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[998b] [1] he observes, e.g., of what parts a bed consists and how they are put together; and then he comprehends its nature. Thus to judge from these arguments the first principles will not be the genera of things.

But from the point of view that it is through definitions that we get to know each particular thing, and that the genera are the first principles of definitions, the genera must also be the first principles of the things defined.And if to gain scientific knowledge of things is to gain it of the species after which things are named, the genera are first principles of the species. And apparently some even of those1 who call Unity or Being or the Great and Small elements of things treat them as genera.

Nor again is it possible to speak of the first principles in both senses.The formula of substance is one; but the definition by genera will be different from that which tells us of what parts a thing is composed.

Moreover, assuming that the genera are first principles in the truest sense, are we to consider the primary genera to be first principles, or the final terms predicated of individuals? This question too involves some dispute.For if universals are always more truly first principles, clearly the answer will be "the highest genera," since these are predicated of everything. Then there will be as many first principles of things [20] as there are primary genera, and so both Unity and Being will be first principles and substances, since they are in the highest degree predicated of all things.But it is impossible for either Unity or Being to be one genus of existing things. For there must be differentiae of each genus, and each differentia must be one2; but it is impossible either for the species of the genus to be predicated of the specific differentiae, or for the genus to be predicated without its species.3 Hence if Unity or Being is a genus, there will be no differentia Being or Unity.But if they are not genera, neither will they be first principles, assuming that it is the genera that are first principles. And further, the intermediate terms, taken together with the differentiae, will be genera, down to the individuals; but in point of fact, although some are thought to be such, others are not. Moreover the differentiae are more truly principles than are the genera; and if they also are principles, we get an almost infinite number of principles, especially if one makes the ultimate genus a principle.

1 The Pythagoreans and Plato.

2 i.e., each differentia must have Being and Unity predicated of it.

3 The reasons are given in Aristot. Topica, 144a 36-b11.

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