Metaphysics

​If, then, both not to posit the good among the principles, and to posit it in this way, are impossible, it is clear that the principles are not correctly assigned, nor are the primary substances. Nor does anyone conceive correctly if he compares the principles of the whole to those of animals and plants, on the ground that the more perfect always come from indefinite and imperfect things, and therefore says that this is so even in the case of the first things, so that the one itself is not even an existing thing. For even here the principles from which these things come are perfect; for man generates man, and the seed is not first. And it is also absurd to make place along with the mathematical solids (for place is peculiar to individual things, which is why they are separate in place, but mathematical things are not somewhere), and to say that they will be somewhere, but not what place is. But those who say that existing things are from elements, and that the first of existing things are numbers, ought to have distinguished in what ways one thing is from another, and so to have stated in what manner number is from the principles. Is it by mixture? But neither is everything mixable, and the product is different, and the one will not be separate nor a distinct nature; yet they wish it to be. Or by composition, like a syllable? But then position must belong to it, and he who thinks of them will think of the one and the multiplicity separately. This, then, will be number—a unit and multiplicity, or the one and the unequal. And since being from certain things can mean either that they are inherent or that they are not, in which way is number so? For in the sense of their being inherent, this is not possible except for things which have generation. Or is it as from a seed? But it is impossible for anything to be shed from the indivisible. Or is it as from a contrary which does not persist? But all things which are in this way are also from something else which persists. Since, then, one person posits the one as contrary to multiplicity, and another as contrary to the unequal, treating the one as the equal, number would be as if from contraries; there must therefore be some other thing, from which as persisting, and from one of the contraries, it is or has been generated. Further, why on earth do all other things which are from contraries or which have contraries perish, even if they are from everything, while number does not? For nothing is said about this. And yet, whether inherent or not inherent, the contrary destroys the contrary, for example, strife destroys the mixture (and yet it ought not, for it is not contrary to that). And nothing has been defined, either, as to in which of the two ways numbers are causes of substances and of being—whether as boundaries (as points are of magnitudes, and as Eurytus determined what number belongs to what, e.g. this number to man and that to horse, like those who bring numbers into the figures of triangle and square, thus assimilating with pebbles the forms of plants), or because harmony is a ratio of numbers, and similarly also man and each of the other things? And how indeed are attributes numbers—the white, the sweet, and the hot? But that numbers are not substance, nor causes of form, is clear; for the ratio is the substance, and number is matter. For example, if the substance of flesh or bone is number in this way, three of fire and two of earth; and whatever number it may be, it is always a number of certain things, either of fire or of earth or of units, but the substance is the being of so much to so much in the mixture; and this is no longer a number, but a ratio of a mixture of numbers, whether bodily or of whatever kind. Therefore, number is not a cause by producing—neither number in general, nor that which consists of units—nor is it the matter, nor the ratio and form of things. Nor indeed is it a cause as that for the sake of which.