on the heavens-第16部分

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ese　thinkers　maintained　was　that　all　else　has　been　generated　and；　as　they　said；　'is　flowing　away；　nothing　having　any　solidity；　except　one　single　thing　which　persists　as　the　basis　of　all　these　transformations。　So　we　may　interpret　the　statements　of　Heraclitus　of　Ephesus　and　many　others。　And　some　subject　all　bodies　whatever　to　generation；　by　means　of　the　composition　and　separation　of　planes。　　　Discussion　of　the　other　views　may　be　postponed。　But　this　last　theory　which　composes　every　body　of　planes　is；　as　the　most　superficial　observation　shows；　in　many　respects　in　plain　contradiction　with　mathematics。　It　is；　however；　wrong　to　remove　the　foundations　of　a　science　unless　you　can　replace　them　with　others　more　convincing。　And；　secondly；　the　same　theory　which　composes　solids　of　planes　clearly　composes　planes　of　lines　and　lines　of　points；　so　that　a　part　of　a　line　need　not　be　a　line。　This　matter　has　been　already　considered　in　our　discussion　of　movement；　where　we　have　shown　that　an　indivisible　length　is　impossible。　But　with　respect　to　natural　bodies　there　are　impossibilities　involved　in　the　view　which　asserts　indivisible　lines；　which　we　may　briefly　consider　at　this　point。　For　the　impossible　consequences　which　result　from　this　view　in　the　mathematical　sphere　will　reproduce　themselves　when　it　is　applied　to　physical　bodies；　but　there　will　be　difficulties　in　physics　which　are　not　present　in　mathematics；　for　mathematics　deals　with　an　abstract　and　physics　with　a　more　concrete　object。　There　are　many　attributes　necessarily　present　in　physical　bodies　which　are　necessarily　excluded　by　indivisibility；　all　attributes；　in　fact；　which　are　divisible。　There　can　be　nothing　divisible　in　an　indivisible　thing；　but　the　attributes　of　bodies　are　all　divisible　in　one　of　two　ways。　They　are　divisible　into　kinds；　as　colour　is　divided　into　white　and　black；　and　they　are　divisible　per　accidens　when　that　which　has　them　is　divisible。　In　this　latter　sense　attributes　which　are　simple　are　nevertheless　divisible。　Attributes　of　this　kind　will　serve；　therefore；　to　illustrate　the　impossibility　of　the　view。　It　is　impossible；　if　two　parts　of　a　thing　have　no　weight；　that　the　two　together　should　have　weight。　But　either　all　perceptible　bodies　or　some；　such　as　earth　and　water；　have　weight；　as　these　thinkers　would　themselves　admit。　Now　if　the　point　has　no　weight；　clearly　the　lines　have　not　either；　and；　if　they　have　not；　neither　have　the　planes。　Therefore　no　body　has　weight。　It　is；　further；　manifest　that　their　point　cannot　have　weight。　For　while　a　heavy　thing　may　always　be　heavier　than　something　and　a　light　thing　lighter　than　something；　a　thing　which　is　heavier　or　lighter　than　something　need　not　be　itself　heavy　or　light；　just　as　a　large　thing　is　larger　than　others；　but　what　is　larger　is　not　always　large。　A　thing　which；　judged　absolutely；　is　small　may　none　the　less　be　larger　than　other　things。　Whatever；　then；　is　heavy　and　also　heavier　than　something　else；　must　exceed　this　by　something　which　is　heavy。　A　heavy　thing　therefore　is　always　divisible。　But　it　is　common　ground　that　a　point　is　indivisible。　Again；　suppose　that　what　is　heavy　or　weight　is　a　dense　body；　and　what　is　light　rare。　Dense　differs　from　rare　in　containing　more　matter　in　the　same　cubic　area。　A　point；　then；　if　it　may　be　heavy　or　light；　may　be　dense　or　rare。　But　the　dense　is　divisible　while　a　point　is　indivisible。　