But the Pythagorean is certainly a stage in advance of the Ionic.
10. In the account which I have hitherto given you of the Pythagorean philosophy, I have taken the statement of its principle from Aristotle, and, founding on his text, I have endeavoured, by means of a few critical reflections of my own, to impart to it some intelligibility, and to show you that there is some meaning, and also some truth in the assertion, that number is the essence of all things. I go on to speak of the Pythagorean philosophy as represented by Philolaus. Philolaus was probably the first of the Pythagoreans who committed to writing any of their master's doctrines; for neither the founder of the school, nor his immediate disciples, appear to have put their opinions on record. Philolaus was, as I said, a contemporary of Socrates. He wrote a work on the Pythagorean system, with which Plato seems to have been acquainted. Some fragments of this work are extant, and were collected and published in 1819 by a German scholar, Augustus Boeckh.
11. In this work we find these words: "Everything," says Philolaus, "which is known has in it number, for it is impossible either to think or know anything without number." He thus makes number the source and condition of intelligence, and the ground of the intelligible universe. But the following is
