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Rh not understand what you meant by water, or air, or earth, or fire, or colour, or sound, or heat, or cold: but whatever his senses were, or whether he had any senses or not, I conceive he would understand what you meant by number, he would know what one meant, and what many meant. He would not understand intuitionally what a tree was, and he could not be made to understand it intuitionally: but he might understand it symbolically, by being informed that it and everything else was a unity which admitted of being resolved into multiplicity, and that each of the fractions was again a unity. Unless he could be made to understand this—in short, unless he could form some conception of number—it seems to me that he would not be an intelligence at all. And therefore it may be said that number is a true universal, that is to say, it is a necessary thought; it expresses something which is the truth for all, and not merely the truth for some, intelligence. At any rate, it is a wider and truer universal than either water or air, or any other sensible thing.

7. We are now able to understand the apparently very paradoxical assertion of the Pythagoreans, namely, that number is the substance of things, the essence of the universe; and we are able, moreover, to perceive in what sense this doctrine is true. The whole paradox is resolved, the whole difficulty is cleared, by attending to the distinction to which I have so often directed your thoughts, the