Aristotle · a new plain-English translation from the original language
1| Book Seven.
2| Everything that is in motion must be moved by something. For if it does not have the principle of its motion within itself, it is clear that it is moved by something else, since the mover will be different from it. But if it does have the principle within itself, let AB be taken as something that moves in its own right, and not because some part of it is moving. Now, in the first place, to suppose that AB is moved by itself, on the grounds that the whole is in motion and is not moved by anything outside it, is like the case where KL is moving LM and is itself in motion, and someone were to deny that KM is being moved by anything, because it is not evident which is the mover and which the moved. Next, what is not moved by anything need not stop moving because something else comes to rest; rather, if something comes to rest because something else has stopped moving, that thing must be moved by something — and once this is granted, everything that is in motion will be moved by something. For since what has been taken as being in motion is AB, it must be divisible, since everything in motion is divisible. Let it, then, be divided at C. Now if CB is not moving, AB will not be moving either; for if it were moving, clearly AC would be moving while CB was at rest, so that AB would not be moving in its own right and primarily. But it was assumed to move in its own right and primarily. So, necessarily, if CB is not moving, AB is at rest. But what is at rest because something else is not moving has been agreed to be moved by something; so everything that is in motion must be moved by something. For what is in motion will always be divisible, and if the part is not moving, the whole must be at rest too.
3| Since everything that is moved must be moved by something — for if something is moved with motion in place by another thing that is itself in motion, and again the mover is moved by something else in motion, and that in turn by yet another, and so on continually — there must be some first mover, and the series must not proceed to infinity. For suppose it does not stop, but let it be infinite. Let A, then, be moved by B, B by C, C by D, and let each thing in the series always be moved by the next. Since, then, it is assumed that the mover, itself being moved, causes motion, the motion of the thing moved and the motion of the mover must occur together (for the mover moves and the thing moved is moved at the same time); it is clear, then, that the motion of A and of B and of C and of each of the movers and things moved will occur together. Let the motion of each, then, be taken, and let E be the motion of A, F the motion of B, and G and H the motions of C and D. For even though each thing is always moved by each thing before it, it will still be possible to take one motion of each in number; for every motion is from something to something, and is not infinite at its limits.
4| I call a motion one in number when it goes from what is numerically the same to what is numerically the same, in what is numerically the same time. For a motion is the same in three ways — in genus, in species, and in number: the same in genus when it belongs to the same category, for instance substance or quality; the same in species when it goes from what is the same in species to what is the same in species, for instance from white to black, or from good to bad, when these do not differ in species; the same in number when it goes from one thing numerically one to one thing numerically one, in the same time — for instance from this white to this black, or from this place to that place, in this time. For if it occurred in a different time, it would no longer be one motion in number, but one in species. This has been discussed earlier. Let the time, too, be taken, in
5| which A has completed its own motion, and let it be K. Since the motion of A is finite, the time too will be finite. Now since the movers and the things moved are infinite in number, the motion EFGH, made up of all of them, will be infinite; for it is possible that the motion of A and of B and of the rest be equal, and it is also possible that the motions of the rest be greater — so that whether they are equal or greater, in either case the whole is infinite, since we are taking what is possible. And since A and each of the others are moved at the same time, the whole motion will occur in the same time as that of A; but that of A occurs in a finite time; so the infinite would occur in a finite time, and this is impossible. In this way
6| it might seem, then, that what was proposed at the outset has been shown; but in fact it has not been demonstrated, because nothing impossible has been shown. For it is possible for there to be an infinite motion in a finite time — not the motion of one thing, but of many. And this is exactly what happens in the present case; for each thing is moved with its own motion, and there is nothing impossible in many things being moved at the same time. But if the thing that primarily causes motion in place, motion of a bodily kind, must either be in contact with the thing moved or be continuous with it — as we see in every case — then the things moved and the things moving them must be continuous with one another or in contact, so that all of them together form a single thing. And whether this is finite or infinite makes no difference for the present purpose; for in any case the motion will be infinite, since the movers are infinite, if indeed it is possible for them to be equal to or greater than one another; for whatever is possible, we shall take as holding. If, then, the thing made up of A, B, C, D is either finite or infinite, and it is moved with the motion EFGH in the time K, and this time is finite, it follows that in a finite time an infinite motion is traversed, whether by the finite thing or by the infinite thing. But both are impossible. So it is necessary for the series to come to a stop, and for there to be some first mover and first thing moved. For it makes no difference that this impossibility results from a hypothesis; for the hypothesis taken was one that is possible, and when what is possible is posited, nothing impossible ought to result from it on that account.
