A case for weak Kleene ST
摘要
The substructural Strict/Tolerant logic based on strong Kleene valuations (sST) was motivated by its ability to express a fully transparent truth predicate and the tolerance principle without falling into the traps of semantic and soritical paradoxes. Even though sST rejects the meta-inferential rule of Cut, it has been shown that many instances of Cut are recoverable. Thus, not only can theories of truth and vagueness based on sST avoid the semantic and soritical paradoxes, but these theories stay very close to classical theories, which is counted as a virtue of sST. In a recent paper by Murzi and Rossi, the authors argue that the notion of (un)paradoxicality plays a major role in recapturing the “safe” instances of Cut. However, the theory of truth based on sST cannot be extended to express the notion (un)paradoxicality on pain of revenge paradox. Similarly, in a recent paper by Bruni and Rossi, the authors argue that the theory of vagueness based on sST cannot be extended to express the notion of determinateness on pain of revenge paradox, even though “determinateness” plays a major role in the theory. In this paper, we argue that given the analysis of these revenge paradoxes, the Strict/Tolerant logician should prefer the weak Kleene variation of the Strict/Tolerant logic (