object of thought or reason. When we look at one colour, what we see is colour, what we think is one, i.e., number; when we look at many colours, what we see is colour, what we think is many, i.e., number. This distinction, the distinction by which number is assigned to reason and not to sense, is, I think, an important aid towards understanding the Pythagorean philosophy.
9. Number is a necessary form of thought under which we place or subsume whatever is presented to the mind. Hence form, which is another name for number, and not matter, is the essence of all things, at least of all intelligible things. It is the truth and substance of the universe—its truth and substance, not only in so far as it exists for us, but in so far as it exists for intelligence generally. Without number they are absolutely incomprehensible to any intelligence. Take away number, that is to say, let the universe and its contents be neither one nor many, and chaos, or worse, is come again. We are involved in contradictory nonsense. Number, then, or form, and not matter, as the Ionic philosophers contended; number, and not the numberless, or ἄπειρον of Anaximander, is the true universal, the common ground, the ultimately real in all things. With Pythagoras form or number is the essential, matter the unessential: with the Ionics matter is the essential, and form or number the unessential. In their respective positions the two schools stand diametrically opposed.
