Tarski’s celebrated model-theoretic explication of the notion of logical consequence left open the question on what grounds to draw a distinction between logical and non-logical constants. This omission gave rise to the demarcation problem of the logical constants, and subsequently led to the search for criteria of logicality – philosophically informative and mathematically precise principles according to which to distinguish logical from non-logical expressions of a given language.  

In this talk, after quickly surveying some of the perceived shortcomings of purely semantic/invariance-based criteria, we will propose a combined criterion of logicality, incorporating both semantic and inferential considerations. We will compare it to another extant combined criterion proposed by S. Feferman (2015), and explore its scope and some of its philosophical implications.

This talk is based on joint work with Denis Bonnay (Université Paris Ouest Nanterre La Défense).