7| The first mover — not in the sense of that for the sake of which, but that from which the origin of the motion comes — is together with the thing moved (by 'together' I mean that there is nothing between them); for this holds in common for every mover and thing moved. Since there are three kinds of motion — that in respect of place, that in respect of quality, and that in respect of quantity — there must also be three kinds of mover: that which carries, that which alters, and that which increases or diminishes. Let us speak first, then, about locomotion; for this is the first of the motions.
8| Now everything that is carried is moved either by itself or by something else. In the case of things moved by themselves, it is clear that the thing moved and the mover are together in them; for the first mover is present within them, so that there is nothing between. But things moved by something else must come about in one of four ways; for there are four kinds of motion by another: pulling, pushing, carrying, and whirling. For all motions in respect of place are reduced to these. Pushing-on is a kind of pushing, when the mover, having set something in motion from itself, follows along and pushes it; pushing-off is when the mover does not follow along after having set it in motion; throwing is when the mover makes the motion away from itself more violent than the thing's natural motion, and the thing is carried just so far as that motion prevails. Again, driving-apart and driving-together are species of pushing-off and pulling: for driving-apart is a pushing-off (pushing-off being either from oneself or from another), while driving-together is a pulling (for pulling too is both toward oneself and toward another). So too are the species of these, such as battening and shuttling: the one is a driving-together, the other a driving-apart. Similarly too the other cases of combination and separation — for all of them will be cases of driving-apart or driving-together — except those that occur in coming-to-be and passing-away.
9| At the same time it is also clear that combination and separation are not some further kind of motion; for all of them are distributed among the ones already mentioned. Further, inhaling is a pulling, exhaling a pushing. Similarly too spitting, and all other motions through the body that are either excretive or receptive; for some of these are pullings, others pushings. And the other motions in respect of place must be reduced in the same way; for all of them fall under these four, and of these, again, carrying and whirling are reduced to pulling and pushing. For carrying occurs in accordance with one of these three ways (for the thing carried is moved accidentally, in that it is in something moving or on something moving, while the thing that carries, carries either while being pulled or being pushed or being whirled, so that carrying is common to all three); while whirling is composed of both pulling and pushing, for what does the whirling must pull one part and push another — for it draws one part away from itself, the other toward itself. So that, if the thing pushing and the thing pulling are together with the thing pushed and the thing pulled, it is clear that between what is moved in place and what moves it there is nothing between.
10| But indeed this is clear also from the definitions: pushing is a motion from oneself or from another toward another, while pulling is a motion from another toward oneself or toward another, when the motion is faster than the one separating continuous things from one another; for in this way the other part is drawn along with it. (Perhaps it might seem that there is also a pulling in another way; for wood draws fire, but not in this way. It makes no difference, though, whether the thing pulling is in motion or at rest when it pulls; for sometimes it pulls from where it is, sometimes from where it was.) But it is impossible to move something from oneself toward another, or from another toward oneself, without touching it; so it is clear that between what is moved in place and what moves it there is nothing between.
11| But surely there is nothing between the thing altered and the thing altering, either. This is clear from induction: in every case it turns out that the last thing altering and the first thing altered are together. For we take it as established that things altered are altered by being affected in respect of what are called affective qualities. For every body differs from every other body in its perceptible qualities, either in having more or fewer of them, or in having the same ones to a greater or lesser degree. But moreover the thing altered is altered by the qualities just mentioned. For these are affections of the underlying quality: we say a thing is altered when it is heated, or sweetened, or condensed, or dried, or whitened, saying this alike of the inanimate and the animate, and again, among animate things, of the parts that have no perception as well as of the perceptions themselves. For the perceptions too are altered in a way: perception in actuality is a motion through the body, the perception being affected in some way. Now whatever the inanimate is altered in respect of, the animate is altered in respect of that too, but not everything the animate is altered in respect of holds also for the inanimate (for it is not altered in respect of the perceptions); and in the one case the being affected escapes notice, in the other it does not. But nothing prevents its escaping notice in the animate as well, whenever the alteration does not occur in respect of the perceptions. If, then, the thing altered is altered by perceptible things, it is evident that in all these cases the last thing altering and the first thing altered are together: for to the one the air is continuous, and to the air the body; and again, color is continuous with light, and light with sight. In the same way too with hearing and smell: the air is the first mover in relation to what is moved. And likewise with taste: the flavor is together with the taste. And the same holds too in the case of inanimate and imperceptive things. So there will be nothing between the thing altered and the thing altering.
