Some Remarks on Proof-Theoretic Semantics

This is a tripartite work. The first part is a brief discussion of what it is to be a logical constant, rejecting a view that allows a particular self-referential “constant” • to be such a thing in favour of a view that leads to strong normalisation results. The second part is a commentary on the flattened version of Modus Ponens, and its relationship with rules of type theory. The third part is a commentary on work (joint with Nissim Francez) on “general elimination rules” and harmony, with a retraction of one of the main ideas of that work, i.e. the use of “flattened” general elimination rules for situations with discharge of assumptions. We begin with some general background on general elimination rules.