MINERS: 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.
In a forthcoming paper, (“’If’s and ‘Ought’s,” JPhil), Niko Kolodny and John MacFarlane argue that the best way to resolve this paradox is to give up modus ponens. Instead, I’ll argue, acceptance of the contextualist semantics for modal expressions I advocate (in “A Flexibly Contextualist Account of Epistemic Modals” and “A Flexible, Contextualist Account of ‘Ought’”, http://www.unl.edu/philosop/people/faculty/dowell/dowell.shtml), together with a Kratzer-style semantics for the indicative conditional, allows for a resolution of the paradox without giving up on MP. This seems to me a clear advantage.
Before getting to my solution, I’ll first briefly summarize the semantic theory my solution presupposes (leaving out some whistles and bells that aren’t required at least for an initial statement of that solution) and the basic Kratzerian semantics for the indicative conditional. On the contextualist semantics I favor, modals may be semantically represented as quantifiers over possibilities. In most uses, including deontic ones, the domains for modal quantifiers are restricted, where the restriction, when not explicit in the linguistic material, is determined by context. The resulting worlds are then ranked, often by a standard that is contextually selected. My view of deontic modals differs from other views in that I recognize two different sorts of domain restrictors, circumstances and information. So, roughly speaking, “ought ɸ” is true whenever all of the best circumstantially alike worlds are ɸ-worlds or whenever all of the best worlds compatible with some body of information are ɸ-worlds.
On Kratzer’s account of indicative conditionals, the antecedent serves to restrict the domain of a covert modal in the consequent. VERY roughly, we can think of ‘if P, then Q” as saying “all the P-worlds are Q-worlds”. That’s only rough because the covert modal’s domain can be further restricted by context; the antecedent will typically not be the only restrictor. (So, we can get, for example: the P-worlds compatible with the circumstances are all Q-worlds”. Ex: “if the summer is unusually rainy, we’ll get mosquitoes” says, roughly, “all the worlds that are circumstantially alike with respect to the ‘local’ circumstances and in which it’s unusually rainy are worlds in which we get mosquitoes”.) Also, the antecedent may provide a clue as to whether circumstances or information provides the additional restriction. Finally, just as the use of an explicit restrictor phrase, such as ‘given what I know’ can make the restriction explicit, the appearance of a modal, such as ‘ought’, in the consequent can make the covert modal overt.
The solution to the paradox, then, lies is seeing that the domain in (1) must be restricted by information; after all, given the circumstances, the best worlds are all the worlds in which we save all the miners and we know that doing nothing won’t save all the miners. So, if the restriction is given by actual circumstances, (1) comes out false. So, when we hear it as true, it must be under an epistemic reading. (In other words, MINERS is a so-called Jackson case and so forces the informational reading. For a detailed contextualist treatment of Jackson cases, see my “A Flexible, Contextualist Account of ‘Ought’,” http://www.unl.edu/philosop/people/faculty/dowell/dowell.shtml.) So, (1) is true, roughly, just in case in all the best worlds compatible with our information, we do nothing.
What about (5)? (5) is compatible with (1) when each disjunct gets a circumstantial reading. It then is true just in case, either, given the circumstances, the best worlds are shaft A-blocking worlds or, given the circumstances, the best worlds shaft B-blocking worlds. But why should we think that the disjuncts have circumstantial modal bases?
There are at least two reasons to think they do. The first is: If they get informational restrictions, then (5) is false, since each disjunct is. But (5) seems true. When we hear (5) as true, it can’t be under an informational reading. Given that the empirically best supported semantic theory of modals recognizes only informational and circumstantial modal bases, the modal base for each disjunct must be circumstantial. The second reason is that the grounds for a modal claim may serve as a clue as to how it’s best understood. One such clue is (4) which is an exhaustive description of possible circumstances; either circumstances are such that all the miners are in A or they are such that they are all in B. If these disjuncts are to support MP with (2) and (3), the modals in the consequents must get circumstantial readings. Since the total grounds for (5) are (2)-(4), each disjunct must get a circumstantial reading. Since (1) gets an informational reading and (5) a circumstantial one, they are compatible. So, all is as it appears in the MINERS scenario; (1) and (5) are both true and (2)-(4) provide conclusive grounds for (5).