Dissolving the Paradoxicality Paradox
Non-classical solutions to semantic paradox can be naturally associated with conceptions of paradoxicality and unparadoxicality defined in terms of entailment facts. For example, in a K3-based theory of truth, it is prima facie intuitive to say that a sentence φ is paradoxical iff φ∨¬φ entails an absurdity. In a recent paper, Julien Murzi and Lorenzo Rossi exploit this to introduce a family of revenge paradoxes for paracomplete, paraconsistent, non-contractive, and non-transitive theories of truth. In this paper, I show that this strategy does not generate genuine revenge paradoxes for these approaches. In the paracomplete and paraconsistent cases, this is because the semantic rules governing these notions of (un)paradoxicality are equivalent to restricted versions of the very negation rules dropped by these logics. In the substructural cases, I show that the theories in question can express the targeted notions of (un)paradoxicality without running into Murzi and Rossi's revenge paradoxes.