Yablo’s Paradox and ω-Inconsistency

Ketland, Jeffrey

doi:10.1007/s11229-005-6201-6

Cited by 50 publications

(31 citation statements)

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“…Alethic reference (just "reference", from now on) is introduced in order to study the reference patterns underlying the semantic paradoxes. Accordingly, it is a relation 11 See Hardy [14] and Ketland [18,19]. A theory formulated in an extension of L is said to be ωinconsistent just in case there is a formula ϕ(x) such that, for each n ∈ ω, ϕ(n) is a theorem and, at the same time, the theory entails ¬∀x ϕ(x).…”

Section: Alethic Referencementioning

confidence: 99%

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Reference and Truth

Picollo

2019

J Philos Logic

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I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide prooftheoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, proof-theoretically strong, and compare well to the most renowned systems in the literature.

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Section: Alethic Referencementioning

confidence: 99%

“…This establishes a link between direct reference and Leitgeb's [21] notion of dependence. 19 More specifically, it follows that ϕ depends on ϕ . The converse doesn't hold, that is, ϕ is not a subset of every set ϕ depends on as, e.g.…”

Section: Well-founded Truthmentioning

confidence: 99%

Reference and Truth

Picollo

2019

J Philos Logic

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“…Let T YA be the axiomatic theory of truth PA 1 ∪ the Local Yablo Disquotation Scheme (LYD) ∪ {Y(n) ↔ ∀k > n, ¬Tr( Y(k) ): n ∈ ω}. 11 As Ketland shows, 12 this theory is ω-inconsistent. 13 In order to appreciate the point with more detail, let A(k) be = Tr(Y(k)).…”

Section: Ii-mentioning

confidence: 99%

“…T YA ∀k > 1, ¬ Tr( Y(k) ) by 2 and Yablo's biconditionals 11 TYA is the weakest theory of truth that can express the sentences of Yablo's sequence. Of course, one could add the Local Yablo Disquotational Scheme to T (PA).…”

Section: Ii-mentioning

confidence: 99%

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Theories of Truth without Standard Models and Yablo’s Sequences

Barrio

2010

Stud Logica

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The aim of this paper is to show that it's not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo's Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn't have models. So, while having an ω-inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.The initial formulation of Yablo's Paradox 1 consists in an infinite set of sentences that is linearly ordered. Each of them claims that all sentences occurring later in the series are not true. At least at a superficial level, the series doesn't seem to involve any kind of self-reference. 2 According to Yablo, the set of sentences would be incapable of having a model and, therefore, it would be unsatisfiable. Of course, this result is controversial. It has been criticized by Priest and Ketland. 3 In particular, starting from a formulation of the series expressed in the language of arithmetic, Ketland shows that it is possible to find a non-standard model for Yablo's sequences. In this paper, I argue that Yablo's sequences introduces new boundaries 1 [23] and [25]. 2 Far from a general consensus on this, there are many who claim that Yablo didn't manage to show that there is not some kind of circularity involved in his sequence. Mainly, Priest and Beall belong to this group and Bueno, Colyvan, Leitgeb, Sorensen and Yablo have maintain that Yablo's list generates a semantic paradox without circularity. See [1, 2, 13, 16, 20] and [25]. 3 See [16] and [11].

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Yablo Sequences in Truth Theories

Cieśliński

2013

Logic and Its Applications

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Yablo’s Paradox and ω-Inconsistency

Cited by 50 publications

References 4 publications

Reference and Truth

Reference and Truth

Theories of Truth without Standard Models and Yablo’s Sequences

Yablo Sequences in Truth Theories

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