And　if　what　is　heavy　must　be　either　hard　or　soft；　an　impossible　consequence　is　easy　to　draw。　For　a　thing　is　soft　if　its　surface　can　be　pressed　in；　hard　if　it　cannot；　and　if　it　can　be　pressed　in　it　is　divisible。　　　Moreover；　no　weight　can　consist　of　parts　not　possessing　weight。　For　how；　except　by　the　merest　fiction；　can　they　specify　the　number　and　character　of　the　parts　which　will　produce　weight？　And；　further；　when　one　weight　is　greater　than　another；　the　difference　is　a　third　weight；　from　which　it　will　follow　that　every　indivisible　part　possesses　weight。　For　suppose　that　a　body　of　four　points　possesses　weight。　A　body　composed　of　more　than　four　points　will　superior　in　weight　to　it；　a　thing　which　has　weight。　But　the　difference　between　weight　and　weight　must　be　a　weight；　as　the　difference　between　white　and　whiter　is　white。　Here　the　difference　which　makes　the　superior　weight　heavier　is　the　single　point　which　remains　when　the　common　number；　four；　is　subtracted。　A　single　point；　therefore；　has　weight。　　　Further；　to　assume；　on　the　one　hand；　that　the　planes　can　only　be　put　in　linear　contact　would　be　ridiculous。　For　just　as　there　are　two　ways　of　putting　lines　together；　namely；　end　to　and　side　by　side；　so　there　must　be　two　ways　of　putting　planes　together。　Lines　can　be　put　together　so　that　contact　is　linear　by　laying　one　along　the　other；　though　not　by　putting　them　end　to　end。　But　if；　similarly；　in　putting　the　lanes　together；　superficial　contact　is　allowed　as　an　alternative　to　linear；　that　method　will　give　them　bodies　which　are　not　any　element　nor　composed　of　elements。　Again；　if　it　is　the　number　of　planes　in　a　body　that　makes　one　heavier　than　another；　as　the　Timaeus　explains；　clearly　the　line　and　the　point　will　have　weight。　For　the　three　cases　are；　as　we　said　before；　analogous。　But　if　the　reason　of　differences　of　weight　is　not　this；　but　rather　the　heaviness　of　earth　and　the　lightness　of　fire；　then　some　of　the　planes　will　be　light　and　others　heavy　（which　involves　a　similar　distinction　in　the　lines　and　the　points）；　the　earthplane；　I　mean；　will　be　heavier　than　the　fire…plane。　In　general；　the　result　is　either　that　there　is　no　magnitude　at　all；　or　that　all　magnitude　could　be　done　away　with。　For　a　point　is　to　a　line　as　a　line　is　to　a　plane　and　as　a　plane　is　to　a　body。　Now　the　various　forms　in　passing　into　one　another　will　each　be　resolved　into　its　ultimate　constituents。　It　might　happen　therefore　that　nothing　existed　except　points；　and　that　there　was　no　body　at　all。　A　further　consideration　is　that　if　time　is　similarly　constituted；　there　would　be；　or　might　be；　a　time　at　which　it　was　done　away　with。　For　the　indivisible　now　is　like　a　point　in　a　line。　The　same　consequences　follow　from　composing　the　heaven　of　numbers；　as　some　of　the　Pythagoreans　do　who　make　all　nature　out　of　numbers。　For　natural　bodies　are　manifestly　endowed　with　weight　and　lightness；　but　an　assemblage　of　units　can　neither　be　composed　to　form　a　body　nor　possess　weight。

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　　The　necessity　that　each　of　the　simple　bodies　should　have　a　natural　movement　may　be　shown　as　follows。　They　manifestly　move；　and　if　they　have　no　proper　movement　they　must　move　by　constraint：　and　the　constrained　is　the　same　as　the　unnatural。　Now　an　unnatural　movement　presupposes　a　natural　movement　which　it　contravenes；　and　which；　however　many　the　unnatural　movements；　is　always　one。　For　naturally　a　thing　moves　in　one　way；　while　its　unnatural　movements　are　manifold。　