2021-2025: Categoricity by Convention (P33708)

• Funder: FWF (Austrian Science Fund).
• 403.000€.
• Applicants: Julien Murzi and Brett Topey
• PI: Julien Murzi.

The project develops a moderate inferentialist view on which our open-ended rules for the higher-order quantifiers determine the full interpretation of second-order logic (and indeed of all logics of finite order), so that, via standard categoricity and quasi-categoricity results, our higher-order mathematical theories can be seen to be categorical or quasi-categorical (pace Skolem, Putnam etc.). The idea is of course old — Vann McGee among others has been arguing for much the same view — but the details are new. Among other things, we provide a new solution to Carnap’s categoricity problem for propositional logic, and strengthen and generalize to higher-order logic a recent result by Denis Bonnay and Dag Westerståhl concerning the categoricity of predicate logic. Our view yields a novel, largely syntactic criterion for logicality, a moderate form of pluralism, and an attractive epistemology of the a priori. (Or so we hope!) In the course of the project, we aim to organize a couple of conferences (online or in person), visit a few places, work on a bunch of papers, and eventually write a short, compact monograph.

2017-2021: The Liar and its Revenge in Context (P29716-G24)

• Funder: FWF (Austrian Science Fund).
• 390.000€.
• Applicants: Julien Murzi and Lorenzo Rossi.
• PI: Julien Murzi.

The project has started in January 2017 and will last until July 2021. It involves (temporal parts of) two (awesome) post-doctoral researchers: Lorenzo Rossi and Brett Topey. Lorenzo is now an Assistant Professor in Munich; we are currently writing a book for OUP. Brett is still in Salzburg; we are currently working on issues surrounding conventionalism and the determinacy of mathematical language. You can visit the website of the project here.

2013-2015: Inference and Logic

• Funder: British Academy.
• £10.000.
• Applicants: Julien Murzi and Florian Steinberger.

The Inference and Logic project was funded by the and led by Julien Murzi and Florian Steinberger. It aimed at investigating inferentialist approaches to logic: approaches according to which (roughly) the meaning of a logical expression is determined by the way we use it, and to know the meaning of a logical expression is to know how to use it. Two controversial but, we think, fecund thoughts! Between April 2013 and July 2015, we wrote a bunch of papers and organised this conference.