Conditional knowledge attributions

I'm going to be discussing an argument that I know Jason Stanley to have given, but I'm away from my copy of his book at the moment, so I can't cite it properly, or check and see who else has discussed it (or even whether it's original to Jason). I'll follow up if citation protocol ends up demanding it.

Here's a naive argument against 'knows' contextualism. (This isn't the Stanley argument I want to discuss; it's part of the set-up for it.) Assume contextualism. Now suppose you're in a nonskeptical context, and I'm in a skeptical one, and we're both talking about me and the proposition that p, a proposition with which I stand in a pretty strong epistemic relation -- one strong enough for your non-skeptical 'knows', but not for my skeptical 'knows'. You say: "Jonathan knows p." Now, according to this naive objection, I'm forced to say this:

(1) I don't know that p, but what you said was true.

This sounds like a crazy thing to say, under the circumstances, but it looks like contextualism predicts that it should be fine.

Of course, contextualism doesn't predict that (1) should be fine; the naive objection is naive. Contextualism avoids the felicity of this utterance by observing that it won't be assertable for me. What you said entails p (even your nonskeptical 'knows' is factive). Since I'm not in a context in which "I know that what you said is true" is true, I therefore can't assert that what you said is true. Indeed, (1) is Moore-paradoxical, or near enough, since it straightforwardly and transparently entails "I don't know that p, but p."

So there's a naive objection to contextualism and a good response on the contextualist's behalf. But Jason Stanley thinks the game isn't over yet, for he has a tweak on the objection to make it less naive in a way that he thinks will avoid the response. Take the same set-up as before; you're in a non-skeptical context and you say "Jonathan knows p," and I'm in a skeptical context where "I know p" is false. Now, Jason asks, why shouldn't I give this sentence?

(2) I don't know that p, but if p is true, then what you said is true.

Here, the second conjunct doesn't entail that p, so the sentence isn't Moore-paradoxical. Insofar as (2) also sounds crazy, we have a version of the objection that isn't susceptible to the quick response given above. (Does (2) sound crazy? Is it a natural enough sentence to generate clear intuitions? I don't know. Let's grant for the purpose of argument that it sucks to have to render this sentence assertible.) The contextualist, I contend, is not committed to the assertibility of (2). Although (2) is not Moore-paradoxical, because the second conjunct does not entail p, its infelicity can still be explained as a violation of the knowledge norm of assertion, since it's second conjunct will, in the relevant cases, be unknown.

'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.