Wolfgang Schwarz

Might

Lewis once proposed that a 'might' counterfactual ("if A had been the case, C might have been the case") is true iff is true. This is sometimes used in defense of controversial philosophical claims, like in Al Hájek's "Most Counterfactuals are False" and in Boris Kment's "Counterfactuals and Explanation". But at least in some cases, the analysis doesn't seem right.

Suppose the laws of nature determine either that A brings about C or that A brings about not-C, but we don't know which. So all we know is that one of these counterfactuals is true:

1)

2)

If were to bring about A, we should take both possible outcomes into account. We shouldn't take it for granted that C would occur, nor that C wouldn't occur. Either could happen. So both of these are true:

3)

4)

But if means , then (3) renders (2) false, and (4) (1), contradicting the assumption that one of (1) and (2) is true.

Unlike Lewis's, Stalnaker's analysis gets this case right. On Stalnaker's analysis, means , with an epistemic diamond. Unfortunately, this breaks down in other cases. Here are two from section 76 of Bennett's Conditionals. First,

5) if I had tossed this fair coin, it might have landed heads.

This seems true. On the other hand,

6) if I had tossed this fair coin, it would have landed heads

is false. The coin is after all fair and could just as well have landed tails. In fact, I know that (6) is false. Hence (5) cannot mean that for all I know, (6) is true.

<update>If you don't share this intuition, recall what it means for the outcome of a quantum mechanical process to be indeterminate: that the electron has a 0.5 chance of going left under such-and-such conditions doesn't mean that we don't know what it would do. Quantum indeterminacy isn't epistemic. There is really no fact of the matter -- until we actually set up the conditions and wait for the wave function to have collapsed. Which we have not if the setup is merely counterfactual. So here there is still no fact of the matter whether the electron would have gone left or right. And then it is certainly not true that the electron would have gone left.</update>

Second, assume John has just given up searching for the needle in the haystack. I say,

7) if John had searched through the haystack more carefully, he might have found the needle.

What I say is true only if the needle is actually in the haystack. If not, there is no chance of him finding it there, no matter how carefully he searches. But if (7) can be made false by the needle not being in the haystack, then (7) isn't made true merely by me or anybody else not being able to rule out that if John had searched more carefully, he would have found the needle.

At another place, Lewis suggested that can mean . The diamond here can hardly be epistemic: when I wonder what might have happened if the dinosaurs hadn't died out, I don't consider what is epistemically possible for me (or for the dinosaurs) in the envisaged counterfactual situation. Lewis thought it's the diamond of nomological possibility. He didn't claim the analysis is always correct, and indeed the counterexample to his first proposal works here, too: either (3) or (4) will most likely come out false. Moreover, the haystack counterexample to Stalnaker will probably work as well: even if the needle is not in the haystack, it is surely nomologically possible that it be there, and therefore also that it be there and be found given that John searches more carefully -- making (7) come out true. In general, whenever the same worlds are diamond-accessible from the actual world and from the closest A-worlds, will come out equivalent to (assuming A is metaphysically possible).

On the other hand, I'm afraid Lewis is right and 'might' counterfactuals sometimes have this interpretation: assume C is possible. So it might have been the case. Assume further C's possibility does not depend on the fact that A is the case; so even if A had not been the case, C still might have been the case; it would still have been possible. Here we get a 'might' counterfactual out of the mere fact that C would be possible given A -- and the "possible" can even be just metaphysical possibility. (Thanks to Dave Chalmers here.)

This is all a little confusing. Are 'might' counterfactuals really so ambiguous? I don't see a good way to square the epistemic reading that's required for the unknown-law case with the non-epistemic reading required for all the other cases. However, one could perhaps unify Lewis's two proposals. One could say that the domain of the diamond in the consequent usually (or always?) is the set of closest worlds selected by the antecedent. Then unless the domain is expanded by something like the reasoning in the last paragraph, and unless this also affects the interpretation of 'would' counterfactuals (which it sometimes appears to do, but sometimes not), the third analysis gives the same result as the first.