Metainferences from a Proof-Theoretic Perspective, and a Hierarchy of Validity Predicates

Golan, Rea

doi:10.1007/s10992-021-09616-6

Cited by 11 publications

(2 citation statements)

References 19 publications

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“…And second, there is still no sequent calculus for Scambler's hierarchy. Nevertheless, there are many sequent calculi for ST ω that have been developed by, e.g., Cobreros et al (2021)-that uses a labeled sequent calculus-, Golan (2021) and Da Ré and Pailos (2021)-both unlabeled options. For these two reasons, we prefer to stick to ST ω instead of going all the way up.…”

Section: Anti-exceptionalism About Logic and The Buenos Aires Planmentioning

confidence: 99%

Anti-exceptionalism, truth and the BA-plan

2021

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Anti-exceptionalism about logic states that logical theories have no special epistemological status. Such theories are continuous with scientific theories. Contemporary anti-exceptionalists include the semantic paradoxes as a part of the elements to accept a logical theory. Exploring the Buenos Aires Plan, the recent development of the metainferential hierarchy of ST-logics shows that there are multiple options to deal with such paradoxes. There is a whole ST-based hierarchy, of which LP and ST themselves are only the first steps. This means that the logics in this hierarchy are also options to analyze the inferential patterns allowed in a language that contains its own truth predicate. This paper explores these responses analyzing some reasons to go beyond the first steps. We show that LP, ST and the logics of the ST-hierarchy offer different diagnoses for the same evidence: the inferences and metainferences the agents endorse in the presence of the truth-predicate. But even if the data are not enough to adopt one of these logics, there are other elements to evaluate the revision of classical logic. Which is the best explanation for the logical principles to deal with semantic paradoxes? How close should we be to classical logic? And mainly, how could a logic obey the validities it contains (just like classical logic)? From an antiexceptionalist perspective, we argue that ST-metainferential logics in general-and STT ω in particular-are the best available options to explain the inferential principles involved with the notion of truth.

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Section: Anti-exceptionalism About Logic and The Buenos Aires Planmentioning

confidence: 99%

Anti-exceptionalism, truth and the BA-plan

2021

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“…al., so they can also be used for our logics. Finally, Golan[41] develops a sequent-calculus for STω which might be adapted for the mc-logics based on LP or K3 without much trouble (the rules for inferential validities should be the ones for LP or K3 that Golan also introduces in his article).…”

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confidence: 99%

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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Introduction

Pailos,

Da Ré

2023

Trends in Logic

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Metainferences from a Proof-Theoretic Perspective, and a Hierarchy of Validity Predicates

Cited by 11 publications

References 19 publications

Anti-exceptionalism, truth and the BA-plan

Anti-exceptionalism, truth and the BA-plan

Meta-Classical Non-Classical Logics

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