Logical pluralism without the normativity

Blake‐Turner, Christopher; Russell, Gillian

doi:10.1007/s11229-018-01939-3

Cited by 16 publications

(16 citation statements)

References 20 publications

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“…Most of them rely on relativising the normatively relevant logic to some plausible parameter. Some authors choose this parameter to be the context [Caret, 2017;Kouri Kissel, 2018], some choose it to be the epistemic goal or purpose [Blake-Turner and Russell, 2021], and yet other choose it to be the domain of inquiry (physics, economics, etc.) [Hjortland, 2017].…”

Section: The Collapse Argumentmentioning

confidence: 99%

Logical Pluralism and Interpretations of Logical Systems

Tajer¹,

Fiore

2022

LLP

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Logical pluralism is a general idea that there is more than one correct logic. Carnielli and Rodrigues [2019a] defend an epistemic interpretation of the paraconsistent logic N4, according to which an argument is valid in this logic just in case it necessarily preserves evidence. The authors appeal to this epistemic interpretation to briefly motivate a kind of logical pluralism: “different accounts of logical consequence may preserve different properties of propositions”. The aim of this paper is to study the prospect of a logical pluralism based on different interpretations of logical systems. First, we give our analysis of what it means to interpret a logic – and make some hopefully useful distinctions along the way. Second, we present what we call an interpretational logical pluralism: there is more than one correct logic and a logic is correct only if it has some adequate interpretation. We consider four variants of this idea, bring up some possible objections, and try to find plausible solutions on behalf of the pluralist. We will argue that interpretations of logical systems provide a promising – albeit not unproblematic – route to logical pluralism.

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Section: The Collapse Argumentmentioning

confidence: 99%

Logical Pluralism and Interpretations of Logical Systems

Tajer¹,

Fiore

2022

LLP

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“…And more generally, if we could determine that the superstructure of a theory for a logic V was accurate, and explosion was among V's E‐sentences, that would tell us whether explosion was valid tout court. (Blake‐Turner & Russell, 2021, p. S4863)…”

Section: Anti‐exceptionalism: Continuity and Logical Theory Choicementioning

confidence: 99%

“…In other words, logical theories are justified by abductive means. (Martin, 2021, p. 9071)In order to make sense of the idea that a theory correctly describes the relevant data, the first step in current anti‐exceptionalism consists in the assumption of a dichotomy between what is valid merely according to a theory , and what is valid simpliciter or valid tout court (Hjortland, 2019, p. 253; Blake‐Turner & Russell, 2021, p. S4863). Knowledge of logic is achieved when that which is valid according to the theory we choose matches with what is really valid.…”

Section: Anti‐exceptionalism: Continuity and Logical Theory Choicementioning

confidence: 99%

Logical anti‐exceptionalism meets the “logic‐as‐models” approach

Arenhart

2022

Theoria

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Logical anti-exceptionalism is the view that logic is not special, it is continuous with science. This continuity is typically understood in terms of the use of the abductive method in logical theory choice, with logical knowledge resulting from our choice of the theory best accounting for the data. In this paper, we argue for two related claims: (i) that this understanding of the continuity between logic and science faces considerable challenges; and (ii) that such challenges may be avoided by elaborating the continuity of logic with science in terms of the "logic-as-models" approach. More specifically, we defend that logical theories should be seen in the lights of the "models-as-epistemic-tools" approach, an approach to the nature of models in empirical science more closely connected with current scientific practice. The result is a version of logical anti-exceptionalism opening new perspectives for the philosophical understanding of logic.

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“…We thus gain a sense of the radical idea of unknowability and ineffability that I am referring to here. It is the type that needs to be distinguished from weaker forms of 23 Aside from the paradoxical representation of both unknowability and ineffability, there is a distinction to be made between them. Hofweber [47] refers to this distinction in the following manner: "Ineffable facts, if there are any, are completely beyond us, unknowable and beyond what we can consider or entertain.…”

Section: A Ahsanmentioning

confidence: 99%

Islamic Contradictory Theology . . . Is there any such Thing?

Ahsan

2021

Log. Univers.

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The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall's (J Anal Theol, 7(1): 400-439, 2019) paper entitled 'Christ-A Contradiction: A Defense of 'Contradictory Christology' is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, 'Contradictory Christology'. There are at least two essential components of Beall's 'Contradictory Christology'. These include the dogmatic statements of Chalcedon and FDE logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction.

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Logical pluralism without the normativity

Cited by 16 publications

References 20 publications

Logical Pluralism and Interpretations of Logical Systems

Logical Pluralism and Interpretations of Logical Systems

Logical anti‐exceptionalism meets the “logic‐as‐models” approach

Islamic Contradictory Theology . . . Is there any such Thing?

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