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  1. Generalized Revenge.Julien Murzi & Lorenzo Rossi - forthcoming - Australasian Journal of Philosophy:1-25.
    Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.
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  • Two-Valued Logics for Naive Truth Theory.Lucas Daniel Rosenblatt - 2015 - Australasian Journal of Logic 12 (1).
    It is part of the current wisdom that the Liar and similar semantic paradoxes can be taken care of by the use of certain non-classical multivalued logics. In this paper I want to suggest that bivalent logic can do just as well. This is accomplished by using a non-deterministic matrix to define the negation connective. I show that the systems obtained in this way support a transparent truth predicate. The paper also contains some remarks on the conceptual interest of such (...)
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  • Omega-Inconsistency Without Cuts and Nonstandard Models.Andreas Fjellstad - 2016 - Australasian Journal of Logic 13 (5).
    This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency (...)
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  • Hypatia's Silence.Martin Fischer, Leon Horsten & Carlo Nicolai - forthcoming - Noûs.
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  • Reaching Transparent Truth.Pablo Cobreros, Paul Égré, David Ripley & Robert van Rooij - 2013 - Mind 122 (488):841-866.
    This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.
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  • From One to Many: Recent Work on Truth.Jeremy Wyatt & Michael Lynch - 2016 - American Philosophical Quarterly 53 (4):323-340.
    In this paper, we offer a brief, critical survey of contemporary work on truth. We begin by reflecting on the distinction between substantivist and deflationary truth theories. We then turn to three new kinds of truth theory—Kevin Scharp's replacement theory, John MacFarlane's relativism, and the alethic pluralism pioneered by Michael Lynch and Crispin Wright. We argue that despite their considerable differences, these theories exhibit a common "pluralizing tendency" with respect to truth. In the final section, we look at the underinvestigated (...)
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  • Naïve Validity.Julien Murzi & Lorenzo Rossi - forthcoming - Synthese:1-23.
    Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...)
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  • Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.
    A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more (...)
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  • Axioms for Determinateness and Truth.Solomon Feferman - 2008 - Review of Symbolic Logic 1 (2):204-217.
    elaboration of the last part of my Tarski Lecture, “Truth unbound”, UC Berkeley, 3 April 2006, and of the lecture, “A nicer formal theory of non-hierarchical truth”, Workshop on Mathematical Methods in Philosophy, Banff , 18-23 Feb. 2007.
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  • Games for Truth.P. D. Welch - 2009 - Bulletin of Symbolic Logic 15 (4):410-427.
    We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.
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  • What Theories of Truth Should Be Like (but Cannot Be).Hannes Leitgeb - 2007 - Philosophy Compass 2 (2):276–290.
  • Does Truth Equal Provability in the Maximal Theory?Luca Incurvati - 2009 - Analysis 69 (2):233-239.
    According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved in (...)
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  • Hypatia's Silence. Truth, Justification, and Entitlement.Martin Fischer, Leon Horsten & Carlo Nicolai - manuscript
    Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment.
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  • Levity.Leon Horsten - 2009 - Mind 118 (471):555-581.
    In this article, the prospects of deflationism about the concept of truth are investigated. A new version of deflationism, called inferential deflationism, is articulated and defended. It is argued that it avoids the pitfalls of earlier deflationist views such as Horwich’s minimalist theory of truth and Field’s version of deflationism.
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  • Truth, Partial Logic and Infinitary Proof Systems.Martin Fischer & Norbert Gratzl - 2017 - Studia Logica:1-26.
    In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an \-rule.
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  • Truth, Partial Logic and Infinitary Proof Systems.Martin Fischer & Norbert Gratzl - 2017 - Studia Logica 106 (3):515-540.
    In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule.
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  • Axiomatizing Semantic Theories of Truth?Martin Fischer, Volker Halbach, Jönne Kriener & Johannes Stern - 2015 - Review of Symbolic Logic 8 (2):257-278.
    We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.
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  • HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
    This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...)
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  • A Robust Non-Transitive Logic.Alan Weir - 2015 - Topoi 34 (1):1-9.
    Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and surreal-valued (...)
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  • Truth, Logical Validity and Determinateness: A Commentary on Field’s Saving Truth From Paradox.P. D. Welch - 2011 - Review of Symbolic Logic 4 (3):348-359.
    We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.
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  • Reducing Compositional to Disquotational Truth.Volker Halbach - 2009 - Review of Symbolic Logic 2 (4):786-798.
    Disquotational theories of truth, that is, theories of truth based on the T-sentences or similar equivalences as axioms are often thought to be deductively weak. This view is correct if the truth predicate is allowed to apply only to sentences not containing the truth predicate. By taking a slightly more liberal approach toward the paradoxes, I obtain a disquotational theory of truth that is proof theoretically as strong as compositional theories such as the Kripket probe the compositional axioms.
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  • S. Feferman. Reflecting on Incompleteness. The Journal of Symbolic Logic, Vol. 56 , No. 1, Pp. 1–49. - W. N. Reinhardt. Some Remarks on Extending and Interpreting Theories with a Partial Predicate for Truth. Journal of Philosophical Logic, Vol. 15 , No. 2, Pp. 219–251. - V. Halbach and L. Horsten. Axiomatizing Kripke’s Theory of Truth. The Journal of Symbolic Logic, Vol. 71 , No. 2, Pp. 667–712 - H. Friedman and M. Sheard. An Axiomatic Approach to Self-Referential Truth.Annals of Pure and Applied Logic, Vol. 33 , No. 1, Pp. 1–21. - V. Halbach. A System of Complete and Consistent Truth. Notre Dame Journal of Formal Logic, Vol. 35 , No. 3, Pp. 311–327. [REVIEW]Graham E. Leigh - 2010 - Bulletin of Symbolic Logic 16 (3):424-428.
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  • Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
    The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].
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  • Revision Revisited.Leon Horsten, Graham E. Leigh, Hannes Leitgeb & Philip Welch - 2012 - Review of Symbolic Logic 5 (4):642-664.
    This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
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  • A Unified Theory of Truth and Paradox.Lorenzo Rossi - 2019 - Review of Symbolic Logic 12 (2):209-254.
    The sentences employed in semantic paradoxes display a wide range of semantic behaviours. However, the main theories of truth currently available either fail to provide a theory of paradox altogether, or can only account for some paradoxical phenomena by resorting to multiple interpretations of the language. In this paper, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory of truth and paradox, that is a theory of truth that also provides a (...)
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  • Logical Disagreement and Aggregation.Diego Tajer - 2017 - Theoria : An International Journal for Theory, History and Fundations of Science 32 (1).
    In this paper, I explore the possibility of applying the methods and results of Judgement Aggregation to the problem of logical disagreement. I develop and evaluate different ways in which individuals who logically disagree can generate a collective logic. I prove a version of the discursive paradox, where the majority voting of a group of structural logicians can give rise to a substructural logic; then I develop a more general impossibility result. After this, I analyze different ways to avoid the (...)
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  • Friedman and the Axiomatization of Kripke's Theory of Truth.John P. Burgess - unknown
    What is the simplest and most natural axiomatic replacement for the set-theoretic definition of the minimal fixed point on the Kleene scheme in Kripke’s theory of truth? What is the simplest and most natural set of axioms and rules for truth whose adoption by a subject who had never heard the word "true" before would give that subject an understanding of truth for which the minimal fixed point on the Kleene scheme would be a good model? Several axiomatic systems, old (...)
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  • Modality in Brandom's Incompatibility Semantics.Giacomo Turbanti - 2011 - In María Inés Crespo, Dimitris Gakis & Galit Weidman-Sassoon (eds.), Proceedings of the Amsterdam Graduate Conference - Truth, Meaning, and Normativity. ILLC Publications.
    In the fifth of his John Locke Lectures, Robert Brandom takes up the challenge to define a formal semantics for modelling conceptual contents according to his normative analysis of linguistic practices. The project is to exploit the notion of incompatibility in order to directly define a modally robust relation of entailment. Unfortunately, it can be proved that, in the original definition, the modal system represented by Incompatibility Semantics (IS) collapses into propositional calculus. In this paper I show how IS can (...)
