Commentary Aristotle Physics
Lecture 7. The types of unity in motion
Since every motion is continuous, a motion that is one in an unqualified sense must (since every motion is divisible) be continuous, and a continuous motion must be one.
There will not be continuity between any motion and any other indiscriminately any more than there is between any two things chosen at random in any other sphere: there can be continuity only when the extremities of the two things are one.
Now, some things have no extremities at all, and the extremities of others differ specifically, although we give them the equivocal name of “end.” How should, for instance, the end of a line and the end of walking touch, or come to be one?
Motions that are not the same either specifically or generically may, it is true, be consecutive (for instance, a man may run and then at once fall ill of a fever), and again, in the spreading of the lamp, we have consecutive but not continuous locomotion. For according to our definition, continuity can only be had when the ends of the two things are one.
Hence, motions may be consecutive or successive in virtue of the time being continuous, but there can be continuity only in virtue of the motions themselves being continuous, that is, when the end of each is one with the end of the other. Thus, motion that is in an unqualified sense continuous and one must be specifically the same, of one thing, and in one time.
Unity is required in respect of time in order that there may be no interval of immobility, for where there is intermission of motion, there must be rest, and a motion that includes intervals of rest will be not one, but many, such that a motion that is interrupted by stationariness is not one or continuous, and it is so interrupted if there is an interval of time.
And, though, of a motion that is not specifically one (even if the time is unintermittent) the time is one, the motion is specifically different, and so cannot really be one.
For motion that is one must be specifically one, though motion that is specifically one is not necessarily one in an unqualified sense. We have now explained what we mean when we call a motion one without qualification.
Further, a motion is also said to be one generically, specifically, or essentially when it is complete, just as completeness and wholeness are characteristics of what is one in other cases, and sometimes a motion, even if incomplete, is said to be one, provided only that it is continuous.
And, besides the cases already mentioned, there is another in which a motion is said to be one, namely, when it is regular.
For in a sense, a motion that is irregular is not regarded as one, that title belonging rather to that which is regular, as a straight line is regular, the irregular being divisible as such. But the difference would seem to be one of degree.
In every kind of motion, we may have regularity or irregularity, and thus there may be regular alteration, and some things which can be moved in a regular path—for instance, in a circle or on a straight line. And it is the same with regard to increase and decrease.
The difference that makes a motion irregular is sometimes to be found in its path: a motion cannot be regular if its path is an irregular magnitude, such as a broken line, a spiral, or any other magnitude that is not such that any part of it taken at random fits on to any other that may be chosen. Sometimes it is found neither in the place nor in the time nor in that to which, but in the manner of the motion, for in some cases, the motion is differentiated by quickness and slowness: if its velocity is uniform, a motion is regular; if not, it is irregular.
So, quickness and slowness are not species of motion, nor do they constitute specific differences of motion, because this distinction occurs in connection with all the distinct species of motion.
The same is true of heaviness and lightness when they refer to the same thing: for instance, earth moves to itself and fire to itself.
Irregular motion, therefore, while one in virtue of being continuous, is so in a lesser degree, as is the case with locomotion in a broken line, and a lesser degree of something always means an admixture of its contrary.
And, since every motion that is one can be both regular and irregular, motions that are consecutive but not specifically the same cannot be one and continuous.
For how should a motion composed of alteration and locomotion be regular? If a motion is to be regular, its parts ought to fit one another.
703. After positing that three things are required in order that a motion be unqualifiedly one—unity of time, unity of that in which the motion takes place, and unity of subject—the Philosopher now intends to prove this.
Now, while there are a number of ways in which things are unqualifiedly one—one being the way in which an indivisible is one, and another, the way in which a continuum is one—no motion can be unqualifiedly one in the way that an indivisible is one, because no motion is indivisible.
Consequently, it remains that a motion is one to the extent that it is continuous and that, insofar as a motion is concerned, to be continuous is to be unqualifiedly one, such that the very continuity of motion suffices for its unity. For if it is continuous, it is one. Accordingly, whatever is required to make a motion be continuous is also required to make it one.
704. Now, in order that a motion be continuous, three things are required.
The first of these is oneness in species. For there will not be continuity between one motion and another indiscriminately any more than there is continuity between just any two continuous things chosen at random in any other sphere. There can be continuity only when the extremities of the two things are one—this is implied in the account of continuity, as was explained above.
