Aristotle · a new plain-English translation from the original language
1| Physics, Book 4. Likewise the student of nature must also know about place, just as about the infinite — whether it exists or not, and how it exists, and what it is. For everyone supposes that the things that are, are somewhere (since what is not is nowhere — for where is a goat-stag or a sphinx?); and of motion, the most common and most fundamental kind is motion with respect to place, which we call locomotion. But there are many puzzles as to what place actually is; for it does not appear to be the same thing to those who survey it in the light of all the relevant facts. Moreover, we have nothing handed down from others, either previously raised as a difficulty or previously worked out, concerning it.
2| That place exists, then, seems to be clear from mutual replacement: where water now is, there air is present in turn once the water has gone out, as if from a vessel, and at other times some other body occupies this same place; and this place seems to be different from all the things that come to be in it and change. For in the place where air now is, water previously was, so that it is clear that place is something, and that the region is different from both — the region into which and out of which they changed. Further, the movements of the natural and simple bodies, such as fire and earth and the like, show not only that place is something, but also that it has a certain power. For each of them, when not prevented, is carried to its own place, one up and the other down; and these — the up and the down and the rest of the six directions — are parts and kinds of place. And such things are not only relative to us — the up and down and right and left. For to us they are not always the same, but come about according to our position, however we turn (which is why the same thing is often right and left, up and down, in front and behind); but in nature each is marked off separately.
3| For up is not just whatever happens to be up, but where fire and what is light are carried; and likewise down is not just whatever happens to be down, but where the things that have weight and the earthy things are carried — since up and down differ not only in position but also in power. Mathematical objects also make this clear: for although they are not in place, they nevertheless have right and left relative to their position toward us, since these are said to belong to them only by position, none of them possessing such a thing by nature. Further, those who assert that the void exists call it place; for the void would be place deprived of body. That place, then, is something over and above bodies, and that every perceptible body is in place, one might suppose from these considerations. And Hesiod too might seem to speak rightly in making chaos come first. At any rate he says, "First of all things chaos came to be, but then next, wide-bosomed earth," as though room had to exist first for the things that are, because he supposed, like most people, that everything is somewhere and in a place. And if this is so, the power of place would be something remarkable, and prior to all other things; for that without which none of the other things can exist, while it itself can exist without the others, must be first; for place does not perish along with the things in it that perish.
4| Still, it does present a puzzle, if it exists, what it is — whether it is some bulk of body or some other nature. For its genus must be sought first. Now it has three dimensions, length and width and depth, by which every body is bounded. But it is impossible for place to be a body; for then two bodies would be in the same place. Further, if there is a place and a region for a body, clearly there is also one for a surface and for the remaining limits; for the same account will fit them — for where the planes of the water were before, there in turn will be the planes of the air. But then again we have no way of distinguishing a point from the place of a point, so that if place is not different even from this, it is not different from any of the others either, nor is place anything over and above each of these. For what, then, could we ever suppose place to be? For, having such a nature, it cannot be either an element or composed out of elements, whether corporeal or incorporeal; for it has magnitude, but is no body — and while the elements of perceptible things are bodies, no magnitude arises out of intelligible things. And further, of what could one posit place to be the cause for the things that are? For none of the four causes belongs to it —
5| for it is neither as matter of the things that are (since nothing is composed out of it), nor as the form and definition of things, nor as an end; nor does it move the things that are. Further, if it itself is one of the things that are, where will it be? For Zeno's puzzle calls for some account: if everything that is is in a place, clearly there will also be a place of the place, and this to infinity. Again, just as every body is in a place, so too in every place there is a body. How then shall we speak about things that grow? For it is necessary, from these premises, that the place grow along with them, if the place of each thing is neither smaller nor larger than it. Through these considerations, then, it is necessary to be puzzled not only about what place is, but even about whether it is.
6| Since one thing is said in its own right, and another in virtue of something else, and place too is in one sense common — the place in which all bodies are — and in another sense proper, namely the primary place in which a thing is (I mean, for example, that you are now in the heavens because you are in the air, and this in the heavens, and you are in the air because you are on the earth, and likewise on the earth because you are in this particular place, which encloses nothing more than you) — if, then, place is the primary thing that encloses each of the bodies, it would be a kind of limit, so that it would seem that the form and the shape of each thing is its place, that by which the magnitude is bounded, and the matter of the magnitude; for this is the limit of each thing. Looked at in this way, then, place is the form of each thing; but insofar as place seems to be the extension of the magnitude, it is the matter; for this is different from the magnitude, and this is what is enclosed and bounded by the form, as by a plane and a limit, and matter and the indeterminate are of this sort; for when the limit and the affections of the sphere are taken away, nothing is left beside the matter. This is why Plato too, in the Timaeus, says that matter and space are the same thing; for the participant and space are one and the same. But though he speaks of the participant in one way there and in another way in his so-called unwritten doctrines, he nevertheless declared place and space to be the same thing. For everyone says that place is something, but he alone attempted to say what it is.
7| It is reasonable, then, that to those examining the question on these grounds it should seem difficult to recognize what place is, if it is indeed either of these two — either the matter or the form; for in any case this requires the most acute observation, and it is not easy to recognize them apart from one another. But that place cannot be either of these two, at any rate, is not hard to see. For the form and the matter are not separated from the thing, but place admits of being separated; for in the place where air was, water in turn comes to be, as we said, the water and the air changing places with one another, and likewise with the other bodies too, so that the place of each thing is neither a part nor a state of it, but is separable. Indeed place does seem to be something of the sort that a vessel is — for a vessel is a portable place — but the vessel is nothing that belongs to the thing. Insofar, then, as it is separable from the thing, in this respect it is not the form; and insofar as it encloses the thing, in this respect it is different from the matter. And it always seems that what is, is somewhere, being itself something and also something else outside itself. (One must say to Plato, however, if we may digress to say so, why the forms and the numbers are not in place, if the participant is place — whether the participant is the great and the small, or the matter, as he wrote in the Timaeus.) Further, how could a thing be carried to its own place, if place is the matter or the form?
8| For it is impossible for that in which there is no motion, and no up or down, to be place. So place must be sought among things of this sort. But if place is in the thing itself (and it must be, if it is either shape or matter), then place will be in a place; for the form and the indeterminate change and move together with the thing, not always being in the same place, but wherever the thing is — so that there will be a place of the place. Further, when water comes to be from air, the place has perished; for the resulting body is not in the same place. What, then, is this perishing? We have now stated the grounds requiring that place be something, together with the grounds that would leave its essence open to doubt.
