(2) There is a difference between touching and being limited. The former is relative to something and is the touching of something (for everything that touches touches something), and further is an attribute of some one of the things which are limited. On the other hand, what is limited is not limited in relation to anything. Again, contact is not necessarily possible between any two things taken at random.
(3) To rely on mere thinking is absurd, for then the excess or defect is not in the thing but in the thought. (15) One might think that one of us is bigger than he is and magnify him ad infinitum. But it does not follow that he is bigger than the size we are, just because some one thinks he is, but only because he is the size he is. The thought is an accident.
(a) Time indeed and movement are infinite, and also thinking, (20) in the sense that each part that is taken passes in succession out of existence.
(b) Magnitude is not infinite either in the way of reduction or of magnification in thought.
This concludes my account of the way in which the infinite exists, and of the way in which it does not exist, and of what it is.
* * *
1 viii. 5.
2 Plato in the Timaeus (52 E, 57 E, 58 A) makes motion depend on inequality.
3 i. e. we can substitute ‘mover’ and ‘moved’ for ‘agent’ and ‘patient’ in the formulation of the hypothesis.
4 Cf. a18–20.
5 Aristotle’s general meaning is fairly plain. He is describing two constructions: in the one odd gnomons are placed round the one, in the other even gnomons are placed round the two.
6 Aristotle does not regard them as elements.
7 The reference is probably to Anaximander.
8 Cf. 203b 15–30.
BOOK IV
1 The physicist must have a knowledge of Place, too, as well as of the infinite—namely, whether there is such a thing or not, and the manner of its existence and what it is—both because all suppose that things which exist are somewhere (the non-existent is nowhere—where is the goat-stag or the sphinx?), (30) and because ‘motion’ in its most general and primary sense is change of place, which we call ‘locomotion’.
The question, what is place? presents many difficulties. An examination of all the relevant facts seems to lead to divergent conclusions. Moreover, we have inherited nothing from previous thinkers, (35) whether in the way of a statement of difficulties or of a solution.
The existence of place is held to be obvious from the fact of mutual replacement. [208b] Where water now is, there in turn, when the water has gone out as from a vessel, air is present. When therefore another body occupies this same place, the place is thought to be different from all the bodies which come to be in it and replace one another. (5) What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both.
Further, the typical locomotions of the elementary natural bodies—namely, fire, earth, and the like—show not only that place is something, (10) but also that it exerts a certain influence. Each is carried to its own place, if it is not hindered, the one up, the other down. Now these are regions or kinds of place—up and down and the rest of the six directions. Nor do such distinctions (up and down and right and left, (15) &c.) hold only in relation to us. To us they are not always the same but change with the direction in which we are turned: that is why the same thing may be both right and left, up and down, before and behind. But in nature each is distinct, taken apart by itself. It is not every chance direction which is ‘up’, (20) but where fire and what is light are carried; similarly, too, ‘down’ is not any chance direction but where what has weight and what is made of earth are carried—the implication being that these places do not differ merely in relative position, but also as possessing distinct potencies. This is made plain also by the objects studied by mathematics. Though they have no real place, they nevertheless, in respect of their position relatively to us, have a right and left as attributes ascribed to them only in consequence of their relative position, not having by nature these various characteristics. Again, (25) the theory that the void exists involves the existence of place: for one would define void as place bereft of body.
These considerations then would lead us to suppose that place is something distinct from bodies, and that every sensible body is in place. Hesiod too might be held to have given a correct account of it when he made chaos first. (30) At least he says:
First of all things came chaos to being, then broad-breasted earth, implying that things need to have space first, because he thought, with most people, that everything is somewhere and in place. If this is its nature, the potency of place must be a marvellous thing, (35) and take precedence of all other things. For that without which nothing else can exist, while it can exist without the others, must needs be first; for place does not pass out of existence when the things in it are annihilated. [209a]
True, but even if we suppose its existence settled, the question of its nature presents difficulty—whether it is some sort of ‘bulk’ of body or some entity other than that, for we must first determine its genus.
(1) Now it has three dimensions, (5) length, breadth, depth, the dimensions by which all body also is bounded. But the place cannot be body; for if it were there would be two bodies in the same place.
(2) Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same statement will apply to them: where the bounding planes of the water were, there in turn will be those of the air. But when we come to a point we cannot make a distinction between it and its place. (10) Hence if the place of a point is not different from the point, no more will that of any of the others be different, and place will not be something different from each of them.
(3) What in the world then are we to suppose place to be? If it has the sort of nature described, it cannot be an element or composed of elements, whether these be corporeal or incorporeal: for while it has size, (15) it has not body. But the elements of sensible bodies are bodies, while nothing that has size results from a combination of intelligible elements.
