Classical Philosophy

In like manner it is necessary that the natural philosopher should know concerning place, as well as concerning the infinite, whether it is or not, and in what manner it is, and what it is: for all men conceive that beings are somewhere; since non-being is nowhere: for where is … Read more

It now remains that we enumerate the reasons through which the infinite appears not only to subsist in capacity, but as that which is definite: for some of these reasons are not necessary; and against others certain other true objections may be urged: for neither is it necessary that there … Read more

Since, however, causes receive a fourfold division, it is evident that the infinite is a cause as matter; that the essence of it is privation; and that the continuous and the sensible are that which is an essential subject. But it is manifest that all others use the infinite as … Read more

It happens, however, agreeably to reason that the infinite should not by addition appear so as to surpass every magnitude, but that this should be effected by division; for as matter is comprehended within, so likewise the infinite. But form comprehends. It is also conformable to reason that in number … Read more

Hence also they assume those venerable conceptions of the infinite; such as, that it comprehends all things, and that it contains the universe in itself, in consequence of possessing a certain similitude with the whole: for the infinite is the matter of the perfection of magnitude; and is the whole … Read more

The infinite, however, happens to subsist in a way contrary to what it is asserted to be by others: for the infinite is not that beyond which there is nothing, but it is that of which there is always something beyond. The truth of this is evidenced in rings, which … Read more

That many absurdities, however, will happen if the infinite has not any subsistence whatever, is evident; for of time there will be some beginning and end; magnitudes also will not be divisible into magnitude; and number will not be infinite. But this being determined, since it does not appear that … Read more

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 … Read more

In the first place, therefore, we must define in how many modes the infinite may be said to subsist. According to one mode, then, that is called infinite which is not naturally adapted to be passed through; just as voice is said to be invisible. But, according to another mode, … Read more

But a belief that there is something infinite is produced in those who consider it, from five arguments especially. From time; for this is infinite. From the division in magnitudes; for mathematicians also use the infinite. Further still; from this, that thus generation and corruption will not fail if that … Read more