Methodological and logicist background

Abstract

Here I shall try to reproduce, briefly, the main direct and indirect influences that served as a context for the origins of Russell’s mathematical philosophy. Boole and Peirce (rather than De Morgan) constituted the main antecedent of all ‘mathematical’ considerations of logic, and then of all logicism. Couturat and Whitehead, whose influence on Russell could not have been more direct, added an essential element: the construction of all mathematics from the simplest operations and elements by trying to form chains of definitions (in the Peanesque style). With regard to Dedekind and Cantor, they were the main precedents of Russell’s constructive methodology in the field of pure mathematical objects; besides, Dedekind explicitly agreed with logicism (without ever detailing his approach) and Cantor reduced arithmetic operations to relations between classes. On the other hand, Bradley and Moore created the philosophical framework providing, as methodological paradigms, respectively, the search for genuine logical forms and definitions as based on simples. In the last section I shall consider the basic ideas of FG, though only in so far as this work, previous to the influence of Moore, already shows some traces of the subsequent method.