Russell and the Bolzanian Conception of Logic

Abstract

In Chapter 3 we examined, from Russell’s point of view, Kant’s account of how propositions that are synthetic can nevertheless be known a priori. Russell’s argument, it will be recalled, was directed against Kant’s model of explanation, which seeks to derive a number of properties of a priori propositions from features characterizing the cognition of these propositions; this was referred to as the relativized model of the a priori (r-model). Russell’s own view is that the source of the synthetic a priori in mathematics is to be found in logic. Since logic is a priori, an acceptable account of its propositions is constrained, among other things, by conditions revealed through an examination of the r-model. On the face of it, apriority implies that the propositions of logic must be true, universal and necessary. Insofar as these characteristics are present, moreover, they should be genuine rather than proxy as in Kant’s theory, according to Russell.