Now, some things have no extremities at all, such as forms and all indivisibles. Therefore, in regard to such things, there can be no continuity.
Other things have extremities that are divisible and have quantity. Some such things are equivocal, that is, not agreeing in name and account. Such things afford no means of forming continuity; indeed, in many cases, no contact is possible. For how could a line and walking be in contact, or how could they possess a common extremity such as to make continuity possible?
This shows that continuity is impossible with things that belong to genera or species that are diverse.
However, motions that differ generically or specifically can be consecutive, that is, follow one upon the other, as a person can start to get a fever immediately after running—getting a fever and running being in diverse genera. And, even in the same genus, such as local motion, one change of place could follow upon another without the motion being continuous, as is evident in the spreading of the lamp, when a torch is passed from hand to hand. In this case, we have diverse non-continuous motions. Or spreading of the lamp could mean that the local motion of the flame, which the name lamp signifies, follows the local motion of the liquid which feeds the flame, which is called spreading.
Therefore, the changes mentioned in the preceding paragraph, since they differ either generically or specifically, are not continuous, since they cannot have one extremity, which is required for a continuum. Consequently, motions that differ generically or specifically may be consecutive and had—that is, in contact somehow without any time interruption—inasmuch as time is continuous and has its continuity in the same way that motion has, namely, because there is one extremity (joining two parts).
Now, there is nothing to prevent one motion from being ended and another of an entirely different kind from beginning at the same instant that two parts of time are being joined. In that case, the two motions will be contiguous, but not continuous.
Therefore, according to our premises, it follows that, in order that a motion be continuous, it is necessary that it be one in species—this unity of species being in the motion from the thing in which the motion is, insofar as it is incapable of division according to species.
705. In the second place, continuity of motion requires unity of subject, for the motions of diverse subjects cannot be continuous, though they can be contiguous, as was said about transferring a lamp from hand to hand.
706. Third, in order that a motion be continuous and one, it must be one in time, such that no period of immobility or rest intervenes. For if there is a time in which it was not moving, then it was at rest during that time, and if a state of rest intervenes, the motion is not one, but many, since motions that are interrupted by rest are not one but many. Consequently, if a motion is interrupted by rest, it will be neither one nor continuous. But it is interrupted by rest if there is a time in the middle of it, as was shown. Hence, for continuity of motion, there must be one continuous time.
But mere continuity of time is not enough, because a motion that is not specifically one is not continuous, even though time is not interrupted, for although it be one in regard to time, it will be other in regard to species. In other words, in order that a motion be one and continuous, it must be specifically one; but it does not follow that a motion specifically one is unqualifiedly one.
Thus, it is clear that the three aforementioned things are required in order that a motion be unqualifiedly one. And, so, he concludes that we have now explained which motion is unqualifiedly one.
707. Then, at “further, a motion is also” (228b11), having posited the three principal ways in which a motion is one, he mentions two secondary ways, although these pertain more to a certain form of unity than to unity itself.
The second of these is given at “and, besides the cases” (228b15; [708]).
He says first (228b11) that, whether a motion be one in genus or in species or in substance (that is, numerically one), it is also called one if it is perfect; likewise, in other things, “perfect” and “whole” pertain to the account of unity. For we do not speak of one man or one shoe, unless they are whole.
However, there are times when we speak of something imperfect as being one, provided it is continuous. And the reason for this is that unity can be regarded from the viewpoint of quantity, in which sense, mere continuity suffices for the unity of a thing, or from the viewpoint of the substantial form, which is the perfection of the whole. Thus, what is perfect and whole is said to be one.
708. Then, at “and, besides the cases” (228b15), he gives the other secondary way: a motion is called one when it is regular, that is, uniform, just as in other things an object is said to be one if its parts are alike.
About this, he does three things: first, he posits this mode of unity, according to which a regular motion is said to be one; second, he shows in which motions regularity and irregularity are found, at “in every kind of motion” (228b19; [709]); third, he explains the modes of irregularity, at “the difference that makes” (228b21; [710]).
He therefore says that, in addition to the above-mentioned ways of being one, a motion is called one if it is regular, that is, uniform. For an irregular or non-uniform motion does not seem to be one, whereas a regular or uniform motion does (as a motion that is entirely straight is uniform).
