THE THEORY OF MATHEMATICAL SUBTRACTION IN ARISTOTLE

Abstract

The problem with most modern accounts of Aristotle’s so-called ‘theory of mathematical abstraction’ or aphairesis (ἀφαίρεσις) is that it is interpreted primarily through the scope of the epistemological process of an immediate reception of mathematical forms by the soul without matter from which the former are said to be ‘abstracted’. However, this interpretation is not present in Aristotle’s texts. Instead, aphairesis presents itself as a method by which the mode of being of the objects of mathematics is explained: it elucidates the location and place of the category of quantity within a particular sensible substance, but not some kind of an abstracting activity of drawing mathematical forms or universals from matter. This latter type of the epistemological abstraction of mathematicals found in most modern commentaries was developed by later commentators of Aristotle. The analysis of the modern scholarship shows a clear trace of influence of the ancient tradition.