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Published online by Cambridge University Press: 25 February 2009
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.
page 197 note 1 Philosophical Quarterly, 1959, p. 302.Google Scholar
page 197 note 2 First edition; Second edition, p. 165-6.Google Scholar
page 197 note 3 p. 304.
page 198 note 1 II, xvi, 1.
page 198 note 2 II, xvi, 2.
page 198 note 3 ib., p. 304.
page 199 note 1 Heyting, A., Intuitionism, An Introduction, Amsterdam, 1965, p. 13.Google Scholar
page 200 note 1 It may be written formally thus: [{P(o)&(n){P(n):⊃P(n + l)]]⊃(n)P(n)].Google Scholar
page 200 note 2 cf. Smith, D. E.: Source Book in Mathematics, p. 73 (Proof of Corollary 12).Google Scholar
page 201 note 1 Eves, H.: An Introduction to the History of Mathematics, p. 261.Google Scholar
page 201 note 2 Oeuvres (ed. Tannery et, Henry) Vol. 2, p. 431, Fermat to Carcari, 1659.Google ScholarKneale, W. (Probability and Induction, p. 37) thinks the principle was formulated by Fermat, and no doubt has this passage in mind.Google Scholar
page 202 note 1 The Foundations of Arithmetic (tr. b y Austin, J. L.), § 31.Google Scholar
page 202 note 2 ib., §§ 37-9.
page 202 note 3 ib., § 39.
page 202 note 4 ib., § 39.
page 203 note 1 ib., 304.
page 203 note 2 intuitionism, p. 13.
page 203 note 3 ib.., p. 15.
page 205 note 1 intuitionism, p. 2.
