## Friday, May 13, 2011

### The Miner Puzzle

Kolodny and MacFarlane give a neat puzzle.

The setup: ten miners are trapped in a shaft—A or B, although we do not know which—and threatened by rising waters. We can block one shaft or neither, but not both. If we block the correct shaft, everyone lives. If we block the wrong shaft, everyone dies. If we do nothing, only one miner dies. (Charlow)
The puzzle is that the following seem to be true:
1. The miners are in A or the miners are in B.
2. If miners are in A, we should block A.
3. If miners are in B, we should block B.
4. It is not the case that we should block A.
5. It is not the case that we should block B.
But assuming modus ponens for (2) and (3), the above claims are contradictory.

Some propose dropping modus ponens. But there is a much better solution. Claims (2)-(5) incompletely identify the relevant action types. Actions types should be identified, in part, by the reasons and intentions for them. Should Jones insert a knife into Smith's heart? The question insufficiently specifies the act. Inserting a knife into Smith's heart could be life-saving cardiac surgery or murder. The intentions and reasons matter. To decide what should be done, we need to expand the action descriptions. Here are some possible expanded descriptions:

1. block A because this has probability 1/2 of killing the miners in B.
2. block A because this has probability 1/2 of saving the miners in A.
3. block B because this has probability 1/2 of killing the miners in A.
4. block B because this has probability 1/2 of saving the miners in A.
5. block neither because that will save nine.
6. block neither because that we will kill one.
7. block A because that will save ten.
8. block B because that will save ten.
I am a reasons-externalist and I take "because" to be factive. Reasons-internalists will want to replace the "because" claims in (10)-(13) with "because you think".

The description "block A" is ambiguous between actions (6), (7) and (12). Once we disambiguate as above, we can say:

1. You shouldn't do (6) or (8).
2. You shouldn't do (7) or (9) if you can do (10) or (12) or (13).
3. If you can do (12), you should do (12).
4. If you can do (13), you should do (13).
5. If you can't do (12) or (13), you should do (10).
But what can you do? If you believe the miners are in A, you can do (12). In that case, you should do (12). If you believe the miners are in B, you can do (13), and so you should. If you have no idea where the miners are, you can't do (12), because it is not possible for you to act because of a reason that isn't available to you. For the same reason, you can't do (13), and so you should do (10).

Can we affirm any conditionals such as (2) or (3)? Not if "should" implies "can". For presumably the way to expand out the "should block" in (2) is not along the lines of (7) but along the lines of (12). And if "should" implies "can", then it is false that if the miners are in A, you should (block A because that will save ten), since you cannot in this case block A because that will save ten, as you are unable to act on that reason.

But suppose you deny that "should" implies "can". Then you can consistently say that:

1. If the miners are in A, you should (block A because that will save ten),
even though the action in the consequent is impossible to you. And then by (18), you can say:
1. Even if the miners are in A, you should (block neither because that will save nine),
since although the action in (19) would be the better one, it is not possible for you. And you are not culpable for failing to do the better action because you have an excellent exculpating excuse: you can't do it.

So we have different stories to tell depending on whether "should" implies "can", but they do not practically differ. Both stories agree that in the event that the miners are in A, you should block neither. The second version of the story also says that you should do something else, thereby placing you in a dilemma, but since that something else is impossible, you have a perfectly fine excuse for acting as you do.

But in any case, there is no real paradox.

So where do I stand with regard to (1)-(5)? Well, we need to have some rigorous disambiguation to the "should block". Here is one proposal. The statement "x should A" has the truth conditions "There is a relevant elaboration A* of A such that x should A*", where an elaboration of an action type is a narrower action type. Then if "should" implies "can", then (2) is false, because the only relevant elaboration of "block A" on which the consequent of (2) would be true is (12), and (12) is not doable in the situation as described, and the same goes for (3). And likewise (4) and (5) are both true, because it is not the case that there is an elaboration of "block A" or of "block B" that we should do.

If "should" does not imply "can", then (2) and (3) are true. But by the same token one of (4) and (5)—the one corresponding to where the miners are—is false.

Moreover, in either case, we can add:

1. You should block neither A nor B.
This may seem to contradict the "should" does not imply "can" statement that one of (4) and (5) is false. But "You should block A" is compatible with "You should block neither A nor B" at least if "should" does not imply "can".

I think Kolodny and MacFarlane would classify my answer as a subjectivist one, since I deny (2) and (3). Their main argument against the subjectivist is this scenario. Suppose the miners are in fact in shaft A. Then we can imagine this dialog. You say you should leave both shafts open because that will save nine. An adviser says: "No, you ought to block shaft A. Doing so will save all ten of the miners." The adviser is disagreeing with you. But how could she be disagreeing with you if your claim that you should leave both shafts open is true?