[Footnote 437: Aristotle's "Metaphysics," bk. i. ch. vi.]
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]
[Footnote 4398: Id., ib., bk. i. ch. ix.]
[Footnote 439: Whewell's "History of Inductive Sciences," vol. i. p. 78.]
These preliminary considerations will have cleared and prepared the way for a fuller presentation of the philosophic system of Pythagoras. The most comprehensive and satisfactory exposition of his "method" is that given by Wm Archer Butler in his "_Lectures on Ancient Philosophy_," and we feel we can not do better than condense his pages.[440]
Pythagoras had long devoted his intellectual adoration to the lofty idea of _order_, which seemed to reveal itself to his mind, as the presiding genius of the serene and silent world. He had, from his youth, dwelt with delight upon the eternal relations of space, and determinate form, and number, in which the very idea of _proportion_ seems to find its first and immediate development, and without the latter of which (number), all proportion is absolutely inconceivable. To this ardent genius, whose inventive energies were daily adding new and surprising contributions to the sum of discoverable relations, it at length began to appear as if the whole secret of the universe was hidden in these mysterious correspondences.