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  1. Rethinking Revision.P. Welch - 2019 - Journal of Philosophical Logic 48 (1):137-154.
    We sketch a broadening of the Gupta-Belnap notion of a circular or revision theoretic definition into that of a more generalized form incorporating ideas of Kleene’s generalized or higher type recursion. This thereby connects the philosophically motivated, and derived, notion of a circular definition with an older form of definition by recursion using functionals, that is functions of functions, as oracles. We note that Gupta and Belnap’s notion of ‘categorical in L’ can be formulated in at least one of these (...)
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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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  • Expressibility and the Liar's Revenge.Lionel Shapiro - 2011 - Australasian Journal of Philosophy 89 (2):297-314.
    There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a (...)
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  • No Fact of the Matter.Hartry Field - 2003 - Australasian Journal of Philosophy 81 (4):457 – 480.
    Are there questions for which 'there is no determinate fact of the matter' as to which answer is correct? Most of us think so, but there are serious difficulties in maintaining the view, and in explaining the idea of determinateness in a satisfactory manner. The paper argues that to overcome the difficulties, we need to reject the law of excluded middle; and it investigates the sense of 'rejection' that is involved. The paper also explores the logic that is required if (...)
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  • A Comparative Taxonomy of Medieval and Modern Approaches to Liar Sentences.C. Dutilh Novaes - 2008 - History and Philosophy of Logic 29 (3):227-261.
    Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...)
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  • Maudlin’s Truth and Paradox. [REVIEW]Hartry Field - 2006 - Philosophy and Phenomenological Research 73 (3):713–720.
    Tim Maudlin’s Truth and Paradox is terrific. In some sense its solution to the paradoxes is familiar—the book advocates an extension of what’s called the Kripke-Feferman theory (although the definition of validity it employs disguises this fact). Nonetheless, the perspective it casts on that solution is completely novel, and Maudlin uses this perspective to try to make the prima facie unattractive features of this solution seem palatable, indeed inescapable. Moreover, the book deals with many important issues that most writers on (...)
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  • The Deflationary Theory of Truth.Daniel Stoljar - 2008 - Stanford Encyclopedia of Philosophy.
    According to the deflationary theory of truth, to assert that a statement is true is just to assert the statement itself. For example, to say that ‘snow is white’ is true, or that it is true that snow is white, is equivalent to saying simply that snow is white, and this, according to the deflationary theory, is all that can be said significantly about the truth of ‘snow is white’.
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  • Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
  • 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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  • 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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  • A Disquotational Theory of Truth as Strong as Z 2 −.Thomas Schindler - 2015 - Journal of Philosophical Logic 44 (4):395-410.
    T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee, the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors ) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus (...)
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  • Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
    We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...)
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  • More on 'A Liar Paradox'.Richard G. Heck - 2012 - Thought: A Journal of Philosophy 1 (4):270-280.
    A reply to two responses to an earlier paper, "A Liar Paradox".
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  • New Grounds for Naive Truth Theory.Stephen Yablo - 2004 - In J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox. Clarendon Press. pp. 312-330.
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  • The Consistency of The Naive Theory of Properties.Hartry Field - 2004 - Philosophical Quarterly 54 (214):78-104.
    If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering paradox. (...)
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  • Some Observations on Truth Hierarchies: A Correction.Philip D. Welch - 2020 - Review of Symbolic Logic 13 (4):857-860.
    A correction is needed to our paper: to the definition contained within the statement of Lemma 1.5 and thus arguments around it in §3.
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  • Ineffability and Revenge.Chris Scambler - 2020 - Review of Symbolic Logic 13 (4):797-809.
    In recent work Philip Welch has proven the existence of ‘ineffable liars’ for Hartry Field’s theory of truth. These are offered as liar-like sentences that escape classification in Field’s transfinite hierarchy of determinateness operators. In this article I present a slightly more general characterization of the ineffability phenomenon, and discuss its philosophical significance. I show the ineffable sentences to be less ‘liar-like’ than they appear in Welch’s presentation. I also point to some open technical problems whose resolution would greatly clarify (...)
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  • Type-Free Truth.Thomas Schindler - 2015 - Dissertation, Ludwig Maximilians Universität München
    This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their model-theoretic, recursion-theoretic and proof-theoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then discuss the prospects of classical type-free truth. (...)
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  • Indeterminate Truth.Patrick Greenough - 2008 - Midwest Studies in Philosophy 32 (1):213-241.
    In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...)
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  • What Theories of Truth Should Be Like (but Cannot Be).Hannes Leitgeb - 2007 - Philosophy Compass 2 (2):276–290.
  • Some Observations on Truth Hierarchies.P. D. Welch - 2014 - Review of Symbolic Logic 7 (1):1-30.
    We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...)
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  • On Artifacts and Truth-Preservation.Shawn Standefer - 2015 - Australasian Journal of Logic 12 (3):135-158.
