Lecture 7 — Refutation of those who say non-being is something

Some thinkers did, in point of fact, give way to both arguments. To the argument that all things are one if “being” means one thing, they conceded that non-being is; to that from bisection, they yielded by positing indivisibles by division.

But obviously it is not true that, if being means one thing and cannot at the same time mean the contradictory of this, then there will be nothing that is not, for even if what is not cannot be without qualification, there is no reason why it should not be a particular non-being.

To say that all things will be one, if there is nothing besides being itself, is absurd. For who understands “being itself” to be anything but a particular substance? But, if this is so, there is nothing to prevent there being many beings, as has been said. It is, then, clearly impossible for being to be one in this sense.

47. After the Philosopher has disproved the argument of Parmenides by bringing forth certain inconsistencies found in it, he here disproves the position of those who have conceded these absurdities.

Concerning this, he makes two points.

First, he sets forth their position.

Second, he disproves it, at but obviously it is not (187a3; [50]).

48. It must be noted first that the Philosopher used two arguments above against the argument of Parmenides. (Lect. 6.)

He used one to show that, because of the diversity of subject and accident, it does not follow from the argument of Parmenides that all is one. This argument led to the absurdity that non-being is being, as is clear from what was said above.

The other argument proceeded to show that the conclusion that all is one does not follow, because, if it were a magnitude, it would follow that magnitude is indivisible. For if it were divisible, there would be some sort of multiplicity.

49. The Platonists, however, gave in to each argument, conceding the impossibilities to which they led. They accepted the first argument, which led to the conclusion that non-being would be being. Suppose that someone were to say that being signifies one thing, either substance alone or accident alone, and because of this, he might also wish to say that all things are one.

In regard to this argument, I say, they accepted the conclusion that non-being would be being. For Plato said that accident is non-being. And, because of this, it is said in Metaphysics 6 (Aristotle, Metaphysics E.2; cf. St. Thomas, Commentary on Metaphysics, bk. 6, lect. 2.) that Plato held that sophistry dealt with non-being, because it treated most of all those things that are predicated per accidens.

Therefore Plato, understanding being to be substance, conceded the first proposition of Parmenides, who said that whatever is other than being is non-being. For Plato held that accident, which is other than substance, was non-being. He did not, however, concede the second proposition, namely, that whatever is non-being is nothing. For although he would say that accident is non-being, he did not say that accident is nothing, but rather that it is something. And, because of this, according to Plato, it does not follow that being is one only.

But Plato, when he made magnitudes to be indivisible by dissection—that is, when he said that a magnitude is terminated in indivisibles by division—did assent to the other argument, which led to the conclusion that a magnitude would be indivisible. For he held that bodies are resolved into surfaces, and surfaces into lines, and lines into indivisibles, as is clear in De caelo et mundo 3.1. (Cf. St. Thomas, Commentary on De caelo, bk. 3, lect. 3.)

50. Next, at but obviously (187a3), he disproves the above position in regard to the point that Plato conceded, namely, that non-being is something. In regard to the other point, namely, that Plato held that there are indivisible magnitudes, this is disproved in its proper place in the following books of natural science. (Bk. 6, lect. 1.)

He disproves the first point in two ways.

First, he shows that it does not follow from the argument of Plato that non-being is something.

Second, at to say that all things (187a6; [52]), he disproves Plato’s remark that, unless we hold this (namely, if the non-being that is an accident is not something), it will follow that all is one.

51. He says, therefore, first (187a3) that the argument by which Plato concluded that being means one thing clearly does not follow. For he held that being is a genus and is predicated univocally of all things by participation in the first being. And further, he held that contradictories cannot be true at the same time. From these two points, he thought that it followed that non-being is not nothing, but something.

For if being signifies one thing, which is substance, it will be necessary that whatever is not substance is non-being. For if it were being, then, since being does not signify anything but substance, it would follow that it would be substance.

And so, it would at once be substance and non-substance, in which case, contradictories would be true at the same time.

If, therefore, it is impossible for contradictories to be true at the same time, and if being signifies one thing, which is substance, it would follow that whatever is not substance is non-being. But there is something that is not substance, namely, accident. Therefore, something is non-being. And so it is not true that non-being is nothing.

But Aristotle shows that this does not follow. For if being signifies principally the one, which is substance, there is nothing to prevent one from saying that accident, which is not substance, is not being simply. But, because of this, it is not necessary to say that that which is not something—that is, not substance—is absolute non-being. Hence, although accident is not being simply, it cannot, indeed, be called absolute non-being.

52. Next, at to say that all things (187a6), he shows further that, if the non-being that is accident is not something, it does not follow that all is one. For if “being” can mean only substance, which truly is, then he says that it is absurd to hold that it would follow that all things are one unless there is something outside of being. For if there is substance, there is nothing to prevent there being a multiplicity of substances, as has already been said, (Lect. 6, n. 45.) even if magnitude and accident are removed. For the definition of “substance” is divided into the many things that are in the genus of substance, as “man” is divided into “animal” and “two-footed.” And further, it follows that, according to the diverse differentiae of a genus, there are many substances in act. And finally, he draws the conclusion that he principally intended, that all things are not one, as Parmenides and Melissus said.