LECTURE 6 (227 b 3-228 a 19)

THE GENERIC, SPECIFIC, AND NUMERICAL UNITY OF MOTION

             695. After the Philosopher has given certain definitions which are necessary for what is to follow, he begins to treat the unity and diversity of motion.

             First he treats the unity and diversity of motion. Secondly, where he says, 'We have further to determine . . .' (229 a 7), he discusses contrariety, which is a species of diversity.

             Concerning the first part he makes two points. First he distinguishes the unity of motion in respect to three common modes. Secondly, where he says, 'Since every motion is continuous . . .' (228 a 20), he subdivides each of these.

             Concerning the first part he makes three points. First he explains how motion is said to be one in genus. Secondly, where he says, 'Motion is one specifically . . .' (227 b 7), he explains how it is said to be one in species. Thirdly, where he says, 'Motion is one . . .' (227 b 22), he explains how it is said to be one in number.

             696. He says, therefore, first that motion is called 'one' in many ways, insofar as 'one' itself, taken in common, is also said in many ways; that is, generically, specifically and numerically.

             Further he says that motion is one in genus according to the figures of predication. For all motions which are in one order of predication can be called one in genus. Thus, all local motions are one in genus because they are in one category; namely, where. But local motion differs in genus from alteration, which is in the category of quality, as was said above.

             697. Next where he says, 'Motion is one specifically . . .' (227 b 7), he explains how motion is one in species.

             First he explains his position. Secondly, where he says, 'A difficulty, however . . .' (227 b 14), he raises a difficulty.

             He says, therefore, first that motion is called one in species when it is one not only in respect to a genus but also in respect to an individual species; that is, in respect to a last species which is not divided into other species. For there are certain species which are divided into other species. Thus colour is a species of quality, but nevertheless it has differentiae by which it is divided into different species. Hence motions in respect to colours can be diverse in species, for example, becoming white and becoming black. But every whitening is the same in respect to species, as is every blackening. For there are no species of whiteness into which it is further divided.

             However, if there are certain things which are both genera and species, it is clear that motions which occur in these subalternate species are in a way one in species, but simply speaking they are not one in species. Thus, science is a species of thought and also the genus of the diverse sciences. Hence all teaching, which is motion toward science, is in a way one in species, but not so simply speaking. For the teaching of grammar is a simply different species than the teaching of geometry.

             Moreover, it must be realized that in the foregoing he treats the unity and diversity of motion in respect to those genera and species in which there happens to be motion. For motion in some way is reduced to the genus of those things in which there is motion.

             698. Next where he says, 'A difficulty, however . . .' (227 b 14), he raises a difficulty concerning the foregoing. The problem is whether motion is necessarily one in species when the same thing is changed many times from the same thing to the same thing. For example, according to geometricians who imagine that a point is moved, let one point be moved many times from this place to that.

             It seems to follow from the above that these motions are one in species. For if motions toward the same species, for example, whiteness, are the same in species, much more would two motions toward the same numerical place be the same in species. But if this be granted, a difficulty follows. For then straight motion and circular motion would be one in species. But to be moved from this place to that circularly, i.e., as if through an arc, occurs first. Only secondarily is there straight motion, i.e., as if through a straight line. And likewise it would follow that in the motions of animals walking, which is through a straight line, would be the same species as rolling, by which an animal is moved through a circular line by revolving itself.

             He answers this difficulty by referring to what he has discussed above. It has been established that if that in which motion occurs is different in species, then the motion is different in species. Thus, in order for motion to be the same in species, there must not only be an identity of termini in respect to species, but also an identity of that through which the motion occurs. But it is clear that a straight line and a circular line are different in species. Hence, circular and straight motion, and walking and rolling, are not the same in species, even though they occur between the same termini. For the path is not the same in respect to species.

             But if there be the same termini and the same path in respect to species, then the motions are the same in respect to species. And furthermore, if the termini and the path are the same in number, then the motions are clearly repeated in respect to the same species.

             699. Next where he says, 'Motion is one . . .' (227 b 22), he gives the third mode according to which motion is called one in number.

             Concerning this he makes two points. First he explains what motion is one in number. Secondly, where he says, 'Suppose, however, that Socrates . . .' (228 a 3), he raises a difficulty about this.

             He says, therefore, first that according to the foregoing modes motion is not called one simply, but only in a qualified way, that is, generically and specifically. But according to the third mode motion is called one simply, which is oneness in number according to its essence.

