A Strongly Differing Opinion on Proof-Theoretic Semantics?

Abstract

Responding to an invitation from Peter Schroeder-Heister, the paper reacts to some criticisms of ‘model theory’ voiced among proof theorists interested in proof-theoretic semantics. It argues that the criticisms are poorly targeted: they conflate model theory with model-theoretic semantics and with the model-theoretic definition of logical consequence, which are three largely unrelated areas of study. On defining the meanings of logical constants, and of natural language expressions in general, the paper lays out some methodological requirements that any satisfactory definitions would need to meet, for example about generalisability from one context of use to other contexts. On defining logical consequence, the paper argues that some points made recently by Schroeder-Heister and Kosta Došen are largely sound and probably uncontroversial if clearly stated, but their impact is blurred by some question-begging formulations.