Читать книгу A Beginner's History of Philosophy, Vol. 1: Ancient and Mediæval Philosophy онлайн

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There are two kinds of reality in the Pythagorean teaching: (1)numbers, and (2)unlimited space. The essential nature of things, the Being that abides, consists in the shaping of this unlimited space into mathematical forms. The numbers or the forms are the limited aspect of Being; space is the unlimited aspect of Being. Actual Being consists in the union of the two aspects. Being therefore has two roots, each being necessary to the other. The later Pythagoreans, indeed, called attention to the fact that their numbers were not the same as the different kinds of matter out of which the other Cosmologists conceived the world to be fashioned. Numbers are not the stuff out of which the world of nature-objects have arisen, but rather are forms of nature-objects. Numbers are the patterns or models of things; things are the copies or imitations of numbers. Unlimited space furnishes the material; numbers or mathematical forms furnish the mould; the result is a material thing. Here we find the early basis of Plato’s doctrine of Ideas, and the correlation in Aristotle of Form and matter. If we were to draw an analogy between the Pythagorean conception of numbers and any part of the preceding cosmological teaching, we should find the similarity between the numbers and the earlier efficient causes and not between the numbers and the elements. For example, Pythagorean numbers have a function more nearly like Love and Hate than like the four elements in Empedocles’ teaching. On the other hand, Pythagorean unlimited space is analogous to the Empedoclean elements.