Supervaluation-Style Truth Revisited

Pablo Dopico; Carlo Nicolai; Johannes Stern

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arXiv · 2510.01883

Supervaluation-Style Truth Revisited

Pablo Dopico·Carlo Nicolai·Johannes Stern

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Abstract

Supervaluational fixed-point semantics for truth cannot be axiomatized because of its recursion-theoretic complexity. Johannes Stern (\emph{Supervaluation-Style Truth Without Supervaluations}, Journal of Philosophical Logic, 2018) proposed a new strategy (supervaluational-style truth) to capture the essential aspects of the supervaluational evaluation schema whilst limiting its recursion-theoretic complexity, hence resulting in ($\nat$-categorical) axiomatizations. Unfortunately, as we show in the paper, this strategy was not fully realized in Stern's original work: in fact, we provide counterexamples to some of Stern's key claims. However, we also vindicate Stern's project by providing different semantic incarnations of the idea and corresponding $\nat$-categorical axiomatizations. The results provide a deeper picture of the relationships between standard supervaluationism and supervaluational-style truth.

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Pablo Dopico, Carlo Nicolai, Johannes Stern. 2025-10-02. Supervaluation-Style Truth Revisited. https://arxiv.org/abs/2510.01883

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