Page:Early Greek philosophy by John Burnet, 3rd edition, 1920.djvu/300

286 accompanied by a singular licence of interpretation. We shall start, then, from what Aristotle tells us about the numbers.

143. In the first place, Aristotle is quite clear that Pythagoreanism was intended to be a cosmological system like the others. "Though the Pythagoreans," he tells us, "made use of less obvious first principles and elements than the rest, seeing that they did not derive them from sensible objects, yet all their discussions and studies had reference to nature alone. They describe the origin of the heavens, and they observe the phenomena of its parts, all that happens to it and all it does." They apply their first principles entirely to these things, "agreeing apparently with the other natural philosophers in holding that reality was just what could be perceived by the senses, and is contained within the compass of the heavens," though "the first principles and causes they made use of were really adequate to explain realities of a higher order than the sensible."

The doctrine is more precisely stated by Aristotle to be that the elements of numbers are the elements of things, and that therefore things are numbers. He is equally positive that these "things" are sensible things, and indeed that they are bodies, the bodies of which the world is