Should the Non‐Classical Logician be Embarrassed?*

Rosenblatt, Lucas

doi:10.1111/phpr.12770

Cited by 8 publications

(4 citation statements)

References 36 publications

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“…Let us call this the hypocrisy objection to non-classical logics. Following Rosenblatt [59], we can say that the non-classical logician is in a dilemma: either she uses classical logic in her metatheory or she does not; if she does, then the hypocrisy objection seems to apply; but if she does not, then it seems that she must give up many important metalogical results.…”

Section: Philosophical Discussionmentioning

confidence: 99%

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Meta-Classical Non-Classical Logics

BARRIO,

FIORE,

PAILOS

2024

The Review of Symbolic Logic

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Recently, it has been proposed to understand a logic as containing not only a validity canon for inferences but also a validity canon for metainferences of any finite level. Then, it has been shown that it is possible to construct infinite hierarchies of 'increasingly classical' logics-that is, logics that are classical at the level of inferences and of increasingly higher metainferences-all of which admit a transparent truth predicate. In this paper, we extend this line of investigation by taking a somehow different route. We explore logics that are different from classical logic at the level of inferences, but recover some important aspects of classical logic at every metainferential level. We dub such systems meta-classical nonclassical logics. We argue that the systems presented deserve to be regarded as logics in their own right and, moreover, are potentially useful for the non-classical logician.

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Section: Philosophical Discussionmentioning

confidence: 99%

“…for the cases of intuitionism and dialetheism, respectively 24. See[42,47] and[32,59] for arguments against and in favor of this strategy, respectively.…”

mentioning

confidence: 99%

Meta-Classical Non-Classical Logics

BARRIO,

FIORE,

PAILOS

2024

The Review of Symbolic Logic

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“…We will not attempt to provide a full defense of this idea here, for one of us has already done this elsewhere (cf. Rosenblatt, 2022), but we will offer a sketch of how that defense would go.…”

Section: Theoretical Faithfulnessmentioning

confidence: 99%

Recapture Results and Classical Logic

Fiore

Rosenblatt

2023

Mind

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An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naive truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence non-classical theorists do not seem entitled to those results. In this paper we analyse these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity, and that once the ambiguity is removed there are no reasons to think that non-classical logicians are not entitled to their recapture results.

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“…operador "bola") (cf. Tajer, 2020;Rosenblatt, 2022). Se alzan una serie de objeciones contra el proyecto de recaptura.…”

Section: Introductionunclassified

Una revisión de la noción de coherencia desde la perspectiva de la lógica definida como secuencia de nociones de consecuencia

Pasqualini

2024

Anál. Filos.

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En el contexto de ofrecer lógicas alternativas que lidien no trivialmente con paradojas semánticas y superen a la vez la objeción de incoherencia que se alza habitualmente contra ellas, el BA-Plan propone una definición de lógica en el sentido de secuencia infinita de nociones de consecuencia que especifica estándares de validez para el nivel inferencial y para los metainferenciales. El presente trabajo argumenta que si se admite la conveniencia de esta definición de lógica es posible desacoplar la noción de coherencia entre estándares de validez de la noción de uniformidad entre estándares de validez.

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Should the Non‐Classical Logician be Embarrassed?*

Cited by 8 publications

References 36 publications

Meta-Classical Non-Classical Logics

Meta-Classical Non-Classical Logics

Recapture Results and Classical Logic

Una revisión de la noción de coherencia desde la perspectiva de la lógica definida como secuencia de nociones de consecuencia

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