August 28, 2007

Most Counterfactuals are False

The title is of Alan Hájek's very interesting paper, which can be found on his website. I mentioned the main argument in a post last January:

1. 'Might' and 'Would' are dual operators. So "If A were the case, B might not be the case" entails "It's false that if A were the case B would be the case":

2. Indeterminism (in particular, chanciness) and indeterminacy (in particular, vagueness) in all the interesting cases underwrite a 'might not' claim. For instance, any chance of both A and not-B (no matter how small) underwrites the 'might not' claim, viz., "If A were the case, B might not be the case":

Hence, in all the interesting cases, its false that if A were the case B would be the case. So most (uttered) counterfactuals are false.

Alan rejects the contextualist response, but I won't develop his arguments. I'll just mention here what I think the contextualist should say. Counterfactuals are context sensitive. Whether apparently bizarre {A, not-B} possibilities are sufficiently close depends on the context. In conversational contexts that involve discussion of quantum indeterminacy, etc., such possibilities are relevant and close. Hence, the would-claim, , is false. But in ordinary conversational contexts, the apparently bizarre {A, not-B} possibilities are irrelevant and remote. Hence, the might-claim, , is false. In neither context is both and true. Luckily for us and the would-claims we ordinarily use, quantum indeterminacy is rarely seriously entertained.


Julien said...

Hé Joe, just a quick question. How to evaluate cross-contextual assessments of might-counterfactual claims? Suppose C1 is a high standards context and C2 is a low standards one. And suppose Hi says, in C1 "A <>--> not-B". Then, it would seem that Lo, in C2, might reply: "What you said (in C1) is true, but, actually, not-(A <>--> not-B)". This doesn't sound intuitively right, however. What do you think?

Joe Salerno said...

Hi Julien. This sounds like the analogue of a Jason Stanley criticism of contextualism about knowledge. However, i'm not sure "epistemic standards" are what shifts with contexts in the case of counterfactuals. Rather the context shifts which background facts are relevant for the proper evaluation of the consequent given the antecedent.

Joe Salerno said...

There's also the disanalogy with epistemic contextualism since there is no subject to which we are attributing an attitude.

That said, there may be an analogous objection to counterfactual contextualist that goes like this:

A: If Caesar had commanded the Korean War he would have used nukes. After all, he was exceedingly ruthless.
B: That may be right, but Caesar lived long before nukes. So it's false that he would have used nukes. Rather, he would have used catapults.
A: I agree, but what I said earlier still stands!

If the truth values of counterfactuals vary with context, then dialogs like the one's above should not violate our semantic intuitions. I don't know how semantically violated I feel about the above dialog. My ears aren't ringing. Perhaps the following is closer to a Stanley-like objection.

A: [uttered in ordinary circumstances]
If I were to jump up, I would come down.
B: However, there is a non-zero probability of a strong gust of wind suspending you in mid-air. Hence, you might not come down, and so, it's false that you would come down.
A: I agree, but what I just said remains true.

I'm not entirely comfortable with this dialog. Will think more about it.