The　same　may　be　shown；　from　the　fact　of　rest。　Rest；　also；　must　either　be　constrained　or　natural；　constrained　in　a　place　to　which　movement　was　constrained；　natural　in　a　place　movement　to　which　was　natural。　Now　manifestly　there　is　a　body　which　is　at　rest　at　the　centre。　If　then　this　rest　is　natural　to　it；　clearly　motion　to　this　place　is　natural　to　it。　If；　on　the　other　hand；　its　rest　is　constrained；　what　is　hindering　its　motion？　Something；　which　is　at　rest：　but　if　so；　we　shall　simply　repeat　the　same　argument；　and　either　we　shall　come　to　an　ultimate　something　to　which　rest　where　it　is　or　we　shall　have　an　infinite　process；　which　is　impossible。　The　hindrance　to　its　movement；　then；　we　will　suppose；　is　a　moving　thing…as　Empedocles　says　that　it　is　the　vortex　which　keeps　the　earth　still…：　but　in　that　case　we　ask；　where　would　it　have　moved　to　but　for　the　vortex？　It　could　not　move　infinitely；　for　to　traverse　an　infinite　is　impossible；　and　impossibilities　do　not　happen。　So　the　moving　thing　must　stop　somewhere；　and　there　rest　not　by　constraint　but　naturally。　But　a　natural　rest　proves　a　natural　movement　to　the　place　of　rest。　Hence　Leucippus　and　Democritus；　who　say　that　the　primary　bodies　are　in　perpetual　movement　in　the　void　or　infinite；　may　be　asked　to　explain　the　manner　of　their　motion　and　the　kind　of　movement　which　is　natural　to　them。　For　if　the　various　elements　are　constrained　by　one　another　to　move　as　they　do；　each　must　still　have　a　natural　movement　which　the　constrained　contravenes；　and　the　prime　mover　must　cause　motion　not　by　constraint　but　naturally。　If　there　is　no　ultimate　natural　cause　of　movement　and　each　preceding　term　in　the　series　is　always　moved　by　constraint；　we　shall　have　an　infinite　process。　The　same　difficulty　is　involved　even　if　it　is　supposed；　as　we　read　in　the　Timaeus；　that　before　the　ordered　world　was　made　the　elements　moved　without　order。　Their　movement　must　have　been　due　either　to　constraint　or　to　their　nature。　And　if　their　movement　was　natural；　a　moment's　consideration　shows　that　there　was　already　an　ordered　world。　For　the　prime　mover　must　cause　motion　in　virtue　of　its　own　natural　movement；　and　the　other　bodies；　moving　without　constraint；　as　they　came　to　rest　in　their　proper　places；　would　fall　into　the　order　in　which　they　now　stand；　the　heavy　bodies　moving　towards　the　centre　and　the　light　bodies　away　from　it。　But　that　is　the　order　of　their　distribution　in　our　world。　There　is　a　further　question；　too；　which　might　be　asked。　Is　it　possible　or　impossible　that　bodies　in　unordered　movement　should　combine　in　some　cases　into　combinations　like　those　of　which　bodies　of　nature's　composing　are　composed；　such；　I　mean；　as　bones　and　flesh？　Yet　this　is　what　Empedocles　asserts　to　have　occurred　under　Love。　'Many　a　head'；　says　he；　'came　to　birth　without　a　neck。'　The　answer　to　the　view　that　there　are　infinite　bodies　moving　in　an　infinite　is　that；　if　the　cause　of　movement　is　single；　they　must　move　with　a　single　motion；　and　therefore　not　without　order；　and　if；　on　the　other　hand；　the　causes　are　of　infinite　variety；　their　motions　too　must　be　infinitely　varied。　For　a　finite　number　of　causes　would　produce　a　kind　of　order；　since　absence　of　order　is　not　proved　by　diversity　of　direction　in　motions：　indeed；　in　the　world　we　know；　not　all　bodies；　but　only　bodies　of　the　same　kind；　have　a　common　goal　of　movement。　Again；　disorderly　movement　means　in　reality　unnatural　movement；　since　the　order　proper　to　perceptible　things　is　their　nature。　And　there　is　also