English

Supervaluation-Style Truth Revisited

Logic 2025-10-03 v1

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\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\nat-categorical axiomatizations. The results provide a deeper picture of the relationships between standard supervaluationism and supervaluational-style truth.

Cite

@article{arxiv.2510.01883,
  title  = {Supervaluation-Style Truth Revisited},
  author = {Pablo Dopico and Carlo Nicolai and Johannes Stern},
  journal= {arXiv preprint arXiv:2510.01883},
  year   = {2025}
}
R2 v1 2026-07-01T06:12:56.797Z