Commentary Aristotle Metaphysics
He gives diagrams (the demonstrative descriptions of geometrical figures) as a second example. For the elements of these diagrams are not said to be the common term “diagram,” but rather those theorems whose demonstrations are found in the demonstrations of other geometrical theorems, either of all or of most of them, because the other demonstrations proceed from the supposition of the first demonstrations. Hence Euclid’s book is called The Elements, because the first theorems of geometry, from which the other demonstrations proceed, are demonstrated therein.
425. Furthermore, those who. Here he gives the second argument, which also employs certain examples drawn from nature. He says that those who hold that the elements of bodies are either one or many say that the principles and elements of bodies are those things of which bodies are composed and made up as intrinsic constituents.
Thus Empedocles says that the elements of natural bodies are fire and water and other things of this kind, which along with these he calls the elements of things. Natural bodies are constituted of these first things inasmuch as they are intrinsic. Moreover, the early philosophers held that in addition to these two principles there are four others—air, earth, strife, and friendship—as was stated in book 1. But neither Empedocles nor the other philosophers of nature said that the genera of things are the principles and elements of these natural bodies.
426. And again if anyone. Here he gives the third argument, which involves things made by art. He says that if someone wished to speculate about the nature, that is, about the definition which indicates the essence of other bodies than natural ones (namely, of bodies made by human art)—for example, if one wished to know a bed—it would be necessary to consider of what parts it is made and how they are put together. In this way he would know the nature of a bed. And after this he concludes that genera are not the principles of existing things.
427. But if we know. Here he argues the other side of the question.
He gives three arguments, the first of which is as follows. Each thing is known through its definition. Therefore, if a principle of being is the same as a principle of knowing, it seems that anything which is a principle of definition is also a principle of the thing defined. But genera are principles of definitions, because definitions are first composed of them. Hence genera are the principles of the things defined.
428. And if in order to. Here he gives the second argument, which runs thus. Scientific knowledge of each thing is acquired by knowing the species from which it gets its being, for Socrates can be known only by understanding that he is man. But genera are principles of species, because the species of things are composed of genera and differences. Therefore, genera are the principles of existing things.
429. Moreover, some of those. Here he gives a third argument, which is based on the authority of the Platonists, who held that the one and being are the principles of things, and also the great and small, which are used as genera. Therefore, genera are the principles of things.
430. But it is not possible. Here he excludes one answer which would say that both of these are principles. He says that it is impossible to say that both of these are principles, that is, both the elements (or the parts of which something is composed) and genera. He proves this by the following argument.
Of each thing there is one definite concept which manifests its substance, just as there is also one substance of each thing. But the definitive concept which involves genera is not the same as the one which involves the parts of which a thing is composed. Hence it cannot be true that each definition indicates a thing’s substance. But the definitive concept which indicates a thing’s substance cannot be taken from its principles. Therefore, it is impossible that both genera and the parts of which things are composed should be simultaneously the principles of things.
431. Again, if genera. Then he treats the second question dialectically.
First, he raises the question;
second, he brings up arguments relative to this question, at for if universals.
Accordingly, he asks: if we hold that genera are the principles of things in the fullest sense, which of these genera should be considered to be the principles of things to a greater degree? Must we consider those genera which are first in number (namely, the most common), or also the lowest genera, which are proximately predicated of the individual (namely, the lowest species)? For this is open to question, as is clear from what follows.
432. For if universals. Here he argues about the question which was proposed, and in regard to this he does three things.
First, he introduces arguments to show that the first genera cannot be principles.
Second, he introduces arguments to show that the last species should rather be called the principles of things, at but, on the other hand.
Third, he debates the proposed question, at but again it is.
In regard to the first he gives three arguments, of which the first runs thus. If genera are principles to the extent that they are more universal, then those which are most universal (namely, those which are predicated of all things) must be the first genera and the principles of things in the highest degree. Hence there will be as many principles of things as there are most common genera of this kind. But the most common of all genera are unity and being, which are predicated of all things. Therefore, unity and being will be the principles and substances of all things.
But this is impossible, because unity and being cannot be genera of all things. For, since unity and being are most universal, if they were principles of genera, it would follow that genera would not be the principles of things. Hence the position which maintains that the most common genera are principles is an impossible one, because from it there follows the opposite of what was held, namely, that genera are not principles.
433. That being and unity cannot be genera he proves by this argument. Since a difference added to a genus constitutes a species, a species cannot be predicated of a difference without a genus, or a genus without a species. That it is impossible to predicate a species of a difference is clear for two reasons.
First, because a difference applies to more things than a species, as Porphyry says.
Second, since a difference is given in the definition of a species, a species can be predicated per se of a difference only if a difference is understood to be the subject of a species, as number is the subject of evenness, in whose definition it is given. This, however, is not the case; but a difference is rather a formal principle of a species. Therefore, a species cannot be predicated of a difference except, perhaps, in an incidental way.
Similarly too neither can a genus, taken in itself, be predicated of a difference by per se predication. For a genus is not given in the definition of a difference, because a difference does not share in a genus, as is stated in Topics 4. Nor again is a difference given in the definition of a genus. Therefore, a genus is not predicated per se of a difference in any way. Yet it is predicated of that which has a difference, namely, of a species, which actually contains a difference.
Hence he says that a species is not predicated of the proper differences of a genus, nor is a genus independently of its species, because a genus is predicated of its differences inasmuch as they inhere in a species. But no difference can be conceived of which unity and being are not predicated, because any difference of any genus is a one and a being, otherwise it could not constitute any one species of being. It is impossible, then, that unity and being should be genera.