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Saving the Truth Schema from Paradox
2002
Journal of Philosophical Logic
The paper shows how we can add a truth predicate to arithmetic (or formalized syntactic theory), and keep the usual truth schema Tr ( A ) ↔ A (understood as the conjunction of Tr ( A ) → A and A → Tr ( A )). We also keep the full intersubstitutivity of Tr ( A )) with A in all contexts, even inside of an →. Keeping these things requires a weakening of classical logic; I suggest a logic based on the strong Kleene truth tables, but with → as an additional connective, and where the effect of
doi:10.1023/a:1015063620612
fatcat:hwltsocl7zhrjkmiyx3a53cm5e