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Gibbardian Collapse and Trivalent Conditionals

Abstract : This paper discusses the scope and significance of the so-called triviality result stated by Allan Gibbard for indicative conditionals, showing that if a conditional operator satisfies the Law of Import-Export, is supraclassical, and is stronger than the material conditional, then it must collapse to the material conditional. Gibbard's result is taken to pose a dilemma for a truth-functional account of indicative conditionals: give up Import-Export, or embrace the two-valued analysis. We show that this dilemma can be averted in trivalent logics of the conditional based on Reichenbach and de Finetti's idea that a conditional with a false antecedent is undefined. Import-Export and truth-functionality hold without triviality in such logics. We unravel some implicit assumptions in Gibbard's proof, and discuss a recent generalization of Gibbard's result due to Branden Fitelson.
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https://halshs.archives-ouvertes.fr/halshs-03090122
Contributor : Paul Égré <>
Submitted on : Tuesday, December 29, 2020 - 11:32:01 AM
Last modification on : Wednesday, December 30, 2020 - 11:36:46 AM

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  • HAL Id : halshs-03090122, version 1
  • ARXIV : 2006.08746

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Paul Egré, Lorenzo Rossi, Jan Sprenger. Gibbardian Collapse and Trivalent Conditionals. Conditionals - Logic, Linguistics, and Psychology, In press. ⟨halshs-03090122⟩

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