ABSTRACT
Following Wittgenstein, I formulate what I call the Paradigm Paradox: “One sentence can never describe the paradigm in another, unless it ceases to be a paradigm.” I argue that this paradox is structurally analogous to Frege's concept of horse paradox and to Russell's paradox. The Paradigm Paradox also occurs if one attempts to self-referentially describe a paradigm using that same paradigm. I argue that such paradoxical sentences can indicate a change in the method of applying the paradigm. Next, I set out the “logic of exemplarity.” The received paraconsistent view has it that an exemplar of X is an X and, at the same time, is not an X. Inspired by Wittgenstein's discussion of the Standard Meter, I propose an alternative paracomplete view whereby we can say of an exemplar of X neither that it is an X nor that it is not an X.
