Lecture 6 — The definition of place

It will now be plain from these considerations what place is. There are just four things of which place must be one: the form, or the matter, or some sort of extension between the bounding surfaces of the containing body, or this boundary itself if it contains no extension over and above the bulk of the body that comes to be in it.

Three of these it obviously cannot be.

The form is supposed to be place because it surrounds, for the extremities of what contains and of what is contained are coincident.

Both the form and the place, it is true, are boundaries, but not of the same thing: the form is the boundary of the thing, while the place is the boundary of the body that contains it.

The extension between the extremities is thought to be something, because what is contained and separate may often be changed while the container remains the same (as water may be poured from a vessel)—the assumption being that the extension is something over and above the body displaced.

But there is no such extension. One of the bodies that change places and are naturally capable of being in contact with the container falls in whichever it may chance to be.

If there were an extension that were such as to exist independently and be permanent, there would be an infinity of places in the same thing.

For when the water and the air change places, all the portions of the two together will play the same part in the whole that was previously played by all the water in the vessel.

At the same time, the place too will be undergoing change, such that there will be another place that is the place of the place, and many places will be coincident.

There is not a different place of the part, in which it is moved, when the whole vessel changes its place, but it is always the same.

For it is in the place where they are that the air and the water (or the parts of the water) succeed each other,

not in that place in which they come to be, which is part of the place that is the place of the whole heavens.

The matter, too, might seem to be place, at least if we consider it in what is at rest and is thus separate but in continuity. For just as in change of quality there is something that was formerly black and is now white, or formerly soft and now hard—this is just why we say that the matter exists—so place, because it presents a similar phenomenon, is thought to exist, but in the one case, we say so because what is now water was previously air, while in the other because where water is now, there was air previously.

But the matter, as we said before, is neither separable from the thing nor contains it, while place has both characteristics.

Well, then, if place is none of the three—neither the form nor the matter nor an extension that is always there, different from and over and above the extension of the thing that is displaced—place necessarily is the one of the four which is left, namely, the boundary of the containing body at which it is in contact with the contained body. (By “the contained body” is meant what can be moved by way of locomotion.)

Place is thought to be something important and hard to grasp, both because the matter and the form present themselves along with it and because the displacement of the body that is moved takes place in a stationary container, for it seems possible that there should be an interval that is other than the bodies that are moved.

The air, which is thought to be incorporeal, also contributes something to the belief: it is not only the boundaries of the vessel that seem to be place, but also what is between them, regarded as empty.

In fact, just as the vessel is a transportable place, so place is a non-portable vessel. So, when what is within a thing that is moved is moved and changes its place, like a boat on a river, what contains plays the part of a vessel rather than that of place.

Place, on the other hand, is rather what wants to be immobile, so it is rather the whole river that is place, for as a whole, it is immobile.

Hence, we conclude that the immobile boundary of that which contains first is place.

This explains why the middle of the heavens and the boundary of circular change of place as to us is seen as “up” and “down” in the strict and fullest sense for all men. For the one is always at rest, while the inner side of the rotating body remains in the same way.

Hence, since the light is what is naturally carried up, and the heavy what is carried down, the boundary that contains in the direction of the middle of the universe and the middle itself are down, and that which contains in the direction of the outermost part of the universe and the outermost part itself are up.

For this reason, too, place is thought to be a kind of surface and, as it were, a vessel, that is, a container of the thing.

Further, place is coincident with the thing, for boundaries are coincident with the bounded.

455. After setting out the preliminary notions required for the search of the definition of place, the Philosopher now begins his search for the definition.

About this, he does three things:

first, he looks into each part of the definition;

second, he concludes the definition, at hence, we conclude (212a20; [470]);

third, he shows that it is a good definition, at this explains why (212a21; [471]).

As to the first, he does two things:

first, he searches for the genus of place;

second, for the differentia that will complete the definition, at place is thought to be (212a7; [467]).

In searching for the genus of place, he divides.

In connection with this, he does three things:

first, he gives the division;

second, he excludes three members of the division, at three of these (211b9; [457]);

third, he argues for the fourth member, at well, then, if place (212a2; [466]).

