on the heavens-第4部分

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nce　in　that　same　time。　Infinite　weight　is　therefore　impossible；　and　the　same　reasoning　applies　also　to　infinite　lightness。　Bodies　then　of　infinite　weight　and　of　infinite　lightness　are　equally　impossible。　　　That　there　is　no　infinite　body　may　be　shown；　as　we　have　shown　it；　by　a　detailed　consideration　of　the　various　cases。　But　it　may　also　be　shown　universally；　not　only　by　such　reasoning　as　we　advanced　in　our　discussion　of　principles　（though　in　that　passage　we　have　already　determined　universally　the　sense　in　which　the　existence　of　an　infinite　is　to　be　asserted　or　denied）；　but　also　suitably　to　our　present　purpose　in　the　following　way。　That　will　lead　us　to　a　further　question。　Even　if　the　total　mass　is　not　infinite；　it　may　yet　be　great　enough　to　admit　a　plurality　of　universes。　The　question　might　possibly　be　raised　whether　there　is　any　obstacle　to　our　believing　that　there　are　other　universes　composed　on　the　pattern　of　our　own；　more　than　one；　though　stopping　short　of　infinity。　First；　however；　let　us　treat　of　the　infinite　universally。

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　　Every　body　must　necessarily　be　either　finite　or　infinite；　and　if　infinite；　either　of　similar　or　of　dissimilar　parts。　If　its　parts　are　dissimilar；　they　must　represent　either　a　finite　or　an　infinite　number　of　kinds。　That　the　kinds　cannot　be　infinite　is　evident；　if　our　original　presuppositions　remain　unchallenged。　For　the　primary　movements　being　finite　in　number；　the　kinds　of　simple　body　are　necessarily　also　finite；　since　the　movement　of　a　simple　body　is　simple；　and　the　simple　movements　are　finite；　and　every　natural　body　must　always　have　its　proper　motion。　Now　if　the　infinite　body　is　to　be　composed　of　a　finite　number　of　kinds；　then　each　of　its　parts　must　necessarily　be　infinite　in　quantity；　that　is　to　say；　the　water；　fire；　&c。；　which　compose　it。　But　this　is　impossible；　because；　as　we　have　already　shown；　infinite　weight　and　lightness　do　not　exist。　Moreover　it　would　be　necessary　also　that　their　places　should　be　infinite　in　extent；　so　that　the　movements　too　of　all　these　bodies　would　be　infinite。　But　this　is　not　possible；　if　we　are　to　hold　to　the　truth　of　our　original　presuppositions　and　to　the　view　that　neither　that　which　moves　downward；　nor；　by　the　same　reasoning；　that　which　moves　upward；　can　prolong　its　movement　to　infinity。　For　it　is　true　in　regard　to　quality；　quantity；　and　place　alike　that　any　process　of　change　is　impossible　which　can　have　no　end。　I　mean　that　if　it　is　impossible　for　a　thing　to　have　come　to　be　white；　or　a　cubit　long；　or　in　Egypt；　it　is　also　impossible　for　it　to　be　in　process　of　coming　to　be　any　of　these。　It　is　thus　impossible　for　a　thing　to　be　moving　to　a　place　at　which　in　its　motion　it　can　never　by　any　possibility　arrive。　Again；　suppose　the　body　to　exist　in　dispersion；　it　may　be　maintained　none　the　less　that　the　total　of　all　these　scattered　particles；　say；　of　fire；　is　infinite。　But　body　we　saw　to　be　that　which　has　extension　every　way。　How　can　there　be　several　dissimilar　elements；　each　infinite？　Each　would　have　to　be　infinitely　extended　every　way。　　　It　is　no　more　conceivable；　again；　that　the　infinite　should　exist　as　a　whole　of　similar　parts。　For；　in　the　first　place；　there　is　no　other　（straight）　movement　beyond　those　mentioned：　we　must　therefore　give　it　one　of　them。　And　if　so；　we　shall　have　to　admit　either　infinite　weight　or　infinite　lightness。　