Multiple-Conclusion Lp and Default Classicality

Beall, Jc

doi:10.1017/s1755020311000074

Cited by 79 publications

(77 citation statements)

References 17 publications

(14 reference statements)

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“…Begin with the assumption that truth naïvely plays capture and release (Beall 2007a(Beall , 2009, in the following minimal sense:…”

Section: Liars and Comentioning

confidence: 99%

“…'paradoxical' sentences are glutty, and ECQ must be given up. 4 But, unless a new conditional is added to the language (about which more in a moment), :-E, and indeed !-E (modus ponens) must be given up too: these rules fail to preserve truth for any / that is both true and false (Priest 2006b;Beall 2009). Kripke (1975) famously showed how to construct models for languages in which the truth-predicate is fully transparent, provided LEM and :-I (among other rules) are suitably restricted.…”

Section: Paracomplete and Paraconsistentmentioning

confidence: 99%

“…Partly for this reason, Beall (2011Beall ( , 2014b has recently advocated, following Goodship (1996), a detachment-free glut-theoretic approach to paradox-one that gives up the project of defining a 'suitable' conditional, and decidedly embraces the failure of !-E displayed by basic paraconsistent logics. Horsten (2009) essentially advocates a dual strategy in a paraconsistent setting.…”

Section: Paracomplete and Paraconsistentmentioning

confidence: 99%

“…4 See e.g. Asenjo (1966), Asenjo and Tamburino (1975), Priest (1979), Goodship (1996) Beall (2009), Beall (2011. 5 The standard conditional-involving Curry Paradox involves a sentence c identical to TrðpcqÞ !…”

Section: Paradoxes Of Naïve Logical Propertiesmentioning

confidence: 99%

“…To be sure, such a revision is not to be taken lightly (see Terzian, THIS VOLUME), and there is no shortage of classical treatments, either hierarchical (Tarski 1936;Parsons 1974b;Burge 1979;Williamson 1998;Glanzberg 2001Glanzberg , 2004aSchurz 2011), or non-hierarchical (Kripke 1975;McGee 1991;Gupta and Belnap 1993;Maudlin 2004;Leitgeb 2005;Simmons 1993, 2000. But, it has been argued, the alternatives are dire (Kripke 1975;Field 2008), the naïve semantic principles are non-negotiable (Field 2008;Beall 2009; for a criticism of their arguments, see Zardini, THIS VOLUME), and there might be independent reasons for putting the blame on the logic in the first place (Ripley, THIS VOLUME; Zardini, THIS VOLUME). So how can logic be revised on the face of semantic paradox?…”

mentioning

confidence: 99%

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Paradox and Logical Revision. A Short Introduction

Murzi¹,

Carrara

2014

Topoi

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“…Begin with the assumption that truth naïvely plays capture and release (Beall 2007a(Beall , 2009, in the following minimal sense:…”

Section: Liars and Comentioning

confidence: 99%

Section: Paracomplete and Paraconsistentmentioning

confidence: 99%

Section: Paracomplete and Paraconsistentmentioning

confidence: 99%

Section: Paradoxes Of Naïve Logical Propertiesmentioning

confidence: 99%

mentioning

confidence: 99%

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Paradox and Logical Revision. A Short Introduction

Murzi¹,

Carrara

2014

Topoi

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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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Annotated Natural Deduction for Adaptive Reasoning

Allo

Primiero

2019

Outstanding Contributions to Logic

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Multiple-Conclusion Lp and Default Classicality

Cited by 79 publications

References 17 publications

Paradox and Logical Revision. A Short Introduction

Paradox and Logical Revision. A Short Introduction

Classicality Lost: K3 and LP after the Fall

Annotated Natural Deduction for Adaptive Reasoning

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