456. He says first (211b5) that, from the previous discussion, the nature of place may already be clear. For it seems that, according to what is ordinarily said of place, it is one of four things: matter, or form, or the space between and within the boundaries of the container; or, if there is no space within the boundaries of the container that has its own dimensions over and above the dimensions of the body existing within the confines of the container, then it will be necessary to posit a fourth possibility, namely, that place is the boundary of the containing body.

457. Then, at three of these (211b9), he excludes three members of this division.

First, he proposes what he intends, saying that it is clear from what follows that place is not any of these three.

Second, he pursues his intention, at the form is supposed (211b10; [458]).

And he says, first, that it is not form;

second, that it is not space, at the extension between (211b14; [460]);

third, that it is not matter, at the matter, too (211b29; [464]).

458. In regard to the first, he does two things.

First (211b10), he sets down why form seems to be place: it is because form is a container, and this seems to be a property of place.

Now, the boundaries of the containing body and those of the contained are together, since the container and the contained are contiguous.

Thus, it does not seem that the containing boundary, which is place, is separate from that of the body contained. Consequently, there does not seem to be any difference between place and form.

459. Second, at both the form and the place (211b12), he shows that form is not place. For although place and form are alike in that each is a kind of boundary, nevertheless they are not the boundary of one and the same thing: form is the boundary of the body of which it is the form, while place is not a boundary of the body of which it is the place, but of the body containing it. So, although the boundaries of the container and of the contained are together, they are not identical.

460. Then, at the extension between (211b14), he takes up the question of space.

First, he sets down why space seems to be place;

second, he shows that it is not place, at but there is no such extension (211b18; [461]).

He first says that, frequently, a body contained by place and distinct from it is changed from one place to another, and any number of bodies can succeed into its original place (but always in such a way that the container remains immobile) in the way that water goes out of a vessel.

For this reason, it seems that place is some middle space between the boundaries of the containing body, as though there were something there besides the body moved from one place to another. For if nothing were there besides the contained body, it would follow either that place is not distinct from the thing in place or that what exists within the confines of the container’s boundaries cannot be place.

Now, just as place must be something over and above the contained body, so it must be something other than the containing body, due to the fact that place remains immobile, while the containing body and everything in it can be changed about. But, in addition to the containing body and the contained body, there is nothing present except the dimensions of space, which exist in no body. Consequently, because place is immobile, it seems that space is place.

461. Then, at but there is no such extension (211b18), he shows that space is not place by two arguments.

As to the first of these, he states that it is not true that there is anything within the confines of the containing body other than the contained body that is transferred from place to place. Rather, within the confines of the containing body, there happens a body of some kind, having, nevertheless, the following two characteristics: that it be a mobile body, and be naturally apt to touch the containing body. But, if, in addition to the dimensions of the contained body, there were present a space that always remained in the same place, the embarrassing conclusion would follow that there would be infinite places together. The reason is that water and air have their own dimensions, and so does each body, and each part of a body. Now, all these parts will do the same thing in the whole body that the whole water does in a vessel.

According to those who hold the opinion that space is place, when the entire water is in the vessel, there are present, in addition to the dimensions of the water, also other dimensions of space.

Now, every part of a whole is contained by the whole as a thing in place is contained by a vessel: the only difference being that the part is not separated from the whole, but the thing in a place is separated from place.

If, therefore, a part be actually separated within the whole, it will follow that, in addition to the dimensions of the part, also other dimensions of the containing whole will be present. But it cannot be said that such division would make new dimensions to exist, for division does not cause dimension; rather, it divides dimension already existing.

Therefore, before that part was divided in the whole, there were present other proper dimensions of the part in addition to the whole’s dimensions that also penetrate that part. Now, there will be as many distinct sets of dimensions, some of which interpenetrate others, as there are parts obtainable by division of the whole, which parts are so divided that one contains another.

But it is possible in a continuous whole to obtain infinitely many parts that contain other parts, because a continuum can be divided to infinity. Consequently, we should have infinite dimensions mutually penetrating themselves. If, therefore, the containing body’s dimensions, penetrating the thing in place, are place, it follows that there are infinite places together—which is impossible.

