We thought a bit about cases in which ‘could’ and ‘might’ come apart. In the paper, Antony discussed sentences like
33b) If we’d left the gate open, the dog could have got out; yet if we’d left the gate open, it isn’t the case that the dog might have got out.
The felicity of such sentences seems to show that at least some ‘might’ counterfactuals shouldn’t be analysed in terms of ‘could’, but instead should be given an epistemic reading. Antony isn’t averse to this idea – in fact, his final view is that ‘might’ is ambiguous in counterfactual contexts between the epistemic reading and the ability reading. However, this does invite the further question of what determines the appropriate reading for some given ‘might’ counterfactual.
Fron 33b we naturally conclude though the dog has the ability to get out, it is so disposed as to not exercise this ability. The only way to interpret someone who expresses the conjunction as not contradicting themselves is to give the ‘might’ and the ‘could’ different readings, and the ‘could’ tends to snaffle the ability reading, leaving the epistemic reading for the ‘might’. 33a, on the other hand, is intuitively clashing:
33a) If we’d left the gate open, the dog might have got out; yet if we’d left the gate open, the dog couldn’t have got out.
An explanation for this would be is that the ‘might’ in the first conjunct naturally takes an ability reading, which the second conjunct then contradicts. If this is right, then it looks like ‘the dog couldn’t have got out’ always takes an ability reading, while ‘the dog might have got out’ can take both the ability and epistemic readings.
This suggests the following difference between ‘might’ and ‘could’ in counterfactual contexts. When used as a predicate, as in the examples above, can/could always takes the ability reading. It only takes the epistemic reading when used as a sentence modifer, as in ‘it could be that the dog escaped’. May/might, on the other hand, can take either the epistemic reading or the ability reading when used as as a predicate. Like can/could, may/might always takes an epistemic reading when used as a sentence modifier.
On a separate issue, I wondered about how use of ‘might’ outside of counterfactual contexts fits with the duality account of the relationship between ‘might’ and ‘would’. Assume Goldbach’s conjecture is necessarily true. On a Lewisian account, there are no worlds in which Goldbach’s conjecture is false, so any counterfactual of the form ‘If x were the case, Goldbach’s conjecture might be false’ comes out false. As Williamson has argued, it seems a plausible principle of counterfactual logic that ‘if, whatever were the case, then p’ entails that necessarily p. Putting this together, the Lewisian account of ‘might’ in counterfactuals contexts entails that ‘Goldbach’s conjecture might be false’ is necessarily false. This is a bad result; we want to say that lots of speakers speak truly when they assert Goldbach’s conjecture might be false’, if their epistemic state is such as not to rule out its falsity. I’m sure this has been observed before; I’d be glad of any references.