Breadcrumb
Limits and Scope of Mathematical Knowledge
17 March 2012 to
18 March 2012
Contact Person: Philip Welch
Organisers: Leon Horsten 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 Gödels 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), ...
One 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.
Other connecting themes will also be discussed.
Main Speakers
- S. Artemov (CUNY)
- T. Carleson (Ohio State)
- W. Dean (Warwick) & S. Walsh (Birkbeck)
- D. Isaacson (Oxford)
- G. Leach-Krause (Notre Dame)
- S. Shapiro (Ohio State)
- T. Williamson (Oxford)