There are five ways in which the infinite is spoken of. In one sense, that which by its nature has no limit, and it is as something impassable and inextricable in that it has no path to tread since it is not a quantity at all, is called infinite, just as we say that the voice is invisible in that it does not fall to sight at all. Of the same kind is both point and quality; for these are limitless: the former, though being itself a limit, has no limit, in that it has no size, and similarly with white and in general with quality in that it has no passage at all.
That which has an endless outlet
In a second sense, that which has an endless outlet, and of which it is impossible for one to find a limit in it, is called infinite, not because we cannot cross it, but because it never results in respect of extend, nor yet is there an end in size.
That which does have a limit but it has not yet been taken
Thirdly, we call infinite that which does have a limit, but due to a difficulty of our own it has not yet been taken. This happens for two reasons: either because of its quantity or because of its quality. Thus, we say that maze is limitless not because there is not a certain limit, but because of the fact that it is full of curves and because of this it is hard for one to go across it. We also say that the ocean is limitless because due to its immenseness we cannot cross it, though it is, at any rate, traversable.
That which is by its nature such as to have but has not
In a forth sense, that which is by its nature such as to have a limit but has not, is called infinite. And as such is a circle; for it is possible for us to assume an actual point in it and from there to make a start, but it has no specific point in actuality, since we may make a start whence we like; for the one who draw a circle by means of a center and a radius does not make a start from a specific point, but does so whence he wishes, and the one who is moving in a circle may start from whatever point he likes as well. Thus, then, a circle is infinite, since though it has no limit of itself — and because of this is called infinite — it may be in connection with another circle (that is, we may constantly draw a new one).
That which is by addition or division or both of them
The fifth significance of the infinite is that which is by addition or division or both of them. By addition, as it is with number and time (for we say that number is infinite in that it may go on to infinity, since it is possible for one to take another bigger one, and for the same reason it is possible for time too to give rise to); by division, by virtue of the capability of a magnitude of being capable of cutting in two constantly; both of these, just as if we conceive a line, then cut it up in two, and over again in two the one of the two received parts, so that on the one hand one part being taken off, on the other the same one being put into the remainder; so then the one may be increased infinitely, the other decreased infinitely.
Bibliography: J. Philoponus in Aristotle’s Physics
Translation: George Kotsalis
