Lecture 11 — Soul as a self-moving number

By far the most unreasonable thing said about the soul is that it is a number moving itself. For in this there are several impossibilities. First, what follows upon “being moved,” and then the special difficulties that follow their assertion that it is a number. For how is one to conceive a unit, being indivisible and undifferentiated, as moving? Or by what? Or in what way? For if it is both mobile and mover, there must be some difference within it.

Further, since they say that a line, being moved, makes a plane, and a point, being moved, a line, the movements of the units will be lines. For a point is a unit having position, whereas the number of a soul must be in some place and have position.

Further, if one subtracts a number or a unit from some number, another number is left. Plants, however, and many animals, live on after being divided and seem to retain specifically the same soul.

It would seem that there is no difference between saying “units” or “small bodies.” For if the spheres of Democritus were to become points and only quantity remained, there would remain in them a certain mover and something moved, as in continuous things. For the distinction spoken of is not due to largeness or smallness, but to quantity. Hence there must necessarily be something moving the units. But if it is the soul that moves the animal, so also in the case of number; then the soul is not both mover and moved, but only a mover.

Now, this would somehow have to be a unit. For there must be some difference from the others in it. But how can one isolated point differ from others except by way of position? But, then, if there are many different units and points in a body, the units will be in the same place; for it will occupy the place of a point. Yet if there are two in the same place, what is there to prevent an infinity of them from being together? For that of which the place is indivisible is itself such. But if the points in the body are the number of the soul, or if the number of points in the body is the soul, why are there not souls in all bodies? For in all things there seem to be points, and an infinity of them.

Furthermore, how is it possible for these points to be separated and released from bodies, if lines cannot be divided into points?

This amounts to saying (as we said before) either, under one aspect, the same as those who posit the soul as a body of very refined elements, or, under another aspect, what Democritus said of the movement of the soul—a thing intrinsically absurd. For if the soul is in every body that senses, there must be two bodies in the same place, if the soul is some sort of body. Moreover, for those who say it is a number, there are many points in one point, or else every body has a soul, unless the soul’s number be other than that of the points in the body. The animal would then come to be moved by a number, precisely as Democritus said. For what difference does it make whether one says small spheres or large units, or, in general, that units are in motion? In any case, the animal necessarily moves when these are moving.

These and many other consequences, then, result for those who would combine number and movement in a single principle. For it is impossible for such to be not only a definition of the soul but even one of its accidents. But it is clear if one attempts by this procedure to account for the soul’s passions and activities, such as thoughts, sensations, pleasures, pains, and so forth. For, as we said before, based on these things, it is not easy even to hazard a conjecture.

168. By far the most unreasonable thing (408b32). After refuting those who asserted that the soul was a thing that moved simply speaking, the Philosopher now critiques the view of Xenocrates, who said, in addition, that soul was a self-moving number—a far less rational opinion than the other philosophers’ opinions already mentioned.

For saying the soul is a self-moving number involves many impossibilities. First, of course, there are those arising from being moved, (Themistius, In De anima, f. 10ra.) that is, due to motion, the things that also result for all who say that the soul moves; and then, in addition, there are the special incongruities that arise for those who say the soul is a number. Therefore, in Xenocrates’s definition of soul, the Philosopher criticizes not merely the terms employed, but also the meaning itself.

This critique has two parts.

First, he shows that the definition does not fit the very substance of the soul;

second, that it does not fit its accidents, at these and many other consequences (409b11; [177]).

The former part subdivides into two:

first, reasons for rejecting the said definition;

and second, reasons for thinking that it involves all the incongruities implicit in the views of the other philosophers, this part beginning at this amounts to saying (409a31; [175]).

169. He shows the unsuitability of the definition by six arguments, the first being as follows. You call the soul a self-moving number, but a number is composed of units; the soul then, in your view, consists of units; if you say the soul is a self-moving number, then the soul is also self-moving units. Now, in any self-moving thing, there are two parts (as is shown in Physics 8): one doing the moving, the other being moved. (Aristotle, Physics 8.5, 257a33–258b9; cf. Aquinas, Commentary on Physics, bk. 8, lect. 10, 11.) Therefore, you must mean that each unit or point is composed of two parts: one doing the moving, the other being moved. But this is impossible. Therefore, the soul is not a self-moving number.

Moreover, he proves the impossibility of a unit having a moving part and a moved part: for what is wholly indivisible and undifferentiated cannot be thought of as moving by itself in such a way that one part moves it and another is moved. For in nothing can these two, that is, the mobile and mover (408b32) exist without being different from each other. Since, then, a unit is indivisible and undifferentiated, it cannot have such parts or move. Therefore, the soul is not a self-moving number.

170. The second argument, at further, since (409a3), runs thus. You say the soul is a number and, therefore, composed of units, as has been said. Now, the only difference between a unit and a point is that a point has position—for it is a unit that possesses position. But if the soul is a number, this number must exist somewhere and have a position. Therefore, the soul will be the units that have positions. And such things are points.

So the soul too will be the points. But according to the Platonists, a point in movement makes a line, a line in movement makes a surface, and a surface in movement makes a body. If, then, the soul is a self-moving number, each of its units is self-moving, and each of these is a self-moving point. But such a point can only make a line; therefore, the soul’s motion makes only a line, and so the soul in motion does not cause life—which is false. Therefore, the soul is not a self-moving number.

