Commentary Aristotle Physics
Lecture 6
The generic, specific, and numerical unity of motion
There are many senses in which motion is said to be “one,” for we use the term “one” in many senses. Motion is one generically according to the different categories to which it may be assigned.
Thus, any locomotion is one generically with any other locomotion, whereas alteration is different generically from locomotion.
Motion is one specifically when, besides being one generically, it also takes place in a species incapable of subdivision. For instance, color has specific differences, and therefore blackening and whitening differ specifically; but at all events, every whitening will be specifically the same with every other whitening, and every blackening with every other blackening.
But white is not further subdivided by specific differences, and hence, any whitening is specifically one with any other whitening. Where it happens that the genus is at the same time a species, it is clear that the motion will then, in a sense, be qualifiedly one.
Learning is an example of this, since, on the one hand, knowledge is a species of apprehension and, on the other hand, it is a genus including the various knowledges.
A difficulty, however, may be raised as to whether a motion is specifically one when the same thing changes from the same to the same, for instance, when one point changes again and again from a particular place to a particular place.
If this motion is specifically one, circular motion will be the same as rectilinear motion, and rolling the same as walking.
But it was determined that, if that in which the motion takes place is specifically different (as the circular path is specifically different from the straight), the motion itself is also different.
We have explained, then, what is meant by saying that motion is one generically or one specifically.
Motion is one in an unqualified sense when it is one essentially or numerically, and the following distinctions will make clear what this kind of motion is.
There are three classes of things in connection with which we speak of motion: the “that which,” the “that in which,” and the “that during which.”
I mean that there must be something that is in motion, such as a man or gold, and it must be in motion in something, such as a place or a passion, and during something, for all motion takes place during a time.
Of these three: it is the thing in which the motion takes place that makes it one generically or specifically; it is the thing moved that makes the motion one in subject; and it is the time that makes it contiguous. But it is the three together that make it one without qualification.
And that in which the motion takes place (the species) must be one and indivisible; that during which it takes place (the time) must be one and without any breaks;
and that which is in motion must be one—not accidentally (that is, it must be one as the white that becomes black is one or Coriscus who walks is one, not in the accidental sense in which Coriscus and white may be one), nor merely in virtue of community of nature
(for there might be a case of two men being restored to health at the same time in the same way—such as from inflammation of the eye—yet this motion is not really one, but only specifically one).
Suppose, however, that Socrates undergoes an alteration specifically the same but at one time and again at another: in this case, if it is possible for that which ceased to be again to come into being and remain numerically the same, then this motion too will be one; otherwise, it will be the same but not one.
And, akin to this difficulty, there is another: is health one, and generally are the states and passions in bodies severally one in essence, although (as is clear) the things that contain them are obviously in motion and in flux?
Thus, if a person’s health at daybreak and at the present moment is one and the same, why should not this health be numerically one with that which he recovers after an interval?
The same argument applies in each case. There is, however, we may answer, this difference: if the states are two, then it follows simply from this fact that the activities must also, in point of number, be two (for only that which is numerically one can give rise to an activity that is numerically one), but if the state is one, this is not in itself enough to make us regard the activity also as one, for when a man ceases walking, the walking no longer is, but it will again be if he begins to walk again.
But, be this as it may, if the health is one and the same in the above instance, then it must be possible for that which is one and the same to come to be and to cease to be many times. However, these difficulties lie outside our present inquiry.
695. After positing some definitions to be used later, the Philosopher now proceeds to discuss unity of motion and contrariety of motions.
First, he treats of the unity and diversity of motion; second, he treats of its contrariety, which is a kind of diversity, at “we have further to determine” (229a7; [715]).
About the first, he does two things: first, he distinguishes the unity of motion according to the three common modes; second, he subdivides the second, at “since every motion is continuous” (228a20; [703]).
About the first, he does three things: first, he shows how motion is said to be generically one; second, how it is specifically one, at “motion is one specifically” (227b6; [697]); third, how it is numerically one, at “motion is one in an unqualified sense” (227b21; [699]).
