Abstract

Bertrand Russell's work on the foundations of mathematics apparently played a decisive role in persuading Wittgenstein to abandon his aeronautical engineering studies in favor of philosophy. Wittgenstein's influence on Russell turned out to be profound as well: two years after they first met, Wittgenstein had delivered an objection to Russell's theory of judgment that was so devastating that it led to the abandonment of a major philosophical project of Russell's, leaving him reportedly “paralysed”. Two fundamental elements are pivotal to the logicism of Russell's Principles of Mathematics: his conception of a proposition, and his commitment to the doctrine of the unrestricted variable. In addition to the ontological problems facing his theory of propositions, Russell also became convinced that his ontology of propositions contained fundamental logical problems, as he encountered recurring contradictions in his attempts to formalize a propositional logic that would comport with his philosophical theory.