Commentary Aristotle Physics
Lecture 8. Which motions are comparable to each other
Similarly, in the case of motion, two things are of the same velocity if they occupy an equal time in accomplishing a certain equal amount of motion.
Suppose that, in a certain time, an alteration is undergone by one half of a body’s length and the other is led by a locomotion. Can we say that, in this, the alteration is equal to the locomotion and of the same velocity?
That would be absurd, and the reason is that there are different species of motion.
And, if we must say in consequence of this that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal time, we have to admit the equality of a straight line and a circumference.
What, then, is the reason of this? Is it that locomotion is a genus or that line is a genus? (We may leave the time out of account, since that is atomic.)
If the lines are specifically different, the locomotions also differ specifically from one another, since locomotion is specifically differentiated according to the specific differentiation of that over which it takes place.
It is also similarly differentiated accordingly as the instrument of the locomotion is different. Thus, if feet are the instrument, it is walking, but if wings, it is flying.
But perhaps this is not so, and, in this case, the differences in the locomotion are merely a diversity of figure in that which is in motion.
We may therefore say that things are of equal velocity if they traverse the same magnitude in an equal time;
when I call it “the same,” I mean that it contains no specific difference and thus no difference in the motion that takes place over it. So, we have now to consider how motion is differentiated.
And this discussion shows that the genus is not a unity, but that genera hide many joined things.
And, in the case of equivocal terms, sometimes the different senses are far removed from one another, while sometimes they have a certain likeness, and sometimes again they are nearly related either generically or analogically.
Hence, they seem not to be equivocal, though they really are.
When, then, is there a difference of species? Is an attribute specifically different if the same thing is found in things that are other, or if differing things are found in differing things? And what is a term?
What will enable us to decide that particular instances of whiteness or sweetness are the same or different? Is it enough that it appears different in one subject from what appears in another? Or must there be no sameness at all?
And further, where alteration is in question, how is one alteration to be of equal velocity with another? One person may be cured quickly and another slowly, and cures may also be simultaneous such that, recovery of health being an alteration, we have here alterations of equal velocity, since each alteration occupies an equal time.
But what alteration? We cannot here speak of an “equal” alteration: what corresponds in the category of quality to equality in the category of quantity is “likeness.”
However, let us say that there is equal velocity where the same change is accomplished in an equal time.
Are we, then, to find the commensurability in the subject of the passion or in the passion itself?
In the case that we have just been considering, it is the fact that health is one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that they are alike.
But if the passion is different in the two cases—for instance, when what is altered becomes white and what is healthy, respectively—here there is no sameness or equality or likeness, inasmuch as the difference in the passions at once makes the alterations specifically different, and there is no unity of alteration, as neither would there be unity of locomotion.
So, we must find out how many species there are of alteration and of locomotion respectively.
Now, if the things that are in motion—the things to which the motions belong essentially and not accidentally—differ specifically, then their respective motions will also differ specifically, but if they differ generically or numerically, the motions also will differ generically or numerically.
But there still remains the question whether, supposing that two alterations are of equal velocity, we ought to look for this equality in the sameness (or likeness) of the passions or in the things altered, to see, for instance, whether a certain quantity of each has become white.
Or ought we not rather to look for it in both? That is to say, the alterations are the same or different according as the passions are the same or different, while they are equal or unequal according as the things altered are equal or unequal.
And now we must consider the same question in the case of generation and corruption: how is one generation of equal velocity with another?
They are of equal velocity if, in an equal time, there are produced two things that are the same and specifically inseparable, such as two men (not generically inseparable, as two animals).
Similarly, one is quicker than the other if, in an equal time, the product is different in the two cases. I state it thus because we do not have two things in which there is an otherness called unlikeness.
If we adopt the theory that it is number that constitutes being, we may indeed speak of a “greater number” and a “lesser number” within the same species.
But there is no common term that will include both relations, nor are there terms to express each of them separately in the same way as we indicate a higher degree or preponderance of a passion by “more” and of a quantity by “greater.”
940. After pointing out in general what is required in order that things be able to be compared, the Philosopher now applies the truth found to the comparison of motions.
He does this first in general;
second, by comparing motions that belong to diverse genera, at suppose that, in a certain time (249a9; [941]);
third, by comparing one motion to another in the same genus, at and, if we must say (249a12; [942]).
He thus says first (249a8) that, just as in other matters the requirements for comparability are that the things compared be not equivocal, that there be an identical first receiver, and that they be of the same species, so also in regard to motion, “equally swift” is said of things that are moved in equal time, through such-and-such an equal length, and in this, that is, with respect to a change of the same kind.
941. Then, at suppose that, in a certain time (249a9), he discusses the comparison of motions in diverse genera. And he asks, in keeping with what went before, whether, if one mobile be altered and another led—that is, moved locally—the alteration can be said to be as swift as the local motion. To say this would be unacceptable, since the two motions are of different species and it has already been said that things not of the same species cannot be compared. Therefore, since local motion is not of the same species as alteration, the swiftness of the two cannot be compared.
942. Then, at and, if we must say (249a12), he discusses the comparison of the motions of one genus within that genus:
first, as to change of place;
second, as to alteration, at and further, where alteration (249a29; [949]);
third, as to generation and corruption, at and now we must consider (249b19; [954]).
He makes no mention of growth and decrease because they share with local motion the common characteristic of being according to some magnitude.
In regard to the first, he does three things:
first, he shows what is required in order that two local motions be able to be mutually compared;
second, he excludes one factor that seems to be required, at “it is also similarly” (249a17; [945]);
third, he comes to the conclusion he chiefly intended, at we may therefore say (249a19; [946]).
About the first, he does two things:
first, he argues that an impossibility would follow if all local motions could be compared;
second, he says why not all can be compared, at what, then, is the reason (249a13; [944]).
943. He says first (249a12) that, if the equally swift are things moved locally through an equal magnitude in equal time, and if it could happen that all local motions should be equally swift, it would follow that what is straight is equal to what is circular.
Now, this statement may be understood in two senses:
first, in respect to a rectilinear motion and a circular one;
second, in respect to a straight line and a circular one.
The latter is the better sense, because it follows from the foregoing. For if all rectilinear and circular motions are equally swift—and they are so when they traverse an equal magnitude in equal time—it follows that a straight line is equal to a circular one, a situation that must be rejected as unsuitable.