs　to　all　B。　Then　the　hypothesis　must　have　been　that　A　belongs



not　to　all　B；　and　the　original　premisses　that　C　belongs　to　all　B；



and　A　belongs　to　all　C；　for　thus　we　shall　get　what　is　impossible。



And　the　original　premisses　form　the　first　figure。　Similarly　if　the



demonstration　establishes　a　particular　proposition：　the　hypothesis



then　must　have　been　that　A　belongs　to　no　B；　and　the　original　premisses



that　C　belongs　to　some　B；　and　A　to　all　C。　If　the　syllogism　is



negative；　the　hypothesis　must　have　been　that　A　belongs　to　some　B；



and　the　original　premisses　that　C　belongs　to　no　A　and　to　all　B；　and



this　is　the　middle　figure。　Similarly　if　the　demonstration　is　not



universal。　The　hypothesis　will　then　be　that　A　belongs　to　all　B；　the



premisses　that　C　belongs　to　no　A　and　to　some　B：　and　this　is　the　middle



figure。



　　It　is　clear　then　that　it　is　possible　through　the　same　terms　to　prove



each　of　the　problems　ostensively　as　well。　Similarly　it　will　be



possible　if　the　syllogisms　are　ostensive　to　reduce　them　ad　impossibile



in　the　terms　which　have　been　taken；　whenever　the　contradictory　of



the　conclusion　of　the　ostensive　syllogism　is　taken　as　a　premiss。　For



the　syllogisms　become　identical　with　those　which　are　obtained　by　means



of　conversion；　so　that　we　obtain　immediately　the　figures　through　which



each　problem　will　be　solved。　It　is　clear　then　that　every　thesis　can　be



proved　in　both　ways；　i。e。　per　impossibile　and　ostensively；　and　it　is



not　possible　to　separate　one　method　from　the　other。







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　　In　what　figure　it　is　possible　to　draw　a　conclusion　from　premisses



which　are　opposed；　and　in　what　figure　this　is　not　possible；　will　be



made　clear　in　this　way。　Verbally　four　kinds　of　opposition　are



possible；　viz。　universal　affirmative　to　universal　negative；



universal　affirmative　to　particular　negative；　particular　affirmative



to　universal　negative；　and　particular　affirmative　to　particular



negative：　but　really　there　are　only　three：　for　the　particular



affirmative　is　only　verbally　opposed　to　the　particular　negative。　Of



the　genuine　opposites　I　call　those　which　are　universal　contraries；　the



universal　affirmative　and　the　universal　negative；　e。g。　'every



science　is　good'；　'no　science　is　good'；　the　others　I　call



contradictories。



　　In　the　first　figure　no　syllogism　whether　affirmative　or　negative　can



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　th