Nor；　secondly；　could　the　body　whose　movement　is　circular　be　infinite；　since　it　is　impossible　for　the　infinite　to　move　in　a　circle。　This；　indeed；　would　be　as　good　as　saying　that　the　heavens　are　infinite；　which　we　have　shown　to　be　impossible。　　　Moreover；　in　general；　it　is　impossible　that　the　infinite　should　move　at　all。　If　it　did；　it　would　move　either　naturally　or　by　constraint：　and　if　by　constraint；　it　possesses　also　a　natural　motion；　that　is　to　say；　there　is　another　place；　infinite　like　itself；　to　which　it　will　move。　But　that　is　impossible。　　　That　in　general　it　is　impossible　for　the　infinite　to　be　acted　upon　by　the　finite　or　to　act　upon　it　may　be　shown　as　follows。　　　（1。　The　infinite　cannot　be　acted　upon　by　the　finite。）　Let　A　be　an　infinite；　B　a　finite；　C　the　time　of　a　given　movement　produced　by　one　in　the　other。　Suppose；　then；　that　A　was　heated；　or　impelled；　or　modified　in　any　way；　or　caused　to　undergo　any　sort　of　movement　whatever；　by　in　the　time　C。　Let　D　be　less　than　B；　and；　assuming　that　a　lesser　agent　moves　a　lesser　patient　in　an　equal　time；　call　the　quantity　thus　modified　by　D；　E。　Then；　as　D　is　to　B；　so　is　E　to　some　finite　quantum。　We　assume　that　the　alteration　of　equal　by　equal　takes　equal　time；　and　the　alteration　of　less　by　less　or　of　greater　by　greater　takes　the　same　time；　if　the　quantity　of　the　patient　is　such　as　to　keep　the　proportion　which　obtains　between　the　agents；　greater　and　less。　If　so；　no　movement　can　be　caused　in　the　infinite　by　any　finite　agent　in　any　time　whatever。　For　a　less　agent　will　produce　that　movement　in　a　less　patient　in　an　equal　time；　and　the　proportionate　equivalent　of　that　patient　will　be　a　finite　quantity；　since　no　proportion　holds　between　finite　and　infinite。　　　　　（2。　The　infinite　cannot　act　upon　the　finite。）　Nor；　again；　can　the　infinite　produce　a　movement　in　the　finite　in　any　time　whatever。　Let　A　be　an　infinite；　B　a　finite；　C　the　time　of　action。　In　the　time　C；　D　will　produce　that　motion　in　a　patient　less　than　B；　say　F。　Then　take　E；　bearing　the　same　proportion　to　D　as　the　whole　BF　bears　to　F。　E　will　produce　the　motion　in　BF　in　the　time　C。　Thus　the　finite　and　infinite　effect　the　same　alteration　in　equal　times。　But　this　is　impossible；　for　the　assumption　is　that　the　greater　effects　it　in　a　shorter　time。　It　will　be　the　same　with　any　time　that　can　be　taken；　so　that　there　will　no　time　in　which　the　infinite　can　effect　this　movement。　And；　as　to　infinite　time；　in　that　nothing　can　move　another　or　be　moved　by　it。　For　such　time　has　no　limit；　while　the　action　and　reaction　have。　　　（3。　There　is　no　interaction　between　infinites。）　Nor　can　infinite　be　acted　upon　in　any　way　by　infinite。　Let　A　and　B　be　infinites；　CD　being　the　time　of　the　action　A　of　upon　B。　Now　the　whole　B　was　modified　in　a　certain　time；　and　the　part　of　this　infinite；　E；　cannot　be　so　modified　in　the　same　time；　since　we　assume　that　a　less　quantity　makes　the　movement　in　a　less　time。　Let　E　then；　when　acted　upon　by　A；　complete　the　movement　in　the　time　D。　Then；　as　D　is　to　CD；　so　is　E　to　some　finite　part　of　B。　This　part　will　necessarily　be　moved　by　A　in　the　time　CD。　For　we　suppose　that　the　same　agent　produces　a　given　effect　on　a　greater　and　a　smaller　mass　in　longer　and　shorter　times；　the　times　and　masses　varying　proportionately。　There　is　thus　no　finite　time　in　which　infinites　can　move　one　another。　Is　their　time　then　infinite？　No；　for　infinite　time　has　no　end；　but　the　movement　communicated　has。　　　