12| Nor, again, is there anything between the thing growing and the thing that makes it grow. For the first thing that causes growth causes growth by being added on, so that the whole becomes one. And again, the thing that diminishes diminishes by something belonging to the diminishing thing being taken away. The growing thing and the diminishing thing must therefore be continuous, and of continuous things there is nothing between. It is clear, then, that between the thing moved and the first and last thing that moves it, in relation to the thing moved, there is nothing in between.
13| That everything that is altered is altered by perceptible things, and that alteration belongs only to those things that are said in their own right to be affected by perceptible things, must be studied from the following considerations. For among the other cases, one might suppose above all that alteration is present in shapes and figures, and in states and the acquisitions and losses of these; but it is present in neither. For when a thing being given shape or figure is completed, we do not call it by the material out of which it is—we do not call the statue bronze, or the pyramid wax, or the bed wood—but by a derived name we call the one bronzen, the other waxen, the other wooden. But what has been affected and altered we do call by the material's name: we call the bronze or the wax wet, or hot, or hard (and not only in that way, but we also call the wet thing or the hot thing bronze), calling the matter by the same name as the affection. So if, in respect of shape and figure, what has come to be is not called by the name of that in which the shape resides, but in respect of affections and alterations it is so called, it is clear that comings-to-be could not be alterations. Further, it would seem strange to say, in this way, that a human being, or a house, or anything else that has come to be, has been altered. Rather, presumably each thing must come to be as a result of something being altered—for instance, the matter being condensed, or rarefied, or heated, or cooled—but the things that come to be are not thereby altered, nor is their coming-to-be an alteration.
14| But moreover, neither are the states—whether of the body or of the soul—alterations. For some states are virtues and others are vices; but neither virtue nor vice is an alteration. Rather, virtue is a kind of completion (for when a thing has received its own virtue, then it is said to be complete—for then it is most in accordance with its nature, just as a circle is complete when it has most fully become a circle and is at its best), while vice is a destruction and departure from this. So then, just as we do not call the completion of a house an alteration (it would be absurd if the coping and the tiling were an alteration, or if the house, in being coped and tiled, were altered rather than completed), in the same way it holds for the virtues and vices too, and for those who possess or are acquiring them: some are completions, others departures, and so they are not alterations.
15| Further, we also say that all the virtues consist in being related to something in a certain way. For the virtues of the body, such as health and good condition, we place in a blending and due proportion of hot and cold things, either of the internal elements in relation to one another, or in relation to the surrounding environment; and likewise too beauty and strength and the other virtues and vices. For each of them consists in being related to something in a certain way, and it disposes what possesses it well or badly with respect to that thing's own proper affections—and the proper affections are those by which it is naturally suited to come to be and to be destroyed. Since, then, relative terms are not themselves alterations, and there is neither alteration nor coming-to-be of them, nor any change at all, it is clear that neither the states nor the losses and acquisitions of the states are alterations; but presumably they must come to be and be destroyed as a result of certain things being altered, just as form and shape do too—for instance, of hot and cold things, or of dry and wet things, or of whatever it is in which they happen to reside in the first instance. For it is with respect to these that each vice and virtue is spoken of, the things by which what possesses them is naturally suited to be altered: virtue makes it either unaffected, or affected in this particular way, while vice makes it affected, or, on the contrary, unaffected.
16| The same holds too for the states of the soul: all of these likewise consist in being related to something in a certain way, and the virtues are completions while the vices are departures. Further, virtue disposes one well with respect to the proper affections, vice badly. So these too will not be alterations, nor indeed will the losses and acquisitions of them. But they must come to be as a result of the perceptive part being altered. And it will be altered by perceptible things: for all ethical virtue concerns bodily pleasures and pains, and these occur either in acting, or in remembering, or in hoping. Those that occur in the acting are in accordance with perception, so that they are set in motion by some perceptible object; those in memory and in hope derive from this—for one takes pleasure either in remembering what one has experienced, or in hoping for what is to come. So it is necessary that all pleasure of this kind arise from perceptible things. And since, when pleasure and pain come to be, vice and virtue also come to be (for they are concerned with these), and pleasures and pains are alterations of the perceptive part, it is clear that it is necessary, as a result of something being altered, to both lose and acquire these too. So their coming-to-be involves alteration, but they themselves are not alterations.
