Indicative Conditionals and Graded Information

Abstract

I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: (i) that a conditional is logically independent from its antecedent; (ii) that a sequence of antecedents behaves like a single conjunctive antecedent (the import-export equivalence); and (iii) that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart.

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Acknowledgements

For inspiring discussions and/or useful feedback on earlier drafts, I am grateful to Maria Aloni, Justin Bledin, Bruno Jacinto, Hannes Leitgeb, Vít Punčochár, Floris Roelofsen, Lorenzo Rossi, Katrin Schulz, Frank Veltman, Malte Willer, Seth Yalcin, and two anonymous reviewers.

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Correspondence to Ivano Ciardelli.

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Ciardelli, I. Indicative Conditionals and Graded Information. J Philos Logic 49, 509–549 (2020). https://doi.org/10.1007/s10992-019-09528-6

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Keywords

  • Indicative conditionals
  • Information semantics
  • Import-export
  • Epistemic modals
  • Non-monotonic reasoning
  • Modus ponens
  • Modus tollens