If　therefore　every　perceptible　body　possesses　the　power　of　acting　or　of　being　acted　upon；　or　both　of　these；　it　is　impossible　that　an　infinite　body　should　be　perceptible。　All　bodies；　however；　that　occupy　place　are　perceptible。　There　is　therefore　no　infinite　body　beyond　the　heaven。　Nor　again　is　there　anything　of　limited　extent　beyond　it。　And　so　beyond　the　heaven　there　is　no　body　at　all。　For　if　you　suppose　it　an　object　of　intelligence；　it　will　be　in　a　place…since　place　is　what　'within'　and　'beyond'　denote…and　therefore　an　object　of　perception。　But　nothing　that　is　not　in　a　place　is　perceptible。　　　The　question　may　also　be　examined　in　the　light　of　more　general　considerations　as　follows。　The　infinite；　considered　as　a　whole　of　similar　parts；　cannot；　on　the　one　hand；　move　in　a　circle。　For　there　is　no　centre　of　the　infinite；　and　that　which　moves　in　a　circle　moves　about　the　centre。　Nor　again　can　the　infinite　move　in　a　straight　line。　For　there　would　have　to　be　another　place　infinite　like　itself　to　be　the　goal　of　its　natural　movement　and　another；　equally　great；　for　the　goal　of　its　unnatural　movement。　Moreover；　whether　its　rectilinear　movement　is　natural　or　constrained；　in　either　case　the　force　which　causes　its　motion　will　have　to　be　infinite。　For　infinite　force　is　force　of　an　infinite　body；　and　of　an　infinite　body　the　force　is　infinite。　So　the　motive　body　also　will　be　infinite。　（The　proof　of　this　is　given　in　our　discussion　of　movement；　where　it　is　shown　that　no　finite　thing　possesses　infinite　power；　and　no　infinite　thing　finite　power。）　If　then　that　which　moves　naturally　can　also　move　unnaturally；　there　will　be　two　infinites；　one　which　causes；　and　another　which　exhibits　the　latter　motion。　Again；　what　is　it　that　moves　the　infinite？　If　it　moves　itself；　it　must　be　animate。　But　how　can　it　possibly　be　conceived　as　an　infinite　animal？　And　if　there　is　something　else　that　moves　it；　there　will　be　two　infinites；　that　which　moves　and　that　which　is　moved；　differing　in　their　form　and　power。　　　If　the　whole　is　not　continuous；　but　exists；　as　Democritus　and　Leucippus　think；　in　the　form　of　parts　separated　by　void；　there　must　necessarily　be　one　movement　of　all　the　multitude。　They　are　distinguished；　we　are　told；　from　one　another　by　their　figures；　but　their　nature　is　one；　like　many　pieces　of　gold　separated　from　one　another。　But　each　piece　must；　as　we　assert；　have　the　same　motion。　For　a　single　clod　moves　to　the　same　place　as　the　whole　mass　of　earth；　and　a　spark　to　the　same　place　as　the　whole　mass　of　fire。　So　that　if　it　be　weight　that　all　possess；　no　body　is；　strictly　speaking；　light：　and　if　lightness　be　universal；　none　is　heavy。　Moreover；　whatever　possesses　weight　or　lightness　will　have　its　place　either　at　one　of　the　extremes　or　in　the　middle　region。　But　this　is　impossible　while　the　world　is　conceived　as　infinite。　And；　generally；　that　which　has　no　centre　or　extreme　limit；　no　up　or　down；　gives　the　bodies　no　place　for　their　motion；　and　without　that　movement　is　impossible。　A　thing　must　move　either　naturally　or　unnaturally；　and　the　two　movements　are　determined　by　the　proper　and　alien　places。　Again；　a　place　in　which　a　thing　rests　or　to　which　it　moves　unnaturally；　must　be　the　natural　place　for　some　other　body；　as　experience　shows。　Necessarily；　therefore；　not　everything　possesses　weight　or　lightness；　but　some　things　do　and　some　do　not。　From　these　arguments　then　it　is　clear　that　the　body　of　the　universe　is　not　infinite。

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　　We　must　now　proceed　to　explain　why　there　can