Locke and the Intuitionist Theory of Number

Abstract

The Purpose of this paper is to ask how far Locke can be said to have anticipated modern theories of number, particularly the intuitionist theory of Brouwer and Heyting. It has in mind Mr Edward E. Dawson's statement that Locke's account of number was not merely ‘a good effort in his own day’ but that ‘what Locke had to say really was quite fundamental, and a good deal of modern mathematics assumes his position, either explicitly or implicitly’. Mr Dawson thinks that some of the central notions of the intuitionist theory are already present in the Essay Concerning Human Understanding, II, xvi, ‘Of Number’. We should like to examine the view.