James Scow

A solution to the liar paradox should meet certain general constraints in addition to blocking the argument to contradiction. One of these constraints is that the solution fit into a semantics for natural language. If that semantics is Davidsonian, then the constraint requires a solution to be finitely axiomatized and inductive and compatible with Convention T. Two further requirements come out of my discussion, that a semantics explain mutual understanding between speakers of a language, and that a solution to the liar also solve the problem of the strengthened liar. These requirements cannot be met if a Davidsonian semantics adopts the orthodox or Tarskian way out of the liar. Using the work of Kripke, Feferman, Parsons, and Burge, I propose alternative ways out that, with certain qualifications, do fit into a Davidsonian semantics, and do so in such a way that the requirements regarding mutual understanding and the strengthened liar are met