(4) Also we may ask: of what in things is space the cause? None of the four modes of causation can be ascribed to it. It is neither cause in the sense of the matter of existents (for nothing is composed of it), (20) nor as the form and definition of things, nor as end, nor does it move existents.
(5) Further, too, if it is itself an existent, where will it be? Zeno’s difficulty demands an explanation: for if everything that exists has a place, (25) place too will have a place, and so on ad infinitum.
(6) Again, just as every body is in place, so, too, every place has a body in it. What then shall we say about growing things? It follows from these premisses that their place must grow with them, if their place is neither less nor greater than they are.
By asking these questions, then, we must raise the whole problem about place—not only as to what it is, but even whether there is such a thing. (30)
2 We may distinguish generally between predicating B of A because it (A) is itself, and because it is something else; and particularly between place which is common and in which all bodies are, and the special place occupied primarily by each. I mean, for instance, that you are now in the heavens because you are in the air and it is in the heavens; and you are in the air because you are on the earth; and similarly on the earth because you are in this place which contains no more than you. (35)
Now if place is what primarily contains each body, it would be a limit, so that the place would be the form or shape of each body by which the magnitude or the matter of the magnitude is defined: for this is the limit of each body. [209b]
If, (5) then, we look at the question in this way the place of a thing is its form. But, if we regard the place as the extension of the magnitude, it is the matter. For this is different from the magnitude: it is what is contained and defined by the form, as by a bounding plane. Matter or the indeterminate is of this na
ture; when the boundary and attributes of a sphere are taken away, (10) nothing but the matter is left.
This is why Plato in the Timaeus1 says that matter and space are the same; for the ‘participant’ and space are identical. (It is true, indeed, that the account he gives there of the ‘participant’ is different from what he says in his so-called ‘unwritten teaching’.2 (15) Nevertheless, he did identify place and space.) I mention Plato because, while all hold place to be something, he alone tried to say what it is.
In view of these facts we should naturally expect to find difficulty in determining what place is, if indeed it is one of these two things, (20) matter or form. They demand a very close scrutiny, especially as it is not easy to recognize them apart.
But it is at any rate not difficult to see that place cannot be either of them. The form and the matter are not separate from the thing, whereas the place can be separated. As we pointed out,3 where air was, (25) water in turn comes to be, the one replacing the other; and similarly with other bodies. Hence the place of a thing is neither a part nor a state of it, but is separable from it. For place is supposed to be something like a vessel—the vessel being a transportable place. But the vessel is no part of the thing.
In so far then as it is separable from the thing, (30) it is not the form: qua containing, it is different from the matter.
Also it is held that what is anywhere is both itself something and that there is a different thing outside it.4 (Plato of course, if we may digress, ought to tell us why the form and the numbers are not in place, (35) if ‘what participates’ is place—whether what participates is the Great and the Small or the matter, as he called it in writing in the Timaeus.) [210a]
Further, how could a body be carried to its own place, if place was the matter or the form? It is impossible that what has no reference to motion or the distinction of up and down can be place. So place must be looked for among things which have these characteristics.
If the place is in the thing (it must be if it is either shape or matter) place will have a place: for both the form and the indeterminate undergo change and motion along with the thing, (5) and are not always in the same place, but are where the thing is. Hence the place will have a place.
Further, when water is produced from air, the place has been destroyed, for the resulting body is not in the same place. (10) What sort of destruction then is that?
This concludes my statement of the reasons why space must be something, and again of the difficulties that may be raised about its essential nature.
3 The next step we must take is to see in how many senses one thing is said to be ‘in’ another.
(1) As the finger is ‘in’ the hand and generally the part ‘in’ the whole. (15)
(2) As the whole is ‘in’ the parts: for there is no whole over and above the parts.
(3) As man is ‘in’ animal and generally species ‘in’ genus.
(4) As the genus is ‘in’ the species and generally the part of the specific form ‘in’ the definition of the specific form.
(5) As health is ‘in’ the hot and the cold and generally the form ‘in’ the matter. (20)
(6) As the affairs of Greece centre ‘in’ the king, and generally events centre ‘in’ their primary motive agent.
(7) As the existence of a thing centres ‘in’ its good and generally ‘in’ its end, i. e. ‘in that for the sake of which’ it exists.
(8) In the strictest sense of all, as a thing is ‘in’ a vessel, and generally ‘in’ place.
One might raise the question whether a thing can be in itself, (25) or whether nothing can be in itself—everything being either nowhere or in something else.
The question is ambiguous; we may mean the thing qua itself or qua something else.
When there are parts of a whole—the one that in which a thing is, the other the thing which is in it—the whole will be described as being in itself. For a thing is described in terms of its parts, as well as in terms of the thing as a whole, e. g. a man is said to be white because the visible surface of him is white, or to be scientific because his thinking faculty has been trained. The jar then will not be in itself and the wine will not be in itself. (30) But the jar of wine will: for the contents and the container are both parts of the same whole.