171. The third argument, at further, if (409a7), is the following. If, as you say, the soul is a number, it must have the nature and passions of number. Now, it is evident that whenever a unit is taken from or added to a number, the number changes its species. For if you add 1 to 3, you change the species of the number: for 4 differs in species from 3. Similarly if you take 1 from 3, leaving 2, you change the species.

Now, it is certain that animals draw their species from their soul, since it is through its own form that each and every thing attains a species. If, then, the soul is a number, any addition to or subtraction from the soul must alter the soul in species. But this is false, for we see that if plants and segmented animals are cut up, the divisions or cuttings go on living and hold on to the same species as before. Therefore, the soul is not a number.

172. The fourth argument, at it would seem that (409a10), is as follows. You say the soul is a number; whence it follows, as we have said, that it is the units having position and, consequently, points. But on this supposition it is obvious that there is no difference between saying, with Democritus, that the soul consists of small indivisible bodies and saying that it is composed of units in position. (Lect. 3, n. 34; lect. 5, n. 56; lect. 7, n. 88.) For each unit with position is a quantity and indivisible. From this, then, I argue: the soul, in your view, is a self-moving number and, consequently, consists of units and points moving themselves.

Let us suppose then that the indivisible bodies of Democritus are points (there is no difference, as we have seen) and are quantities (as they must be, since, properly speaking, they are not moved unless they are quantities). Now, these points will move themselves if the soul is a self-moving number. But every self-mover, as has been said, is twofold; hence, there will be in the point itself one thing that is the mover and another that is moved; and this, no matter whether they be large parts or small, provided they have some quantity, for every self-moving continuum contains the two things: a moving one and a moved one.

So there must be something moving the units. But in animals, the mover is the soul; therefore, in the case of number, what moves the number would be the soul; whence it follows that the soul is not what is being moved but the mover. And thus, the definition of the soul as a self-moving number is a bad one; it should rather be defined as what moves the moved number.

173. The fifth argument begins at now, this would somehow have to be a unit (409a18). In Xenocrates’s opinion, this, that is, the soul, is a unit. But if so, then it is a point; for the soul must, as a unit, differ from other units, (Themistius, In De anima, f. 10ra, 8 ab imo.) and it cannot differ from them except through position. For what is it that differentiates isolated points, that is, units, as here understood, except their position? Nothing. Moreover, only through position are units points. The soul, then, is not units but points. Yet the soul exists in the body, and every body has points throughout itself. I ask, then, are the soul-points identical with the body-points or not? If they are not, then, since the soul is in every part of the body, and in every part of the body there will be the soul’s points, thus there will be two points in the same place at the same time. And if two, why not more than two, ad infinitum? For things whose place is indivisible are themselves indivisible and do not require more space. (Themistius, In De anima, f. 10ra–rb.) Whence if two can be in an indivisible place, there is no reason why an infinite number should not be there. On the other hand, if the body-points are identical with the soul-points, then every body has a soul, since every body has points. But this is false; therefore the soul is not a self-moving number.

174. The sixth argument, at furthermore, how (409a28), continues the preceding one. As has been said, it follows from Xenocrates’s position that the soul is the points. But we see that points are inseparable and undetachable from bodies, for lines are not separable from surfaces, nor points from lines. (Themistius, In De anima, f. 10rb.) But the soul is separable and detachable from the body; hence it is not the points or a number. Clearly then, Xenocrates’s definition of the soul is incongruous as regards the things placed in the definition.

175. Then, at this amounts to saying (409a31), he finds this definition incongruous in its consequences. For these consequences involve all the objectionable consequences flowing from the opinions of all who have philosophized about the soul.

For some of these fell into the mistake of saying that the soul was a body made up of extremely fine parts, from which it followed that two bodies would be together in the same place, for the soul is wherever sensation occurs, and this is everywhere in the body. (Lect. 6, n. 68.) And the same would follow, as has been said, if the soul were the points: two points, or even an infinite number of points, would exist together in the same place; this would follow if the soul-points differed from body-points. But if there is not a different number of soul-points, that is, if there is no difference between soul-points and body-points, then every body contains a soul, since it must contain points.

176. Others, like Democritus, erred in saying that the soul itself is moved, and the body is moved because of the soul’s motion. (Lect. 3, n. 34.) And from Democritus’s statement that the soul was made up of indivisible spheres whose movement caused the body to move, it followed that indivisible bodies were the cause of bodily movements. The same incongruity follows from the definition which states that an animal is moved by a number and so by points. It makes no difference whether one says small spheres or large units, for in any case, that is, with spheres or with units, the origin of the soul’s movement is the movement of bodily spheres and points or units.

177. Next, at these and (409b11), he shows the inadequacy of the above definition with respect to accidents. An adequate definition, he says, must give knowledge not only of the substance of the thing defined, but even of its accidents. But if we combine number and movement in our definition of the soul, we shall find ourselves involved in many other consequences besides those that concern the soul’s very substance. For these two things, number and movement, not only cannot be a definition of the soul, that is, its substance, but it is impossible even that they (that is, number and motion) are accidents of the soul, nor do they lead one to a knowledge of these accidents. Hence the definition itself is unsuitable. And that it does not help us to know the accidents of the soul is manifest if someone were to try, from such a definition, to designate the soul’s passions and activities, such as reasonings, delights, pains, and the like. If we started on these things, namely, number and movement, we should not only find it not easy to reach any knowledge of the soul’s accidents and activities, but we could not even begin to hazard any conjecture about them based on the soul’s passions and activities themselves.