17| But surely the states of the intellectual part are not alterations either, nor is there any coming-to-be of them. For it is above all in the case of what is knowing that we speak of being in some condition relative to something. And further it is also evident that there is no coming-to-be of them: for what is potentially knowing does not become knowing by being itself moved, but by something else's coming to be the case. For when the particular instance comes to be, it knows the universal in a certain way through the particular. Again, there is no coming-to-be of the using and the exercising of knowledge, unless someone thinks there is a coming-to-be of the recovery of sight or of touch as well; for using and exercising are like these. But the initial acquiring of knowledge is not a coming-to-be nor an alteration: for it is by the thought's coming to rest and standing still that we are said to know and to be wise, and there is no coming-to-be into a state of rest; for in general there is no coming-to-be of any change at all, as has been said before. Further, just as when someone changes from being drunk, or asleep, or sick, into the opposite states, we do not say he has become knowing again (although he was previously unable to exercise his knowledge), so too it is not the case when he acquires the state from the beginning: for it is by the soul's settling down out of its natural disturbance that something becomes practically wise and knowing. That is why children can neither learn, nor judge by their perceptions as well as older people do; for there is much disturbance and motion in them. And the soul settles down and grows calm — with respect to some things by nature itself, with respect to others by other agencies — while in both cases certain things in the body are being altered, just as in the case of using and exercising knowledge, when a person becomes sober and wakes up. It is evident, then, from what has been said, that being altered and alteration occur both in the objects of perception and in the perceptive part of the soul, and in nothing else except accidentally.
18| One might raise the difficulty whether every motion is comparable with every other or not. If, then, every motion is comparable, and what is equal in speed is what moves an equal distance in an equal time, then some arc will be equal to a straight line, and indeed one greater and one lesser. Further, an alteration and a locomotion will be equal, whenever in an equal time the one thing is altered and the other is carried an equal amount. There will, then, be an affection equal to a length. But that is impossible. But is it rather this: whenever an equal magnitude is traversed in an equal time, then it is equal in speed, while an affection is not equal to a length, so that an alteration is not equal in speed to a locomotion, nor less than it, so that not every motion is comparable? But in the case of the circle
19| and the straight line, how will it turn out? For it is odd if this thing cannot move on the circle in the same way as that thing on the straight line, but must instead necessarily be either faster or slower, as though one were downhill and the other uphill; nor does it make any difference to the argument if someone says it is necessary for it to be simply faster or slower rather than equal. For then the arc will be greater and less than the straight line, and so also equal to it. For if in time A it has traversed distance B, and the other has traversed C, B would be greater than C — for that is what 'faster' meant. So too, if an equal distance is traversed in a lesser time, that is faster; so that there will be some part of A in which something traverses a distance on the circle equal to B, and C in the whole of A. But indeed, if they are comparable, what was just said follows: that a straight line is equal to a circle. But they are not comparable, and so neither are the motions; rather, whatever things are not synonymous are all incomparable. For instance — why is it not comparable which is sharper, the stylus or the wine or the top string? Because they are homonymous, they are not comparable; but the top string is comparable with the string next to it, because 'sharp' signifies the same thing in both. Is it, then, the case that 'fast' is not the same here and there, and still much less so in alteration and locomotion?
20| Or is it, first of all, not true that things are comparable so long as they are not homonymous? For 'much' signifies the same thing in water and in air, and yet they are not comparable. Or if not that example, at least 'double' is the same in different things (for it means two to one), and yet things called double are not comparable. Or does the same account hold in these cases too? For 'much' is also homonymous. But in some cases even the definitions are homonymous — for instance, if someone says that 'much' is 'so much and more,' the 'so much' is different in different cases. And 'equal' is homonymous too, and 'one,' if it comes to that, is straightaway homonymous. And if this is so, so is 'two' — since otherwise why are some things comparable and others not, if there were a single nature in each case? Is it because they are present in a different primary recipient? So a horse and a dog are comparable as to which is whiter — for the primary recipient, the surface, is the same — and likewise as to size; but water and sound are not, for they are in a different recipient. Or is it clear that, on this reasoning, everything will end up made one, while each thing is said to be in a different recipient, and 'equal' and 'sweet' and 'white' will be the same thing, yet different in different things? Further, the recipient is not just any recipient of just anything, but the primary recipient of one thing is one thing.
