The miners paradox

Source: as presented by Niko Kolodny and John MacFarlane (2010), Ifs and Oughts, Journal of Philosophy vol. 107: pp. 115-143.

“Ten miners are trapped either in shaft A or in shaft B, but we do not know which. Flood waters threaten to flood the shafts. We have enough sandbags to block one shaft, but not both. If we block one shaft, all the water will go into the other, killing any miners inside it. If we block neither shaft, both shafts will fill halfway with water, and just one miner, the lowest in the shaft will be killed.

Action	If miners are in A	If miners are in B
Block shaft A	All saved	All drowned
Block shaft B	All drowned	All saved
Block neither shaft	One drowned	One drowned

We take it as obvious that the outcome of our deliberation should be:

(1) We ought to block neither shaft.

Still, in deliberating it is natural to accept:

(2) If the miners are in shaft A, we ought to block shaft A.

(3) If the miners are in shaft B, we ought to block shaft B.

We also accept:

(4) The miners are in shaft A or shaft B.

But (2), (3) and (4) seem to entail:

(5) Either we ought to block shaft A or shaft B.

And this is incompatible with (1), so we have a paradox.”

Note: Kolodny and MacFarlane did not invent this paradox. They took it from Derek Parfit’s paper ‘What We Together Do,’ and Parfit in turn references Donald Regan’s book Utilitarianism and Co-operation.

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