Perhaps, however, this inquiry is more universal, whether it be possible that the infinite can subsist in mathematical entities, in intelligible, and in things which have no magnitude. But we consider with respect to sensibles, and those things which we make the subject of our discussion, whether body, infinite in augmentation, is in these or not. To those, therefore, who consider the affair logically, it may seem that there is not, from the following arguments: for if the definition of body is that which is bounded by superficies, there will not be an infinite body, neither intelligible, nor sensible. But neither will there be number, so as to be separate and infinite: for number, or that which possesses number is numerable. If, therefore, that which is numerable can be numbered, it will be possible for the infinite to be passed through. But to those who consider the affair more physically, it will be evident that there cannot be a body of infinite magnitude from the following arguments; for it can neither be composite, nor simple. An infinite body, therefore, will not be a composite, if the elements are finite in number: for it is necessary that contraries should always be more than one, and be equalized, and that one of them should not be infinite; for if the power in one body should be in any manner whatever surpassed by the power of another; as, for instance, if fire is finite, but air is infinite, and equal fire surpasses in power equal air, however much it may be multiplied, if it only possesses a certain number; yet at the same time it is manifest that the infinite will surpass and corrupt that which is finite. But it is impossible that each of the elements should be infinite. For that is body which has interval on all sides; and that is infinite which has extension without bound. So that an infinite body will be extended on all sides to infinity. Neither can an infinite body be one and simple; nor as some say, that which is beside the elements from which these are generated; nor in short can it have any subsistence: for there are some who make this infinite to be neither air nor water, list other things should be destroyed by the infinity of these; since they possess contrariety to each other. Thus air is cold, but water is moist, and fire is hot: of which if there is one infinite, other things would have been already corrupted. But now they say that is different from which all these are produced. It is, however, impossible that there can be a thing of this kind, not because it is infinite (for concerning this something common must be said, which similarly accords with every body, namely, with air and water, and any other whatever), but because there is no such sensible body, beside those that are called the elements: for everything is dissolved into that from which it is composed. So that here there would be something else beside air and fire, earth and water. But there does not appear to be any such thing period neither fire, therefore nor any other of the elements, can be infinite. For, in short, exclusively of some one of them being infinite, it is impossible that the universe, although it be finite, can either be or be generated some one of them; conformably to what Heraclitus says, that all things once were fire. There is also the same reason in one body, which natural philosophers introduce beside the elements: for all things are changed from 1 contrary into another; as, for instance, from the hot into the cold. But it is necessary also from these things to consider respecting every body, whether it is possible or not, that there can be an infinite sensible body. In short, however, that it is impossible there can be a body sensible and infinite, is evident from hence, that everything sensible is naturally adapted to be somewhere; that there is some place of everything; and that there is the same place of the part and of the whole, as of the whole earth, and one clod, and of fire and a spark. So that if this infinite sensible body is of one form, it will either be immovable, or always borne along; though this is impossible: for why should it rather be carried downward than upward, or anywhere else? I mean, for instance, if it is a clod of the earth, where will it be moved? Or where will it abide? For the place is infinite of a body kindred to it. Whether, therefore, will it occupy the whole place? And in what manner? What likewise, and where will be its permanence, and its motion? Or will it be everywhere permanent? It will not, therefore, be moved. Or will it be everywhere moved? It will not therefore be at rest. But if the universe is dissimilar, places also will be dissimilar. And first there will not be one body of the universe, except by contact. Secondly, these will either be finite, or infinite in species. And they cannot, indeed, be finite: for some will be infinite, and others not, if the universe be infinite; as for instance, water or fire. But a thing of this kind brings destruction to contraries, as we have before observed. Hence no one of the physiologists has made either fire or earth to be one and infinite, but water or air, or that which is a medium between these; because the place of each (namely, of fire and earth) is evidently definite. And these verge to the upper and lower region. But if the parts are infinite and simple, the places also will be infinite, and there will be infinite elements. If, however, this is impossible, and places are finite, it is also necessary that the whole should be finite: for it is impossible that body and place should not be equal in dimensions; since neither is the whole place so great as not to be able to admit at the same time body, though at the same time neither will body be infinite; nor is body greater than place: for otherwise there will either be a vacuum, or a body which is naturally adapted to be nowhere.
Anaxagoras, however, speaks absurdly concerning the permanency of the infinite: for he says that the infinite itself supports itself; and this because it is in itself: for nothing else contains it. As if where anything is it is naturally there. But this is not true: for a thing may be situated in a certain place by force, and not where it is naturally adapted to be. If, therefore, the whole is by no means moved; for that which is established in itself, and is in itself, is necessarily immovable; yet it should be said why it is not naturally adapted to be moved: for it is not just that he who thus speaks should be dismissed; since there may be anything else which is not moved; but nothing hinders it from being naturally adapted to be moved: for earth also is not borne along; nor if it were infinite could it be locally moved, in consequence of being restrained by the middle. It would not, however, remain in the middle, because there is not any other place into which it could be moved, but because it is not natural to it so to be moved. Though, indeed, it might be said, that the earth supports itself. If, therefore, this is not the cause of the permanency of the earth if it were infinite, but its gravity is the cause; and that which is heavy abides in the middle, and the earth is in the middle: in like manner also, the infinite will abide in itself, through some other cause, and not because it is infinite, will itself support itself. At the same time likewise, it is manifest, that it is necessary every part of it should abide: for as the infinite abides supported in itself; so likewise whatever part of it is assumed, will abide in itself: for the places of the whole and the part are of the same species; as of the whole earth and a clod, the place is downward; and of the whole of fire, and a spark, the place is upward. So that if the place of the infinite is in itself, there will be the same place also of a part of the infinite. It will abide therefore, in itself. And, in short, it is evident that it is impossible to say that there is an infinite body, and at the same time that there is a certain place for bodies, if every sensible body either possesses gravity or levity. And if it is heavy, it has a natural tendency to the middle; but if light, it naturally tends upward: for it is necessary that an infinite body should be such. but it is impossible that the whole should be passive in either way, or the half in both ways: for how will you divide? Or how will one part of the infinite be above, and another below? Or how will it have extremes or a middle? Further still; Every sensible body is in place; but the species and differences of place are upward and downward, before and behind, to the right hand and to the left: and these things not only thus subsist with relation to us, and by position, but have a definite subsistence in the universe itself. But it is impossible that these things should be in the infinite: and, in short, it is impossible that there should be an infinite place. But every body is in place: and, therefore, it is also impossible that there should be an infinite body. That, likewise, which is somewhere, is in place; and that which is in place is somewhere. If, therefore, the infinite cannot be a quantum (for in this case it would be of some definite quantity, as, for instance, of two cubits, or three cubits, since these signify a definite quantity), so likewise with respect to that which is in place, because it is somewhere: but this is either upward or downward, or in some other of the six intervals, each of which is a certain boundary period from these things, therefore, it is evident that there is not an infinite body in energy.
