On Williamson's new Quinean argument against nonclassical logic

Beall, Jc

doi:10.26686/ajl.v16i7.5915

Cited by 5 publications

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“…See(Williamson, 2007(Williamson, , 2017b(Williamson, , 2020Priest, 2008Priest, , 2014Priest, , 2021Russell, 2014Russell, , 2015Russell, , 2019Beall, 2017Beall, , 2019Hjortland, 2017Hjortland, , 2019Hjortland, , 2022Martin, 2021cMartin, ,a,b, 2022Zanetti, 2021; Australasian Journal of Logic (20:3) 2023, Article no. 1…”

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Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality

Andersen

2023

AJL

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A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory.

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Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality

Andersen

2023

AJL

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“… But on this, see In Contradiction, p. 66, and [Mortensen and Priest, 1981]. 17 For some discussion, see[Priest, 2014], and similarly[Beall, 2019].…”

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A Tale of Excluding the Middle

Beall

Priest

2021

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he paper discusses a number of interconnected points concerning negation, truth, validity and the liar paradox. In particular, it discusses an argument for the dialetheic nature of the liar sentence which draws on Dummett’s teleological account of truth. Though one way of formulating this fails, a different way succeeds. The paper then discusses the role of the Principle of Excluded Middle in the argument, and of the thought that truth in a model should be a model of truth.

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Logical Maximalism in the Empirical Sciences

Brîncuş

2021

Karl Popper's Science and Philosophy

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Karl R. Popper (1947a, b) took the central topic of logic to be the theory of deductive inference and the main problem he was concerned with in his early writings on deductive logic was to give a satisfactory definition for the notion of "deductive valid inference". Although his definition was supposed to be a generalization of Tarski's definition of logical consequence, Popper showed that the notion of "truth" can be avoided, even though its use is not objectionable. In addition, unlike Tarski's modeltheoretic (or, better, group-theoretic) criterion, he proposed an inferential criterion to draw a line between the formative (i.e., logical) and the non-formative signs (i.e., non-logical) and defined the validity of deductive inferences on the basis of inferential definitions. 1 Although the notion of truth can be avoided in this inferential foundational approach to deductive inferences, in some latter writings Popper acknowledged that the validity of deduction goes beyond the signs and the rules that govern their use, and emphasized the constitutive role that the notion of truth has for logical deduction: Deduction, I contend, is not valid because we choose or decide to adopt its rules as a standard, or decree that they shall be accepted; rather, it is valid because it adopts, and incorporates, the rules by which truth is transmitted from (logically stronger) premises to (logically weaker) conclusions, and by which falsity is re-transmitted from conclusions to premises. (This retransmission of falsity makes formal logic the Organon of rational criticism -that is, of refutation). (Popper 1962, 64) In addition, Popper et al. (1970, 18) took the notion of truth to be crucial for the applications of logic in the other areas of inquiry. With regard to these applications,

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On Williamson's new Quinean argument against nonclassical logic

Cited by 5 publications

References 25 publications

Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality

Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality

A Tale of Excluding the Middle

Logical Maximalism in the Empirical Sciences

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