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  • Models of Positive Truth.Mateusz Łełyk & Bartosz Wcisło - 2019 - Review of Symbolic Logic 12 (1):144-172.
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  • Model-Theoretic Semantics and Revenge Paradoxes.Lorenzo Rossi - 2019 - Philosophical Studies 176 (4):1035-1054.
    Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field and argue that it does not offer a way out of the revenge problem. More generally, I argue (...)
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  • The Paradox of the Knower Revisited.Walter Dean & Hidenori Kurokawa - 2014 - Annals of Pure and Applied Logic 165 (1):199-224.
    The Paradox of the Knower was originally presented by Kaplan and Montague [26] as a puzzle about the everyday notion of knowledge in the face of self-reference. The paradox shows that any theory extending Robinson arithmetic with a predicate K satisfying the factivity axiom K → A as well as a few other epistemically plausible principles is inconsistent. After surveying the background of the paradox, we will focus on a recent debate about the role of epistemic closure principles in the (...)
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  • Book Reviews. [REVIEW]Vann Mcgee - 1993 - Mind 102 (408):518-.
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  • A Note on Contraction-Free Logic for Validity.Colin R. Caret & Zach Weber - 2015 - Topoi 34 (1):63-74.
    This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.
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  • Alternative Logics and Applied Mathematics.Timothy Williamson - 2018 - Philosophical Issues 28 (1):399-424.
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  • Adding a Conditional to Kripke’s Theory of Truth.Lorenzo Rossi - 2016 - Journal of Philosophical Logic 45 (5):485-529.
    Kripke’s theory of truth, 690–716; 1975) has been very successful but shows well-known expressive difficulties; recently, Field has proposed to overcome them by adding a new conditional connective to it. In Field’s theories, desirable conditional and truth-theoretic principles are validated that Kripke’s theory does not yield. Some authors, however, are dissatisfied with certain aspects of Field’s theories, in particular the high complexity. I analyze Field’s models and pin down some reasons for discontent with them, focusing on the meaning of the (...)
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  • Book Reviews. [REVIEW]Vann McGee - 2013 - Studia Logica 101 (3):641-646.
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  • Norms of Truth and Logical Revision.Giulia Terzian - 2015 - Topoi 34 (1):15-23.
    Many take the lesson of the paradoxes to be that we ought to impose some form of logical revision. It is argued here that this kind of move should not be taken lightly.
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  • Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth.Carlo Nicolai - 2018 - Studia Logica 106 (1):101-130.
    We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...)
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  • Response to Heck.David Ripley - 2012 - Thought: A Journal of Philosophy 1 (4):254-257.
    In Heck, Richard Heck presents variants on the familiar liar paradox, intended to reveal limitations of theories of transparent truth. But all existing theories of transparent truth can respond to Heck's variants in just the same way they respond to the liar. These new variants thus put no new pressure on theories of transparent truth.
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  • One Hundred Years of Semantic Paradox.Leon Horsten - 2015 - Journal of Philosophical Logic (6):1-15.
    This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.
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  • A Proof-Theoretic Account of Classical Principles of Truth.Graham E. Leigh - 2013 - Annals of Pure and Applied Logic 164 (10):1009-1024.
    This paper explores the interface between principles of self-applicable truth and classical logic. To this end, the proof-theoretic strength of a number of axiomatic theories of truth over intuitionistic logic is determined. The theories considered correspond to the maximal consistent collections of fifteen truth-theoretic principles as isolated in Leigh and Rathjen.
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  • Truth, Revenge, and Internalizability.Kevin Scharp - 2014 - Erkenntnis 79 (S3):597-645.
    Although there has been a recent swell of interest in theories of truth that attempt solutions to the liar paradox and the other paradoxes affecting our concept of truth, many of these theories have been criticized for generating new paradoxes, called revenge paradoxes. The criticism is that the theories of truth in question are inadequate because they only work for languages lacking in the resources to generate revenge paradoxes. Theorists facing these objections offer a range of replies, and the matter (...)
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