Wednesday, September 08, 2010

Counterfactuals and Modals

I like the approach to counterfactuals that treats them as modals. The sentence 'if A were the case, C would be the case' says that, out of some restricted class of possibilities, all the A possibilities are C possibilities. Which restricted class is in play is of course in part a context-sensitive matter. The relevant class of possibilities is relevant for other modal language, too. I've argued, controversially, that this is the case for 'knows'. But there are much less contentious cases, too. Consider bare modals like 'might' and 'must'; these definitely take context-sensitive domains, and those domains look to play central roles in the interpretation of counterfactual conditionals, too.

There is a kind of conflict between sentences like these, uttered back to back in a given conversational context:

(1) If he were to break thorough his chains, he would save the girl.

(2) He couldn't possibly break through his chains.

The 'kind of conflict' here isn't necessarily a matter of semantic inconsistency. (The approach to modals and counterfactuals I have in mind has the second entailing the first -- if there's no possibility of his breaking his chains, then, trivially, all possibilities in which he breaks through his chains are ones in which he kills his captors.) It's rather something like a pragmatic tension. The 'couldn't possibly' claim requires the modal base to be devoid of cases in which he breaks through his chains; such a base renders the counterfactual trivial -- so the counterfactual strongly prefers a context in which there are some chain-breaking possibilities among the modal base. (Compare: "There's nothing in this bottle." "All the air in the bottle is musty.")

Given this connection between bare modals and counterfactual conditionals, it's pretty straightforward to see that certain equivalences will hold as well. In particular, these two sentences will, in any given context, have the same truth value:

(3) He can't phi.

(4) If he were to phi, then p and not-p.

The necessity claim says that there are no him-phi-ing worlds. The counterfactual says that, of all the him-phi-ing worlds, all of them are p-and-not-p worlds; this is false if there are any him-phi-ing worlds, and vacuously true if there are. (I'm assuming that no worlds -- in particular, none of the him-phi-ing worlds, are p-and-not-p worlds.)

I say that (3) and (4) are equivalent in all contexts. This is not, however, to say that, in any conversational situation, the expression of (3) would take the same truth-value as would the expression of (4). For in many situations, (3) and (4) will have divergent effects on the conversational score, for just the sorts of reasons given above. I've used very strong chains, and also drugged him; he definitely will not succeed in his attempts to break the chains. If you and I are speaking in an ordinary villain-and-henchman context, rather than a esoteric metaphysician's one, I might very well express a truth with "he can't break through his chains." We are, in Lewis's useful terminology, legitimately ignoring certain genuine but irrelevant possibilities, like the possibility that his chains suddenly and spontaneously transform to dust. I would not, however, plausibly express a truth by the sentence "if he were to break through his chains, then p and not-p." If I were to utter this counterfactual, the relevant domain would expand in order to accommodate the presupposition that there are some possibilities in which he breaks through his chains; relative to this new, wider set of possibilities, the modal claim of the counterfactual would be false. We accommodate by treating sincere utterances, when possible, as non-vacuous. Relative to that new, wider set of possibilities, the bare modal would be false too; but it's not most naturally evaluated there.

What I say for (3) and (4) generalises to (5) and (6):

(5) Necessarily, p.

(6) If not-p were the case, A and not-A would be the case.

That is to say, first, both sentences are context-sensitive, second, the two sentences are semantically equivalent in the sense of having the same truth value relative to any particular context, and third, that they can and often will have divergent capacities for updating the context.

Timothy Williamson bases his treatment of modal epistemology on the fact that (5) and (6) are semantically equivalent. But I think that an appreciation of the rest of the story makes trouble for his epistemological story. I'll try to develop my worry in some detail in future posts.

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