Second Workshop on the Limits and Scope of Mathematical Knowledge

One particular theme of the First Workshop ran as follows: in 1951, Gödel argued convincingly fora 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), ... Thus one research question of the conference was 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; however, the Conference is not limited to this topic. (Details of the First Workshop can be found here: https://www.bris.ac.uk/philosophy/department/events/mathematicalknowledge)

Please see: https://www.bris.ac.uk/philosophy/department/events/mathematicalknowledge2  for further details.   

Attendance is free, but registration for numbers is required. Please contact Sam Pollock ([email protected]) with your affiliation (if any) and email address.