Over at PEA Soup, Janice Dowell discusses an interesting argument for a moral paradox. This is how she presents it:
10 miners are trapped in a flooding mine; they are either all in shaft A or all in shaft B. Given our information, each location is equally likely. We have just enough sandbags to block one shaft, saving all the miners, if they are in the blocked shaft, but killing them all if they are in the other. If we do nothing, the water will distribute between the two shafts, killing only the one miner positioned lowest. On the basis of these considerations, (1) seems true:
(1) We ought to block neither shaft.
While deliberating, though, we accept both
(2) If the miners are in A, we ought to block A
(3) If the miners are in B, we ought to block B.
We also accept
(4) Either the miners are in A or they are in B.
And (2)-(4) seems to entail
(5) Either we ought to block A or we ought to block B.
She mentions a paper in which some philosophers respond by rejecting modus ponens. That seems much too severe and unattractive. Dowell suggests another line of attack which is quite sophisticated--it involves semantic theory, which is not something I want to get into right now. I think a simpler solution can be found. In a nutshell, I think the paradox argument requires the false assumption that ought's can be unprincipled.
Consider what principle would have to be applied to block one of the shafts. It couldn't be a principle based on one's knowledge of where the miners are. It would have to be a haphazard principle akin to flipping a coin. Such a "principle" (if we can even call it that) would only minimize harm in those worlds where the coin happened to come up the right way every time. I think we'd do less harm in more possible worlds by applying a different principle.
The point is, what one ought to do is a matter of what principle one ought apply in cases of a particular type, and not merely a matter of the consequences of applying that principle in any particular case. Thus, there are possible worlds in which all the miners are in A, but in which one ought not block A. Similarly for B, of course. So we should reject (2) and (3), and thereby resolve the paradox.
Update (July 15, 2010, 14:09 GMT): A moral noncognitivist (such as myself) would not let the paradox argument get off the ground, as stated, because it supposes that "we ought to X" can be either true or false. Yet, I think the paradox argument can proceed without that supposition. While the subjects in the scenario may say, "If the miners are in A, we ought to block A," what they mean (truth functionally) is this: If the miners are in A, we are justified in blocking A. The difference is subtle enough to not really matter, but it preserves the argument without offending the noncognitivist.