Juliet Floyd

Truth in Early Wittgenstein and Gödel

The Tractatus engages directly with both Frege and Russell on the nature of truth, developing responses to each, particularly to Frege’s view that true thoughts have a common objectual referent, “The True”, and Russell’s view that true belief may be analyzed in terms of external relations of greater than 2-adicity. Schlick explicitly rejected Russell’s view in favor of a form of correspondence theory, one tipping easily into forms of conventionalism and verificationism. But, quite differently, Wittgenstein’s picture conception draws in 2 further ideas: a medium of representation and the idea of modality as fundamental to logic. 

Aware of the Tractatus, Gödel engaged with Russell’s theory of truth, particularly in the period leading up to his incompleteness paper (1929) and in 1942-3. The parallel yet distinct engagements of Gödel and Wittgenstein with Russell on truth (and Vienna positivism) are fascinating.  Each regarded Russell’s view as requiring amendment, but whereas Gödel focused on the need for an actual infinite for the foundations of mathematics, and a metaphysical and phenomenological basis for the extensionalism this requires, Wittgenstein articulated, from the Tractatus onward, a non-extensional view of the foundations of mathematics.  This highlighted step-by-step, “mechanical”, purely “formal” procedures as a central aspect of proof in mathematics.  In the end, Wittgenstein and Gödel took Turing’s analysis of the notion of a formal system to clinch this aspect, but each drew radically different philosophical morals from this

Juliet Floyd is Professor of Philosophy at Boston University. Her research focuses on the history of early analytic philosophy, foundations of logic, mathematics and language and, more recently, philosophies of data and emerging media.  She has published most recently (with A. Bokulich) Philosophical Explorations of the Legacy of Alan Turing: Turing 100 (Boston Studies in the Philosophy of Science, Springer, 2017),  (with Felix Mühlhölzer) Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics: An Investigation of Wittgenstein’s Non-Extensionalist Understanding of the Real Numbers (Springer, 2020) and Wittgensein’s Philosophy of Mathematics (Cambridge Element in Philosophy of Mathematics, forthcoming).