He also totally misrepresents Plato's doctrine of "Ideas." "Plato's Ideas," he says, "are substantial existences--real beings" ("Metaphysics," bk. i. ch. ix.). Whereas, as we shall subsequently show, "they are objects of pure conception for human reason, and they are attributes of the Divine Reason. It is there they substantially exist." (Cousin, "History of Philosophy," vol. i. p. 415). It is also pertinent to inquire, what is the difference between the "formal cause" of Aristotle and the archetypal ideas of Plato? and is not Plato's τὸ ἀγαθόν the "final cause?" Yet Aristotle is forever congratulating himself that he alone has properly treated the "formal" and the "final cause!"] [Footnote 434: This, however, was not the doctrine of Plato. He does not say "forms are numbers." He says: "God formed things as they first arose according to forms _and_ numbers." See "Timaeus," ch. xiv. and xxvii.] [Footnote 435: Aristotle's "Metaphysics," bk. i. ch. vi.] 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: "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: Aristotle's "Metaphysics," bk. i. ch. vi.]