Williamson on modal epistemology and counterfactuals

This post is an exercise in Williamson exegesis. I'm looking primarily at chapter five -- the modal epistemology chapter -- of The Philosophy of Philosophy. (That chapter substantially overlaps a couple of earlier papers as well.) As many readers will know, Williamson emphasises the equivalence of claims of metaphysical modality with particular counterfactuals (such as the ones discussed in my recent post here), and suggests, therefore, that our ordinary imagination-based capacity for the evaluation of counterfactual conditionals brings along with it a capacity for knowledge of metaphysical modality. As Williamson says, "the epistemology of metaphysical thinking is tantamount to a special case of the epistemology of counterfactual thinking."

There are important interpretive questions that are too easily overlooked. The question I'm after right now is just: what in particular is Williamson trying to accomplish in this material? I think that many people are not always clear about this question. (Williamson is one of these people.)

One candidate project is to answer what I'll call the 'how' question:

How do we have modal knowledge?

A possible answer to the how question suggested by Williamson's work, which emphasizes the equivalence of modal claims with certain counterfactuals, is that we acquire modal knowledge by coming to have counterfactual knowledge, and exploiting the connection between counterfactual truths and modal truths. I think understanding Williamson's project in this way would be a mistake.

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.

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).

Quantifiers, Knowledge, and Counterfactuals

Quantifiers, Knowledge, and Counterfactuals, forthcoming in Philosophy and Phenomenological Research.

Many of the motivations in favor of contextualism about knowledge apply also to a contextualist approach to counterfactuals. I motivate and articulate such an approach, in terms of the context-sensitive ‘all cases’, in the spirit of David Lewis’s contextualist view about knowledge. The resulting view explains intuitive data, resolves a puzzle parallel to the skeptical paradox, and renders safety and sensitivity, construed as counterfactuals, necessary conditions on knowledge.