Gödel vis-à-vis Russell: Logic and Set Theory to Philosophy

Gödel’s work from the beginning to his first substantive explorations in philosophy would to a significant extent be contextualized by, reactive to, and reflective of, Russell’s. Russell was the towering figure who set the stage for analytic philosophy in the first two decades of the 20th Century; Gödel insisted that his mathematical work was substantively motivated by his own philosophical outlook; and so it becomes especially pertinent to draw out and highlight the interconnections between the two. What follows is a narrative focussing on the interplay of several arching motifs: Russell’s theory of types and Axiom of Reducibility; definability as analysis; Gödel’s incompleteness theorems and constructible sets; and Russell’s and Gödel’s respective construals of the nature of truth as a, if not the, philosophical problem. More specifically, Gödel’s reflections on Russell’s so-called “multiple relation theory of judgment” (MRTJ), the theory of truth at work in Principia Mathematica and later writings of Russell, especially his William James Lectures (1940), will be set forth and framed. This will allow us to draw out, in a provisional way, some of the philosophical significance of Gödel’s recently transcribed Max Phil notebooks. Russell’s MRTJ was an idiosyncratic version of the correspondence theory of truth, framed in terms of complex (non-dual) relations between judgers, the