Getting One for Two, or the Contractors’ Bad Deal. Towards a Unified Solution to the Semantic Paradoxes

Abstract

The paper concerns transparent theories of truth, i.e. theories treating ‘ ‘ϕ’ is true’ as fully intersubstitutable with ϕ, and examines what the prospects are of maintaining a suitably refined version of transparency in view of the problem posed by the semantic paradoxes. In particular, three kinds of transparent theories—theories denying the law of excluded middle, theories denying the law of non-contradiction and theories denying the metarule of contraction—are compared with respect to the two most prominent semantic paradoxes: the Liar and Curry’s. It is argued that there are versions of the Liar paradox that do not rely on the law of excluded middle or the law of non-contradiction, and that such versions are blocked by the first two kinds of theories only by (implausibly) severing important connections between logical consequence and negation. Similarly, it is argued that Curry’s paradox does not rely on the law of excluded middle or the law of non-contradiction, and that it is blocked by the first two kinds of theories only by (implausibly) severing important connections between logical consequence and the conditional. All the paradoxes discussed are shown however to rely on the metarule of contraction, and so the third kind of theory is revealed to have the advantage of offering a unified solution to such paradoxes.