Aristotle on Continuity in Physics VI

Abstract

Abstract Aristotle’s favourite model of the continuum is the same as ours, namely a geometrical line, or line-segment. He does not also have, as we do, the numerical model of the real numbers, but that is scarcely a handicap. After all, one of our main ways of understanding the structure of the real numbers (namely via the notion of a ‘Dedekind cut’) is very naturally viewed as drawing upon our prior grasp of the structure of a geometrical line, with the real numbers understood as corresponding to the points on that line. There are some features of this structure which Aristotle grasps very clearly, notably that no two points on a line are ever next to one another, for between any two points there is always a whole line-segment, which in turn will always contain further points within it. Undoubtedly, this is a major achievement on his part, but its importance should not be over-exaggerated, as it appears to be (for example) in Ross’s classic edition of the Physics. (Looking at the issue from our contemporary point of view, we may observe that the fact that between any two points there are always others does not yet distinguish the structure of the real numbers from that of the rational numbers.)