The Scope and Limits 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 alii), progressions of formal theories (Feferman, Beklemishev, et alii), the logic of proofs (Artemov), and so on. 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. 

About one year after the first conference, there will be a second follow-up conference on the same theme. The hope is that in the one-year interval, real progress has been made on some of the key issues discussed at the first conference.

Conference programme Saturday, March 17th 10.45: welcome 11.00-13.00: S. Shapiro - 'Idealization, Mechanism and Knowability' 13.00-14.30: Lunch 14.30-16.30: D. Isaacson - 'How to express knowledge about numbers and sets that cannot be formally expressed' 16.30-17.00: Break 17.00-19.00: G. Leach-Krouse - 'Some Modal Omega Logic' Conference dinner Sunday, March 18th 9.00-11.00: W. Dean and S. Walsh - 'Reversals and Sameness of Computational Resource' 11.00-11.30: Break 11.30-13.30: S. Artemov - TBC 13.30-15.00: Lunch 15.00-17.00: T. Williamson - TBC 17.00-17.30: Break 17.30-19.30: T. Carlson - TBC Registration Attendance is free, but registration is required. Please contact Marianna Antonutti ([email protected]).

For further details about the venue and the conference programme, see: 

https://www.bris.ac.uk/philosophy/department/events/mathematicalknowledge