ABSTRACT
Aristotle's implicit claim that numbers have intelligible matter is much more problematic because, quite simply, it is difficult to make much sense of the idea, and the problems are compounded by the fact that the examples of intelligible matter that he presents are always geometrical. In the case of geometry, Aristotle employs some different kinds of abstraction. Aristotle considers that all spatial magnitudes can be generated from lines and points and this allows him to carry the abstraction that yields the three-dimensional substratum further so that it yields planes and finally lines and points. In Aristotle's work, as in Greek mathematics generally, the basic entity that we operate with is the line length, so that arithmetical operations are performed by manipulating line lengths. Aristotle represents numbers by line lengths and sometimes by letters, and he also represents times and motions in this way.
