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Limits and Scope of Mathematical Knowledge

Contact Person: Sam Pollock

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Organisers: Philip Welch

Description
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's arguments for the first disjunct are widely regarded as unconvincing. At the same time, formal frameworks have in the decades following Goedel'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 Goedel's disjunctive thesis.

This is a second follow-up conference on the same theme as the first.

Main Speakers

• Y. Gurevich (Microsoft); Y. Moschovakis (UCLA); D. Achourioti (ILLC Amsterdam); G. Leach-Krouse (Notre-Dame); W.H. Woodin (Berkeley); T. Carlson (Ohio State); L. Hortsen & M Antonutti (Bristol); J. Moschovakis; P. Koellner (Harvard)