The logic of paradox

Priest, Graham

doi:10.1007/bf00258428

Cited by 826 publications

(398 citation statements)

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“…In particular, we refer to [21,22] or [3] for details. We rehearse some prominent features of these logics: both logics validate the classical rules of conjunction introduction, conjunction elimination, De Morgan laws for conjunction and negation, double negation introduction as well as elimination, universal generalization, and universal instantiation.…”

Section: Definition 13 An Mv-model M Is a Tuple D I Such Thatmentioning

confidence: 99%

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Tolerant, Classical, Strict

et al. 2010

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In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.

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Section: Definition 13 An Mv-model M Is a Tuple D I Such Thatmentioning

confidence: 99%

“…In particular, they bear an unexpected connection to more familiar many-valued logics: the Logic of Paradox (LP) proposed by Priest in [21], and its dual, so-called "Strong Kleene" logic (K3). Because of this, they cast a new light on these many valued approaches, as applied to vagueness.…”

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confidence: 99%

Tolerant, Classical, Strict

et al. 2010

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“…The addition of a third truth value to deal with vague predicates or with the truth predicate leaves a number of issues open, however, starting with the interpretation of the third truth value, and with the choice of an appropriate consequence relation. Let us agree to call the value 1 'true-only', value 0 'false-only', and leave open what to call the value 1 2 (see [Priest, 1979], [Lewis, 1982]). Depending on the view, 1 2 may be called 'neither true nor false', or 'both true and false'.…”

Section: Introductionmentioning

confidence: 99%

“…On paracomplete approaches, the Liar sentence is fundamentally viewed as neither true nor false, and borderline cases of vague predicates are cases for which it is neither true nor false that the predicate applies. On the dual, paraconsistent approaches to vagueness and the Liar paradox ( [Priest, 1979]), the Liar sentence is fundamentally viewed as both true and false, and similarly borderline cases of vague predicates are cases for which it is both true and false that the predicate applies. Importantly, distinct logics result depending on which interpretation of the third truth value is favored, and on whether logical consequence is defined as the preservation of the value 1 (the true-only), or as the preservation of non-0 values (the non-(false-only)).…”

Section: Introductionmentioning

confidence: 99%

Vagueness, Truth and Permissive Consequence

Cobreros

Égré

Ripley

et al. 2015

Unifying the Philosophy of Truth

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We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

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“…Let us give two examples. First, the identity function (ϕ) = ϕ conservatively maps the Logic of Paradox (LP ) [14] into classical propositional logic, because LP has exactly the same valid formulas as classical propositional logic. Second, the function (ϕ) = p ∧ ¬p (where p is some atomic formula) conservatively maps Strong Three-valued Logic (K 3 ) [10,11] into classical propositional logic, because K 3 does not have any valid formulas.…”

Section: Introductionmentioning

confidence: 99%

Three-valued Logics in Modal Logic

Kooi

Tamminga

2012

Stud Logica

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Abstract.Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any threevalued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In general, our Translation Manual gives rise to translations that are exponentially longer than their originals. This fact raises the question whether there are three-valued logics for which there is a shorter translation into S5. The answer is affirmative: we present an elegant linear translation of the Logic of Paradox and of Strong Three-valued Logic into S5.

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The logic of paradox

Cited by 826 publications

References 10 publications

Tolerant, Classical, Strict

Tolerant, Classical, Strict

Vagueness, Truth and Permissive Consequence

Three-valued Logics in Modal Logic

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