Logicism and the Analysis of Mathematical Propositions

Abstract

According to Peter Hylton, ‘Russell was both a metaphysician and a working logician. The two are completely intertwined in his work: metaphysics was to provide the basis for logic; logic and logicism were to provide the basis for arguments for the metaphysics’ (Hylton, 1990, p. 9).¹ On this account, Russell’s metaphysical commitments were adopted along with Moore’s new logic and significantly informed the logic that grew out of Russell’s break with idealism. Russell’s logic and his metaphysics are indeed intertwined in the ‘philosophical approach to analysis’ that arose out of his initial anti-Hegelian commitment to the part/whole approach to analysis. The approach, as we have seen, involves the decomposition of propositions into constituent concepts and complex concepts into indefinable simple constituents, where conceptual differences indicate the real differences logic must preserve. ² Though he dispenses with the part/whole approach to analysis as he adopts symbolic logic and formulates logicism, the new logic informs Russell’s view that logical analysis has philosophical as well as technical requirements, so that, on the decompositional approach, analyses must be philosophically exact (must preserve sense) as well as preserving the relevant formal features of the analysandum in the analysans. ³