Now the Pythagoreans did not accept numbers in this indifferent way, but as Notion. “At least they say that phenomena must be composed of simple elements, and it would be contrary to the nature of things if the principle of the universe pertained to sensuous phenomena. The elements and principles are thus not only intangible and invisible, but altogether incorporeal.”[41] But how they have come to make numbers the original principle or the absolute Notion, is better shown from what Aristotle says in his Metaphysics (I. 5), although he is shorter than he would have been, because he alleges that elsewhere (infra., p. 214) he has spoken of it. “In numbers they thought that they perceived much greater similitude to what is and what takes place than in fire, water, or earth; since a certain property of numbers (_τοιονδὶ πάθος_) is justice, so is it with (_τοιονδὶ_) the soul and understanding; another property is opportunity, and so on. Since they further saw the conditions and relations of what is harmonious present in numbers, and since numbers are at the basis of all natural things, they considered numbers to be the elements of everything, and the whole heavens to be a harmony and number.” In the Pythagoreans we see the necessity for one enduring universal idea as a thought-determination. Aristotle (Met. XII. 4), speaking of ideas, says: “According to Heraclitus, everything sensuous flows on, and thus there cannot be a science of the sensuous; from this conviction the doctrine of ideas sprang. Socrates is the first to define the universal through inductive methods; the Pythagoreans formerly concerned themselves merely with a few matters of which they derived the notions from numbers—as, for example, with what opportuneness, or right, or marriage are.” It is impossible to discern what interest this in itself can have; the only thing which is necessary for us as regards the Pythagoreans, is to recognize any indications of the Idea, in which there may be a progressive principle.