Insolubility?

This chapter examines the more purely philosophical aspect of the question of the paradoxes of truth. It first considers a particular paradoxical derivation that uses the equivalence principle not in the form of the T-biconditionals (which immediately raise questions about what kind of conditional is involved), but of rules of T-introduction and T-elimination. It then explains the concept of revenge as well as logical and contextualist “solutions” and the so-called “paraconsistency.” It concludes with a discussion of inconsistency theories such as defeatism and deflationism. The background assumptions about meaning behind an integrated deflationist/defeatist theory might run as follows. Meaning can be given by rules, but rules can be inconsistent. There is even a result in mathematical logic (Church's theorem) to the effect that there is no mechanical test for inconsistency of rules, making it unlikely we have any filter preventing us from ever internalizing inconsistencies.