Paraconsistent logic

Priest, Graham

doi:10.4324/9780415249126-y053-1

Cited by 40 publications

(61 citation statements)

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“…It would take us too far afield to try to rationally evaluate the various nonclassical proposals for a theory of truth (e.g., Kripke 1975;Priest 2002;Field 2008). Fortunately, we do not have to do so and neither does Maya for the special MERF principle to come into play.…”

Section: Fallibility About Specific Laws Of Logicmentioning

confidence: 96%

“…"This statement is not true"). All Maya needs to know is that prominent philosophers such as Kripke (1975) and Field (2008) have advocated the view that the instance of the law of excluded middle [L is true v -L is true] is not true, for it to be rational for Maya to assign it confidence of less than 1.0; and all she needs to know is that prominent philosophers such as Priest (2002) have advocated the view that the following explicit contradiction is true: [L is true & -L is not true], for it to be rational for Maya to assign it confidence of greater than zero. The special MERF principle easily explains this result, because Maya's MCS would acknowledge that the relative frequency of truth of propositions that have been defended by prominent philosophers even though they were at one time intuitively unattractive is greater than zero.…”

Section: Fallibility About Specific Laws Of Logicmentioning

confidence: 99%

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A non-probabilist principle of higher-order reasoning

Talbott

2015

Synthese

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The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency (MERF) principle. These are used to explain the rationality of revisions to an agent's degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them-especially reductions in confidence assignments to propositions antecedently regarded as certain-including certainty-reductions to instances of the law of excluded middle or the law of noncontradiction in logic or certainty-reductions to the certainties of probabilist epistemology. The author proposes special and general versions of the MERF principle and uses them to explain the examples, including the reasoning that would lead to thoroughgoing fallibilism-that is, to a state of being certain of nothing (not even the MERF principle itself). The author responds to the main defenses of probabilism: Dutch Book arguments, Joyce's potential accuracy defense, and the potential calibration defenses of Shimony and van Fraassen by showing that, even though they do not satisfy the probability axioms, degrees of belief that satisfy the MERF principle minimize expected inaccuracy in Joyce's sense; they can be externally calibrated in Shimony and van Fraassen's sense; and they can serve as a basis for rational betting, unlike probabilist degrees of belief, which, in many cases, human beings have no rational way of ascertaining. The author also uses the MERF principle to subsume the various epistemic akrasia principles in the literature. Finally, the author responds to Titelbaum's argument that epistemic akrasia principles require that we be certain of some epistemological beliefs, if we are rational.

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Section: Fallibility About Specific Laws Of Logicmentioning

confidence: 96%

Section: Fallibility About Specific Laws Of Logicmentioning

confidence: 99%

A non-probabilist principle of higher-order reasoning

Talbott

2015

Synthese

View full text Add to dashboard Cite

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“…See [33](361) for discussion of expressing the extensionality axiom with a material biconditional. 6 Cantor goes on to relate his definition to the "Platonic ιδoς or ιδ α.…”

Section: Naive Setsmentioning

confidence: 99%

“…A theory is trivial if it contains every Φ. Any inconsistent but non-trivial theory must be based on a paraconsistent logic [37](151).…”

Section: Logicmentioning

confidence: 99%

Extensionality and Restriction in Naive Set Theory

Weber

2010

Stud Logica

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The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads to triviality.

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“…This passage has remained unchanged from its original version inPriest and Tanaka (1997).3 There is a separate question about whether anyone who accepts a contradiction could be ideally rational, and a further question whether everyone who uses an inconsistent theory accepts, or is committed to, that theory. SeeMichael (2013).…”

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confidence: 96%

On a “most telling” argument for paraconsistent logic

Michael

2015

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Priest and others have presented their "most telling" argument for paraconsistent logic: that only paraconsistent logics allow non-trivial inconsistent theories. This is a very prevalent argument; occurring as it does in the work of many relevant and more generally paraconsistent logicians. However this argument can be shown to be unsuccessful. There is a crucial ambiguity in the notion of non-triviality. Disambiguated the most telling reason for paraconsistent logics is either question-begging or mistaken. This highlights an important confusion about the role of logic in our development of our theories of the world. Does logic chart good reasoning or our commitments? We also consider another abductive argument for paraconsistent logics which also is shown to fail.

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Paraconsistent logic

Cited by 40 publications

References 0 publications

A non-probabilist principle of higher-order reasoning

A non-probabilist principle of higher-order reasoning

Extensionality and Restriction in Naive Set Theory

On a “most telling” argument for paraconsistent logic

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