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.