Gaps, gluts, and theoretical equivalence

Carlo Nicolai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants of Kripke–Feferman truth. The first, KF+ CONS, features a consistent but partial truth predicate. The second, KF+ COMP, an inconsistent but complete truth predicate. It is known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability, under natural assumptions, coincides with definitional equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of KF+ CONS and KF+ COMP raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth.

Original languageEnglish
Article number366
JournalSYNTHESE
Volume200
Issue number5
DOIs
Publication statusPublished - Oct 2022

Keywords

  • Paradox
  • Theoretical equivalence
  • Truth

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