Response to MacFarlane and Kolodny on Modus Ponens

One of the most interesting arguments I have encountered recently is John MacFarlane and Niko Kolodny's argument that modus ponens is not actually a valid formulation in logic. They present it in a paper entitled Ifs and Oughts and provide some apparent counterexamples to the rule. I shall take their key example, and demonstrate that it relies upon false premises.

Ten miners are trapped either in shaft A or 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 shaft, killing any miners inside it. If we block neither shaft, both shaft will fill halfway with water, and just one miner, the lowest in the shaft, will be killed.

Action                               if miners in A               if miners 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 ought to be:

(1) We should block neither shaft

Still, in deliberating about what to do, it seems natural to accept:

(2) If the miners are in shaft A, we should block shaft A

(3) If the miners are in shaft B, we should block shaft B

We also accept:

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

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

(5) Either we should block shaft A or we should block shaft B

And this is incompatible with (1). So we have a paradox.

Taken from MacFarlane, J. & Kolodny, N (2010), Ifs and Oughts, accessed at http://johnmacfarlane.net/ifs-and-oughts.pdf ; the thought experiment they credit to Donald Regan in Utilitarianism and Cooperation, via Derek Parfit in What We Together Do

The authors argue that the best resolution of this paradox is to reject the assumption that modus ponens is a valid logical formation. I shall disarm their argument by demonstrating the falsity of premises (2) and (3), which removes the necessary support for (5) and so avoids the paradox.

My disproof runs as follows:

(1) We cannot act upon facts of which we are not aware. [I take this as obvious]
(2) That we should do something implies that we "can" do it. [The classic "ought" implies "can", a generally accepted principle]
(3) That we should act upon a fact implies that we are aware of the fact. [from (1) and (2)]
(4) If we are not aware of a fact, it is not the case that we should act upon it. [from (3)]
(5) If the miners are in shaft A, we are not aware of this fact. [from the original problem]
(6) If the miners are in shaft A, we should not act based on this fact. [from (4) and (5)]
(7) If the miners are in shaft B, we are not aware of this fact. [from the original problem]
(8) If the miners are in shaft B, we should not act based on this fact. [from (4) and (7)]

(9) Hence premises (2) and (3) in MacFarlane and Kolodny's argument are false. [from (6) and (8)]

I believe that MacFarlane and Kolodny confuse the false premises "If the miners are in shaft A, we should block shaft A" and "If the miners are in shaft B, we should block shaft B" with the true premises "If we are aware that the miners are in shaft A, we should block shaft A" and "If we are aware that the miners are in shaft B, we should block shaft B".

HT: Nathan Duckett