Gibbardian Collapse and Trivalent Conditionals

Paul Egré , Lorenzo Rossi (1) , Jan Sprenger (2)

1 LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München
2 UNITO - Università degli studi di Torino = University of Turin

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.

Domaines: Sciences de l'Homme et Société; Linguistique; Philosophie

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