The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning

Abstract

The semantic tradition in logic descends from Tarski's seminal work on truth and logical consequence. In the introduction to this volume, Sagi and Woods remind us that this tradition prominently uses model theory to study languages and their interpretations. Tarski's model-theoretic definition of logical consequence is the prime example of this approach, seeking as it does to reduce logical properties to a class of operations on classical, iterative (ZF) sets. Sagi and Woods explain with admirable clarity the origins, implications, and philosophical questions surrounding this project. The contributions to the volume go on to address whether this approach successfully elucidates logicality and how it intersects with the foundations of mathematics and natural language semantics. One of the most enduring topics in the semantic tradition is the divide between logical and non-logical vocabulary. This plays an important role in Tarski's definition of logical consequence, but does the value and success of this definition require an absolute criterion of logicality? Gila Sher previously developed the view that vocabulary are properly called ‘logical’ when they express operations that are stable under certain transformations of the domain of quantification. This is known as invariantism. Mario Gómez-Torrente previously argued not only against invariantism, but more generally against the need for any such criteria. He contends that the semantic approach functions fine even if the demarcation of logical term is merely pragmatic and interest relative. In the first two chapters of the present volume, Sher and Gómez-Torrente rehash and expand on this debate.