             He will show what motion is one in this mode by distinguishing those things which are required for motion. The unity of motion consists in three things. These are the object which is moved, the genus or species in which there is motion, and the time when it is moved. He explains each of these individually. He mentions that which is moved because in any motion it is necessary for there to be something which is moved, for example, a man or gold or some body. And likewise it is necessary that any mobile object be moved in some genus or species, for example, in place or in passive quality. And likewise it is necessary to consider when it is moved. For everything that is moved is moved in time. Among these three things the unity of genus or species is found in that in which there is motion, for example, in place or in quality. But in respect to the unity of motion, the unity of genus or species is not due to the time, since there is only one species of time. Rather the continuity of motion without interruption is due to time.

             However the unity of motion, according to which it is called one simply, consists in the unity of all three of these. For that in which motion occurs must be one and indivisible in the way in which a last species is called indivisible. Further the time when the motion occurs must be one continuum without interruption. And thirdly that which is moved must be one.

             Furthermore he excludes two types of unity in the subject which are not sufficient for motion to be one simply.

             The first type is accidental unity. For example, Coriscus and white are one accidentally. Nevertheless, the motion proper to Coriscus and the motion proper to white are not one. For the motion proper to white is to become black. And the motion proper to Coriscus is to walk. These motions, indeed, are different.

             The second type is the unity of genus or species. In order for motion to be one in number, it is not sufficient for the subject to be some common genus or species. For it might happen that two men are cured at the same time and in respect to the same species of health, for example, they are cured of ophthalmia, which is a disease of the eyes. In this case there is unity of time, and unity of that in which the motion occurs, and unity of the subject in respect to species. Nevertheless, these two cures are not one in number, but only one in species.

             700. Next where he says, 'Suppose, however, that Socrates . . .' (228 a 3), he raises a difficulty.

             Concerning this he makes three points. First he gives what at first sight appears to be an example of the numerical unity of motion. Secondly, where he says, 'And akin to this difficulty . . .' (228 a 6), he raises a difficulty about this. Thirdly, where he says, 'The same argument applies . . .' (228 a 12), he determines the truth.

             He says, therefore, first that the same mobile object, for example, Socrates, might undergo specifically the same alteration at two different times. For example, he might be cured twice of ophthalmia. At first glance it seems that this repeated alteration will be numerically one motion if the health which is acquired is the same in number. This would be true if that which was corrupted would again come to be as one in number. But this seems to be impossible. For the health which was acquired in the first alteration was later corrupted. And numerically the same health cannot be recovered.

             If numerically the same health were recovered, it would seem that the subsequent alteration would be numerically the same motion as the first. But if numerically the same health were not recovered, the motion will be the same in species, but not in number.

             701. Next where he says, 'And akin to this difficulty . . .' (228 a 6), he raises a difficulty about this.

             The problem is as follows. If one continuously maintains health, or any other accident, will this health, or any other state or passion in bodies, be one? It seems not, because according to some philosophers all subjects which have qualities or states seem to be in continuous motion and flux.

             Suppose that, for one who remains healthy, the health which he had in the morning is one and the same as the health which he has at noon or in the evening. Now if he loses his health and later recovers it, there seems to be no reason [ratio] why the second recovered health is not one in number with the health that he previously had.

             Aristotle does not answer this difficulty because it is not pertinent here. It pertains rather to the metaphysician who considers in common the one and the many, and the same and different. Moreover this difficulty is based on a false premise; namely, that all things are in continuous motion and flux. This is what Heraclitus thought, and Aristotle refutes this in Metaphysics, IV. But this is not the same argument. For, while health remains, even though a man's health may vary, that is, he becomes more or less healthy, his being healthy is not interrupted. His being healthy is interrupted when health is totally corrupted.

             702. Next where he says, 'The same argument applies . . .' (228 a 12), he determines the truth concerning this problem. He has said above that, if the quality which is recovered is the same, then the second alteration will be numerically the same motion as the first. But if numerically the same quality is not recovered, it follows that there is not numerically one act. After interposing this difficulty, he adds, as though giving a reason [ratio] for the foregoing, that he has said this because it seems at first glance that the nature [ratio] of the unity of quality and of motion is the same.

             But they differ as follows. If two motions are the same in such a way that they are one in number, then it necessarily follows that the quality acquired by that motion is one. For the numerically one quality acquired by that act is numerically one act.

             But if the quality which is recovered is one, because of this it does not seem that there is one act. For if the terminus of motion is numerically one, it is not necessary for the motion to be numerically one. This is clear in local motion. For when a walking man pauses, that walking ceases. But when he begins to walk again, then there will be walking again. Therefore, if it be said that the walking is one and the same, then one and the same thing both is and is corrupted many times. But this is impossible. Therefore, if it should happen that numerically the same health were restored, it would not follow that the second curing is numerically the same motion as the first. Likewise, the second walking is not numerically the same as the first, even though they are both directed to numerically the same place.

             Finally he concludes that these difficulties are outside his main intention, and therefore are dismissed.