Showing posts with label lottery paradox. Show all posts
Showing posts with label lottery paradox. Show all posts

Saturday, October 24, 2009

Counterfactuals and Knowledge

I'm on the record as thinking there are tight connections between counterfactuals and knowledge.

Robbie Williams, in his "Defending Conditional Excluded Middle," denies this. At least, he argues for a strong disconnect between them. Robbie argues, among other things, that there are strong reasons to accept both (A) and (B):
(A) If I were to flip a fair coin a billion times, it would not land heads a billion times.

(B) If I were to flip a fair coin a billion times, it would not be knowable that it would not land heads a billion times.

Since, Robbie says, (A) and (B) are both true, it can't be that (A) entails the negation of (B) -- therefore Bennett's view, which connects knowledge and counterfactuals in a way implying that entailment, is false. Robbie's argument for (A) is that rejecting it would require rejecting the truth of too many of our ordinary counterfactuals, since they enjoy no stronger metaphysical grounds than those for (A) -- since there's a genuine physical probability of really wacky things happening all the time, we have nothing better than this kind of probabilistic connection between antecedent and consequent in lots of counterfactuals that we want to maintain.

The way Robbie puts the point is that denying (A) would be to commit oneself to an error theory, since it would make our ordinary judgments about ordinary counterfactuals wrong all the time. This move seems to me a bit odd; to my ear, (A) does not look obviously true. Indeed, it looks like we should reject it. That's not to say I can't be moved by an argument in favor of it -- I can -- but if we're in the game of respecting pre-theoretic intuitions, it seems to me that to accept (A) is to embrace something of an error theory, too. We can make it worse if we make the problematic possibility more salient:
(A*) If I were to flip a fair coin a billion times, the possibility of its landing heads a billion times would not be the one to become actual.

If you agree with me that (A*) is equivalent to (A), and that (A*) sounds false, then you must likewise agree with me that Robbie, in embracing (A), commits to a bit of error theory himself. That's not to say it's therefore a bad view; it's just to say that we're already in the game of weighing various intuitive costs. It's not so simple as error theories are bad, therefore (A) must be true.

(Another observation: Robbie thinks it'd be bad to deny (A) because it would make us deny the truth of many ordinary counterfactuals, which play important roles in philosophy. He writes:
Error-theories in general should be avoided where possible, I think; but an error-theory concerning counterfactuals would be especially bad. For counterfactuals are one of the main tools of constructive philosophy: we use them in defining up dispositional properties, epistemic states, causation etc. An error-theory of counterfactuals is no isolated cost: it bleeds throughout philosophy.

Perhaps this is right. But if it is true that counterfactuals play really important roles in construction of philosophical theories, then it's not just their truth that matters -- it's also our knowledge of them. So a view that preserves many of these counterfactuals as true, but that leaves us with very little knowledge about counterfactuals, seems to have a lot of what is problematic in common with the error theory Robbie discusses.)

Robbie gives three arguments for (B). I'll discuss the first two in this blog post; I think that they have analogues against (A).