Counterepistemic indicative conditionals and probability

Abstract
Two major themes in the literature on indicative conditionals are (1) that the content of indicative conditionals typically depends on what is known;1 (2) that conditionals are intimately related to conditional probabilities.2 In possible world semantics for counterfactual conditionals, a standard assumption is that conditionals whose antecedents are metaphysically impossible are vacuously true.3 This aspect has recently been brought to the fore, and defended by Tim Williamson, who uses it in to characterize alethic necessity by exploiting such equivalences as: A⇔¬A A. One might wish to postulate an analogous connection for indicative conditionals, with indicatives whose antecedents are (in some relevant sense) epistemically impossible being vacuously true: and indeed, the modal account of indicative conditionals of Brian Weatherson has exactly this feature.4 This allows one to characterize an epistemic modal by the equivalence A⇔¬A→A. For simplicity, in what follows we write A as KA and think of it as expressing that subject S knows that A.5 The connection to probability has received much attention. Stalnaker (1970) suggested, as a way of articulating the ‘Ramsey Test’, the following very general schema for indicative conditionals relative to some probability function P: P(A→B) = P(B|A) 1For example, Nolan (2003); Weatherson (2001); Gillies (2007). 2For example Stalnaker (1970); McGee (1989); Adams (1975). 3Lewis (1973). See Nolan (1997) for criticism. 4‘epistemically possible’ here means incompatible with what is known (where ‘what is known’ is to be cashed out in some relevant sense). 5This idea was suggested to me in conversation by John Hawthorne. I do not know of it being explored in print. The plausibility of this characterization will depend on the exact sense of ‘epistemically possible’ in play—if it is compatibility with what a single subject knows, then can be read ‘the relevant subject knows that p’. If it is more delicately formulated, we might be able to read as the epistemic modal ‘must’..
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