Counterfactual Triviality: A Lewis-Impossibility Argument for Counterfactuals

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  • My interest in the theses explored in this paper was sparked after reading an early version of (Moss, ms.). Moss cites a range of interesting evidence in favour of a connection between credence and chances—of which the generalizations below are in the spirit (though the reader should read Moss's paper to determine exactly how her position relates to the thesis I explore). I’d like to thank Rachael Briggs, Ross Cameron, Ant Eagle, Brandon Fitelson, Daniel Elstein, David Etlin, Al Hájek, Barry Loewer, Sarah Moss, Jason Turner, Rich Woodward, an anonymous reviewer, and all others with whom I’ve discussed this material. Versions were presented at departmental seminars at Rutgers and Maryland. The work in this paper was supported by a British Academy Research Development Award (BARDA: 53286). I have also benefited from the events funded by the Spanish Government's research grant FFI2008-06153 (MICINN).

Abstract

I formulate a counterfactual version of the notorious ‘Ramsey Test’. Whereas the Ramsey Test for indicative conditionals links credence in indicatives to conditional credences, the counterfactual version links credence in counterfactuals to expected conditional chance. I outline two forms: a Ramsey Identity on which the probability of the conditional should be identical to the corresponding conditional probability/expectation of chance; and a Ramsey Bound on which credence in the conditional should never exceed the latter.

Even in the weaker, bound, form, the counterfactual Ramsey Test makes counterfactuals subject to the very argument that Lewis used to argue against the indicative version of the Ramsey Test. I compare the assumptions needed to run each, pointing to assumptions about the time-evolution of chances that can replace the appeal to Bayesian assumptions about credence update in motivating the assumptions of the argument.

I finish by outlining two reactions to the discussion: to indicativize the debate on counterfactuals; or to counterfactualize the debate on indicatives.

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