Note (return) — Chapter IX

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.