The reason that an irregular motion does not seem to be one is that it can be divided into parts that are not alike, whereas indivisibility pertains to the account of unity, because that which is one is undivided. However, an irregular motion is one in a sense. But the unity of irregular and regular motions seem to differ according to more and less, because a regular motion is more perfectly one than an irregular motion, just as a body whose parts are alike is more perfectly one than a body of parts that are not alike.
709. Then, at “in every kind of motion” (228b19), he shows in which motions irregularity and regularity are found. And he says that they are found in every genus and species of motion: some things can be altered in a regular manner, as when the entire alteration is uniform, and some things can be moved along a magnitude that is regular and uniform, as things that are in circular motion or in rectilinear motion. The same is true of growing and decreasing.
710. Then, at “the difference that makes” (228b21), he approaches the task of deciding about irregular motion.
First, he mentions ways of being irregular; second, he shows how an irregular motion is one, at irregular motion, therefore (229a1; [713]).
About the first, he does two things: first, he assigns two ways in which irregularity is present in motions; second, he draws certain conclusions from all this, at so, quickness and slowness (228b28; [712]).
He first says, therefore (228b21), that the variations that make for irregularity in motion are caused sometimes from the thing in respect to which there is motion. This is evident especially in local motions, for it is impossible for a motion to be regular and uniform unless it passes over a magnitude that is regular, that is, uniform. Now, a magnitude is said to be regular or uniform when each part of it follows its neighbor in a uniform manner, such that any part could be superimposed upon any other, as is clear in the case of arcs or straight lines. But a magnitude is irregular if one part does not uniformly follow another, as is evident in two lines that form an angle, of which one part does not fit perfectly over the other in the way that one part of a line fits perfectly over another.
Therefore, a circular motion is regular, and so is a rectilinear one, but reflected or oblique motions, whose path forms an angle, are not regular and do not take place on a uniform magnitude; neither is any motion on a magnitude that is not such that any part of it taken at random fits on any other taken at random. For if the part that contains the angle is superimposed on a part that does not form an angle, they will not match.
711. The second difference that makes for irregularity is found neither in the place, nor in the time, nor in that to which—that is, neither from that part of it which is called that to which (for a motion is not merely in a place, but also in quality or in quantity), or this can refer to the subject in which there is motion. But this second kind of irregularity in motion is in the manner of the motion. For in some cases, the motion is differentiated by swiftness and slowness, because a motion that has the same velocity throughout is said to be uniform, while one in which one part is swifter than another is said to be irregular.
712. Then, at “so, quickness and slowness” (228b28), he draws two conclusions from the foregoing.
The first is that swiftness and slowness are neither species of motion nor specific differences, because they can be found in all types of motion, since they determine regularity and irregularity, which follow upon each species of motion, as was said above. And no species or difference is common to every species of a genus.
The second corollary is that swiftness and slowness are not the same as heaviness and lightness, because each of the latter has its own motion, for the motion of earth, which is heavy, is always to itself and the motion of fire is always to itself. On the other hand, swiftness and slowness are common to diverse motions, as was said.
713. Then, at “irregular motion, therefore” (229a1), 1121he does two things: first, he shows how an irregular motion is one;
second, he draws a corollary, at “and, since every motion” (229a3; [714]).
He says first that an irregular motion can be said to be one insofar as it is continuous, but it is less perfectly one than a regular motion, just as a line having an angle is less perfectly one than a straight line. This is especially clear in a reflected motion, which seems to be two motions, as it were.
Now, since an irregular motion is less perfectly one, it appears to share in the notion of multitude, for a thing is said to be less because it has an admixture of the contrary, as what is less perfectly white has an admixture of black, at least in being closer to black than a perfectly white object is. And thus it is clear that an irregular motion is both one (insofar as it is continuous) and multiple in a certain way, insofar as it is less perfectly one.
714. Then, at “and, since every motion” (229a3), he concludes from the immediately foregoing the conclusion that he had previously proposed: motions that are specifically diverse cannot form a continuity. For every motion that is one can be either irregular or regular. But a motion that is composed of specifically distinct motions cannot be regular. For how could a regular motion be composed of alteration and local motion? For in order that a motion be regular, its parts must agree. Consequently, the conclusion is that diverse motions that are consecutive but not all of the same species do not form a motion that is one and continuous, as was stated above and explained by examples.