and that outside of this there is “neither space, nor vacuum, nor time.” One would expect these words to mean that the Universe extends to infinity in all directions; but, on the other hand, Aristotle attributes a definite circular shape to the “outside” of the Universe, which would be incompatible with the idea of infinite extension. In fact, his arguments to prove the above untenable position are curious abstract quibbles, which may be quoted to show how oddly a philosopher of the 4th century B.C. could reason on the physical construction of the Universe. He says (‘On the Heavens,’ I. ix.) that there can be neither space nor vacuum outside the circumference of the Cosmos, for, if there were, then body might be placed therein; but this is impossible, because every physical body is naturally endowed with one of three motions: it is either naturally centripetal, or naturally centrifugal, or naturally revolving round the earth. Now each of these three kinds of body has its natural place within the Universe; the stone being centripetal has its natural place on or in the earth; fire being centrifugal has its natural place above the air; the stars which revolve have their natural place in the revolving Heaven. Thus there is no kind of body which can naturally exist outside the Universe, and therefore there can be no Space, for Space is that in which bodies exist! That there is no Time beyond the limits of the Universe, Aristotle proves by the more legitimate argument that “if there is no motion there can be no time, since Time is the measure of motion.” But his conception of the “natural” motions inherent