9| After this we must grasp in how many ways one thing is said to be in another. In one way, as the finger is in the hand, and generally the part in the whole. In another way, as the whole is in its parts; for the whole is not something beside the parts. In another way, as man is in animal, and generally species in genus. In another way, as the genus is in the species, and generally the part of the species is in the definition. Further, as health is in what is hot and cold, and generally the form is in the matter. Further, as the affairs of the Greeks are in the king, and generally as effects are in their primary moving cause. Further, as something is in the good, and generally as it is in the end; and this is the that-for-the-sake-of-which. But the most proper sense of all is as something is in a vessel, and generally as a thing is in place. One might be puzzled whether it is even possible for a thing to be in itself, or whether nothing is, but everything is either nowhere or in something else. This is so in two ways, either in its own right or in virtue of something else. For when the thing in which something is and the thing that is in it are parts of a whole, then the whole will be said to be in itself;
10| for a thing is also called something in respect of its parts, as it is called white because its surface is white, and knowledgeable because its rational part is knowledgeable. So the jar itself will not be in itself, nor will the wine be in itself; but the jar-of-wine will be in itself; for both the containing thing and that which is in it are parts of the same whole. In this way, then, it is possible for a thing to be in itself, but not primarily. For example, the white is in a body — for the surface is in a body — and knowledge is in a soul; and it is in virtue of these, as parts, that such designations apply, as indeed is the case in a man (whereas the jar and the wine, taken apart, are not parts, but taken together they are; hence, when they are parts, the thing will be in itself). For example, the white is in a man because it is in his body, and in this because it is in the surface; but in the surface it is no longer there in virtue of anything else. And these — the surface and the white — are different in kind, and each has a different nature and power. So, whether we look at the matter inductively, we see nothing that is in itself under any of these distinctions, and by argument too it is clear that it is impossible; for it would be necessary for each of the two to have both characters, for instance for the jar to be both a vessel and wine, and for the wine to be both wine and a jar, if indeed it is possible for a thing to be in itself.
11| So that even if they were, as far as possible, in one another, the jar would receive the wine not insofar as it is itself wine but insofar as the other thing is wine, and the wine would be in the jar not insofar as it is itself a jar but insofar as the other thing is a jar. That they are different, then, in respect of their being, is clear; for the account of the container and the account of the thing contained are different. But indeed it is not possible either, even accidentally; for then two things would be in the same thing at once; for the jar itself would be in itself, if that whose nature it is to receive something can be in itself, and further that which it receives as well — for instance, if it receives wine, the wine too. That it is impossible, then, for anything to be in itself primarily, is clear. As for the puzzle Zeno raised — that if place is something, it will be in something — this is not hard to resolve; for nothing prevents the primary place from being in something else, not, however, as being in a place in that thing, but just as health is in what is hot as a state, while the hot is in a body as an affection. So there is no necessity of going on to infinity. But this much is evident: since the vessel is nothing that belongs to the thing in it — for what is in something primarily and that in which it is are different — place would be neither the matter nor the form, but something else; for these, the matter and the shape, belong to that which is in the place. Let these points, then, stand as having been set out as puzzles.
12| What place is will become clear in the following way. Let us take up, concerning it, all the things that seem truly to belong to it in its own right. We hold, then, that place is, first, what contains that of which it is the place, and is nothing that belongs to the thing itself; further, that the primary place is neither less nor greater than the thing; further, that it is left behind by each thing and is separable; and besides these, that every place has an up and a down, and that each of the bodies is carried by nature to, and remains in, its own proper places, and that it does this either upward or downward. With these laid down, we must examine what remains. And the inquiry should be conducted in such a way that the what-it-is will be given, so that the puzzles will be resolved, the things that seem to belong to place will turn out to belong to it, and further the cause of the difficulty and of the puzzles about it will become clear; for in this way each point would be shown to best effect. First, then, we must understand that place would not have been sought if there were no motion with respect to place; and it is for this reason, above all, that we think the heaven is in a place, because it is always in motion. Of this motion, one kind is locomotion, another is growth and decay;
13| for indeed in growth and decay a thing changes, and what was previously here has now shifted into something smaller or larger. And of things that move, some move in their own right, in actuality, others accidentally; and of the things that move accidentally, some are capable of moving in their own right, for example the parts of the body and the nail in a ship, while others are not capable of it but always move accidentally, for example whiteness and knowledge — for these have changed place in this way, because the things in which they are present change place. Now since we say that a thing is, as it were, in a place, in the heaven, because it is in the air, and this in turn is in the heaven; and it is not in the whole of the air either, but we say it is in the air on account of the outer limit of the air that contains it (for if the whole air were its place, the place of a thing and the thing itself would not be equal, though the place is thought to be equal, and the primary place in which a thing is, is of this sort) — so then, whenever the containing thing is not divided off but continuous, the contained thing is said to be in it not as in a place, but as a part in a whole; but whenever the containing thing is divided off and in contact, the contained thing is in the primary limit of the container, which is neither a part of the thing in it nor greater than its extension, but equal to it;
14| for the limits of things in contact are in the same place. And when a thing is continuous with its container, it does not move in it but along with it, whereas when it is divided off, it moves in it; and this holds no less whether the container is moving or not. From this, then, it is already clear what place is. For there are, roughly, four things of which place must be one: either shape, or matter, or some extension between the limits, or the limits themselves, if there is no extension over and above the magnitude of the body that comes to be in it. Now it is clear that three of these cannot be place; but because it contains, shape is thought to be place, since the limits of the containing thing and of the contained thing are in the same place. Both, then, are limits, but not of the same thing: rather, the one is the form of the thing, the other is the place of the containing body. And because the contained and divided-off thing often changes while the containing thing remains — as water flows out of a vessel — the intervening extension is thought to be something, as if it were something over and above the body that shifts. But it is not; rather, whatever body happens to be among those that shift and are naturally in contact falls into it. And if there were some extension that was by nature fixed and remained, there would be infinitely many places in the same place (for as the water and the air shift, all the parts within the whole would do the same thing that the whole water does within the vessel);
15| and at the same time the place itself would be changing, so that there would be another place of the place, and there would be many places at once. But the place of the part in which it moves is not different when the whole vessel shifts, but the same; for within that in which it is, the air and the water, or the parts of the water, exchange places with each other, but not within the place in which they come to be, which is a part of the place that is the place of the whole heaven. And matter, too, might seem to be place, if one considered a thing that is at rest and not divided off but continuous. For just as, if something is altered, there is something that is now white though formerly black, and now hard though formerly soft (and this is why we say matter is something), so too place is thought to be something on account of some such appearance — except that in the former case it is because what was air is now water, whereas in the case of place it is because where there was air, there is now water in that same place. But matter, as was said earlier, is neither separable from the thing nor does it contain it, whereas place does both. If, then, place is none of the three —
16| the form, the matter, or some extension that always exists as something distinct from that of the thing that shifts — then place must be the remaining one of the four: the limit of the containing body at which it is in contact with the contained body. By the contained body I mean the body that is capable of locomotion. Place seems to be something great and difficult to grasp, both because matter and shape are made to appear together with it, and because the shifting of the moving thing takes place while the containing thing is at rest; for it appears possible that there is some other extension between the moving magnitudes. The air, too, since it is thought to be incorporeal, contributes something to this; for it appears that place is not only the limits of the vessel, but also the space between them, as if it were void. And just as the vessel is a place that can be carried about, so too place is a vessel that cannot be moved. And this is why, when a thing moves and its contents change within something that is itself moving, as a ship on a river, it uses that as a vessel rather than as the place that contains it. But place wants to be unmoved; and this is why it is rather the whole river that is place, because the whole is unmoved. So the primary unmoved limit of the containing body — this is place.
