Comparing Fixed-Point and Revision Theories of Truth

Kremer, Philip

doi:10.1007/s10992-009-9107-9

Cited by 13 publications

(36 citation statements)

References 14 publications

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“…Sections 2 and 3 of Kremer [8] develop the fixed-point semantics [9,10] and the revision theoretic semantics [6] for languages expressing their own truth concepts. Here, we repeat the main definitions without the discussion and motivation.…”

Section: Fixed-point and Revision Theories Of Truthmentioning

confidence: 99%

“…We will define ten fixed-point theories of truth and three revision theories. As pointed out in [8], each of these thirteen theories relies on what M. Kremer [7] calls the supervenience of semantics: the intuition that the interpretation of T should be determined by the interpretation of the nonsemantic names, function symbols and relation symbols, as represented by a ground model. M. Kremer argues both that that Kripke [9] does not endorse this proposal, and that this proposal misinterprets the fixed-point semantics.…”

Section: Fixed-point and Revision Theories Of Truthmentioning

confidence: 99%

“…And yet lfp(μ M ) and lfp(κ M ) are nonclassical: thus it seems that neither of the least-fixed-point theories T lfp,μ or T [8].) Gupta and Belnap introduce their notion of a Thomason model (see [8], Definition 4.7) in order to clarify the advantage that they claim for their approach: "its consequence that truth behaves like an ordinary classical concept under ... conditions that can roughly be characterized as those in which there is no vicious reference in the language." The notion of a Thomason model is a formalization of the notion of a nonpathological ground model, i.e.…”

Section: Truth Behaving Like a Classical Conceptmentioning

confidence: 99%

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How Truth Behaves When There’s No Vicious Reference

Kremer

2010

J Philos Logic

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In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth "its consequence that truth behaves like an ordinary classical concept under certain conditionsconditions that can roughly be characterized as those in which there is no vicious reference in the language." To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of "no vicious reference" generated both by revision theories of truth and by fixedpoint theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.

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Section: Fixed-point and Revision Theories Of Truthmentioning

confidence: 99%

Section: Fixed-point and Revision Theories Of Truthmentioning

confidence: 99%

Section: Truth Behaving Like a Classical Conceptmentioning

confidence: 99%

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How Truth Behaves When There’s No Vicious Reference

Kremer

2010

J Philos Logic

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“…Martin [45], with a response by Gupta [22]. A systematic comparison between fixedpoint and revision theories of truth was provided by Kremer [36]. There was a critical evaluation of the motivations for adopting revision rules presented by Shapiro [54], with a response by Gupta [25,[160][161]].…”

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Guest Editors’ Introduction

Bruni

Standefer

2018

J Philos Logic

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by Hans Herzberger, revision theory appears as a proposal to deal with a type-free concept of formal truth that preserves the classical scheme [7,20,28,29]. Though the story is well-known, we think it would be useful to recapitulate here, in a brief and obviously incomplete summary, some of the main events by means of which the original proposals developed into the current, broader field of investigation, to give the uninitiated reader a rough idea of the context for the contributions in this volume. 1 In his seminal work from the 1930's, Alfred Tarski proved the existence of a fundamental inconsistency emerging in a situation where: (i) there is a formal language L respecting some modest assumptions on its strength in expressive capabilities; (ii) the language contains a unary, unrestricted predicate T for (codes of) formulas working as a truth predicate, verifying natural principles that require that the formula T ( ϕ ) be equivalent to ϕ, for every sentence ϕ of L; (iii) a classical relation of satisfaction for formulas of L in any interpretation, or model M, is retained, therefore each sentence ϕ of L is assumed to take either semantic value 1 or 0. Tarski's contradiction took the form of a theorem about the (arithmetical) undefinability of such predicate T for any L, granted (i)-(iii). Tarski's theorem shows that no sufficiently expressive, classical formal language can consistently contain its own truth predicate. As a solution, he proposed a typed theory of formal truth, asserting that every language L for 1 The interested reader should consult [38] for a more detailed introduction to revision theory.

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“…See, for example,Kremer [1988],Gupta and Belnap [1993], orKremer [2009].15 In this connection, it is worth briefly mentioningField [2008]. Field uses a revisiontheoretic construction to interpret a conditional, which does not obey the conditional form of contraction, and at each stage of revision, he constructs a fixed-point to interpret the truth predicate, holding fixed the interpretation of the conditional.…”

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Contraction and revision

Standefer

2016

AJL

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An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.

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Comparing Fixed-Point and Revision Theories of Truth

Cited by 13 publications

References 14 publications

How Truth Behaves When There’s No Vicious Reference

How Truth Behaves When There’s No Vicious Reference

Guest Editors’ Introduction

Contraction and revision

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