462. Then, at at the same time (211b23), he gives a second reason, which is the following. If the dimensions of the space that is between the boundaries of the containing body are place, it follows that place can be transported. For it is clear that, when a body is transported, such as a jug, the space within the jug is transported, since that space can never be except where the jug is. Now, whatever is transported to another place is penetrated (according to those who hold the doctrine of space as place) by the dimensions of the space into which it is transported. Therefore, it follows that other dimensions enter the dimensions of the jug’s space; consequently, there would be another place of place, and many places would be existing together.

463. This unacceptable consequence arises from positing one place for the contained body (for example, the water) and another place for the vessel (for example, the jug). For according to the opinion we are discussing, the place of the water is the space within the boundaries of the jug, while the place of the whole jug is the space within the boundaries of the body containing the jug. We, however, do not assign a special place for the part in which the part moves, as distinct from the whole, when the entire vessel is transported (by part, he means the body contained in the vessel, as the water contained in the jug), for according to Aristotle, the water is moved per accidens when the vessel is transported, and it changes place only inasmuch as the jug changes its place.

Hence, it is not necessary that the place into which the transfer is made be the place of the part per se, but only inasmuch as it becomes the place of the jug. But, according to those who hold the opinion about space as place, it follows that the new place would belong per se both to water and to the jug. Likewise, space would be transported and would have a place per se, and not only per accidens.

Now, although the containing body is sometimes moved, it does not follow according to the opinion of Aristotle that the place is moved, or that there is a place of a place. For it does indeed happen that a containing body, in which something is contained, is sometimes moved, as are air or water or certain parts of the water. For example, if a boat is in a river, the parts of the water that surround the boat from below are in motion, but the boat’s place is not moved. Hence, he adds, not in that place in which they come to be; that is, that in which things come to be as in a place is not moved.

How this is true he makes clear by adding, which is a part of the place that is the place of the whole heavens. For although this container be moved inasmuch as it is this body, yet in regard to its relation to the whole body of the heavens, it is not moved: the body that succeeds it has the same order or position in relation to the whole heavens as had the body that previously flowed on. This, therefore, is what he says: although the water or the air be moved, the place is not, considered precisely as a certain part of the place of the whole heavens and as having a definite position in the universe.

464. Then, at the matter, too (211b29), he continues by considering matter.

First, he shows why matter seems to be place;

second, that it is not place, at but the matter (211b36; [465]).

He first says, therefore, that matter appears to be place if one should consider the changing of the bodies that succeed each other in the same place, as this occurs in some one subject that is at rest in a place, with attention being paid not to the fact that place is separate, but only to the fact that the change is occurring in one and the same continuum.

For some continuous body is at rest according to place when it is being altered in quality, now white or black, or now hard, while previously soft. Yet it remains one and the same in number. And, on account of this changing of forms in the subject, we say that matter is something that remains one whole when change takes place with respect to forms. Because of this, place seems to be something, for in it, as remaining, different bodies succeed each other. Nevertheless, we use different terminology when referring to these two cases:

to designate matter or the subject, we say, what is now water was previously air;

to designate unity in place, we say, where water is now, there was air previously.

465. Then, at but the matter (211b36), he shows that matter is not place, for as we said above, (Lect. 3, n. 429.) matter is not separated from the thing of which it is the matter, nor does it contain the latter, both of which characteristics belong to place. Place, therefore, is not matter.

466. Then, at well, then, if place (212a2), having eliminated the first three members, he argues for the fourth. And he says that, since place is not any of these three—form, matter, or some space other than the internal distances of the things in place—it must be the fourth of the above named: the boundary of the containing body. And lest anyone understand that the thing contained or in place is some middle space, he adds that the contained body is what is apt to be moved in respect to change of place.

467. Then, at place is thought to be (212a7), he tracks down the specific difference of place, namely, that it is immobile.

In regard to this, he does two things:

first, he shows that an error arose from improperly considering this difference;

second, he shows how we must understand the immobility of place, at in fact, just as the vessel (212a14; [468]).

