Combined Criteria of Logicality
Abstract: 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.
Recent decades have seen the development of a multitude of such criteria, mostly either along semantic/invariance-based or inferential/proof-theoretic lines. After quickly surveying some of the shortcomings of purely semantic/invariance-based approaches this talk will explore the prospect of a combined criterion of logicality, a criterion trying to combine both inferential and semantic elements. In doing so we will first point out deficiencies of extant criteria of this kind, to then formulate and defend our own criterion based on the idea that what makes an expression logical is its ability to ‘pin down’ an appropriate semantic value. This talk is based on joint work with Denis Bonnay (Université Paris Ouest Nanterre La Défense).