17| And this is why the center of the heaven, and the limit of the circular motion that faces us, are thought by everyone, most properly of all, to be down and up respectively: because the one always remains, while the limit of the circular motion, though it revolves, remains the same in its condition. So then, since the light is what is by nature carried upward, and the heavy what is carried downward, the containing limit toward the center is down, and so is the center itself, while the limit toward the outer boundary is up, and so is the outer boundary itself. And this is why place is thought to be a kind of plane, and, as it were, a vessel and something that contains. Further, place is together with the thing; for the limits are together with the thing that is bounded.
18| A body that has some other body outside it, containing it, is in place; one that does not is not. This is why, even if water were to become such a thing, its parts will be in motion (for they are contained by one another), while the whole is in one way in motion and in another way not. For as a whole it does not change its place all at once, but it moves in a circle — for this is the place of its parts — and some things move neither up nor down but only in a circle, while others move both up and down, namely those that have condensation and rarefaction. And as was said, some things are in place potentially, others actually. So when the homogeneous thing is continuous, its parts are in place potentially; but when it is divided yet still in contact, like a heap, they are in place actually. And some things are in place in their own right (every body, for instance, that is movable either by locomotion or by growth is in some place in its own right; but the heaven, as has been said, is not as a whole anywhere, nor in any place at all, given that no body contains it — though in respect of that in which it moves, in that respect there is a place for its parts, since one part of it is next to another);
19| while other things are in place accidentally — for example the soul, and the heaven. For all the parts of the heaven are in some sense in place, since on the circle each part contains another. This is why the upper part moves in a circle, while the whole is not anywhere. For what is somewhere is itself something, and there must further be something else beside it, in which it is, that contains it; but beside the universe and the whole there is nothing outside the whole, and this is why all things are in the heaven — for the heaven, presumably, is the universe. But place is not the heaven, but a certain limit of the heaven, the part that touches the movable body. This is why earth is in water, water is in air, air is in aether, and aether is in the heaven — but the heaven is no longer in anything else. And it is clear from this that also
20| the puzzles would all be resolved if place is spoken of in this way. For place need not grow along with the thing that is in it, nor is there a place of a point, nor are there two bodies in the same place, nor is there any bodily interval (for whatever body happens to lie between the limits of a place is a body, not a bodily interval). And place is also somewhere, though not as being in a place, but as a limit is in what is limited — for not everything that is, is in place, but only the movable body. And indeed it is reasonable that each thing is carried to its own place: for what is next to something and in contact with it without force is akin to it; and things that have grown together are unaffected by one another, while things that are merely in contact are affected by and act on one another. And it is not without reason that each thing by nature stays in its proper place; for the part too — the part that is in place stands to the whole as a divisible part stands to it, as when someone sets in motion a portion of water or of air. And air stands to water in the same way: the one is, so to speak, matter, the other form; water is matter for air, and air is, as it were, a kind of actuality of water, since water is potentially air, and air is potentially water, in another way. These matters must be determined more precisely later; but for the present occasion something must be said, even if what is said now is unclear and will be clearer then. If, then, the same thing is both matter and realization (for both are water, but the one potentially and the other in realization), it would stand as a sort of part to the whole. This is why there is contact between them; and there is organic union when both come to be actually one. And about place, both that it is and what it is, we have now spoken.
22| In the same way it must be supposed to belong to the student of nature to examine the void as well — whether it exists or not, and how it exists, and what it is — just as with place. For the subject involves a similar mix of distrust and credence, based on what people assume. Those who assert it treat the void as a kind of place or container, and a thing seems to be full when it holds the bulk it is receptive of, and void when it is deprived of that — as though the void, the full, and place were the same thing, though what it is to be each of them is not the same. We must begin the inquiry by taking up what those who say it exists claim, and again what those who deny it claim, and third, the common opinions held about it. Now those who try to show that it does not exist do not refute what people actually mean by 'void'; they speak mistakenly — as do Anaxagoras and those who refute it in his manner. For they show that air is something by twisting wineskins and demonstrating how strong the air is, and by trapping it in water-clocks. But what people mean by void is an interval in which there is no perceptible body; and since they suppose that everything that is, is body, they say that whatever contains nothing at all is void, and hence that what is full of air is void. So what needs to be shown is not that air is something, but that there is no interval distinct from bodies — neither one that is separable nor one that actually exists — which divides the whole body up so that it is not continuous, as Democritus and Leucippus and many other natural philosophers say; nor, for that matter, whether there is anything outside the whole body, given that it is continuous.
23| These thinkers, then, do not come at the problem by the front door,
24| but rather those who assert that it exists do. They say, first, that there could be no motion with respect to place (that is, locomotion and growth); for motion would not seem to be possible unless there were void, since what is full cannot possibly receive anything. But if it can receive something, so that two things are in the same place at once, then any number whatsoever of bodies could be together at once — for one cannot state the difference by which this would fail to hold. And if this is possible, then even the smallest thing will receive the largest, since a large thing is many small things; so that if many equal things can be in the same place, so can many unequal ones. Melissus, then, actually uses these considerations to show that the universe is unmoved: for if it were to move, he says, there would have to be void, and void is not among the things that are. From these facts, then, they establish the existence of void in one way; in a second way, from the fact that certain things visibly draw together and grow denser — they say, for example, that storage jars take up the wine along with their skins, on the ground that a body, as it grows compact, gathers into the voids it already contains. Again, growth too is thought by everyone to occur through the void, since nourishment is a body, and it is impossible for two bodies to be in the same place at once. And they offer as evidence what happens with ash, which takes in as much water as the empty vessel does. The Pythagoreans, too, said that void exists, and that it enters the heaven itself out of the boundless breath, on the ground that the heaven, as it were, breathes it in; and that the void marks off natures, as though the void were a kind of separation and differentiation of things that stand in a row — and that this is found first of all among the numbers, since the void marks off their nature. Such, roughly, and so many, are the grounds on which some say that void exists and others deny it.
