Fixed Points for Consequence Relations

This paper provides a way of dealing with paradoxes associated with consequence relations via a generalisation of Kripke’s fixed point technique. In particular, we focus on Beall and Murzi’s paradox, although the framework outlined should have more general application. We first attempt to locate this problem among the existing corpus of semantic paradoxes. We then examine two canonical approaches to the issue and conclude with an inductive construction which, in some fashion, goes beyond those approaches.