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This paper discusses proof-theoretic semantics, the project of specifying themeanings of the logical constants in terms of rules of inference governingthem. I concentrate on Michael Dummett's and Dag Prawitz' philosophicalmotivations and give precise characterisations of the crucial notions ofharmony and stability, placed in the context of proving normalisation resultsin systems of natural deduction. I point out a problem for defining the meaningof negation in this framework and prospects for an account of the meanings ofmodal operators in terms of rules of inference.

Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality