You say, “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.”

The problem for me is that this seems perfectly natural, as do all of the following:
“Of course it’s possible that not-p. Heck, anything’s POSSIBLE. But we know it aint’ gonna happen.”
“Yeah, there’s a chance that not-p. But c’mon, it’s completely insignificant. You know it’s not true.”
“I know that the small chance that not-p won’t obtain.”

Or, more specifically,
“Of course it’s possible that the large hadron collider will produce black holes. Heck, anything’s POSSIBLE. But we know it ain’t gonna happen.”
“Yeah, there’s a chance that not a single free will be made in the upcoming NBA playoffs. But c’mon, it’s completely insignificant. You know it’s not true.”
“I know that the small chance that I’ll die in the next 2 seconds won’t obtain.”

I don’t, then, take difficulties with the above to be problems for fallibilism. I take the naturalness of the above to be data on par with the unnaturalness of “I know that p but p might be false.”

I’m not sure that the view you propose allows for the naturalness of all of these. Dougherty and Rysiew’s view does. Now, I gather, you don’t think that these sound natural. But what sort of theory should someone accept who DOES hear them as perfectly natural? It looks (putting contextualist moves aside) like there is going to have to be a Gricean explanation somewhere — either for these or for the simpler concessive knowledge attributions. Fallibilists, obviously, should be interested in plumping for the Gricean explanation for the original concessive knowledge attributions.

Just as a matter of contemporary history of epistemology, I don’t think of Unger as (merely) defending a rival to contextualism. Rather, I think of Unger as an important precursor to contemporary contextualism — that’s certainly the way DeRose talks about it, and I think there’s something to that.

Maybe you and I agree that my claims about knowledge and certainty are as plausible as Unger’s about circles and perfect circles. I’d like that. I do take that data seriously, although I see that you don’t agree with it. I agree that it might be interesting to see what the folk think. I suspect they’re friendlier to the Unger line than you suggest. (But if I’m wrong about that, I’m not too worried. They’re only the folk.)

First, while it may work for some things that philosophers do in this neighborhood, I don’t think that your deflationary line on intuitions is going to make sense of some sizeable chunks philosophical practice, and at the very least, it fails to make any sense of _ Lewis_. Go back and re-read the relevant bits of “Elusive Knowledge”, and it’s just obvious that he, at least, doesn’t have any further “considerations that do count in that direction” of his claims about the infallibility of knowledge. It’s just something he takes to be a psychologically powerful datum, and if someone disagrees with him about that, then he thinks that all they can do is agree to disagree. First, his appeal is of a frankly psychological nature: “Yet fallibilism is the less intrusive madness [compared to skepticism]. It demands less frequent corrections of what we want to say. So, if forced to choose, I choose fallibilism. (And so say all of us.) We can get used to it, and some of us have done. No joy there - we know that people can get used to the most crazy philosophical sayings imaginable. If you are a contented fallibilist, I implore you to be honest, be naive, hear it afresh. ‘He knows, yet he has not eliminated all possibilities of error.’ Even if you’ve numbed your ears, doesn’t this overt, explicit fallibilism still _sound_ wrong?” (And note, by the way, that he is precisely asking us to step _away_ from any ways in which our epistemological expertise may be informing our judgments here.)

If Lewis had other considerations to muster, he would have mustered them, or at least gestured towards where they might be mustered from (the historical record or empirical observation or a mathematical proof published elsewhere or whatever it might be). And it’s not surprising that he proceeds — or, rather, doesn’t even try to proceed — in that manner, since indeed it’s hard to see what further considerations there are to be mustered here at all. We’re at bedrock, he thinks. E.g., he writes,

“I started with a puzzle: how can it be, when his conclusion is so silly, that the sceptic’s argument is so irresistible? My Rule of Attention, and the version of the proviso that made that Rule trivial, were built to explain how the sceptic manages to sway us - why his argument seems irresistible, howevertemporarily. If you continue to find it eminently resistible in all contexts, you have no need of any such explanation. We just disagree about the explanandum phenomenon.”

