Paradoxes About Belief

Abstract

Referentialism is the view that all there is to the meaning of a singular term is its referent. Referentialism entails Substitutivity, i.e., that co-referring terms are intersubstitutable salva veritate. Frege's Paradox shows that Referentialism is inconsistent given two principles: Disquotation says that if S assents to 'P', then S believes that P, and Consistency says that if S believes that P and that not-P, then S is not fully rational. Kripke's strategy was to save Substitutivity by showing that those intuitively plausible principles already led to paradox. I argue that this generalising strategy fails. The Descriptivist, who thinks that a singular term has descriptive meaning, will reject Substitutivity in Frege's Paradox, and deny that Consistency finds application in Kripke's Paradox. The Referentialist, however, may reject Consistency: if the logical properties of the contents of S's beliefs are not reflectively accessible, then S can hold contradictory beliefs without being irrational. Even if successful against Frege's and Kripke's Paradox, this response is ineffective against a strengthened version of the former which rests on Disquotation and Substitutivity, and a strengthened version of the latter which rests only on Disquotation.