Aristotle's arguments about the void present special interests and problems because of their long history in Aristotle's commentators. A full accounting of the responses to these arguments lies beyond the scope of my analysis, although some special cases will be taken up. One point however has been crucial for interpretations of these arguments: Euclidean geometry requires a three-dimensional infinite space. Euclid flourished (probably) one generation after Aristotle, and his geometry was enormously influential. Because Aristotle defines place as the limit of the first containing body, place was often thought to be both finite and, as we have seen, a two-dimensional surface. Hence on this view, Aristotle's notion of place fails on both counts to meet the requirements of Euclidean geometry. Taken together, the requirements of Euclidean geometry and the apparent failure of Aristotle's account of place to meet them often motivated first a commitment to the void and then criticism of Aristotle's arguments rejecting the void. Therefore, these criticisms derive from the conjunction of Euclidean geometry and a common misunderstanding of Aristotle's account of place. My interest lies in a direct analysis of the arguments concerning the void in Physics IV.

Place has not been established as the exclusive answer to the question “where are things?” because void [κενόν, i.e., “empty”] presents an alternate answer. Consequently, void must be examined, and, Aristotle says, the same questions must be posed for it as for place, namely, “if it is or not, and how it is and what it is.”