696. He says therefore (227b3) that there are a number of ways in which a motion is one, just as one itself has many senses: that is, generically, specifically, and numerically. A motion is said to be generically one according to the different predicaments. For all motions that are assigned to one and the same predicament can be called generically one; thus, every local motion is one generic motion, because each is in the predicament “where” and differs generically from alteration, which is in the predicament quality, as has been said above.
697. Then, at “motion is one specifically” (227b6), he shows how motions are specifically one.
First, he shows this; second, he raises a question, at “a difficulty, however” (227b14; [698]).
He says first (227b6) that a motion is called specifically one when, besides being one according to its genus, it also takes place in a species incapable of subdivision, that is, in the most particular one, which is not divided into other species. For some species can be subdivided into other species, as color, which is a species of quality, is capable of differences that make for sub-species. Hence, motions in regard to color can be diverse in species, as whitening and blackening; but all cases of whitening are specifically the same (just as all cases of blackening are), for there are no sub-species of whitening.
But, when it happens that the species is at the same time a genus, then the motions found in a subalternate species are qualifiedly one, although, strictly speaking, they are not of the same species. Thus, science is a species of knowledge, as well as a genus of the various types of science. Hence, all teaching, which is a motion toward science, is in some sense specifically the same, although, strictly speaking, it is not, for the teaching by which grammar is taught is, simply speaking, different in species from that by which geometry is taught.
Now, it should be observed that, in the foregoing, the Philosopher has based the unity and diversity of motion on the genera and species in which motion can occur, because motion is in a certain way reduced to the genus in which the motion is.
698. Then, at “a difficulty, however” (227b14), he raises a question about the foregoing: whether a motion is specifically one and the same when the same thing changes frequently from the same thing to the same thing—for instance, when a point (according to the geometers who imagine that a point can be moved) changes again and again from this place to that. Now, according to the foregoing, it seems that the answer should be yes. For if all motions that tend to the same species, such as whiteness, are specifically the same, all the more should two motions from the same origin to the same terminus be specifically one. But, if that were so, then it would follow that a rectilinear motion is specifically the same as a circular motion. For it is possible to pass from this place to that by means of a circular motion—that is, by describing an arc—and afterward by going in a straight line. Likewise, it would follow that, in the motions of animals, walking (which is in a straight line) would be specifically the same as rolling, which consists in turning oneself in circles.
However, he answers this difficulty in the light of the foregoing.
For it has been decided that, if that in which the motion takes place is specifically different (as in the present instance the circular path is specifically different from the straight), the motion itself is also different.
Consequently, in order that two motions be specifically the same, not only must the goal be specifically the same, but also that through which the motion passes.
Now, it is clear that a straight line is specifically different from the curved. Consequently, a circular and a rectilinear motion, as well as walking and rolling, are not specifically the same, even though they tend to the same goal, because the paths are not specifically the same.
But, if the goals are identical and the paths specifically the same, then the motions are specifically the same; and much more so, if the goals and the path are numerically the same, then the same repeated motions will be specifically the same.
699. Then, at “motion is one in an unqualified sense” (227b21), he posits the third way in which a motion is said to be one, namely, numerically.
About this, he does two things: first, he explains when a motion is numerically one; second, he raises some question on this point, at “suppose, however, that Socrates” (228a3; [700]).
He says first (227b21) that, in the first two senses, motions are not unqualifiedly one, but they are one only in a sense, that is, in genus and species. But, in the third sense, a motion is one in an unqualified sense, namely, when it is numerically one in its essence.
Which motion is one in this way will be clear if we distinguish the things required for motion, for there are numerically three things on which the unity of a motion depends: first, the subject that is being moved; second, the genus or species of the motion; third, the time in which the motion takes place.
And he explains each of these individually.
A subject of motion is required, for in every case of motion, there must be something that is being moved, like a man or gold or some body. Likewise, the subject must be affected by some genus or species of motion, such as place or a passion. Again, the time must be considered, because whatever is moved is moved in time.
Now, among these three things, the generic or specific unity of the motion can depend on the thing in which there is motion, such as the place or quality. But the time does not account for the generic or specific unity of the motion, for there is only one species of time; rather, it accounts for the contiguous, that is, that it flows on without interruption.