He says, therefore, that it is a large undertaking and a difficult one to understand what place is, both because some have thought it is matter or form—both of which involve lofty speculation, as was said above (Lect. 3, n. 428.)—and because the change that occurs when things change place occurs in something both at rest and containing. Now, since nothing seems to be containing and immobile except space, it seems that place is a sort of middle space distinct from the magnitudes that are moved in respect to place. And the fact that air seems to be incorporeal helps to make this opinion credible, for where air is, there appears to be no body, but a certain empty space. Thus place seems to be not only the boundaries of a vessel, but something between the boundaries as a vacuum or void.

468. Then, at in fact, just as the vessel (212a14), in order to exclude this stated opinion, he shows how we must understand the immobility of place. And he says that a vessel and place are seen to differ in that a vessel can be transported but place cannot. Hence, just as a vessel can be called “a transportable place,” so place can be called “an immobile vessel.” Therefore, when something is being moved in a body that is in motion, as a ship in a river, we speak of that in which it is being moved as a vessel rather than of a containing place, because place wants to be immobile; that is, it is of the very nature and aptitude of place to be immobile. On this account, it is better to speak of the whole river as being the place of the ship, because the river as a whole is immobile. Thus, the whole river inasmuch as it is immobile is the common place.

However, since proper place is a part of common place, we must consider the proper place of the ship in flowing water—not the water inasmuch as it is flowing, but in its relation to the order or position that this flowing water has to the river as a whole. It is this order or position that remains constant while the water flows on. Therefore, although the water materially passes on, yet, insofar as it has the account of place—that is, insofar as it is considered as having a certain order and position with respect to the whole river—it does not change.

This also shows how we ought to consider how the boundaries of natural mobile bodies are place with respect to the entire spherical body of the heavens, which is fixed and immobile on account of the immobility of the center and of the poles. Therefore, although this part of air that contains, or this part of water, flows by and moves as this water, yet, insofar as this water has the account of place—namely, a position and order to the whole spherical body of the heavens—it always remains. This is like the same fire, remaining as to its form but, as to its matter, varying as wood is consumed and other wood added.

469. This removes an objection that could be lodged against positing place as the boundary of the container, for since the container is mobile, its boundary will also be mobile; consequently, a thing at rest will have diverse places. But this does not follow, because the boundary of the container is not place insofar as it is this surface of this particular mobile body, but by reason of the order or position it has in the immobile whole. From this, it is evident that the whole account of place in all containers is taken from the first container and locator, namely, the heavens.

470. Then, at hence, we conclude (212a20), he concludes from the foregoing the definition of place: place is the immobile boundary of that which contains first. He says first to designate proper place and exclude common place.

471. Then, at this explains why (212a21), he shows that the definition is well assigned, because the things said about place concur with this definition. And he gives three such things.

The first is that, since place is an immobile container, the middle of the heavens (namely, the center) is seen as down, and the boundary of circular change of place (that is, of the bodies moved in a circle, and the boundary as to us, namely, the surface of the sphere of the moon), is seen as up, and the middle as down. The middle or center is seen to be said most properly of all to be permanent, for the center of a sphere is always at rest. Now, in relation to us, that which is the boundary of the bodies moved in a circle, although it moves in a circle, nevertheless remains permanent insofar as it remains in the same way, that is, at the same distance from us.

Hence, since natural bodies are moved to their proper places, it follows that light bodies naturally move up and heavy bodies down—for both the middle and the containing boundary in the direction of the middle are called “down”; likewise, the boundary in the other sense, and what is in the direction of that boundary, are called “up.”

He uses this manner of speaking because it is the center that is the place of the earth, which is simply heavy, while toward the center, the place of water is found. In like manner, the place of fire, which is simply light, is the outermost, while the place of air is toward the outermost.

He gives the second reason at for this reason, too (212a28), saying that, because place is a boundary, place seems to be like a certain surface and like a containing vessel, but not like the space of the containing vessel.

He gives the third reason at further, place is coincident (212a29), when he says that, because place is a boundary, the place and the thing in place are together.

For the limits of the thing in place and the boundary of the container, which is place, are together (for the boundaries of things that touch are together). This also explains why place is equal to the thing in place: namely, because they are equated as to their boundaries.