    In Saving Truth from Paradox, Hartry Field presents and defends a theory of truth with a new conditional. In this paper, I present two criticisms of this theory, one concerning its assessments of validity and one concerning its treatment of truth-preservation claims. One way of adjusting the theory adequately responds to the truth-preservation criticism, at the cost of making the validity criticism worse. I show that in a restricted setting, Field has a way to respond to the validity criticism. I (...)
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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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  • 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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  • 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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  • Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.
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  • Self-Reference and the Languages of Arithmetic.Richard Heck - 2007 - Philosophia Mathematica 15 (1):1-29.
    I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of self-reference.
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  • Field’s Logic of Truth.Vann McGee - 2010 - Philosophical Studies 147 (3):421-432.
  • Truth and the Unprovability of Consistency.H. Field - 2006 - Mind 115 (459):567-606.
    It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...)
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  • The Inexpressibility of Validity.Julien Murzi - 2014 - Analysis 74 (1):65-81.
    Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...)
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  • Paths to Triviality.Tore Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.
    This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An (...)
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  • More Reflections on Consequence.Julien Murzi & Massimiliano Carrara - 2014 - Logique Et Analyse 57 (227):223-258.
    This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections (...)
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  • Compositional Principles Vs. Schematic Reasoning.Hartry Field - 2006 - The Monist 89 (1):9-27.
  • 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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  • Super Liars.Philippe Schlenker - 2010 - Review of Symbolic Logic 3 (3):374-414.
    Kripke’s theory of truth succeeded in providing a trivalent semantics for a language that contains its own truth predicate and means of self-reference; but it did so by radically restricting the expressive power of the logic. In Kripke’s analysis, the Liar (e.g. This very sentence is not true) receives the indeterminate truth value; but the logic cannot express the fact that the Liar is something other than true: in order to do so, a weak negation not* would be needed, but (...)
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  • Weak Systems of Determinacy and Arithmetical Quasi-Inductive Definitions.P. D. Welch - 2011 - Journal of Symbolic Logic 76 (2):418 - 436.
    We locate winning strategies for various ${\mathrm{\Sigma }}_{3}^{0}$ -games in the L-hierarchy in order to prove the following: Theorem 1. KP+Σ₂-Comprehension $\vdash \exists \alpha L_{\alpha}\ models"\Sigma _{2}-{\bf KP}+\Sigma _{3}^{0}-\text{Determinacy}."$ Alternatively: ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}-{\mathrm{C}\mathrm{A}}_{0}\phantom{\rule{0ex}{0ex}}$ "there is a β-model of ${\mathrm{\Delta }}_{3}^{1}-{\mathrm{C}\mathrm{A}}_{0}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17 em}}{\mathrm{\Sigma }}_{3}^{0}$ -Determinacy." The implication is not reversible. (The antecedent here may be replaced with ${\mathrm{\Pi }}_{3}^{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left({\mathrm{\Pi }}_{3}^{1}\right)-{\mathrm{C}\mathrm{A}}_{0}:\text{\hspace{0.17em}}{\mathrm{\Pi }}_{3}^{1}$ instances of Comprehension with only ${\mathrm{\Pi }}_{3}^{1}$ -lightface definable parameters—or even weaker theories.) Theorem 2. KP +Δ₂-Comprehension +Σ₂-Replacement + ${\mathrm{\Sigma }}_{3}^{0}\phantom{\rule{0ex}{0ex}}$ -Determinacy. (Here AQI (...)
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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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  • Ultimate Truth Vis- À- Vis Stable Truth.P. D. Welch - 2008 - Review of Symbolic Logic 1 (1):126-142.
    We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...)
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  • Contextual-Hierarchical Reconstructions of the Strengthened Liar Problem.Christine Schurz - 2015 - Journal of Philosophical Logic 44 (5):517-550.
    In this paper we shall introduce two types of contextual-hierarchical approaches to the strengthened liar problem. These approaches, which we call the ‘standard’ and the ‘alternative’ ch-reconstructions of the strengthened liar problem, differ in their philosophical view regarding the nature of truth and the relation between the truth predicates T r n and T r n+1 of different hierarchy-levels. The basic idea of the standard ch-reconstruction is that the T r n+1-schema should hold for all sentences of \. In contrast, (...)
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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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  • On Heck's New Liar.Julien Murzi - 2012 - Thought: A Journal of Philosophy 1 (2):258-269.
    Richard Heck has recently drawn attention on a new version of the Liar Paradox, one which relies on logical resources that are so weak as to suggest that it may not admit of any “truly satisfying, consistent solution”. I argue that this conclusion is too strong. Heck's Liar reduces to absurdity principles that are already rejected by consistent paracomplete theories of truth, such as Kripke's and Field's. Moreover, the new Liar gives us no reasons to think that (versions of) these (...)
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  • 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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