Talk: Sebastian Speitel (Bonn)

Title:

Logical Constants between Inference and Reference

Abstract:

Tarski’s model-theoretic definition of logical consequence relies on a prior division of the expressions of a language 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, I want to propose a novel criterion of logicality designed to solve the demarcation problem. It combines insights from the model-theoretic as well as from the inferentialist approaches to the issue: a notion qualifies as logical if its inferential behaviour determines a unique denotation among its consistent, formal (i.e., invariant) 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. The talk presents joint work with Denis Bonnay.