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  1. Axiomatic theories of truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
    Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...)
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  • The Implicit Commitment of Arithmetical Theories and Its Semantic Core.Carlo Nicolai & Mario Piazza - 2019 - Erkenntnis 84 (4):913-937.
    According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...)
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  • Deflationary truth and the ontology of expressions.Carlo Nicolai - 2015 - Synthese 192 (12):4031-4055.
    The existence of a close connection between results on axiomatic truth and the analysis of truth-theoretic deflationism is nowadays widely recognized. The first attempt to make such link precise can be traced back to the so-called conservativeness argument due to Leon Horsten, Stewart Shapiro and Jeffrey Ketland: by employing standard Gödelian phenomena, they concluded that deflationism is untenable as any adequate theory of truth leads to consequences that were not achievable by the base theory alone. In the paper I highlight, (...)
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  • The Logical Strength of Compositional Principles.Richard Heck - 2018 - Notre Dame Journal of Formal Logic 59 (1):1-33.
    This paper investigates a set of issues connected with the so-called conservativeness argument against deflationism. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for a first-order language, taken (...)
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  • Equivalences for Truth Predicates.Carlo Nicolai - 2017 - Review of Symbolic Logic 10 (2):322-356.
    One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated (...)
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  • Soundness arguments for consistency and their epistemic value: A critical note.Matteo Zicchetti - 2024 - Philosophical Quarterly.
    Soundness Arguments for the consistency of a (mathematical) theory S aim to show that S is consistent by first showing or employing the fact that S is sound, i.e., that all theorems of S are true. Although soundness arguments are virtually unanimously accepted as valid and sound for most of our accepted theories, philosophers disagree about their epistemic value, i.e., about whether such arguments can be employed to improve our epistemic situation concerning questions of consistency. This article provides a (partial) (...)
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  • (1 other version)Gaps, Gluts, and Theoretical Equivalence.Carlo Nicolai - manuscript
    When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants 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 well-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 (...)
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  • (1 other version)Gaps, gluts, and theoretical equivalence.Carlo Nicolai - 2022 - Synthese 200 (5):1-22.
    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, \, features a consistent but partial truth predicate. The second, \, 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 (...)
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