Paradox and Logical Revision. A Short Introduction

Murzi, Julien; Carrara, Massimiliano

doi:10.1007/s11245-014-9286-z

Cited by 6 publications

(2 citation statements)

References 69 publications

(75 reference statements)

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“…Non-classical logics figure out interesting tools for dealing with paradoxes. As Murzi and Carrara (2015) observe, such logical revision should go through substructural logics, which abandon some structural rules, since semantic theories based on nonclassical structural logics are usually subjected to v-Curry. 6 In what follows, we will analyze two non-classical solutions: a structural solution given by Pailos (2020) and a substructural solution given by Barrio et al (2016).…”

Section: Non-classical Solutionsmentioning

confidence: 99%

On validity paradoxes and (some of) their solutions

Bezerra

2023

Principia

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Many semantic theories become trivial when extended with a naïve validity predicate due to the validity paradoxes. The non-classical semantic theories are the ones that allegedly preserve the naïveté of the validity predicate while being capable of avoiding the validity paradoxes. This blocking, on the other hand, usually comes at a high cost. In this paper, we argue that the pre-theoretical notion of validity that the naïve validity predicate intends to capture is unattainable.

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Section: Non-classical Solutionsmentioning

confidence: 99%

On validity paradoxes and (some of) their solutions

Bezerra

2023

Principia

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“…For a survey see, again,(Murzi and Carrara, 2015b). See also the special issue edited byMurzi and Carrara (2015a) on Paradox and Logical Revision for an extensive number of papers on this topic.5 Substructural approaches can be either of the SContr-free (from Γ , φ, φ ⊢ ψ it follows that Γ , φ ⊢ ψ) or Cut-free (from Γ ⊢ φ and ∆, φ ⊢ ψ it follows that Γ, ∆ ⊢ ψ).…”

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confidence: 99%

A Note on Gödel, Priest and Naïve Proof

Carrara

Martino

2020

LLP

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In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel's first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel's conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between Gödel's theorem and naïve proof so understood, both from a classical and a dialetheic perspective.

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Classicality Lost: K3 and LP after the Fall

Jenny

2017

Thought: A Journal of Philosophy

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It is commonly held that the ascription of truth to a sentence is intersubstitutable with that very sentence. However, the simplest subclassical logics available to proponents of this view, namely K3 and LP, are hopelessly weak for many purposes. In this paper, I argue that this is much more of a problem for proponents of LP than for proponents of K3. The strategies for recapturing classicality o ered by proponents of LP are far less promising than those available to proponents of K3. This undermines the ability of proponents LP to engage in public reasoning in classical domains. IntroductionGottlob Frege famously held that "nothing is added to [a] thought by . . . ascribing to it the property of truth" ( , ). This idea is commonly expressed with the slogan that truth is transparent: φ and T r ( φ ) -the sentence that says that φ is true-are fully intersubstitutable in extensional contexts. Unfortunately, in classical logic, the law of excluded middle, i.e.φ ∨ ¬φ, and the rule of explosion, i.e. φ, ¬φ ∴ ψ, allow us to derive any sentence from the liar sentence if we have transparency. It's tempting to put the blame on transparency here.However, it isn't entirely obvious what to replace transparency with. That is why a number of authors have instead blamed classical logic. Saul Kripke ( ), Robert Martin and Peter ' φ ' is a term for φ in the object language. Note that the corner quotes here are Gödel quotes, not Quine quotes. To be fully precise, I would need to use both kinds of quotes; however, since corner quotes are commonly used for both, I allow myself the usual use-mention sloppiness here and throughout.See McGee ( ) and Halbach ( ) for surveys of some of the options.

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Paradox and Logical Revision. A Short Introduction

Cited by 6 publications

References 69 publications

On validity paradoxes and (some of) their solutions

On validity paradoxes and (some of) their solutions

A Note on Gödel, Priest and Naïve Proof

Classicality Lost: K3 and LP after the Fall

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