LECTURE 6 (211 b 5-212 a 30)

THE DEFINITION OF PLACE

             455. Having set forth those things which are necessary to investigate the definition of place, he here investigates the definition of place.

             Concerning this he makes three points. First he investigates the parts of the definition. Secondly, where he says, 'Hence we conclude . . .' (212 a 20), he concludes to the definition. Thirdly, where he says, 'This explains why . . .' (212 a 22), he shows that the definition has been well established.

             Concerning the first part he makes two points. First he investigates the genus of place, and secondly the complementary differentia of its definition, where he says, 'Place is thought to be . . .' (212 a 7).

             Furthermore to investigate the genus of place he makes use of a certain division. Concerning this he makes three points. First he proposes the division. Secondly, where he says, 'Three of these . . .' (211 b 9), he rules out three members of this division. Thirdly, where he says, 'Well, then, if place . . .' (212 a 2), he concludes to the fourth.

             456. He says, therefore, first that what place is can now be made clear from what has been set forth.

             According to the things that are customarily said about place, it seems that place is one of four things: either the matter, or the form, or the space between the extremities of the container, or if, between the extremities of the container which has dimensions, there is no space outside of the magnitude of the body which is within the containing body, then it will be necessary to mention a fourth possibility, that is, that place is the extremities of the containing body.

             457. Next where he says, 'Three of these . . .' (211 b 9), he rules out three members of the given division.

             First he states his intention by saying that is clear through what follows that place is not one of the first three.

             Secondly, he carries out his intention, first in regard to form, where he says, 'The shape is supposed . . .' (211 b 10), secondly in regard to space, where he says, 'The extension between . . .' (211 b 13), and thirdly in regard to matter, where he says, 'The matter, too . . .' (211 b 30).

             458. Concerning the first part he makes two points. First he explains why form would seem to be place. For the form contains, and this seems to be proper to place. The extremities of the containing body and the contained body are together, for the container and that which is contained are contiguous to each other. Thus the containing terminus, which is place, does not seem to be separated from the terminus of the contained body. And thus it seems that place does not differ from form.

             459. Secondly, where he says, 'Both the shape and the place . . .' (211 b 11), he shows that form is not place.

             Although both place and form agree in that each of them is a certain terminus, nevertheless they are not termini of one and the same thing. Rather form is the terminus of the body of which it is the form, while place is not the terminus of the body of which it is the place, but of the body containing it. And although the termini of the container and of that which is contained are together, nevertheless they are not the same.

             460. Next where he says, 'The extension between . . .' (211 b 13), he treats space.

             First he explains why space seems to be place. Secondly, where he says, 'But there is no such extension' (211 b 16), he shows that space is not place.

             He says, therefore, first that a body contained by place, and divided from it, is frequently changed from place to place. And bodies reciprocally succeed each other in the same place, such that the container remains immobile, in the way in which water goes out of a vase. Because of this it seems that place is a certain intermediate space between the extremities of the containing body; as if there were something there other than the body which is moved from one place to another. For if there were not something there other than that body, it would follow either that place is not different from that which is located in place or that that which is an intermediate between the extremities of the container could not be place. Moreover just as place must be something other than the contained body, likewise it seems that place would have to be something other than the containing body, because place remains immobile, but the containing body and everything in it is subject to change. However, nothing other than the containing body and the contained body can be understood to be there except the dimensions of space existing in no body. Therefore since place is immobile, it seems that space is place.

             461. Next where he says, 'But there is no such extension' (211 b 16), he shows with two arguments that space is not place.

             In the first argument he says that it is not true that there is something there within the extremities of the containing body and other than the contained body, which is borne from place to place. Rather within the extremities of the containing body there is a body, whatever it happens to be, which is a mobile body and which is one of those things which are suitably constituted to touch the containing body. But if there could be some intermediate containing space, which is other than the dimensions of the contained body, and which always remains in the same place, then this inconsistency would follow--an infinite number of places would be together. This is so because since water or air or any body or any part of a body would have proper dimensions, then every part will do the same thing in the whole as the water as a whole does in the vase. According to the position of those who believe in space, while the water as a whole is in the vase, there are there other dimensions of space besides the dimensions of the water. However every part is contained by the whole as that which is located is contained by the vase. They differ only in that the part is not divided, while that which is located is divided. Therefore if a part is actually divided, it follows that other dimensions of the whole container are there besides the dimensions of the part.

