LECTURE 2 (209 a 2-30)

SIX PROBABLE ARGUMENTS ARE GIVEN TO SHOW THAT PLACE DOES NOT EXIST

             415. After the Philosopher has given arguments to show that place exists, he here gives six arguments to show that place does not exist. In order to begin inquiring whether something is, it is necessary to state what it is, at least to state what is signified by the name. And therefore he says that, although it has been shown that place exists, nevertheless there is still a doubt about what it is if it is. Is it a certain corporeal mass or a nature of some other kind?

             416. Regarding this he argues as follows. If place is something, it must be a body, for place has three dimensions--length, breadth, and depth. Moreover, a body is determined by these dimensions, because everything that has three dimensions is a body. But it is impossible for place to be a body. For since place and that which is located in place exist together, it would follow that two bodies exist together, which is impossible. It is, therefore, impossible that place be something.

             417. He gives the second argument where he says, 'Further, if body has . . .' (209 a 8). The argument is as follows.

             If the place of a body is a certain receptacle of the body other than the body itself, then the place of the surface must be some receptacle other than the surface itself. The same is true of the other terminations of quantity, the line and the point. He proves this condition as follows. Place was shown to be other than bodies from the fact that a body of air now exists where a body of water formerly was. But likewise the surface of air now exists where the surface of water formerly was. Therefore the place of the surface is other than the surface. And similar arguments can be given in regard to the line and the point.

             He argues, therefore, by denying the consequent. There cannot be any difference between a point and the place of a point. For since place does not exceed that which is located in place, the place of a point can only be something indivisible. But two indivisible quantities, like two points joined together, are only one. Therefore for the same reason the place of a surface will not be other than the surface, nor will the place of a body be other than the body.

             418. He gives the third argument where he says, 'What in the world . . .' (209 a 13). The argument is as follows.

             Whatever is is either an element or composed of elements. But place is neither of these. Therefore place does not exist.

             He proves the minor as follows. Whatever is an element or composed of elements is included in the number of either corporeal or incorporeal things. But place is not included in the number of incorporeal things because it has magnitude. And it is not included in the number of corporeal things because it is not a body, as has been proven. Therefore place is neither an element nor composed of elements.

             But someone might say that, although place is not a body, nevertheless it is a corporeal element. To refute this he adds that the elements of sensible bodies are corporeal, because elements are not outside of the genus of things composed of the elements. For no magnitude is constituted by intelligible principles which are incorporeal. Hence if place is not a body, it cannot be a corporeal element.

             419. He gives the fourth argument where he says, 'Also we may ask . . .' (209 a 18). The argument is as follows.

             Whatever is is in some way a cause of something. But place cannot be a cause according to any of the four types of causes. It is not a material cause because things which are are not constituted out of place, which is the meaning of matter. It is not a formal cause because then everything which occupies one place would be of the same species, since the principle of the species is the form. It is not a final cause of things because it seems that place exists for the sake of that which is located in place rather than vice versa. Nor is it an efficient or moving cause because it is the terminus of motion. It seems, therefore, that place is nothing.

             420. He gives the fifth argument where he says, 'Further, too, if it is . . .' (209 a 24). This is the argument of Zeno and it is as follows.

             Whatever is is in place. Therefore, if place is something, it follows that it is in place, and this latter place is in another place, and so on to infinity, which is impossible. Thus place is not something.

             421. He gives the sixth argument where he says, 'Again, just as every body . . .' (209 a 27). The argument is as follows.

             Every body is in a place, and in every place there is a body, as many probably think. From this it follows that place is neither smaller nor greater than that which is located in place. Since, therefore, that which is located in place increases in size, then place must also increase in size. But this seems impossible because place is immobile. Therefore place is not something.

             And finally he concludes that these arguments make us doubt not only what place is but also whether it is.

             However these arguments are answered in what follows.