The Dennes Room

Event Detail

Fri Apr 18, 2008
60 Evans Hall, 4:10–6 PM
Logic Colloquium
John MacFarlane (UC Berkeley)
Ifs and Oughts

Consider the following problem, from the ethics literature: Ten miners are trapped either in shaft A or in shaft B, but we don’t 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 leave both shafts open, both shafts will fill halfway with water, and just one miner, the lowest in the shaft, will be killed.

In deliberating about what to do, it seems natural to accept:

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

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

We also accept:

(3) Either the miners are in shaft A or they are in shaft B.

But it seems we cannot conclude:

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

For this is incompatible with the correct prescription:

(5) We ought to block neither shaft.

In this talk, we consider four options for resolving the paradox:

(a) Distinguish objective and subjective senses of “ought”.

(b) Take “ought” in (1) and (2) to have wide scope over the conditional.

(c) Analyze (1) and (2) using a two-place conditional obligation operator.

(d) Reject modus ponens for the indicative conditional.

We argue that (d) is the best option. Rejecting modus ponens is not ad hoc, because it follows from independently-motivatable semantics for “ought” and the indicative conditional. (On this semantics, the counterexample to modus ponens above works for the same reasons as Vann McGee’s counterexamples involving nested conditionals.) Nor does it cripple reasoning, since we can give precise and broad conditions under which modus ponens can be used safely in reasoning.

This talk is based on joint work with Niko Kolodny (UC Berkeley, Philosophy).