Now the writings of Plato are all extant to-day, and accessible in an excellent English translation to any of our readers. Cousin has shown, [436] most conclusively (and we can verify his conclusions for ourselves), that Aristotle has totally misrepresented Plato. And if, in the same connection, and in the course of the same argument, and in regard to the same subjects, he misrepresents Plato, it is most probable he also misrepresents Pythagoras.
[Footnote 436: ][ (return) ] "The True, the Beautiful, and the Good," pp. 77-81.
It is, however, a matter of the deepest interest for us to find the evidence gleaming out here and there, on the pages of Aristotle, that he had some knowledge of the fact that the Pythagorean numbers were regarded as symbols. The "numbers" of Pythagoras are, in the mind of Aristotle, clearly identified with the "forms" of Plato. Now, in Chapter VI. of the First Book he says that Plato taught that these "forms" were παραδείγµατα--models, patterns, exemplars after which created things were framed. The numbers of Pythagoras, then, are also models and exemplars. This also is admitted by Aristotle. The Pythagoreans indeed affirm that entities subsist by an imitation (µίµησις) of numbers. [437] Now if ideas, forms, numbers, were the models or paradigms after which "the Operator" formed all things, surely it can not be logical to say they were the "material" out of which all things were framed, much less the "efficient cause" of things. The most legitimate conclusion we can draw, even from the statements of Aristotle, is that the Pythagoreans regarded numbers as the best expression or representation of those laws of proportion, and order, and harmony, which seemed, to their eyes, to pervade the universe. Their doctrine was a faint glimpse of that grand discovery of modern science--that all the higher laws of nature assume the form of a precise quantitative statement.
[Footnote 437: ][ (return) ] 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 438: ][ (return) ] Id., ib., bk. i. ch. ix.
[Footnote 439: ][ (return) ] 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]
[Footnote 440: ][ (return) ] Lecture VI. vol. i.