on the heavens-第20章
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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。
2
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
