on the heavens-第22章
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mocomerous bodies。 They do not pretend that a face is composed of faces； or that any other natural conformation is composed of parts like itself。 Obviously then it would be better to assume a finite number of principles。 They should； in fact； be as few as possible； consistently with proving what has to be proved。 This is the common demand of mathematicians； who always assume as principles things finite either in kind or in number。 Again； if body is distinguished from body by the appropriate qualitative difference； and there is a limit to the number of differences （for the difference lies in qualities apprehended by sense； which are in fact finite in number； though this requires proof）； then manifestly there is necessarily a limit to the number of elements。 There is； further； another view…that of Leucippus and Democritus of Abdera…the implications of which are also unacceptable。 The primary masses； according to them； are infinite in number and indivisible in mass： one cannot turn into many nor many into one； and all things are generated by their combination and involution。 Now this view in a sense makes things out to be numbers or composed of numbers。 The exposition is not clear； but this is its real meaning。 And further； they say that since the atomic bodies differ in shape； and there is an infinity of shapes； there is an infinity of simple bodies。 But they have never explained in detail the shapes of the various elements； except so far to allot the sphere to fire。 Air； water； and the rest they distinguished by the relative size of the atom； assuming that the atomic substance was a sort of master…seed for each and every element。 Now； in the first place； they make the mistake already noticed。 The principles which they assume are not limited in number； though such limitation would necessitate no other alteration in their theory。 Further； if the differences of bodies are not infinite； plainly the elements will not be an infinity。 Besides； a view which asserts atomic bodies must needs come into conflict with the mathematical sciences； in addition to invalidating many common opinions and apparent data of sense perception。 But of these things we have already spoken in our discussion of time and movement。 They are also bound to contradict themselves。 For if the elements are atomic； air； earth； and water cannot be differentiated by the relative sizes of their atoms； since then they could not be generated out of one another。 The extrusion of the largest atoms is a process that will in time exhaust the supply； and it is by such a process that they account for the generation of water； air； and earth from one another。 Again； even on their own presuppositions it does not seem as if the clements would be infinite in number。 The atoms differ in figure； and all figures are composed of pyramids； rectilinear the case of rectilinear figures； while the sphere has eight pyramidal parts。 The figures must have their principles； and； whether these are one or two or more； the simple bodies must be the same in number as they。 Again； if every element has its proper movement； and a simple body has a simple movement； and the number of simple movements is not infinite； because the simple motions are only two and the number of places is not infinite； on these grounds also we should have to deny that the number of elements is infinite。
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Since the number of the elements must be limited； it remains to inquire whether there is more than one element。 Some assume one only； which is according to some water； to others air； to others fire； to others again something finer than water and denser than air； an infinite body…so they say…bracing all the heavens。 Now those who decide for a single element； which is either water or air or a body finer than water and denser than air； and proceed to generate other things out of it by use of the attributes density and rarity； all alike fail to observe the fact that they are depriving the element of its priority。 Generation out of the elements is； as they say； synthesis； and generation into the elements is analysis； so that the body with the finer parts must have priority in the order of nature。 But they say that fire is of all bodies the finest。 Hence fire will be first in the natural order。 And whether the finest body is fire or not makes no difference； anyhow it must be one of the other bodies that is primary and not that which is intermediate。 Again； density and rarity； as instruments of generation； are equivalent to fineness and coarseness； since the fine is rare； and coarse in their use means dense。 But fineness and coarseness； again； are equivalent to greatness and smallness； since a thing with small parts is fine and a thing with large parts coarse。 For that which spreads itself out widely is fine； and a thing composed of small parts is so spread out。 In the end； then； they distinguish the various other substances from the element by the greatness and smallness of their parts。 This method of distinction makes all judgement relative。 There will be no absolute distinction between fire； water； and air； but one and the same body will be relatively to this fire； relatively to something else air。 The same difficulty is involved equally in the view elements and distinguishes them by their greatness and smallness。 The principle of distinction between bodies being quantity； the various sizes will be in a definite ratio； and whatever bodies are in this ratio to one another must be air； fire； earth； and water respectively。 For the ratios of smaller bodies may be repeated among greater bodies。 Those who start from fire as the single element； while avoiding this difficulty； involve themselves in many others。 Some of them give fire a particular shape； like those who make it a pyramid； and this on one of two grounds。 The reason given may be…more crudely…that the pyramid is the most piercing of figures as fire is of bodies； or…more ingeniously…the position may be supported by the following argument。 As all bodies are composed of that which has the finest parts； so all solid figures are composed of pryamids： but the finest body is fire； while among figures the pyramid is primary and has the smallest parts； and the primary body must have the primary figure： therefore fire will be a pyramid。 Others； again； express no opinion on the subject of its figure； but simply regard it as the of the finest parts； which in combination will form other bodies； as the fusing of gold…dust produces solid gold。 Both of these views involve the same difficulties。 For （1） if； on the one hand； they make the primary body an atom； the view will be open to the objections already advanced
against the atomic theory。 And further the theory is inconsistent with a regard for the facts of nature。 For if all bodies are quantitatively commensurable； and the relative size of the various homoeomerous masses and of their several elements are in the same ratio； so that the total mass of water； for instance； is related to the total mass of air as the elements of each are to one another； and so on； and if there is more air than water and； generally； more of the finer body than of the coarser； obviously the element of water will be smaller than that of air。 But the lesser quantity is contained in the greater。 Therefore the air element is divisible。 And the same could be shown of fire and of all bodies whose parts are relatively fine。 （2） If； on the other hand； the primary body is divisible； then （a） those who give fire a special shape will have to say that a part of fire is not fire； because a pyramid is not composed of pyramids； and also that not every body is either an element or composed of elements； since a part of fire will be neither fire nor any other element。 And （b） those whose ground of distinction is size will have to recognize an element prior to the element； a regress which continues infinitely； since every body is divisible and that which has the smallest parts is the element。 Further； they too will have to say that the same body is relatively to this fire and relatively to that air； to others again water and earth。 The common error of all views which assume a single element is that they allow only one natural movement；
