Page:Early Greek philosophy by John Burnet, 3rd edition, 1920.djvu/303

Rh Again, Plutarch says: "In the division of numbers, the even, when parted in any direction, leaves as it were within itself a field; but, when the same thing is done to the odd, there is always a middle left over from the division." It is clear that all these passages refer to the same thing, and that can hardly be anything else than the "terms" or dots with which we are already familiar (§ 47). The division must fall between these; for, if it meets with an indivisible unit, it is at once arrested.

145. Now there can be no doubt that by his Unlimited Pythagoras meant something spatially extended; for he identified it with air, night, or the void. We are prepared, then, to find that his followers also thought of the Unlimited as extended. Aristotle certainly regarded it so. He argues that, if the Unlimited is itself a reality, and not merely the predicate of some other reality, then every part of it must be unlimited too, just as every part of air is air. The same thing is implied in his statement that the Pythagorean Unlimited was outside the heavens. Further than this, it is not safe to go. Philolaos and his followers cannot have regarded the Unlimited as Air; for, as we shall see, they adopted the theory of Empedokles as to that "element," and accounted for it otherwise. One of them, Xouthos, argued that rarefaction and condensation implied the void; without it the universe would overflow. We do not know, however, whether he was earlier than the Atomists or not. 19