ON A SIDE EFFECT OF SOLVING FITCH’S PARADOX BY TYPING KNOWLEDGE
By Volker Halbach
It has been proposed to block Fitch’s paradox by disallowing a predicate or sentential operator of knowledge that can be applied to sentences containing the same predicate or operator of knowledge. Furthermore it has been claimed that this move is not ad hoc as there is independent motivation for this restriction, because this restriction provides a solution also to paradoxes arising from selfreference like the paradox of the Knower. A solution to paradoxes arising from selfreference is only needed if knowledge is treated as a predicate that can be diagonalized. However, if knowledge and possibility are conceived as such predicates with type restrictions, a new paradox arises. Very basic, jointly consistent assumptions on the predicates of knowledge and possibility yield an inconsistency if (a typed version of) the verifiability principle is added.
Analysis 68 (2008), to appear