Commentary Aristotle Physics
Lecture 2. Six probable arguments that place does not exist
But, even if we suppose the existence of space 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.
Now, it has three dimensions: length, breadth, depth—the dimensions by which all body also is bounded. But place cannot be body, for if it were, there would be two bodies in the same place.
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.
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.
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, it has not body. But the elements of sensible bodies are bodies, while nothing that has size results from a combination of intelligible elements.
We may also ask, “of what in things is space the cause?” None of the four modes of causation can be ascribed to it. It is neither in the sense of the matter of existents (for nothing is composed of it); nor as the form and definition of things; nor as end; nor does it move existents.
Further, too, if it is itself an existent, where will it be? Zeno’s difficulty demands an explanation: if everything that exists has a place, place too will have a place, and so on to infinity.
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 premises 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.
415. After giving reasons to show that place exists, the Philosopher now gives six reasons showing that place does not exist. Now, the way to begin investigating the question whether a thing exists is to settle on what it is, at least as to what its name means. Therefore, he says that, although it has been shown that place exists, there is a difficulty, a question about what it is, even if it does exist: is it a bodily mass or a nature of some other kind?
416. Hence, he argues thus. If place is anything, it must be a body, for place has three dimensions—length, width, and depth—and such things determine a body, because whatever has three dimensions is body. But place cannot be a body, because, since place and the body in it are together, there would be two bodies together, which does not work. Therefore, it is impossible for place to be anything.
417. He gives a second reason at “further, if body has” (209a7), which is this. If the place of a body is a receptacle distinct from the body, then the place of its surface must be a receptacle distinct from this surface, and similarly for the other limits of quantity, such as the line and the point.
He proves this conditional proposition in the following manner. Place was proved to be distinct from bodies on the grounds that, where the body of air now is, there was the body of water previously. But, similarly, where the surface of the water was, there is now the surface of the air; therefore, the place of the surface is distinct from the surface, and the same holds for the line and the point.
He argues, therefore, by the destruction of the consequent, starting from the fact that there can be no difference between the place of the point and the point itself. For since a place is not greater than the thing in place, the place of a point can be only an indivisible.
Now, two quantitative indivisibles—such as two points joined together—are just one point. For the same reason, therefore, neither will the place of the surface be different from the surface itself nor the place of the body be different from the body itself.
418. He gives a third reason at “what in the world” (209a13), which is this: whatever exists is either an element or composed of elements; but place is neither of these; therefore, place does not exist. The middle premise he proves thus. Whatever is an element or composed of elements is either corporeal or incorporeal; but place is not incorporeal, for it has magnitude, nor is it corporeal, because it is not a body, as we have already shown. Therefore, it is neither an element nor composed of elements. Now, since someone might say that, even though it is not a body, it is nevertheless a bodily element, he excludes this by adding that all sensible bodies have corporeal elements, because the elements are not outside the genus of their compounds. For no magnitude results from intelligible principles that are incorporeal. Hence if place is not a body, it cannot be a corporeal element.
419. He gives the fourth reason at “we may also ask” (209a18), which is this. Everything that exists is somehow a cause in relation to something else, but place cannot be a cause in any of the four ways. It is not a cause as matter, because things that exist are not composed out of place, which belongs to the concept of matter. Nor is it a formal cause, for then, all things that have the same place would be of the same species, since the principle of the species is the form. It is not like the final cause in things, since places seem to be for the sake of the things in place, rather than those things being for the sake of the places. Finally, it is not an efficient or moving cause, since place is the terminus of a motion. Therefore, it seems place is nothing.
420. He gives the fifth reason at “further, too” (209a23), which is Zeno’s reason. Whatever exists is in place; hence, if place is anything, it follows that it is itself in place, and that place in another place, and so on to infinity. But this is impossible. Consequently, place is not anything.
421. He gives the sixth reason at “again, just as every body” (209a26), which is this. Every body is in a place and in every place is a body (according to the opinion of many). From this, it is taken that place is neither smaller nor larger than the thing in place. When a thing in place grows, therefore, its place also should grow. However, this seems impossible, for place is an immobile something. Therefore, place is not anything.
In summary, he says that, for reasons of this sort, doubts are raised not only as to the nature of place but also as to its very existence. However, these reasons will be answered by what follows.