25| To settle the question either way, we need to grasp what the name means. The void is thought to be a place in which there is nothing. The reason for this is that people suppose what exists to be body, and every body to be in a place, and a void to be a place in which there is no body, so that if there is somewhere no body, there is nothing there. Again, they suppose every body to be tangible, and a thing is of this sort if it has weight or lightness. It follows, then, by syllogism, that this is void in which there is nothing heavy or light. So these conclusions, as we said before too, follow by syllogism. But it would be absurd if a point were void; for there must be a place in which there is an interval of tangible body. Still, the void is evidently spoken of in one way as what is not full of perceptible body in respect of touch — and a thing is perceptible in respect of touch if it has weight or lightness (hence one might also raise the puzzle: what would people say if the interval had color or sound — void or not? Surely it is clear that if it admits tangible body, it is void, and if not, it is not) — and in another way as that in which there is no this-something, nor any bodily substance. That is why some say the void is the matter of body (the same people who also say this about place), speaking incorrectly; for matter is not separable from the things it belongs to, whereas the void they seek is something separable.
26| Now since we have determined the account of place, and the void must
27| be a place, if it exists, deprived of body — and since we have said both how place exists and how it does not — it is clear that in this sense the void does not exist, neither as separated nor as unseparated. For the void is not a body, but is meant to be an interval of body; that is also why the void seems to be something, because place does too, and for the same reasons. For indeed, motion with respect to place lends support both to those who say that place is something over and above the bodies that occupy it, and to those who say the void is. They suppose the void to be a cause of motion in this way, as that in which motion occurs; and this would be the sort of thing that some say place is. But there is no necessity, if motion exists, that void should exist. This holds not at all for motion in general — which is why it escaped Melissus's notice too; for the full can undergo alteration. But it does not even hold for motion with respect to place; for it is possible for things to give way to one another simultaneously, there being no separate interval over and above the bodies that are moved. This is clear too in the rotations of continuous bodies, as also in those of liquids. And it is possible for a thing to become denser not into the void but through the squeezing out of what is contained in it (as when water is compressed, it squeezes out the air contained in it), and to grow not only by something entering it but also by alteration, as when air comes to be out of water. And in general, the argument about growth and about the water poured into ashes gets in its own way. For either nothing grows, or not by body, or it is possible for two bodies to be in the same place (in which case they are trying to solve a common puzzle, but are not showing that void exists), or it is necessary that the whole body be void, if it grows in every part and grows through void. The same argument applies also to the case of the ashes. It is clear, then, that it is easy to refute the void from the very grounds on which they show it exists.
28| Let us say again why there is no void that is separate in this way, as some claim. For if each of the simple bodies has by nature some motion — fire, for instance, upward, and earth downward and toward the middle — clearly the void would not be a cause of motion. Of what, then, will the void be a cause? It is thought to be a cause of motion with respect to place, but it is not the cause of this. Again, if there is something like a place deprived of body, when it is void, where will a body placed into it be carried? Surely not into all of it. The same argument applies also against those who suppose place to be something separate, into which a thing is carried; for how will the thing placed into it be carried, or will it remain at rest? And the same argument will fit reasonably both the case of up and down and the case of the void; for those who claim the void exists make it a place. And how, then, will a thing be present, either in a place or in the void? For it does not turn out so when a whole is placed as if in a separate and persisting place — some body; for the part, if it is not placed separately, will not be in a place but in the whole. Again, if there is no place, there will be no void either.
29| But for those who say the void exists as something necessary, if there is to be motion, the opposite turns out to be the case instead, if one examines it: it is not even possible for a single thing to move, if there is a void. For just as those who say the earth is at rest because of its uniformity say this, so too in the void a thing must be at rest; for there is no place where it will move more or less, since insofar as it is void, it admits no differentiation. Next, every motion is either forced or in accordance with nature. And if the forced motion exists, the natural motion must exist too (for forced motion is contrary to nature, and what is contrary to nature is posterior to what is in accordance with nature); so that if there is no motion in accordance with nature for each of the natural bodies, none of the other motions will exist either. But then how will there be motion in accordance with nature, when there is no differentiation at all in respect of the void, any more than in the infinite? For insofar as it is infinite, there will be no up, no down, no middle; and insofar as it is void, up is no different from down (for just as there is no differentiation in what is nothing, so too in the void; for the void is thought to be a kind of not-being, and a privation). But motion in accordance with nature is differentiated, so that there will be natural differentiations. Either, then, there is nowhere by nature any motion for anything, or, if this is so, there is no void.
30| Again, as things stand, projectiles keep moving after the thing that threw them is no longer touching them, either because of mutual replacement, as some say, or because the air that has been pushed pushes the projectile with a motion faster than the natural motion by which the projectile is carried to its proper place; but in the void none of this can occur, nor will anything be carried except as what is merely conveyed along. Again, no one could say why a thing once moved will come to rest anywhere; for why here rather than there? So it will either remain at rest, or it must be carried on to infinity, unless something stronger gets in its way. Again, currently a thing is thought to move into the void because it yields; but in the void this holds everywhere alike, so that it will be carried in every direction. Further, what has been said is clear from the following considerations as well.
31| For we see the same weight, that is, the same body, carried faster for two reasons: either because the medium through which it moves differs, as through water or earth, or through water or air, or because the moving body itself differs, other things being equal, on account of an excess of weight or of lightness. Now the medium through which a thing moves is a cause of this because it impedes — most of all if it moves in the opposite direction, but also if it simply remains at rest; and what is not easily divided impedes more, and the thicker medium is of this kind. Let A, then, be carried through B in a time C, and through D, which is thinner, in a time E, if the length of B is equal to that of D, in proportion to the impeding body. Let B be water and D be air; then by as much as air is thinner than water and less bodily, by that much A will be carried faster through D than through B. Let the speed to the speed, then, have the same ratio as air has to water. So that if air is twice as thin, A will traverse the distance B in twice the time it takes to traverse the distance D, and the time C will be double the time E.
32| And always, indeed, the more incorporeal, less obstructive, and more easily divisible the medium through which a thing is carried, the faster it will be carried. But the void has no ratio by which it is exceeded by body, just as nothing has no ratio to a number. For if four exceeds three by one, and exceeds two by more, and exceeds one by more still than it exceeds two, yet it no longer has a ratio by which it exceeds nothing; for the excessive term must be divided into the excess and the thing exceeded, so that four will be both the amount by which it exceeds and nothing. That is why a line does not exceed a point either, unless it is composed of points. Likewise the void can have no ratio at all to the full, and so neither can motion through the one have a ratio to motion through the other; rather, if a body is carried a given distance in a given time through the thinnest medium, then through the void it exceeds every ratio. For let
33| Ζ be a void, equal to Β and to Δ. Now if Α passes through it and is moved in a certain time — the time designated Η — and in less time than the one designated Ε, then the void will bear to the full this same ratio, namely that of Η to Ε. But in as much time as Η, Α passes through Θ of Δ. And indeed it would also pass through some body differing in fineness from Δ, one bearing to Δ the ratio which the time designated Ε bears to the time designated Η. For if the body is thinner than Δ by as much as Ε exceeds Η, then Α, moving in inverse proportion to its speed, will pass through the distance in as much time as Η, if it is carried through it. If, then, there is no body at all in Ζ, it will be carried through still faster. But it was assumed to be carried through in the time Η. So it will pass through an equal distance in an equal time whether the medium is full or void. But that is impossible. It is clear, then, that if there is any time in which a body will be carried through any part of the void, this impossibility will follow: for it will turn out that the same distance is passed through in an equal time whether the medium is full or void, since there will be some body bearing to another body the ratio that one time bears to another time. To put it briefly, the cause of this outcome is plain: between any motion and any motion there is a ratio, since each is in time, and between any two finite times there is a ratio — but between void and full there is none.
