Commentary Aristotle Metaphysics
163. The second difference is that Plato held that numbers are separate from sensible things, and this in two ways. For he said that the forms themselves are numbers, as was pointed out above. He also held, as was stated above, that the objects of mathematics are an intermediate genus between the forms and sensible things, and that they are numbers by their very essence.
But the Pythagoreans said that sensible things themselves are numbers, and did not make the objects of mathematics an intermediate species between the forms and sensible things. Nor again did they hold that the forms are separate from things.
164. Therefore, his making. Here he gives the reason for the difference.
First, he gives the reason for the second difference;
second, the reason for the first difference, at but his making.
He says, then, that the Platonists adopted the position that both the one and numbers exist apart from sensible things and not in sensible things, as the Pythagoreans claimed. They also introduced separate forms because of the investigation into the ideas of things, that is, because of their investigation of the definitions of things, which they thought could not be attributed to sensible substances, as has been stated. This is the reason they were compelled to hold that there are certain things to which definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of dialectic, whose office it is to investigate definitions and universals of this kind, the study of which led to the introduction of the ideas.
165. But his making. Here he gives the reason for the other difference, the one concerning matter.
First, he gives the reason for such a difference.
Second, he shows that Plato was not reasonably motivated, at yet what happens is the contrary.
He accordingly says that the Platonists made the dyad to be a number of a different nature than the forms, because all numbers with the exception of prime numbers are produced from it. They called prime numbers those which are not measured by any other number (such as three, five, seven, eleven, and so on), for these are produced immediately from unity alone. But numbers which are measured by some other number are not called prime numbers, but composite ones (for example, the number four, which is measured by the number two). And in general every even number is measured by the number two. Hence even numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to them, as has been stated above. This is why he posited the dyad, from which as a matrix, or exemplar, all other even numbers are produced.
166. Yet what happens. Here he proves that Plato made unreasonable assumptions; in regard to this he does two things.
First, he proves this by an argument from nature.
Second, he gives the argument based on the nature of things, which led Plato to adopt this position, at and from one matter.
He says that although Plato posited a dyad on the part of matter, still what happens is the contrary of this, as the opinions of all the other natural philosophers testify; for they claimed that contrariety pertains to form and unity to matter, as is clear in Physics 1. For they held that the material principle of things is air or water or something of this kind, from which the diversity of things is produced by rarefaction and condensation, which they regarded as formal principles. For Plato’s position is not a reasonable one.
Now the natural philosophers adopted this position because they saw that many things are generated from matter as a result of a succession of forms in matter. For that matter which now supports one form may afterward support many forms as a result of one form being corrupted and another being generated.
But one species or form generates only once, that is, constitutes the thing which is generated. For when something is generated it receives a form, and the same form numerically cannot become the form of another thing that is generated, but ceases to be when that which was generated undergoes corruption. In this argument it is clearly apparent that one matter is related to many forms, and not the reverse (one form to many matters).
Thus it seems more reasonable to hold that unity pertains to matter but duality or contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato held.
167. And from one matter. Here he gives an opposite argument taken from sensible things according to the opinion of Plato. For Plato saw that each thing is received in something else according to the measure of the recipient. Hence receptions seem to differ according as the capacities of recipients differ. But one matter is one capacity for reception. And Plato also saw that the agent who induces the form, although he is one, causes many things to have this form; this comes about because of diversity on the part of matter. An example of this is evident in the case of male and female, for a male is related to a female as an agent and one who impresses a form on matter. But a female is impregnated by one action of a male, whereas one male can impregnate many females. This is why he held that unity pertains to form and duality to matter.
168. Now we must note that this difference between Plato and the philosophers of nature is a result of the fact that they considered things from different points of view.
For the philosophers of nature considered sensible things only insofar as they are subject to change, in which one subject successively acquires contrary qualities. Hence they attributed unity to matter and contrariety to form. But Plato, because of his investigation of universals, went on to give the principles of sensible things. Therefore, since the cause of the diversity of the many singular things that come under one universal is the division of matter, he held that diversity pertains to matter and unity to form. And such are the changes in these principles which Plato posited—that is, participations, or, as I may say, influences in the things generated. For Pythagoras understands the word “change” in this way. Or Aristotle says “changes” inasmuch as Plato changed the opinion which the first philosophers of nature had about principles, as is evident from the foregoing. Hence it is evident from the foregoing that Plato dealt thus with the causes which we are investigating.
169. From the foregoing. Here he shows to what genus of cause the principles given by Plato are referred. He says that it is evident from the foregoing that Plato used only two kinds of causes. For he used as one cause of a thing the cause of its whatness (that is, its quiddity, or its formal cause, which determines its quiddity), and he also used matter itself. This is also evident from the fact that the forms which he posited are the cause of the whatness in other things, that is, the causes of the whatness of sensible things (namely, their formal causes).
But the formal cause of the forms themselves is what I call the one, which seems to be the substance of which the forms are composed. And just as he holds that the one is the formal cause of the forms, in a similar fashion he holds that the great and small are their material cause, as was stated above. And these causes—the formal and the material cause—are referred not only to the forms but also to sensible substances, because there is some subject of which the one is predicated in the forms. That is to say, that which is related to sensible substances in the same way as the one is to the forms is itself a form, because that duality which relates to sensible things as their matter is the great and small.
170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with reference to each of the elements which he posited. For he made form the cause of good and matter the cause of evil. However, some of the first philosophers attempted to investigate the cause of good and evil, such as Anaxagoras and Empedocles, who established certain causes in the world with the end of giving the principles of good and evil by means of these causes. And in touching upon these causes of good and evil they came very close to positing the final cause, although they did not posit this cause directly, but only indirectly, as is stated below.