(Now I happen to think that it's not at all clear how to make sense of that last stipulation. This basically amounts to a worry whether there is any correct generalization characterizing the difference between the shifty SSI-like views from 'classical invariantism'. But I'm setting that aside for now, assuming, as is usual in this discussion, that the sense in which Howie and Louie are in the same 'epistemic position' is tractable -- and does not at least really trivially entail that they're alike with respect to knowledge. I'll here use 'epistemic position' technically to mean the stuff that traditional invariantists affirm, but shifty people deny, comprise a supervenience base for knowledge.)
Contextualists and the relevant invariantists each have no trouble making Louie and Howie's utterances both true; the invariantist says that Howie and Louie just differ in what they know -- because of their interests or attention or whatever. (I'm not interested in 'classical invariantism' for the purposes of this post; the only invariantists I'm discussing are the shifty ones.) And the contextualist says that 'know' in Howie's mouth expresses some know-high relation, while 'know' in Louie's mouth demands only some know-low relation. If you're a contextualist who is also an intellectualist -- someone who thinks that stuff like interests and attention are irrelevant to the correct applicability of know-high, or know-low, or any other thing that 'know' can pick out, then you're also committed to thinking that both Howie and Louie know-low, but neither knows-high.
But each view, one might think, has a harder time when we consider what Howie and Louie say about each other. Suppose Louie and Howie are each talking about one another, cognizant of their respective epistemic positions. Howie says "Louie does not know that p." The standard intuition in these cases is typically taken to be that Howie's utterance is true. That's good for the contextualist (Howie's saying that Louie doesn't know-high, which he doesn't) but bad for the invariantist (Howie says that Louie doesn't know, but he does -- because he's so relaxed). Similarly, Louie says "Howie doesn't know that p" -- here, the standard intuition is that Louie's utterance is true. That's good for the invariantist (Howie doesn't know, because he cares so much and thinks about skepticism), but bad for the (intellectualist) contextualist (Louie is saying Howie doesn't know-low, but he does).
So is it a wash? Everybody gets one kind of intuition wrong, and now we're in the game of explaining intuitions away, or arguing that there are other theoretical reasons to go one way or the other, or whatever. People do often seem to write like this -- Jason Stanley's pretty explicit about seeing the dialectic in this way. But Keith DeRose cries foul -- the contextualist has more choices, he says. He's right -- she does. The contextualist can handle this last case ok. But there are other similar cases that she has to get wrong, if, like DeRose, she is an intellectualist. So I think DeRose claims too much when he says, on p. 226 of his new book, that "only contextualism adequately handles all of the relevant cases, and that it thereby obtains a very serious advantage over SSI on this issue." (At least supposing that the contextualist is an intellectualist, which DeRose's is.)
So what's DeRose say about the case above? The troublesome case was Louie's intuitively true utterance, "Howie doesn't know p". The thought was, since Louie's in such a chill context, 'knows' in his mouth will pick out know-low, but Howie does have that. DeRose's observation -- which I think is 100% right as far as it goes -- is that Louie doesn't have to pick out know-low by 'knows', just because he's so chill. If he knows that Howie is thinking about skepticism, or that it's really important to Howie whether p, then he can tailor his language to be talking about the thing relevant to Howie's situation. Suppose Howie's situation is such that he should phi only if he knows-high that p, and he's now trying to decide whether to phi. If Louie knows all this, then it's entirely natural for him to be talking about know-high. As DeRose says,
On contextualism, the speaker's context does call the shots. ... But sometimes speakers' own conversational purposes call for employing standards that are appropriate to the practical situation of the far-away subjects they are discussing, and so the shot that the speakers' context calls can be, and often quite naturally will be, to invoke the standards appropriate to the practical situation faced by the subject being discussed. (240)
So the contextualist can make "Howie doesn't know p" true in Louie's mouth. So far, we have one case the invariantist gets wrong, but the contextualist has gotten them all right. Yee haw. This is where DeRose sees the situation.
However, DeRose's treatment, though it seems to work just fine in this case, doesn't look sufficiently general. Notice that it relied on Louie's knowledge about Howie's situation. This is an accidental feature of the relevant set-up. Let's relax the assumption that Louie knows these facts about Howie; let's suppose, indeed, that Louie falsely believes Howie to be like Louie -- he thinks that p is no big deal to Howie, that Howie isn't thinking about skeptical scenarios, or whatever. I take it the intuitive data is the same: if Louie says "Howie doesn't know," it's true. (Maybe now we should consider a more likely utterance: "Howie does know," which we intuit to be false.) DeRose's explanation won't work here. Louie is not going to choose the knows-high relation to suit Howie's skeptical situation, because Louie doesn't know about that situation. And indeed, it doesn't look very plausible that there is any other way that Louie's 'know' is going to express know-high. The intellectualist contextualist is going to deliver a counterintuitive result about this case.
I think the contextualist has three choices.
First, she can question the data. I've made claims about what verdicts are intuitive; she can deny that those claims are true. In particular, she can maintain that contextualism respects the intuitively important difference between the informed Louie case and the ignorant Louie case.
Second, she can give up on claiming to enjoy an advantage over the invariantist with respect to intuitions about the truth third-person knowledge attributions, admitting that each view has counterintuitive consequences.
Third, she can give up intellectualism. A contextualist intellectualist would think that 'knows' sometimes picks out different know-relations, but denies that (some/all) of these relations supervene on the subject's epistemic situation. If she goes this way, then she can claim that Louie and Howie differ with respect even to the referent of Ignorant Louie's 'knows'.
I think option three is worth taking seriously. Stanley says that intellectualism is an important motivation for contextualism, and DeRose seems to agree. One might worry that once you're either a contextualist or an anti-intellectualist, you lose motivation for having the other view as well. But this blog post shows that there's at least some advantage: if you're either an intellectualist or an invariantist, you're going to get some intuitive verdicts wrong; if you're an anti-intellectualist contexualist, you can get all the cases right.
Is the resulting view more like a best-of-both-worlds view, or a worst-of-both-worlds view? We just need to think a lot more about various consequences, but so far, I'm not seeing much downside.