That it can’t make sense of this very famous paper is some indication that, despite your protests to the contrary, your proposal is substantially more revisionary than you’re trying to make it out to be. Now, if philosophers had, upon reading the paper, tended to go, “wow, some interesting stuff here, but what in the world is Lewis doing with those weird psychological premises? You can’t go about making serious philosophical arguments that way,” etc., then that would go some distance in your favor. But that’s not at all the reception the paper has garnered, however. The baldly psychological aspects of what he’s doing have gone unremarked, because they are part & parcel of the mainstream practice.

Turning to the Unger stuff, I think it’s important to keep in mind that he is just plain wrong about the linguistic data here. If someone says, say, that southern Illinois is flat, and Unger says, “aha! but it really does have lots of ups and downs and peaks and valleys and roughnesses … I mean, just compare it to, say, this piece of paper here. Isn’t this piece of paper much, much flatter?” , then the first person is likely to agree to that comparative judgment. But if Unger presses them, “aha, so don’t you want to say that southern Illinois isn’t _really_ flat? It’s not _perfectly_ flat, right?”, then they are likely to respond with some combination of (i) “whoa, you think southern Illinois isn’t really flat? dude, try driving through it sometime”; (ii) “well, right, so it’s not _perfectly_ flat. no one would think it is. but it’s still _flat_. Really, really flat, in fact”; and (iii) rolling their eyes and looking to renew their earlier commitment not to talk to philosophers, who so often have wasted their time with tin-eared sillinesses. Pretty much no one is going to say, “gosh, maybe southern Illinois isn’t really flat!” It’s just not going to happen. More generally, there’s just nothing amiss with utterances like, “Sure, it’s got some little bumps here and there, but it’s flat” said of, say, a football field. It doesn’t seem to So that whole premise of the discussion is basically off.

This is probably very good fodder for some x-phi treatment, btw; I found a tiny bit of data informally reported here: http://www.gap5.de/proceedings/pdf/157-168_blome-tillmann.pdf Couldn’t find anything else that seemed to have taken a real look at Unger’s outrageous claims, though.

Even setting that aside, although claims like “all circles are perfect circles” are the stock-in-trade of the standard Ungerian line, they are meant to support a _rival_ to the contextualist line — it’s the line of the invariantist skeptic! So if you’re making a case for contextualist certaintism, you don’t want to go that way. The parallel claim would be “all knowledge requires perfect certainty”, and you don’t want that. On the picture you’re trying to paint, you want something like, simply, “all knowledge requires certainty”, plus a story about how the contextually-determined certainty threshhold gets driven higher once it is pointed out that one is currently operating short of some still-higher possible such threshhold. Generally speaking, the contextualist in these debates wants to hook up to gradable terms, maybe even ones that are absolutizable, but they don’t want to hook up their target term to the _absolutized_ form of any such term. Flat enough is flat enough, and need not be perfectly flat, for the contextualist.

Now, it should be noted that Lewis himself does do this a bit differently. He does seem to embrace the absolutized form, only to un-embrace it; he jumps all the way out to it — and then walks it all back a ways, with his “psst!”s. This is another area where the infallibilist may have resources that the certaintist might not. The infallibilist can try to use the Lewisian machinery of “properly ignoring”, because she can point out, in her theory, those possibilities that are to be properly ignored, and of course he has lots of rules on offer to guide such ignorings. Certainty doesn’t seem to have the right structure for that. You’re just certain to a greater or lesser degree, end of story. There’s nothing like the infallibilist’s possibilities for any such walking-back machinery to get a hold of, when dealing with certainty.

Clarification: in your response to Garret, are you just rejecting that any _contemporary_ belief in the Euclidean structure of space is justified, or are you also rejecting that _past_ (in particular, pre-modern-physics) beliefs of that sort are justified? If it’s just the former, then I think Garret’s point still holds.

Garret: why should we think that the claim that all space must be Euclidean is justified a priori? I’m not sure I see why we should think it’s justified at all.