34| This, then, is what follows in respect of the difference between the media through which things are carried; but in respect of the excess of the things carried, the following holds. For we see that things having a greater tendency, whether of weight or of lightness, if everything else is alike, are carried faster over an equal distance, and in the ratio that their magnitudes bear to one another. So it would also be through the void. But that is impossible: for what cause will make it carried faster? In full media it is of necessity so, since the greater body divides faster by its strength — for it divides either by its shape, or by the impulse that the moving or thrown thing possesses; so in the void all things will move at equal speed. But that is impossible. It is clear, then, from what has been said, that if there is a void, the opposite follows from what those who assert that there is a void mean to establish. Now some think that the void exists, if there is to be motion with respect to place, as something separated in its own right; but this is the same as saying that place is something separate — and that this is impossible has been said already.
35| And if one examines it in its own right, what is called the void would appear to be a void in truth. For just as, if one puts a cube in water, as much water is displaced as the cube's size, so too in air — though this is imperceptible to sense. And indeed, always in every body capable of displacement, wherever it naturally shifts to, it is necessary, unless it is compressed together, that it be displaced — either always downward, if its motion is downward as with earth, or upward, if it is fire, or in both directions, whatever the thing inserted may be. But in the void this is impossible, since there is no body there; rather, an equal interval has been passed through by way of the cube, the very interval that was there before in the void — as if the water were not displaced by the wooden cube, nor the air either, but they passed everywhere straight through it. But surely the cube has just as much magnitude as the void it occupies; and this magnitude, even if it is hot or cold or heavy or light, is nonetheless something different in being from all these affections, even if it is not separable from them — I mean the bulk of the wooden cube. So that even if it were separated from all the others and were neither heavy nor light, it will occupy an equal void and will be in the same place both as the place and as the portion of void equal to itself.
36| What, then, will distinguish the body of the cube from an equal void and place? And if two such things can occupy the same place, why will not any number whatever be in the same place? This, then, is one absurd and impossible consequence. Further, it is clear that the cube, even when it shifts elsewhere, will retain this bulk, which all the other bodies also have. So if it differs in no way from place, why must we posit a place for bodies beyond each thing's own bulk, if the bulk is unaffected? For nothing is gained if some other, equal interval of this sort surrounds it. That there is, then, no separated void is clear from these considerations.
37| There are some who think it is evident, from the rare and the dense, that there is a void. For if there is no rare and dense, then it is not possible for things to condense and be compressed either; and if this were not possible, then either there will be no motion at all, or the whole heaven will bulge outward, as Xuthus said, or air and water must always change into an equal amount of each other — I mean, for example, that if air has come to be from a ladleful of water, an equal amount of water must at the same time have come to be from an equal amount of air — or else there must, of necessity, be a void; for it is not possible for things to be compressed and to expand in any other way. Now if by 'rare' they mean that which has many separated voids in it, it is clear that, if it is no more possible for a void to exist separately than for place to have an interval of its own, then the rare cannot exist in this way either. But if it is not separate, and yet some void is nonetheless present in it, this is less impossible — but the consequence is, first, that the void is not the cause of every motion but only of upward motion (for the rare is light, which is why they also say fire is rare); and next, that the void is a cause of motion not in the way of that in which motion occurs, but rather — just as wineskins, by being carried upward themselves, carry along with them what is attached to them — so the void carries things upward. And yet how can there be motion of a void, or a place of a void? For a void of a void results — the very thing it moves into. Further, how will they account for a heavy thing's moving downward? And it is clear that if a thing is carried upward in proportion as it is rarer and more void, then, if it were void outright, it would be carried upward fastest of all. But perhaps it too is incapable of being moved — the argument being the same as the one showing that, just as all things are motionless in the void, so the void itself is motionless; for speeds through it are incommensurable.
38| But since we say there is no void, while the other difficulties raised are genuine — namely, that either there will be no motion, if there is to be no condensation and rarefaction, or the heavens will bulge outward, or an equal amount of water must always come to be from air, and air from water (for it is clear that more air comes to be from water) — it is necessary, then, if there is no compression, either that the outermost adjoining part, being pushed outward, causes the whole to bulge, or that, somewhere else, an equal amount of water changes from air, so that the whole bulk of the universe remains equal, or that nothing moves at all — for this will always result from something being displaced, unless it goes round in a circle; and motion is not always circular, but also rectilinear. For these reasons, then, some would say there is some void. But we say, on the basis of what has been laid down, that there is a single matter underlying the contraries — hot and cold and the other natural contrarieties — and that what exists in actuality comes to be out of what exists potentially; and that matter is not separable, though it is different in being, and is one in number, it may be, for color and for hot and for cold. And there is matter also for body, both large and
39| ...is the same as that of the small. This is clear: when air comes to be from water, the same matter has come to be air without taking on anything else in addition; rather, what was potentially air has become actually air. And again water comes from air in the same way, sometimes changing from smallness to greatness, sometimes from greatness to smallness. So likewise, when a large quantity of air comes to occupy a smaller bulk, and a smaller quantity becomes larger, it is the matter existing potentially that becomes both. For just as the matter that becomes hot from cold, and cold from hot, is the same matter, because it was potentially hot or cold, so too the matter that becomes hotter from hot is the same: nothing has come to be hot in the matter that was not already hot when it was less hot. It is just the same as with the curvature and convexity of a larger circle when it becomes that of a smaller circle, whether the curvature is the same or different: in no case has the convex come to be in something that was not convex but straight (for the more and the less do not come about through any discontinuity). Nor is it possible to take any magnitude of flame in which heat and whiteness are not both present. So too, then, is the earlier heat related to the later heat. Hence both the largeness and the smallness of the perceptible bulk are extended not because the matter has taken on anything additional, but because the matter is potentially both. So the dense and the rare are the same matter, and there is one matter for both. The dense is heavy, and the rare is light. For there are two things involved in each, in the dense and in the rare: the heavy and the hard both seem to be dense, and their opposites, the light and the soft, seem to be rare; but the heavy and the hard come apart from each other in the case of lead and iron.