             But it cannot be said that division makes some new dimensions to be there. For division does not cause dimension, rather it divides pre-existing dimension. Therefore before the part would be divided from the whole, there were other proper dimensions of the part besides the dimensions of the whole which pass into the parts. Therefore as many parts as are taken by division in some whole, such that one part contains another, so many dimensions had been distinct there from each other, certain of which passed into others. However, since a continuum is divided to infinity, this means that one takes in some continuous whole an infinity of parts which contain others. It follows, therefore, that there is an infinity of dimensions passing into each other. If, therefore, place is the dimensions of the containing body which pass into that which is located, then it follows that an infinity of places exist together, which is impossible.

             462. Next where he says, '. . . at the same time . . .' (211 b 23), he gives the second argument which is as follows.

             If the dimensions of the space which is between the extremities of the containing body are place, it follows that place would be changed. For it is clear that when a body, for example, a jar, is changed, the space which is between the extremities of the jar is changed, since the space is only where the jar is. Moreover according to their position everything which is changed to some place is penetrated by the dimensions of the space into which it is changed. It follows, therefore, that some other dimensions enter under the dimensions of the space of the jar. And thus there will be a place of place, and many places are together.

             463. Now this difficulty occurs because the place of the contained body, or water, is taken as different from the place of the vase or jar. For according to their opinion the place of the water is the space which is within the extremities of the jar, and the place of the whole jar is the space which is within the extremities of the body which contains the jar. But we do not say that the place of the part, in which the part is moved, is different, since the whole vase is moved in the same way (by 'part' here he means the body contained in the vase, as water is contained in the jar). For according to Aristotle, when the vase is moved, the water is moved per accidens, and it does not change its place except insofar as the jar changes its place. Hence it is not necessary that the place into which it goes is the place of the part per se, but only insofar as it is the place of the jar. But according to those who believe in space, it follows that this place corresponds per se to both the water and the jar. It also follows that space corresponds to them per se, and properly speaking space will be moved and will have place, and not just per accidens.

             Now although the containing body is sometimes moved, nevertheless it does not follow according to Aristotle's opinion that place is moved or that there is a place of place. For indeed it does happen that a containing body, in which something is contained, is moved, as air or water or some parts of water. For example, if a ship is on a river, the parts of the water which contain the ship from below are moved, but nevertheless the place is not moved. And he adds, 'sed non in quo fiunt loco', which means, 'but that in which things come to be as in a place does not move' (211 b 28).

             He explains how this is true when he adds, '. . . which is part of the place which is the place of the whole world' (211 b 29). For although this container is moved insofar as it is this body, nevertheless, considered according to the order which it has to the whole body of the world, it is not moved. For the other body which succeeds it has the same order and site in comparison to the whole world which the body which previously left had. He, therefore, says that although the water or air is moved, nevertheless the place, considered as a certain part of the place of the whole world having a determined site in the universe, is not moved.

             464. Next where he says, 'The matter, too . . .' (211 b 30), he treats matter.

             First he explains why matter seems to be place. Secondly, where he says, 'But the matter . . .' (212 a 1), he shows that matter is not place.

             He says, therefore, first that matter seems to be place if one considers the transmutation of bodies succeeding each other in the same place, in some one subject which is at rest in respect to place. Attention is not directed here to the fact that place is separated, but rather only to a transmutation in some one continuum. For when a body, which is a continuum and at rest in respect to place, is altered, then that which is one and the same in number is now white, then black, now soft, then hard. Because of this transmutation of forms in a subject, we say that matter is something which remains one when a transmutation of form occurs. And through similar evidence it seems that place is something. For diverse bodies succeed each other in a place which remains permanent.

             But we use a different way of speaking in each of these cases. For to designate matter or a subject we say that that which is now water formerly was air. But to designate the unity of place we say that where water now is, there formerly was air.

             465. Next where he says, 'But the matter . . .' (212 a 1), he shows that matter is not place. For, as was said above, matter is not divided from that of which it is the matter, nor does it contain it. But both of these characteristics belong to place. Therefore place is not matter.

             466. Next where he says, 'Well, then, if place . . .' (212 a 2), having ruled out three members, he concludes to the fourth. He says that, since place is not one of these three, that is, neither the form, nor the matter, nor the space which is other than the dimensions of that which is located, then it is necessary that place is the one member that remains of the four named above, that is, that place is the terminus of the containing body. And lest someone think that that which is contained or located is some intermediate space, he adds that the contained body is called that whose nature it is to be moved in respect to change of place.

             467. Next where he says, 'Place is thought to be . . .' (212 a 7), he investigates the differentia of place, that is, that it is immobile.

             Concerning this he makes two points. First he shows that a certain error about place arises if this differentia is not properly considered. Secondly, where he says, 'Just, in fact, as the vessel . . .' (212 a 14), he shows how the immobility of place must be understood.

