13 April 2023, The Utrecht Logic in Progress Series (TULIPS), Sebastian Speitel

Abstract: Tarski’s model-theoretic definition of logical consequence relies on a division of the expressions of the language under considerations into logical and non-logical. Finding a philosophically motivated and mathematically precise criterion to delineate the logical expressions of a language constitutes the demarcation problem of the logical constants.

In this talk, we propose a novel criterion of logicality designed to address the demarcation problem. It combines insights from the model-theoretic as well as from the inferentialist approaches to meaning. According to it a notion qualifies as logical if its inferential behaviour determines a unique denotation among logically acceptable interpretations.

I will motivate the criterion and investigate its scope and limits by considering expressions from the category of generalized quantifiers. The talk concludes by discussing some consequences of the proposed criterion for the debate concerning determinate reference to the natural number structure in the philosophy of mathematics. This talk presents joint work with Denis Bonnay.