40| Given the points just established, no void exists as a separated thing — not unqualifiedly, not within the rare, and not even potentially — unless someone insists on using 'void', in every application of the word, for whatever causes locomotion. In that sense the matter of the heavy and the light, insofar as it is such, would be the void. For the dense and the rare, in respect of this opposition, are productive of locomotion, but in respect of the hard and the soft they are productive of being affected and not being affected, and of alteration rather than locomotion. Let this, then, be our determination about the void — in what sense it exists and in what sense it does not. Following what has been said, the next thing is to go through the subject of time. It is well, first, to work through the puzzles about it, using the arguments from outside as well, as to whether it belongs among the things that are or among the things that are not, and then what its nature is. That it either does not exist at all, or barely and dimly, one might suspect from the following. Part of it has been and is not; part is going to be and is not yet. And both infinite time and time taken in any given case are composed out of these. But what is composed out of things that are not would seem to be incapable of sharing in substance.
41| Besides this, of everything divisible, if it exists, it is necessary, when it exists, that either all its parts exist or some of them. But of time, though it is divisible, part has been and part is going to be, and none of it exists. The now is not a part; for a part measures the whole, and the whole must be composed out of its parts — but time does not seem to be composed out of nows. Further, it is not easy to see whether the now, which appears to mark the boundary between the past and the future, always remains one and the same, or is always different. For if it is always different and different, and no two of the different parts within time exist together at once (except where one does not include the other, but is included by it, as the lesser time is included by the greater), then the now, since it does not exist now but existed before, must have perished at some point, and the nows will not exist together with one another — the earlier one must always have perished. Now it cannot have perished in itself, because it existed then; but it is not possible for the earlier now to have perished in another, later now. For let it be granted that it is impossible for nows to be next to one another, just as a point cannot be next to a point. If, then, it has not perished in the next now but in some other one, it would exist at once together with the nows in between, which are infinite in number —
42| but this is impossible. But then again, neither is it possible for it to remain always the same; for nothing divisible and finite has a single limit, whether it is continuous in one direction or in several — but the now is a limit, and it is possible to take a finite stretch of time. Further, if being simultaneous in time, and being neither earlier nor later, consists in being in one and the same now, then, if the things that happened ten thousand years ago and the things happening today are both in this now, they would be simultaneous with each other, and nothing would be earlier or later than anything else.
43| Let this many puzzles, then, be raised about the attributes belonging to time. But what time is, and what its nature is, is equally unclear both from the traditional accounts and from the discussions we have just gone through. Some say it is the motion of the whole, others that it is the sphere itself. Yet a part of the revolution too is some amount of time, but it is not a revolution; for what is taken is a part of the revolution, not the revolution. Further, if there were several heavens, the motion of any one of them would equally be time, so that there would be many times at once. The sphere of the whole seemed to those who made this claim to be time because all things are both in time and in the sphere of the whole; but the claim is too naive to be worth examining for its impossibilities. Since time seems above all to be motion and a kind of change, this is what we must examine. Now the change and motion of each thing is only in the thing that is changing, or wherever the very thing that is moving and changing happens to be; but time is alike everywhere and present with everything. Further, change can be faster or slower, but time cannot; for the slow and the fast are defined by time — the fast being what moves a great deal in a little time, the slow what moves a little in a great deal of time. But time is not defined by time, neither by being some quantity of it nor some quality of it. That time, then, is not motion is clear; and let it make no difference to us for the present whether we say motion or change.
44| But then again, it does not exist without change either; for whenever we ourselves undergo no change in our thinking, or fail to notice that we are changing, no time seems to us to have passed — just as it does not seem to have passed, either, to those who are said in legend to sleep among the heroes in Sardinia, when they wake up. For they join the earlier now to the later now and make them one, cutting out the interval because they did not perceive it. So then, just as there would be no time if the now were not different each time but were the same and one, so too, since it escapes notice that it is different, the interval does not seem to be time. If, then, it happens to us that we do not think time has passed just when we mark off no change, but the soul appears to remain in one undivided state, while whenever we perceive and mark a change off, then we say time has passed, it is clear that time does not exist without motion and change. That time, then, is neither motion nor exists without motion, is clear. But since we are inquiring what time is, we must take this as our starting point: what feature of motion it is. For we perceive motion and time together; even if it is dark and we are affected by nothing through the body, but some motion is present in the soul, at once some time too seems to have passed along with it. And moreover, whenever some time seems to have passed, at the same time some motion too seems to have occurred. So time is either motion or something belonging to motion. Since, then, it is not motion, it must be something belonging to motion.
45| Since what is moved moves from something to something, and every magnitude is continuous, motion follows magnitude; for because the magnitude is continuous, motion too is continuous, and because of motion, time is continuous; for time is always thought to have become as great as the motion. Now the before and after is first of all in place. Here it is by position; but since the before and after is in magnitude, the before and after must also be in motion, corresponding to what holds there. But indeed the before and after is also in time, because each of them always follows the other. Now the before and after, in motion, is at any given time motion, yet its being is something different, and not motion. But indeed we also come to know time when we mark off motion, marking it off by the before and after; and we say time has elapsed when we perceive the before and after in motion. We mark them off by taking them as one thing and then another, with something else between them; for when we think of the extremes as different from the middle, and the soul pronounces the two 'nows' — one before, one after — then we say this is time too; for what is marked off by the 'now' is held to be time, and let this be assumed. So whenever we perceive the 'now' as one, and not either as before and after in the motion, or as the same thing but belonging to some before and after, no time seems to have elapsed at all, because no motion has either. But whenever we perceive the before and after, then we speak of time; for this is what time is: a number of motion with respect to before and after.
46| Time, then, is not motion, but motion in so far as it admits of number. Here is a sign of this: we judge more and less by number, but more and less motion by time; time, then, is a kind of number. But since number is spoken of in two ways (for we call both what is counted — the countable — a number, and also that with which we count), time is what is counted, and not that with which we count. And that with which we count is different from what is counted. And just as motion is always different and different again, so too is time (though the whole of time taken together is the same; for the 'now' is the same as whatever it once was — though its being is different — and the 'now' marks off time, as before and after). The 'now' is in one sense the same, in another sense not the same; for in so far as it is in one thing and then another, it is different (and this was what it was for it to be a 'now'), but in so far as it is whatever it is at any given time, it is the same. For, as was said, motion follows magnitude, and time follows motion, as we say; and likewise the moving thing follows the point — by means of which we come to know the motion, and the before and after in it.
47| This — whatever it is at a given time — is the same thing (for it is a point, or a stone, or some other such thing), but different in account, just as the sophists take it that Coriscus being in the Lyceum is different from Coriscus being in the marketplace. And this too is different by being now in one place, now in another. The 'now' follows the moving thing, just as time follows motion (for it is by the moving thing that we come to know the before and after in motion, and in so far as the before and after is countable, the 'now' exists). So here too, whatever the 'now' is at a given time is the same (for what it is at a given time is the before and after in motion), but its being is different — for it is in so far as the before and after is countable that the 'now' exists. And this is the most knowable thing; for motion too is known through what is moved, and locomotion through what is carried along — for what is carried along is a 'this', whereas motion is not. So the 'now' is in one sense always the same, in another sense not the same; for so too is what is carried along.
