Husserl and Frege on substitutivity
pp. 113-140
in: Leila Haaparanta (ed), Mind, meaning and mathematics, Berlin, Springer, 1994Abstract
In the critical discussion of Gottlob Frege's logic in Edmund Husserl's Philosophy of Arithmetic,1 Husserl outlines his objections to the use Frege makes of Leibniz's principle of the substitutivity of identicals in the Foundations of Arithmetic. 2 In the 1903 appendix to Basic Laws II,3 Frege linked these same criticisms with Russell's paradox when, without mentioning Husserl's name, he traced the source of the paradox to points Husserl had made in the Philosophy of Arithmetic. For many philosophical, linguistic and historical reasons4 these two facts have gone virtually uncommented. In the belief that Husserl's discussion of identity and substitutivity in Frege's theory of number may actually be able to shed light on some dark areas surrounding the significance of Russell's paradox for logic and epistemology, I propose here to examine Husserl's criticisms and systematically tie his arguments in with observations made by Bertrand Russell and others who have studied Frege's work.
