'Significant Possibilities' and Concessive Knowledge Attributions

Suppose you think that it's possible to know that p, even though your epistemic position vis-a-vis p is weak enough for 'it might be that not-p', in its epistemic reading, to be true. I don't really see why you'd want to think this myself, but I guess some people think that (a) this is a good reading of 'fallibilism' and (b) fallibilism is true. If you think this, then you face the problem to explain the infelicity of concessive knowledge attributions. Why's it sound so bad to say "I know that p but p might be false"?

The obvious explanation is that it's a contradiction: according to standard epistemic modal logic, 'might', in its epistemic reading, is just the dual of 'know'. But the fallibilist of this stripe has closed off that response. What's he say instead? Dougherty and Rysiew propose a pragmatic line: "p might be false," they say, implicates but does not entail that there is a significant chance of not-p. And while a chance of not-p is consistent with knowledge that p, a significant chance of not-p is not. Fantl and McGrath supplement the story by suggesting that the significance of various chances can be a stakes-sensitive matter; the same possibility, with the same likelihood, can be significant if the stakes are high, and insignificant if the stakes are low.

Now I get nervous when Gricean pragmatic stories are asked to do work like this. Too often, the data don't generalize the right ways. Here's one problem: the pragmatic effect doesn't seem appropriately cancelable. Consider:

It's possible that it will rain today, but I know it won't rain today.

The badness of this sentence is explained, on the view in question, by suggesting that the first conjunct pragmatically implicates that there is a significant chance that it will rain today. It predicts, then, that if we cancel the implication, we're left with felicity. But this prediction is not borne out; this is still bad:

It's possible that it will rain today, but there's no significant chance that it will rain today, so I know it won't rain today.

Also, there's a point that Derek Ball raised in Jason Stanley's seminar last week, inspired by Seth Yalcin: the infelicity of concessive knowledge attributions persists in non-assertoric contexts. "Suppose that you know it will rain today and it might not rain today." "If you know it will rain today and it might not rain today, then you know something that might not happen." Etc. The Gricean story is peculiar to assertions, and therefore insufficiently general.

I think there's a better view in the same spirit. (Well, maybe in the same spirit; I'm not quite sure what the intuitive motivation behind this project is. My suggestion won't vindicate the coherence of concessive knowledge propositions. But like I said, I'm not sure I see why anyone would want to do that.) The line we've been considering is one in which "there is some possibility of p" pragmatically implicates that there is some significant possibility of p. But the existential quantifier is going to have a context-sensitive domain restriction anyway. We could suppose that in the relevant contexts, we're only quantifying only significant possibilities. Then "there is some possibility of p" would, in the relevant context, entail that there is some significant possibility of p.

On this approach, you can still get a lot of the stuff that Fantl and McGrath want. On this view, whether there is a possibility of p will depend on the stakes, since all possibilities are significant possibilities, and whether a possibility is significant depends on stakes. So their 'impurism' would infect 'possibility' talk too. (This is not a result of the view they actually offer, which I'm criticizing: they have 'pure' possibilities, where talk of them implicates results about 'impure' significant possibilities.) But the concessive knowledge attributions will be genuine contradictions.

What is fallibilism?

I've long been troubled by failing to understand what 'fallibilism' and 'infallibilism' are supposed to amount to. Here's an example of the sort of discussion I find puzzling.

Bohghossian and Peacocke write:

A priori justification is not infallible justification. Just as one may be justified in believing an ordinary empirical proposition that is empirically revealed on empirical grounds to be false, so one may be justified (non-conclusively) in believing an a priori proposition that is subsequently revealed on a priori grounds to be false.

I find this passage puzzling, for at least two reasons. First, Boghossian and Peacocke characterize a priori propositions for Boghossian and Peacocke as those which can be known a priori; so the idea of an a priori proposition that turns out to be false looks to me to be incoherent.

Second, it's not clear what the second sentence has to do with the first. The second sentence is about what may happen when you're justified in believing something -- that thing may turn out, either empirically or a priori, to be fase. The first sentence, however, isn't a claim about all justification; it's a claim about a priori justification. It can't be that a priori justification is fallible merely because it's possible to be justified in believing some a priori proposition that turns out false; if a priori justification is fallible, then there has to be a sense in which you can be wrong even if you're a priori justified. And that just isn't established or claimed in this passage. Is the idea supposed to be that any time you are justified in believing some a priori proposition, you're justified a priori? That would fill out the enthymeme, but it has the disadvantage to being totally implausible.

So I don't really know what Boghossian and Peacocke are up to here. Or, in general, what people who talk about a priori justification being fallible are up to.

What is infallibility supposed to be?

This week I'm thinking about Laurence Bonjour's In Defense of Pure Reason. In §4.4, Bonjour offers what he takes to be a very straightforward argument against the infallibility of rational insight: just look, he says, at all the examples of alleged cases of rational insight that are false — some have been empirically refuted, and some been shown a priori to be incoherent, and some are just inconsistent with others in a way that guarantees that at least some are false.

He qualifies the charge of fallibility, recognizing that it's open to deny that such cases of seeming rational insight into something that ends up being fall are genuine rational insights at all; this, he says, is a "mere terminological or conceptual stipulation" and "fails to secure infallibility in any epistemologically useful sense".

I don't see what infallibility was ever going to amount to if it was to be something stronger than what Bonjour thinks is an uninteresting sense. Did or could anybody ever have thought that anything that seemed to be a rational insight thereby guaranteed its truth? Descartes, for example, recognized the possibility that human reason might be deceived by a God or demon, or imperfectly designed, such that it led into error.

What is the correct characterization of a strong form of infallibility?