48| It is also clear that if time did not exist, the 'now' would not exist, and if the 'now' did not exist, time would not exist. For just as the thing carried along and its locomotion go together, so too do the number of the thing carried along and the number of the locomotion. For time is the number of the locomotion, and the 'now' is like the thing carried along — as it were, a unit of number. And time is continuous by means of the 'now', and is divided at the 'now'; for this too follows the locomotion and the thing carried along. For motion and locomotion are one by reference to the thing carried along, because it is one (not one in the sense of whatever it is at a given moment — for it could be interrupted — but one in account); and this marks off the before and after of the motion. And this too corresponds, in a way, to the point; for the point both makes the length continuous and marks it off — for it is the beginning of one part and the end of another. But when one takes it this way, treating the one point as two, a halt is necessary, if the same point is to be both beginning and end; whereas the 'now', because what is carried along is always in motion, is always different. So time is a number, not in the sense that belongs to the same point, because it is both beginning and end, but rather in the sense that belongs to the extremities of a line — and not in the sense that belongs to its parts, both for the reason stated (for one will be treating the middle point as two, so that a state of rest will result), and, further, it is clear that the 'now' is no part of time, nor is the division a part of the motion, just as the point is no part of the line;
49| rather, the two lines are parts of the one line. So in so far as the 'now' is a limit, it is not time, but is incidental to it; but in so far as it counts, it is a number. For limits belong only to that of which they are the limits, but a number — say, the ten of these horses — belongs elsewhere too. That time, then, is a number of motion with respect to before and after, and that it is continuous (since it belongs to something continuous), is clear. The smallest number, without qualification, is two; but a number of a particular kind exists in one sense, and in another sense does not — for instance, the smallest number of a line, in point of plurality, is two, or one, but in point of magnitude there is no smallest; for every line is always divisible. So it is likewise with time: the smallest in point of number is one, or two, but in point of magnitude there is none. It is also clear that time is not called fast or slow, but much and little, and long and short. For in so far as it is continuous, it is long and short; in so far as it is a number, it is much and little. But it is not fast or slow; for no number by which we count is fast or slow either.
50| And it is the same everywhere at once; but in respect of before and after it is not the same, because the change too is one when present, but the change that has occurred and the one to come are different. Time is a number, not that with which we count but that which is counted, and this — the before and after — always turns out different; for the 'nows' are different. The number of a hundred horses and the number of a hundred men is one and the same number, but the things of which it is the number are different — the horses are different from the men. Further, just as it is possible for a motion to be the same and one again and again, so too with time — for instance, a year, or a spring, or an autumn. Not
51| Not only do we measure motion by time, but also time by motion, because each is defined by the other: for time defines motion, being its number, and motion defines time. And we speak of much or little time by measuring it with motion, just as we measure a number by what is counted, for example the number of horses by one horse. For by number we come to know the multitude of horses, and again by one horse we come to know the number of horses itself. It is the same with time and motion: we measure motion by time, and time by motion. And this happens reasonably enough, for motion follows magnitude, and time follows motion, in that all three are quantities, continuous, and divisible: motion has these features because magnitude is of this sort, and time has them because of motion. And we measure magnitude by motion, and motion by magnitude: for we say the road is long if the journey is long, and the journey is long if the road is long; and likewise the time is long if the motion is long, and the motion is long if the time is long.
52| Since time is a measure of motion and of being in motion, and it measures motion by marking off some motion that will measure out the whole (just as a cubit measures length by marking off some magnitude that will measure out the whole), and for motion, being in time is being measured by time, both itself and its being (for time measures at once the motion and the being of the motion, and this is what being in time is for it: that its being is measured) — clearly for other things too this is what being in time is: that their being is measured by time. For being in time is one of two things: one, existing at the time when time exists; the other, as we say of some things that they are in a number. This signifies either that a thing is a part of a number and an attribute of it, and in general something belonging to the number, or that there is a number of it. Since time is a number, the now and the before and all such things are in time in the way a unit or the odd and the even are in number (for the latter are something belonging to number, and the former something belonging to time);
53| but things are in time as in a number. And if this is so, they are contained by time just as things in a number are contained by number, and things in place are contained by place. It is also clear that being in time is not the same as existing when time exists, any more than being in motion or being in place is existing when motion and place exist. For if being in something worked this way, all things would be in anything whatever, and the heaven would be in a grain of millet; for when the millet exists, the heaven also exists. But this is merely coincidental, whereas the other follows of necessity: for whatever is in time, there must be some time when it too exists, and for whatever is in motion, there must then be motion. Since being in time is like being in a number,
54| a time will be found greater than anything that is in time. Hence everything that is in time must necessarily be contained by time, just as everything else that is in something is contained by it — for example, things in place are contained by place. And a thing is indeed affected by time, just as we habitually say that time wastes things away, and that all things grow old through time, and that a thing is forgotten because of time — but we never say it has learned because of time, or become young or beautiful because of time. For time is in its own right a cause of decay rather than of anything else, since it is the number of motion, and motion displaces what belongs to a thing. So it is clear that things that always are, insofar as they always are, are not in time: for they are not contained by time, nor is their being measured by time. A sign of this is that they are not affected by time at all, as things not in time are. Since time is a measure of motion, it will also be a measure of rest, for all rest is in time. For it is not the case that, just as what is in motion must be moving, so too what is in time must be moving; for time is not motion but the number of motion, and what is at rest can also fall within the number of motion.
55| For not everything unmoved is at rest, but only what is deprived of motion while naturally fitted to move, as has been said earlier. Being in a number is there being some number belonging to the thing, and its being measured by the number it is in — so that if it is in time, it is measured by time. Time will measure what is moving and what is at rest, insofar as one is moving and the other at rest: for it will measure their motion and their rest, how much each is. So what is moving will not, without qualification, be measurable by time simply insofar as it is some quantity, but insofar as its motion is a quantity. So whatever neither moves nor rests is not in time: for being in time is being measured by time, and time is a measure of motion and rest. It is clear, then, that not everything that is not will be in
56| time — for example, whatever cannot be otherwise, such as the diagonal's being commensurable with the side. For in general, if time is in its own right a measure of motion, and of other things only incidentally, it is clear that for all the things whose being it measures, their being will consist in resting or moving. So whatever is perishable and subject to coming-to-be, and in general at one time is and at another is not, must necessarily be in time (for there is some greater time, which will exceed both their being and whatever measures their substance). And among things that are not, whatever time contains: some were, as Homer once was; others will be, as something among things to come — depending on which direction it contains them; and if in both directions, then both. But whatever it does not contain in either direction neither was nor is nor will be. Such are those among the things that are not whose opposites always are — for example, the diagonal's being incommensurable always is, and this will not be in time. Nor, then, will its being commensurable be in time either; hence it always is not, because it is contrary to what always is. But whatever has a contrary that does not always exist can both be and not be, and there is coming-to-be and passing-away of it.
