A really interesting paper this week - it can be found here, and the presentation is here.

Kment's main proposal is that match of matters of particular fact should be relevant to closeness of two worlds for the purposes of evaluating counterfactuals if and only if the matters of fact have the same explanation in both worlds. Secondarily, he proposes that we should allow for laws to have exceptions, and hence that all worlds which share the same laws as ours should be closer to actuality than any world with different laws.

We quite liked the main proposal, but worried about the individuation of explanations it relies upon. What are the conditions for two events to have the same explanation? For example, consider the counterfactual 'if I had tossed the coin five minutes earlier, it would still have come up heads'. This seems false, but perhaps Kment can account for this falsity by saying that the coin's coming up heads in the various A-worlds would have a different explanation from its explanation in the actual world, because it would have been caused by a different event of tossing.

However, what about 'if I had tossed the coin one nanosecond earlier, it would still have come up heads'? Here we were much more inclined to take the counterfactual as true. Perhaps this difference goes along which goes along with the intuition that the actual tossing and the 1-nano-second earlier tossing count as the same event (or as counterparts according to some very natural counterpart relation), while the actual tossing and the 5-minute-earlier tossing count as different events. But if this is the line Kment would want to take, we'd need to hear more about how it is to work.

Finessing the individuation critera for explanations might also afford a solution to the problem case (25) which Kment mentions inconclusively. If the explanation for the lottery's having the result it did does not include that phone A was used to make the call, but just includes that some phone of such-and-such qualitative character was used to make a call, then we would get the right result that even if phone B had been used, the result of the lottery would have been the same. This requires that the explanation of the lottery's result should only include qualitative features of certain early-enough explanatory factors, rather than the whole fully-detailed causal story. That is, explanations should comprise roughly the minimal information required to determine their explanandum.

This solution involves dropping the transitivity of explanation which Kment explicitly assumes - because it is plausible that a call being made explains the outcome of the lottery, and that the use of phone A explains that a call was made. However, perhaps dropping transitivity of explanation is any case desirable. Consider the well-known counterexample to transitivity of causation - the boulder's rolling down the mountain is the cause of the hiker's ducking, and the ducking is the cause of his survival, but the boulder's rolling is not the cause of survival. The same counterexample seems to work against transitivity of explanation - the rolling explains the ducking, and the ducking explains survival, but the rolling does not explain survival.

Another issue we thought about was the degree to which a Humean could adopt the notion of laws as having exceptions. Clearly it's incompatible with Lewis' own theory of laws, according to which the laws are those true universal generalizations which provide the best balance of simplicity and strength, but perhaps (as Antony suggested) a Humean view which took laws to be more like habitual statements would work. Habituals tolerate exceptions, but they still explain their instances.

Maria had a potential objection to this approach for the Humean (and to any view according to which there are restrictions on how many exceptions are possible before the laws have to be different) - suppose the number of exceptions in a world are right on the borderline for it's having some particular laws. Then the extra small exception needed to accommodate some antecedent would involve consideration of an A-world with too many exceptions to have the same laws as the original world. Then the A-world which, intuitively, is the right one for evaluating the counterfactual would not come out as closest according to Kment's criteria. So it looks like the view might only in fact be compatible with strong 'immanent' views of laws where any arbitrary number of exceptions are possible while the laws remain the same.

One final thought; it would be possible to hold that exceptions are possible to all special-scientific laws, but not to the fundamental laws, if such there be. This seems to fit well with usage: we talk of the 'laws' of statistical mechanics, even though they only hold with high probability, but we are much less willing to admit that the laws of fundamental physics might have exceptions. Someone who took this view of laws could carry over everything Kment says about ordinary counterfactuals, though might have to say something a little more counterintuitive about counterfactuals concerning fundamental physics (perhaps in a deterministic world we would have to count as true 'if this electron had been over here and not over there, the matter distribution at the big bang would have been different'). However, this consequence might be ameliorated by the indeterminacy of fundamental physics.