Commentary Aristotle Metaphysics
However, it can be understood in two other ways. First, it can mean the definition itself of the last species, which is not further divided by essential differences. In this sense his statement can mean that we do not have complete knowledge of a thing until we reach its last species, for one who knows the genus to which a thing belongs does not yet have a complete knowledge of that thing.
According to this interpretation, we must say that just as the first argument concluded that it is impossible to have an infinite regress in an upward direction among formal causes, in a similar fashion this second argument concludes that it is impossible to have an infinite regress in a downward direction, otherwise it would be impossible to reach a last species. Therefore, this position destroys any complete knowledge.
324. Now a formal division exists not only when a genus is divided by differences (and when such division is no longer possible the last species can be said to be undivided), but also when the thing defined is divided into its definitive parts, as is evident in Physics 1. Therefore, in this place “undivided” can also mean a thing whose definition cannot be resolved into any definitive parts.
Now, according to this the supreme genus is undivided, and from this point of view his statement can mean that we cannot have scientific knowledge of a thing by definition unless we reach its supreme genera, because when these remain unknown it is impossible to know its subsequent genera. And according to this, the second argument concludes (as the former one did) that it is impossible to proceed to infinity in an upward direction among formal causes.
325. Or, in order to reach the same conclusion, “undivided” can be explained in another way, namely, in the sense that an immediate proposition is undivided. For if it were possible to proceed to infinity in an upward direction in the case of definitions, there would be no immediate proposition, and thus science as such (which is about conclusions derived from immediate principles) would be destroyed.
326. Nor will knowledge. He gives the third argument, which proceeds to show that such an infinite regress would destroy not only science but any kind of human knowing whatsoever. In regard to this argument he does two things.
First, he gives his argument.
Second, he refutes an objection raised against it, at this case is not like.
The argument is as follows. We know each thing by understanding its form. But if there were an infinite regress in forms, these forms could not be understood, because the intellect is incapable of understanding the infinite as infinite. Therefore, this position destroys knowing in its entirety.
327. This case is not like. He disposes of an objection, for someone could say that a thing having an infinite number of forms can be understood in the same way as a line which is divided to infinity. But he denies this. He says that this case is not the same as that of a line, whose divisions do not stop but go on to infinity. For it is impossible to understand anything unless some limit is set to it. Therefore, a line can be understood inasmuch as some actual limit is given to it by reason of its extremes. However, it cannot be understood insofar as its division does not terminate. Hence no one can count the divisions of a line insofar as they are infinite.
But as applied to forms “infinite” means actually infinite, and not potentially infinite as it does when applied to the division of a line. Therefore, if there were an infinite number of forms, there would be no way in which a thing could be known either scientifically or in any way at all.
328. But it is necessary. He gives the fourth argument, which runs thus. Matter must be understood to exist in everything that is moved, for whatever is moved is in potency, and what is in potency is matter. But matter itself has the character of the infinite, and nothingness belongs to the infinite in the sense of matter, because matter taken in itself is understood without any kind of form. And since nothingness belongs to the infinite, it follows contrariwise that the principle by which the infinite is a being is itself not infinite, and that it does not belong to the infinite (or to matter) to be infinite in being. But things are by virtue of their form. Hence there is no infinite regress among forms.
329. However, it must be noted that in this place Aristotle holds that the infinite involves the notion of nothingness, not because matter involves the notion of privation (as Plato claimed when he failed to distinguish between privation and matter), but because the infinite involves the notion of privation. For a potential being contains the notion of the infinite only insofar as it comes under the nature of privation, as is evident in Physics 3.
330. Again, if the species. He shows that the species of causes are not infinite in number, and he uses the following argument. We think that we have scientific knowledge of each thing when we know all its causes. But if there were an infinite number of causes in the sense that one species of cause may be added to another continuously, it would be impossible to traverse this infinity in such a way that all causes could be known. Hence in this way too the knowing of things would be destroyed.
Lecture 5. The method of metaphysics
The way in which people are affected by what they hear depends upon the things to which they are accustomed. For it is in terms of such things that we judge statements to be true, and anything over and above these does not seem similar, but less intelligible and more remote. For it is the things to which we are accustomed that are better known.
The great force which custom has is shown by the laws, in which legendary and childish elements prevail over our knowledge of them, because of custom.
Now some men will not accept what a speaker says unless he speaks in mathematical terms; others, unless he gives examples; while others expect him to quote a poet as an authority.
Again, some want everything stated with certitude, while others find certitude annoying, either because they are incapable of comprehending anything or because they consider exact inquiry to be quibbling—for there is some similarity.
Hence it seems to some men that just as liberality is lacking when a fee is charged for a banquet, so also is it lacking in arguments.
For this reason one must be trained how to meet every kind of argument, and it is absurd to search simultaneously for knowledge and for the method of acquiring it. Neither of these is easily attained.
But the exactness of mathematics is not to be expected in all cases, but only in those which have no matter. This is why its method is not that of natural philosophy; for perhaps the whole of nature contains matter. Hence we must first investigate what nature is, for in this way it will become evident what the things are with which natural philosophy deals, and whether it belongs to one science or to several to consider the causes and principles of things.
331. Having shown that the study of truth is in one sense difficult and in another easy, and that it belongs preeminently to first philosophy, the Philosopher now exposes the proper method of investigating the truth. In regard to this he does two things.
First, he gives the different methods which men follow in the study of truth.
Second, he shows which method is the proper one, at for this reason one must.
First, he shows how powerful custom is in the study of truth.
Second, he concludes that the different methods which men employ in the study of truth depend on the different things to which they are accustomed, at now some men.
First, he shows how powerful custom is in the study of truth.
Second, he makes this clear by an example, at the great force.