Paradoxicality Without Paradox

Rosenblatt, Lucas

doi:10.1007/s10670-021-00405-w

Erkenn

2021

DOI: 10.1007/s10670-021-00405-w

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Paradoxicality Without Paradox

Lucas Rosenblatt

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Cited by 5 publications

(3 citation statements)

References 27 publications

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“…For example, see Williamson (2018), Murzi andRossi (2020) and Halbach and Nicolai (2018). Answers by non-classical logicians can be found in Rosenblatt (2021) and Field (2022.…”

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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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“…For example, see Williamson (2018), Murzi andRossi (2020) and Halbach and Nicolai (2018). Answers by non-classical logicians can be found in Rosenblatt (2021) and Field (2022.…”

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confidence: 99%

Recapture Results and Classical Logic

Fiore

Rosenblatt

2023

Mind

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“…For a number of related worries, see(Murzi and Rossi, 2020),(Halbach and Nicolai, 2018), and(Woods, 2019). I have addressed some of these other worries elsewhere, see(Rosenblatt, 2020b) and(Rosenblatt, 2021b).…”

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confidence: 99%

“…For example, given that the main aim of the paper is to show that classical recapture is in good standing, I have not said a word on the issue of whether there are revenge paradoxes involving the groundedness predicate, nor about whether one can express other modal-like notions besides groundedness, such as paradoxicality or hypodoxicality. I take up these matters elsewhere, see(Rosenblatt, 2020b) and(Rosenblatt and Gallovich, 2021).…”

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confidence: 99%

Should the Non‐Classical Logician be Embarrassed?*

Rosenblatt

2021

Philos Phenomenol Research

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Towards a Non-classical Meta-theory for Substructural Approaches to Paradox

Rosenblatt

2021

J Philos Logic

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Paradoxicality Without Paradox

Cited by 5 publications

References 27 publications

Recapture Results and Classical Logic

Recapture Results and Classical Logic

Should the Non‐Classical Logician be Embarrassed?*

Towards a Non-classical Meta-theory for Substructural Approaches to Paradox

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