One particular theme of the First Workshop ran as follows: in 1951\, Gö\;del 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&rsquo\; arguments for the first disjunct are widely regarded as unconvincing. At the same time\, formal frameworks have in the decades following Gö\;del&rsquo\;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 Gö\;del&rsquo\;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)
\nPlease see: \;https://www.bris.ac.uk/philosophy/department/events/mathematicalknowledge2 \; for further details. \; \;
\nAttendance is free\, but registration for numbers is required. Please contact Sam Pollock (sp8777@bristol.ac.uk) with your affiliation (if any) and email address.
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