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Logic Without Gaps or Gluts

Part of the Synthese Library Book Series (volume 458)

DOI: 10.1007/978-3-030-94624-1

ISBN: 978-3-030-94623-4

Publisher: Springer International Publishing - Springer Journals

Feb 25, 2022

Available

Logic and the Liar Paradox

Burgis, Benjamin Alan

Pages: 1 –15

[The Liar and related paradoxes create a prima facie conflict between two equally important principles of classical logic—the Law of the Excluded Middle (LEM) and the Law of Non-Contradiction (LNC). Dialetheists such as Graham Priest and JC Beall solve the paradoxes by accepting the negations of...
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Graham Priest and Dialetheism

Burgis, Benjamin Alan

Pages: 17 –29

[Most dialetheists and most non-dialetheists agree that the argument from the semantic paradoxes to the existence of true contradictions is the strongest argument for dialetheism. Indeed, apart from Graham Priest, most dialetheists regard contradicts about the alethetic status of paradoxical...
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How to Solve Priest’s Paradoxes Without Sacrificing Classical Logic

Burgis, Benjamin Alan

Pages: 31 –48

[Objections are made to (almost) all of the “priestly” arguments for dialetheism discussed in Chap. 2. For example, we can accept normative dilemmas either in the law or in other domains without having any particularly compelling reason to postulate the existence of true normative contradictions....
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Dialetheism and the Laws of Logic

Burgis, Benjamin Alan

Pages: 49 –64

[Graham Priest accepts the traditional definition of validity as truth-preservation, but conceptual headaches arise when we try to dialetheically make sense of truth-preservation. Does truth-preservation mean that true premises always lead to true conclusions, or that they never lead to false...
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Dialetheism, Rejection, and Curry’s Paradox

Burgis, Benjamin Alan

Pages: 65 –101

[The dialetheist proposes to block the inference from paradox to triviality not by blocking the inference from paradox to contradiction but by blocking the inference from contradiction to triviality. This strategy is undermined by Curry’s Paradox, in which the inference goes from paradox to...
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Dialetheism, Rejection, and Probability Theory

Burgis, Benjamin Alan

Pages: 103 –124

[If Principle R and related attempts to substitute rejection-talk for negation-talk fail, what remaining options does the dialetheist have at her disposal? Priest has suggested that, since the statistical frequency of true contradictions is quite low, classical laws that are not deductively valid...
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Hartry Field and Paracompleteness

Burgis, Benjamin Alan

Pages: 125 –146

[The paracomplete solution to the semantic paradoxes championed by Hartry Field might seem to be more promising than its paraconsistent competitor. Embracing some logical contradictions is more initially implausible than rejecting both disjuncts of some instances of the LEM. On closer...
Available

How to Solve the Liar Paradox Without Sacrificing Classical Logic

Burgis, Benjamin Alan

Pages: 147 –180

[After seven chapters of seeing how important proposed solutions to the paradoxes can go wrong, several important things learned along the way are pulled together to propose a positive alternative (rooted in a non-standard way of parsing disquotationalism about truth called Content Inheritance...

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