Note (return) — Chapter IX

The fact seems to be this, the Pythagoreans busied themselves chiefly with what Aristotle designates "the formal cause," and gave little attention to the inquiry concerning "the material cause." This is admitted by Aristotle. Concerning fire, or earth, or the other bodies of such kind, they have declared nothing whatsoever, inasmuch as affirming, in my opinion, nothing that is peculiar concerning sensible natures. 438 They looked, as we have previously remarked, to the relations of phenomena, and having discovered certain "numerical similitudes," they imagined they had attained an universal principle, or law. "If all the essential properties and attributes of things were fully represented by the relations of numbers, the philosophy which supplied such an explanation of the universe might well be excused from explaining, also, that existence of objects, which is distinct from the existence of all their qualities and properties. The Pythagorean doctrine of numbers might have been combined with the doctrine of atoms, and the combination might have led to results worthy of notice. But, so far as we are aware, no such combination was attempted, and perhaps we of the present day are only just beginning to perceive, through the disclosures of chemistry and crystallography, the importance of such an inquiry." 439