             He says, therefore, first that to establish what place is is something important and difficult. One reason for this is that to some it seems that place is matter or form, which require the highest contemplation, as was said above. Another reason is that change in respect to place occurs in something which is at rest and which contains. Since, therefore, nothing seems to contain and to be immobile except space, it seems that place is a certain intermediate space which is different from the magnitudes which are moved in respect to place. The fact that air seems to be incorporeal contributes much to the credibility of this opinion. For where air is, there seems to be no body, but rather a certain spatial vacuum. And thus it seems that place not only is the terminus of the vase but also a certain medium, a vacuum as it were.

             468. Next where he says, 'Just, in fact, as the vessel . . .' (212 a 14), in order to exclude the above opinion, he explains how the immobility of place must be understood.

             He says that a vase and place seem to differ in that the vase is moved but place is not. Hence, as the vase can be called a movable place, likewise place can be called an immobile vase. Therefore, when something is moved in some body which is moved, as a ship in a river, he refers to that in which it is moved more as a vase than as a containing place. For place 'wishes to be immobile', that is, it is appropriate and natural to place for it to be immobile. Because of this it is better to say that the whole river is the place of the ship, for the whole river is immobile. Thus, therefore, the whole river, insofar as it is immobile, is a common place.

             However since proper place is part of common place, it is necessary to assign the proper place of the ship in the water of the river, insofar as it has an order to the whole river as immobile. Therefore the place of the ship is determined in the flowing water, not in respect to this water which flows, but in respect to the order or site which this flowing water has to the whole river. And indeed this order or site remains the same in the water which succeeds. Therefore, although the water flows by materially, nevertheless it does not change insofar as it has the nature place, that is, insofar as it is considered in such an order and site in the whole river.

             In like manner we ought to say that the extremities of natural mobile bodies are place in respect to the whole spherical body of the heavens, which is fixed and immobile because of the immobility of the centre and the poles. Thus, although this part of air contains, or this part of water flows and is moved insofar as it is this water, nevertheless, insofar as this water has the nature of place, that is, a site and order in the whole sphere of the heavens, it always remains permanent.

             In a similar way fire is said to remain the same in respect to form, although in respect to matter it changes as different wood is added and consumed.

             469. By means of this an objection which can be made against our position that place is the terminus of the container is overcome. Since the container is mobile, the terminus of the container will also be mobile. And thus a thing existing at rest will have diverse places. But this does not follow. For the terminus of the container is not a place insofar as it is these surfaces of this mobile body, but insofar as it has an order or site in an immobile whole. From this it is clear that the whole nature [ratio] of place in everything that contains is from the first container and ocator, that is, the heavens.

             470. Next where he says, 'Hence we conclude . . .' (212 a 20), he concludes the definition of place from the above; that is, place is the immobile terminus of that which contains primarily. He says 'primarily' in order to designate proper place and exclude common place.

             471. Next where he says, 'This explains why . . .' (212 a 22), he shows that this definition has been well established because the things which are said of place agree with this definition.

             He makes three points. The first is that, since place is an immobile container, the middle of the heavens, that is, the centre, and the extremity of circular local motion, that is, the extremity of bodies moved in a circle (the extremity, I say, towards us, that is, the surfaces of the moon), are such that the one--the extremity--seems to be upward, and the other--the middle--seems to be downward. And above all things it is most properly said that the centre of the sphere always remains permanent. And although the extremity of bodies moved towards us in a circle moves in a circle, nevertheless it remains permanent insofar as it is similarly related, that is, it is the same distance from us. And since natural bodies are moved to their proper places, light bodies are naturally moved upwards and heavy bodies downwards. For both the middle itself and the terminus containing towards the middle are called downwards. And likewise both the extremity and that which is towards the extremity are said to be upwards. Moreover he uses such a way of speaking because the middle is the place of earth, which is heavy simply. But the place of water is towards the middle. And likewise the extremity is the place of fire, which is light simply. But the place of air is towards the extremity.

             He gives the second point where he says, 'For this reason, too . . .' (212 a 28). He says that since place is a terminus, place seems to be like certain surfaces and like a certain containing vase, but not like the space of a containing vase.

             He gives the third point where he says, 'Further, place is coincident . . .' (212 a 30). He says that since place is a terminus, place and that which is located exist together. For the boundary of that which is located and the terminus of the container, which is place, exist together, because the extremities of things which touch exist together. And according to this it is also understood that place is equal to that which is located, because they are equal in respect to the extremities.