Meanwhile, he had a logical machine ready to hand, which could be used with terrible effect against the Platonic Ideas. Any of these—and there were a great number—that could be brought under one of the last nine categories were at once deprived of all claim to independent existence. Take Equality, for instance. It cannot be discovered outside quantity, and quantity is always predicated of a substance. And the same is true of number, to the utter destruction of the Neo-Pythagorean theory which gave it a separate existence. Moreover, the categories served not only to generalise and combine, but also to specificate and divide. The idea of motion occurs in three of them; in quantity, where it means increase or diminution; in quality, where it means alteration, as from hot to cold, or _vice versâ_; and in place, implying transport from one point to another. The Idea of Good, which stands at the very summit of Plato’s system, may be traced through all ten categories.[242] Thus, the supposed unity and simplicity of such conceptions was shown to be an illusion. Platonism was, in truth, so inconsistent with the notions embodied in common language, that it could not but be condemned by a logic based on those notions. Aristotle next takes the Idea of Substance and subjects it to a fresh analysis.[243] Of all things none seem to possess so evident an existence as the bodies about us—plants and animals, the four elements, and the stars. But each of these has already been shown to consist of Form and Matter. A statue, for instance, is a lump of bronze shaped into the figure of a man. Of these two constituents, Matter seems at first sight to possess the greater reality. The same line of thought which led Aristotle to place substance before the other categories now threatens to drive him back into materialism. This he dreaded, not on sentimental or religious grounds, but because he conceived it to be the negation of knowledge. He first shows that Matter cannot be the real substance to which individuals owe their determinate existence, since it is merely the unknown residuum left behind when every predicate, common to them with others, has been stripped off. Substance, then, must be either Form alone or Form combined with Matter. Form, in its completest sense, is equivalent to the essential definition of a thing—the collection of attributes together constituting its essence or conception. To know the definition is to know the thing defined. The way to define is to begin with the most general notion, and proceed by adding one specific difference after another, until we reach the most particular and concrete expression. The union of this last with a certain portion of Matter gives us the individual Socrates or Callias. There are no real entities (as the Platonists pretend) corresponding to the successive stages of generalisation, biped, animal, and so forth, any more than there are self-existing quantities, qualities, and relations. Thus