Second Workshop on the Limits and Scope of Mathematical Knowledge

In 1951, Gödel argued convincingly for a disjunctive thesis: either the human mathematical mind exceeds the output of a Turing machine, or there exist absolutely undecidable mathematical propositions. Since then, attempts have been made to decide one or both of the disjuncts, but no decisive progress has been made so far. For instance, Lucas’ arguments for the first disjunct are widely regarded as unconvincing. At the same time, formal frameworks have in the decades following Gödel’s publication been developed which could be fruitfully applied to this question: epistemic arithmetic (Shapiro et al.), progressions of formal theories (Feferman, Beklemishev, et al.), the logic of proofs (Artemov), ...

The research question of the conference is whether some of these formal frameworks (or combinations of these frameworks) can be used to obtain arguments for statements that are stronger than Gödel’s disjunctive thesis.

This is a second follow-up conference on the same theme as the first. The hope is that in the one-year interval between the two, real progress has been made on some of the key issues discussed at the first conference.

The conference is generously supported by a grant awarded by the Templeton Foundation.