Weak Assertion

We present an inferentialist account of the epistemic modal operator 'might'. Our starting point is the bilateralist programme. A bilateralist explains the operator 'not' in terms of the speech act of rejection; we explain the operator 'might' in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of 'might' provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. This demonstrates that an inferentialist approach to meaning can be successfully extended beyond the core logical constants.