In this sense then, but not primarily, a thing can be in itself, namely, as ‘white’ is in body (for the visible surface is in body), and science is in the mind.
[210b] It is from these, which are ‘parts’ (in the sense at least of being ‘in’ the man), that the man is called white, &c. But the jar and the wine in separation are not parts of a whole, though together they are. So when there are parts, a thing will be in itself, as ‘white’ is in man because it is in body, and in body because it resides in the visible surface. (5) We cannot go further and say that it is in surface in virtue of something other than itself. (Yet it is not in itself: though these are in a way the same thing,) they differ in essence, each having a special nature and capacity, ‘surface’ and ‘white’.
Thus if we look at the matter inductively we do not find anything to be ‘in’ itself in any of the senses that have been distinguished; and it can be seen by argument that it is impossible. (10) For each of two things will have to be both, e. g. the jar will have to be both vessel and wine, and the wine both wine and jar, if it is possible for a thing to be in itself; so that, however true it might be that they were in each other, the jar will receive the wine in virtue not of its being wine but of the wine’s being wine, (15) and the wine will be in the jar in virtue not of its being a jar but of the jar’s being a jar. Now that they are different in respect of their essence is evident; for ‘that in which something is’ and ‘that which is in it’ would be differently defined.
Nor is it possible for a thing to be in itself even incidentally: for two things would be at the same time in the same thing. (20) The jar would be in itself—if a thing whose nature it is to receive can be in itself; and that which it receives, namely (if wine) wine, will be in it. Obviously then a thing cannot be in itself primarily.
Zeno’s problem—that if Place is something it must be in something—is not difficult to solve. There is nothing to prevent the first place from being ‘in’ something else—not indeed in that as ‘in’ place, (25) but as health is ‘in’ the hot as a positive determination of it or as the hot is ‘in’ body as an affection. So we escape the infinite regress.
Another thing is plain: since the vessel is no part of what is in it (what contains in the strict sense is different from what is contained), place could not be either the matter or the form of the thing contained, (30) but must be different—for the latter, both the matter and the shape, are parts of what is contained.
This then may serve as a critical statement of the difficulties involved.
4 What then after all is place? The answer to this question may be elucidated as follows.
Let us take for granted about it the various characteristics which are supposed correctly to belong to it essentially. We assume then—
(1) Place is what contains that of which it is the place.
(2) Place is no part of the thing. [211a]
(3) The immediate place of a thing is neither less nor greater than the thing.
(4) Place can be left behind by the thing and is separable.
In addition:
(5) All place admits of the distinction of up and down, and each of the bodies is naturally carried to its appropriate place and rests there, and this makes the place either up or down. (5)
Having laid these foundations, we must complete the theory. We ought to try to make our investigation such as will render an account of place, and will not only solve the difficulties connected with it, but will also show that the attributes supposed to belong to it do really belong to it, and further will make clear the cause of the trouble and of the difficulties about it. (10) Such is the most satisfactory kind of exposition.
First then we must understand that place w
ould not have been thought of, if there had not been a special kind of motion, namely that with respect to place. It is chiefly for this reason that we suppose the heaven also to be in place, because it is in constant movement. Of this kind of change there are two species—locomotion on the one hand and, (15) on the other, increase and diminution. For these too involve variation of place: what was then in this place has now in turn changed to what is larger or smaller.
Again, when we say a thing is ‘moved’, the predicate either (1) belongs to it actually, in virtue of its own nature, or (2) in virtue of something conjoined with it. In the latter case it may be either (a) something which by its own nature is capable of being moved, (20) e. g. the parts of the body or the nail in the ship, or (b) something which is not in itself capable of being moved, but is always moved through its conjunction with something else, as ‘whiteness’ or ‘science’. These have changed their place only because the subjects to which they belong do so.
We say that a thing is in the world, in the sense of in place, because it is in the air, and the air is in the world; and when we say it is in the air, (25) we do not mean it is in every part of the air, but that it is in the air because of the outer surface of the air which surrounds it; for if all the air were its place, the place of a thing would not be equal to the thing—which it is supposed to be, and which the primary place in which a thing is actually is.
When what surrounds, then, is not separate from the thing, (30) but is in continuity with it, the thing is said to be in what surrounds it, not in the sense of in place, but as a part in a whole. But when the thing is separate and in contact, it is immediately ‘in’ the inner surface of the surrounding body, and this surface is neither a part of what is in it nor yet greater than its extension, but equal to it; for the extremities of things which touch are coincident.
The Basic Works of Aristotle (Modern Library Classics) Page 39