21| But is it, then, not only
22| necessary that the things being compared not be homonymous, but also that they have no differentia, either in what is compared or in that in which it is present? I mean, for instance, that color admits of division; accordingly it is not comparable in respect of this — that is, which is colored more, not in respect of some particular color, but qua color — but it is comparable in respect of white. So too with motion: equal in speed is defined by moving an equal distance in an equal time. If, then, of a given length one part was altered and another was carried, is this alteration then equal to the locomotion, and equal in speed with it? But that is absurd. The reason is that motion has species, so that if things carried an equal length in an equal time will be equal in speed, then the straight line and the arc are equal. Is the reason, then, that locomotion is a genus, or that the line is a genus? For the time is the same, but if the things involved differ in species, then those motions too differ in species. For indeed locomotion has species, if that over which the motion occurs has species — and sometimes if that by which it occurs does, for instance if by feet, walking, if by wings, flight. Or is that not so, but rather locomotion differs by its shapes? So that things moving through an equal magnitude in an equal time are equal in speed, and what is the same and undifferentiated in species is also undifferentiated in motion; so that this must be investigated: what is the differentia of motion. And this argument shows that the genus is not some single thing, but that many things lie hidden alongside it, and that among homonymies some are far apart, some have a certain similarity, and some are close either in genus or by analogy, which is why they do not seem to be homonymies, though they are. When, then, is the species different — when the same thing is in a different subject, or when a different thing is in a different subject? And what is the criterion? Or shall we judge whether white and sweet are the same or different by this: whether it appears different because it is in a different subject, or because it is simply not the same at all?
23| Now concerning alteration, how will one alteration be equal in speed to another? If, then, being healed is being altered, it is possible for one person to be healed quickly and another slowly, and for some at the same time as each other, so that there will be an alteration equal in speed to another, since it occurred in an equal time. But what was altered? For 'equal' is not properly what is said here; rather, just as there is equality in quantity, here there is likeness. But let it be granted that what changes the same thing in an equal time is equal in speed. Should we, then, compare in respect of that in which the affection occurs, or in respect of the affection itself? Here, at any rate, because the health is the same, we can grasp that it is present neither more nor less, but in like manner. But if the affection is different — as when what is being whitened and what is being made healthy are both being altered — for these there is nothing the same, nor equal, nor alike, inasmuch as these already make different species of alteration, and it is not a single kind, any more than locomotions are. So we must grasp how many species of alteration there are, and how many of locomotion. If, then, the things moved differ in species — the things of which the motions are motions in their own right and not accidentally — the motions too will differ in species; if in genus, in genus; if in number, in number. But then should we look to the affection, asking whether it is the same or alike, to see if the alterations are equal in speed, or to the thing being altered — for instance, whether this much of the one has been whitened, and that much of the other?
24| Or into both, and whether it is the same or different with respect to what is affected — if it is the same or not the same — and equal or unequal, if the other thing is equal or unequal? And the same question must be examined in the case of coming-to-be and passing-away. How is coming-to-be equally fast? If in an equal time the same and indivisible thing comes to be — for example a man, and not merely an animal (for the one is indivisible) — but in cases where, in an equal time, a different thing comes to be (for we do not have any two things in which the difference is of the same kind as dissimilarity), or, if substance is a number, then it is a matter of a greater or smaller number of the same species; but there is no name for what is common to both cases, nor for either one taken alone — just as the greater is called an affection, or rather the exceeding thing is called so more properly, while the quantity is called "larger."
25| Since what moves something always moves it in something and up to some point (I mean by "in something" that it moves it in a time, and by "up to some point" that there is a definite length; for what moves something is always simultaneously moving it and has moved it, so that what has been moved will be some definite quantity, and in some definite time) — suppose, then, that A is what moves, B is what is moved, the length through which it has been moved is Γ, and the time in which it moved it is Δ. Then in an equal time, a force equal to A will move half of B twice the distance of Γ, and will move Γ itself in half of Δ; for that is how the proportion will work out. And if the same force moves the same thing a given distance in a given time, and moves half of it that same distance in half the time, then half the force will move half the thing an equal distance in an equal time. For example, let E be half the force A, and let half of B be taken as well; then they stand in the same ratio, and the force is proportional to the weight, so that they will move an equal distance in an equal time. But if E moves Z a distance Γ in time Δ, it does not follow that, in an equal time, E will move twice Z half the distance of Γ. So if A moves B a distance equal to Γ in Δ, half of A, namely E, will not move B in the time Δ, nor will it move, in any part of Δ, a part of Γ proportional to the whole of Γ as A is to E; for it may well be, quite generally, that it will move nothing at all.
26| For it does not follow that, if the whole force moved something a certain distance, half the force will move it some distance, in some period of time whatsoever; otherwise one man alone could move a ship, provided that the combined force of the ship-haulers is divided according to their number, and so too the distance which all of them together moved it. This is why Zeno's argument is not true, that any part whatever of a bushel of millet makes a sound as it falls; for there is nothing to prevent a given part from failing to move, in any length of time, the amount of air that the whole bushel moved in falling. Nor does it even move as much of the air as it would move of the whole amount, if this part existed by itself; for nothing exists in the whole except potentially. But if there are two things that cause motion, and each of them separately moves such-and-such an amount in such-and-such a time, then the forces, when combined, will move the object composed of the two weights an equal distance and in an equal time; for this holds in proportion.