57| The now is a continuity of time, as was said, for it holds together the time that has passed and the time to come, and it is a limit of time: it is the beginning of one and the end of the other. But this is not evident in the way it is with a point that stays fixed. It divides potentially. And insofar as it is this, the now is always different; but insofar as it binds together, it is always the same — as with mathematical lines (for the point is not always the same to the understanding: as one divides, it is one point and then another; but insofar as it is one, it is the same throughout) — so too the now: in one respect it is a division of time potentially, in another it is the limit of both parts and their unity. The division and the union are the same thing and in the same respect, but their being is not the same. This, then, is one way the now is spoken of; another is when the time belonging to it is near. He will arrive now, meaning he will arrive today; he has arrived now, meaning he came today. But the events at Troy did not happen now, nor did the flood happen now — and yet time is continuous down to them, only they are not near. 'At some time' is a time marked off in relation to the earlier now, for example: Troy was taken at some time, and there will at some time be a flood.
58| For it must be bounded in relation to the now. There will, then, be some determinate time from this point to that one, and there was also a determinate time stretching into the past. But if there is no time of which it is not the case that it exists at some point, then all time would be finite. Will time, then, give out? Or will it not, since motion always exists? Is it, then, a different time, or the same time occurring many times over? Clearly time is however motion is: for if the motion is one and the same at some point, time too will be one and the same, but if not, it will not be. And since the now is both an end and a beginning of time — not of the same stretch of time, however, but an end of the time that has passed and a beginning of the time to come — time would be always at once at a beginning and at an end, the way a circle has, in a sense, the convex and the concave in the same point. And this is why time is thought to be always different: for the now is not the beginning and end of the same stretch, since then opposite things would hold at once and in the same respect. And so time will not give out; for it is always at a beginning. And 'just now' is what is close to the present
59| now — an indivisible part of the time to come (When are you walking? 'Just now,' because the time in which one is about to walk is near) — and also the part of past time not far from the now (When are you walking? 'I have just now walked'). But we do not say that Troy has just now been captured, because that is too far from the now. And 'lately' is the part of the past close to the present now. When did you come? 'Lately,' if the time is close to the present now. But 'long ago' refers to what is far off. And 'suddenly' is what has departed from its former state in an imperceptible time, on account of its smallness; and every change is by nature apt to make things depart from their former state. Now everything comes to be and perishes in time; and for this reason some called it the wisest thing, while the Pythagorean Paron called it the most ignorant, on the ground that people also forget in it — and he speaks more correctly. It is clear, then, that time will in its own right be a cause of perishing rather than of coming to be, as was said before as well (for change, in its own right, is apt to make things depart from their former state), but a cause of coming to be, and of being, only accidentally. A sufficient sign of this is that nothing comes to be without itself being in some way moved and acting, whereas a thing perishes even without being moved at all. And this is the kind of perishing we are most accustomed to call destruction by time. Not that time itself brings this about, all the same; rather, it merely happens that this change too takes place in time. We have now said, then, that time exists, and what it is, and in how many senses 'the now' is spoken of, and what 'at some time,' 'just now,' 'lately,' 'long ago,' and 'suddenly' are.
60| Now that these points have been settled for us in this way, it is clear that every change and everything that moves is in time. For quicker and slower hold with respect to every change (in all cases this is how it appears); and I call that motion quicker which, moving over the same interval and with a uniform motion, changes into the underlying subject earlier than another (for example in locomotion, if both move along the circular path, or both along the straight one; and likewise in the other cases as well). But surely the 'before' is in time; for we speak of 'before' and 'after' in terms of distance from the now, and the now is the boundary between the time that has passed and the time to come. So then, since the nows are in time, the before and after will also be in time; for wherever the now is, there too is the distance from the now. (But 'before' is spoken of in opposite ways with respect to past time and to future time: for in the past we call 'before' what is farther from the now and 'after' what is nearer, whereas in the future we call 'before' what is nearer and 'after' what is farther.) So then, since the before is in time, and the before accompanies every motion, it is clear that every change and every motion is in time.
61| It is also worth examining how time is related to the soul, and why time is thought to exist in everything — on earth, and in the sea, and in the heaven alike. Is it because time is some affection or state of motion, being indeed a number, and all these things are movable (for they are all in place), and time and motion exist together, both with respect to potentiality and with respect to actuality? One might raise the puzzle whether, if soul did not exist, time would exist or not. For if it is impossible for there to be something that will count, it is also impossible for there to be something countable, so that it is clear that there would then be no number either; for a number is either what has been counted or what is countable. And if nothing else is by nature capable of counting except soul, and the intellect of soul, then it is impossible for time to exist if soul does not exist — except perhaps for that underlying thing of which time is the attribute, whenever it exists, that is, if it is possible for motion to exist without soul. For the before and after are in motion, and time is these insofar as they are countable. One might also raise the puzzle
62| as to what sort of motion time is the number of. Or is it of any sort whatever? For a thing comes to be in time, and perishes, and grows, and is altered, and is carried along; so then, insofar as there is motion, in that respect there is, for each motion, a number. Hence time is, without qualification, the number of continuous motion, not of any particular motion. But it is possible that at the same time something else too has been moved, of which there would likewise be a number for each of the two motions. Is there, then, a different time, and would there at once be two equal times? Or not? For time that is equal and simultaneous is one and the same time; but even times that are not simultaneous are the same in kind. For example, if there were dogs, and there were horses, and each group were seven, the number is the same. So too, of motions completed at the same time, the time is the same, even though one may be fast and the other not, and one may be locomotion and the other alteration; nevertheless the time is the same for the alteration and for the locomotion, provided it is equal and simultaneous. And for this reason the motions are different and separate from one another, but the time is everywhere the same, because the number too is one and the same everywhere, being the number of things that are equal and simultaneous. And since there is locomotion,
63| and among locomotion, circular motion, and each thing is counted by some one thing akin to it — units by a unit, horses by a horse — so too time is counted by some determinate time, and, as we said, time is measured by motion and motion is measured by time (and this means that both the quantity of the motion and the quantity of the time are measured by the determinate motion that occupies the time). If, then, among things of the same kind the first is the measure, uniform circular motion is the measure most of all, because its number is the most familiar. Now alteration, and growth, and coming to be are not uniform, but locomotion is. This is why time is also thought to be the motion of the sphere, because the other motions are measured by this one, and time is measured by this motion. And this is also why the customary saying arises: for people say that human affairs form a circle, and so too do the affairs of the other things that have natural motion and coming to be and perishing. This is because all these things are determined by time, and take their end and their beginning as if in accordance with some cycle. For time itself too is thought to be a kind of circle; and this in turn is thought to be so because time is the measure of this sort of locomotion and is itself measured by this sort of locomotion. So that to say that the things that come to be form a circle is to say that there is a kind of circle of time; and this is because it is measured by circular locomotion. For beyond the measure, nothing else is disclosed about the thing measured, except that the whole is a number of measures.