Abstract
It is known that indicative and subjunctive conditionals interact differently with a rigidifying “actually” operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing “actually” instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they preserve material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed.
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Notes
One can observe that sentences such as (1i) and (2i) are truisms prior to taking any theoretical stance on whether indicative conditionals are truth-functional.
Of course, we do not expect \( {\varvec{\models^{*}}} \) p → Ap, since the conditional may have a true antecedent and a false consequent with respect to a counterfactual circumstance of evaluation.
Such an account of propositional attitudes would be incompatible with Stalnaker’s; his is coarse-grained and gives much less weight to the agent’s reaction to a sentence that expresses the proposition at issue, even when the agent understands the sentence.
The agent’s assumed rationality allows us to ignore objections to TAUTOLOGY that concern agents who are not omniscient about truth-functional logic.
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Acknowledgements
Thanks to participants in the 2008 First Formal Epistemology Festival in Konstanz for stimulating comments on an earlier version of this material, and to Franz Huber for written comments.
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Williamson, T. Conditionals and Actuality. Erkenn 70, 135–150 (2009). https://doi.org/10.1007/s10670-008-9144-8
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DOI: https://doi.org/10.1007/s10670-008-9144-8