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68 even more important: "It is necessary," says Philolaus, "that everything should be either limiting or unlimited, or that everything should be both limiting and unlimited. Since, then, it appears, that things are not made up of the limiting only, nor of the unlimited only, it follows that each thing consists both of the limiting and the unlimited, and that the world, and all that it contains, are in this way formed or adjusted." This is a remarkable extract, for it shows that the Pythagoreans had to some extent anticipated the great principle of Heraclitus, namely, that every thing and every thought is the unity or conciliation of contraries; a principle, the depth and fertility of which have never to this day been rightly apprehended or appreciated, far less fathomed and exhausted.

12. In his dialogue entitled Philebus, Plato touches on this Pythagorean doctrine. For the word , which is Philolaus's expression for the limiting, he substitutes , the limit; and the union of the two (the limit and the unlimited) he calls , the mixed. So that, according to Pythagoras (and Plato seems to approve of the doctrine), everything is constituted out of the , and the , the limit and the unlimited, and the result is the , that is, the union of the two. This principle, afterwards applied to morals, led to Aristotle's doctrine of the , or of virtue as a mean between two extremes. The ; in the physical world was a limit or law