Commentary Aristotle Metaphysics
But an individual is man by participation inasmuch as the specific nature is participated in by this designated matter. For that which is something in its entirety does not participate in it but is essentially identical with it, whereas that which is not something in its entirety but has this other thing joined to it is said properly to participate in that thing.
Thus, if heat were a self-subsistent heat, it would not be said to participate in heat, because it would contain nothing but heat. But since fire is something other than heat, it is said to participate in heat.
155. In a similar way, since the separate idea of man contains nothing but the specific nature itself, it is man per se; and for this reason it was called by him man-in-itself. But since Socrates and Plato have in addition to their specific nature an individuating principle, which is designated matter, they are therefore said to participate in a form, according to Plato.
156. Now Plato took this term “participation” from Pythagoras, although he made a change in the term. For the Pythagoreans said that numbers are the causes of things, just as the Platonists said that the ideas are, and claimed that sensible things of this kind exist as certain imitations of numbers. For inasmuch as numbers, which have no position of themselves, received positions, they caused bodies. But because Plato held that the ideas are unchangeable in order that there might be scientific knowledge of them, he did not agree that the term “imitation” could be used of the ideas, but in place of it he used the term “participation.” However, it must be noted that even though the Pythagoreans posited participation or imitation, they still did not investigate the way in which a common form is participated in by individual sensible things or imitated by them. But the Platonists have treated of this.
157. Further, he says. Here he gives Plato’s opinion about the mathematical substances. He says that Plato posited other substances—the objects of mathematics—in addition to the forms and sensible things. Moreover, he said that beings of this kind were an intermediate genus among the three kinds of substances, or that they were above sensible substances and below the forms, and differed from both.
The mathematical substances differed from sensible substances because sensible substances are corruptible and changeable, whereas the mathematical substances are eternal and immobile. The Platonists got this idea from the way in which mathematical science conceives its objects, for mathematical science abstracts from motion.
The mathematical substances also differed from the forms, because the objects of mathematics are found to be numerically different and specifically the same—otherwise the demonstrations of mathematics would prove nothing. For unless two triangles belonged to the same species, geometry would attempt in vain to demonstrate that some triangles are similar; and the same thing is true of other figures.
But this does not happen in the case of the forms. For, since a form is just the specific nature itself of a thing, each form can only be unique. Even though the form of man is one thing, and the form of ass another thing, nevertheless the form of man is unique, and so is the form of ass; the same thing is true of other things.
158. Now to one who carefully examines Plato’s arguments it is evident that Plato’s opinion was false, because he believed that the mode of being which the thing known has in reality is the same as the one which it has in the act of being known.
Therefore, since he found that our intellect understands abstractions in two ways—in one way as we understand universals abstracted from singulars, and in another way as we understand the objects of mathematics abstracted from sensible things—he claimed that for each abstraction of the intellect there is a corresponding abstraction in the essences of things. Hence he held that both the objects of mathematics and the forms are separate.
But this is not necessary. For even though the intellect understands things insofar as it becomes assimilated to them through the intelligible form by which it is put into act, it still is not necessary that a form should have the same mode of being in the intellect that it has in the thing known. For everything that exists in something else exists there according to the mode of the recipient.
Therefore, considering the nature of the intellect (which is other than the nature of the thing known) the mode of understanding by which the intellect understands must be one kind of mode, and the mode of being by which things exist must be another. For although the object which the intellect understands must exist in reality, it does not exist there according to the same mode.
Hence, even though the intellect understands mathematical entities without simultaneously understanding sensible substances, and understands universals without understanding particulars, it is not therefore necessary that the objects of mathematics should exist apart from sensible things, or that universals should exist apart from particulars.
For we also see that sight perceives color apart from flavor, even though flavor and color are found together in sensible substances.
159. And since the forms. Here he gives Plato’s opinion concerning the principles of things; and in regard to this he does two things.
First, he states the principles which Plato assigned to things;
second, the genus of cause to which they are reduced, at from the foregoing.
First, he tells us what kind of principles Plato had assigned to things.
Second, he shows in what respect Plato agreed with the Pythagoreans, and in what respect he differed from them, at yet Plato.
He first says that since the forms are the causes of all other beings according to Plato, the Platonists therefore thought that the elements of the forms are the elements of all beings. Hence, they assigned as the material principle of things the great and small, and said that the substance of things (that is, their form) is the one. They did this because they held these to be the principles of the forms. For they said that just as the forms are the formal principles of sensible things, in a similar way the one is the formal principle of the forms.
Therefore, just as sensible things are constituted of universal principles by participation in the forms, in a similar way the forms (which he said are numbers) are constituted from these, that is of the great and small. For the unit constitutes different species of numbers by addition and subtraction, in which the notion of the great and small consists.
Hence, since the one was thought to be the substance of being (because he did not distinguish between the one which is the principle of number and the one which is convertible with being), it seemed to him that a plurality of different forms might be produced from the one, which is their common substance, in the same way that a plurality of different species of numbers is produced from the unit.
160. Yet Plato. Here he compares the position of Plato with that of Pythagoras.
First, he shows in what respect they agreed;
second, in what respect they differed, at but to posit.
Now they agreed in two positions. The first is that the one is the substance of things. For the Platonists, like the Pythagoreans, said that what I call the one is not predicated of some other being as an accident is of a subject, but signifies a thing’s substance. They said this, as we have pointed out, because they did not distinguish between the one which is convertible with being and the one which is the principle of number.
161. The second position follows from the first, for the Platonists, like the Pythagoreans, said that numbers are the causes of the substance of all beings; they held this because number is just a collection of units. Hence if the one is substance, number must also be such.
162. But to posit. Here he shows in what respect they differed. In regard to this he does two things.
First, he states how they differed.
Second, he gives the reason for this difference, at therefore, his making.
Now this difference involves two things. First, the Pythagoreans, as has already been stated, posited two principles of which things are constituted—the limited and the unlimited—of which one, the unlimited, has the character of matter.
But in place of this one principle, the unlimited, which the Pythagoreans posited, Plato created a dyad, holding that the great and small have the character of matter. Hence the unlimited, which Pythagoras claimed to be one principle, Plato claimed to consist of the great and small. This is his own opinion in contrast with that of Pythagoras.