But unity of motion in the sense of unqualified unity depends on all three.
For that in which the motion exists must be one and indivisible in the way that the most particular species, incapable of further subdivision, is said to be one.
Further, the time during which the motion occurs must be continuous, without any breaks.
Third, the subject in motion must be one.
However, there are two types of unity of subject that are not sufficient to guarantee that the motion is unqualifiedly one.
The first type is accidental: for example, Coriscus and white are accidentally one, but the motion proper to Coriscus is not the same as the motion proper to white. For the proper motion of white is to become black, and the motion proper to Coriscus is to walk, and these are different.
The second type is generic and specific unity. For in order that a motion be numerically one, it is not enough that the subject be one as something common either generically or specifically. For it is possible that two men are being healed during the same period of time in regard to the same thing (for example, from inflammation of the eye), such that the time is one and the species is one, and the subject is one in species. Yet these two healings are not one numerically, but only specifically.
700. Then, at “suppose, however, that Socrates” (228a3), he raises a question.
And about this, he does three things: first, he mentions what at first glance seems to be a motion numerically one; second, he raises a question about this, at “and, akin to this difficulty” (228a6; [701]); third, he gives the true solution, at “the same argument applies” (228a12; [702]).
He says first (228a3) that it is possible for one mobile—for instance, Socrates—to be altered at two different times with respect to the same specific disease, such as if he is twice healed of eye inflammation. This repeated healing will at first sight be numerically one motion, if the health acquired is numerically the same in both cases. And this will be so if it is possible for that which ceased to be to come again into being as the same numerical thing—which seems impossible. For the health acquired after the first alteration was later lost, and the same numerical health cannot be regained.
But it seems that, if the same numerical health were regained, the second alteration would be numerically the same motion as the first. But, if the same numerical health is not regained, the motion will not be numerically the same, but specifically.
701. Then, at “and, akin to this difficulty” (228a6), he raises another difficulty on this point: if someone continually perseveres in health or any other accident, could the health, or any other habit or passion in bodies, be one? It seems not, because certain philosophers believe that all subjects that possess certain qualities or habits are in continuous motion and flux.
If, therefore, in the case of a person who remains healthy, there is one and the same health at dawn and at noon and in the evening, there seems to be no reason why, in the case of a person who gets sick and then recovers, the health recovered is not numerically the same as the one previously possessed.
Aristotle does not settle this question for two reasons: first, because it is not to the point, since it pertains to metaphysics, whose province is to consider the one and the many, the same and the diverse; second, he refrains from answering because this difficulty is based on the false assumption that all things are in a state of continuous change and flux, as Heraclitus believed—an opinion that Aristotle refutes in Metaphysics 4. Moreover, the two cases are not the same: as long as health remains in spite of fluctuations in degree, the original health is not interrupted, as it is in the case of one who completely loses his health.
702. Then, at “the same argument applies” (228a12), he determines the truth in regard to the case mentioned above. He mentioned there that, if it is the same quality that is recovered, the second alteration will be numerically the same motion as the first; if the same numerical quality is not recovered, then it is not numerically the same act.
Having presented a certain difficulty as though giving a reason for what was set down above, he adds that the reason for raising the difficulty was that, at first sight, it seemed that the same argument would hold good for the unity of quality and of motion.
But there is a difference: it does follow that, if two motions are the same in the manner in which a motion is said to be numerically one, then the state, the quality, acquired by the motion is one, because numerically the same quality is produced by an act numerically one. However, if the quality that returns is one, not everyone would agree that the act is one. For if the terminus of two motions is numerically one, it does not mean that the motions were numerically one.
This is evident in local motion. For when a person interrupts his walk, the act of walking ceases; but when he resumes, the act resumes.
Now, if you were to say that the whole journey is one act of walking that ceases to be and is then revived, then it would follow that one and the same thing can exist and cease to exist any number of times—which is impossible.
In like manner, if the same numerical health is again and again recovered, it does not follow that the second healing was the same motion as the first, any more than a second walk is the same as a first, even though both go toward the same numerical goal.
Finally, he concludes that these difficulties lie outside the present inquiry and are for that reason to be passed over.