If Stephen's argument from the (alleged) transparency of speaker-meaning works against DeRose and other contextualists, it works against much of contemporary linguistic semantics, for semantics posits hidden indexicals, or at least non-obvious context-dependence, all over the place.  Since I think there are good semantic arguments for such posits, I infer that the argument fails by proving too much.
    I join Stephen in thinking that the argument applies about equally to the first two of his three ways of implementing contextualist semantics, hidden-indexical and indexical-verb.  (The third way, vagueness, is irrelevant for the reasons Stephen gives.)  I doubt that it applies to the Millikan variant I mentioned in class.  Millikan's idea is that contextual factors affect truth-value without being in any way represented in the target sentence's logical form.  If they do, then it is not surprising that speakers could not as readily recover them under questioning.  I shall not pursue that reply here, because I don't remember Millikan's presentation well enough. (I expect the idea is expressed somewhere in On Clear and Confused Ideas.)  But recall my distinction in "Reply to Ted's Argument" between hidden-parameter and similarity theories of conditionals.  The hidden-parameter theory is subject to Stephen's argument even if the argument fails; the similarity theory is not even subject to it.
    Obviously Stephen is right that, for some entirely uncontroversial hidden indexicals, competent speakers can be expected to recover the parameters under questioning.  So what the contextualist must say is that some hidden indexicals are more deeply hidden than others.  And that is also what I think is true, though with DeRose, I shall argue as well that the parameter of knowing is not as deeply hidden as Stephen thinks.
    Here are a few examples of hidden indexicals posited by semanticists.  (I am not counting philosophers who have philosophical rather than linguistic agendas, such as Gil Harman in arguing for moral relativism.)  (1) We've talked about time zone.  (2) We've talked (earlier) about conditionals--and, n.b., no one disputes that conditionals are context-sensitive in a way that is quite hard for anyone, much less an ordinary speaker, to articulate.  (3) Then there is season predication: "It's spring now." --Not in Sydney, it isn't.   Season predication is relative to hemisphere.  (4) Lots of expressions are indexed to assumed vantage points, notably verbs like "come" and "go."  Robert Frost: "I'm going out to clean the pasture spring;.... --You come too."  (Notice that the vantage point shifts between clauses.)  And lots more.
    Let me begin by conceding that Stephen's "different concept" move is sometimes appropriate.  I think it is for Matthew's case of relativistic apacetime.  Einstein added an argument place to each of the pre-existing spatiotemporal concepts, thereby producing a paronym; it's not that English words like "before" and "after" had had a hidden Einsteinian parameter all along.  And perhaps Stephen is right about three-year-olds and time zones.  Maybe the child's concept is, "The big hand is on the 12 and the little hand is on the 5."  But this move won't work for fluent adults mobilizing nontechnical concepts.  For example, I don't think it works for seasons and hemispheres; someone who forgets that relativity doesn't have a concept of "spring" different from what the public English word means.
    OK, so why are some hidden indexicals more deeply hidden than others?  Good question, and I don't have a pat answer.  Just this morning, Dorit suggested that it may be because there are different varieties of context-dependence, perhaps more than the four we have mentioned so far; that would afford one kind of answer.  A second type of answer would be syntactic and technical: A linguist or psycholinguist might tell us why some hidden parameters are psychologically harder for a speaker to recover than others.
    The best cases for Stephen are the ones he takes as his paradigm, the hidden temporal and spatial indexicals ("It's raining [now][here]"), because nearly all English sentences make temporal references, if only through tense, and nearly as many make spatial references.  Thus, of course speakers can readily explain those references even when they are hidden as in "It's raining."  Slightly less good cases are those based on attributive adjectives, because I doubt that the average speaker realizes that "big," "fast," heavy," etc. always mean "big [etc.] for an F."  But I agree that if subjected to directed questioning as DeRose calls it ("Do you mean big for a midget or big for a moose?"), such speakers will normally be able to cough up a correct answer.
    It does not follow that the same is or should be true of all hidden indexicals.  The parameters that drive indicative and subjunctive conditionals are hard even for the sophisticated theorist to articulate, and they have to do with merely possible states of affairs; ordinary people are not accustomed to thinking of such items as grouped into domains.  The behavior of the vantage point parameter is complex (see Kenneth Taylor's "We've Got You Coming and Going," Linguistics and Philosophy (1988)), and it would be tricky even to frame the appropriate directed question.
    I still have not given a general answer to the question, "Why are some hidden indexicals more deeply hidden than others?," because I don't have one.  But I have tried to indicate some possible reasons, and I have tried to convince you that some indexicals are more deeply hidden than others.

    Turning to DeRose:  I take Stephen's points against him--that Stephen's point is about directed questions, so that everything up to the middle of p. 3 is irrelevant, and that acknowledging ordinary vagueness does not make one a contextualist in a sense relevant to addressing skepticism.  But now I'd like to defend DeRose's claim that in any case the putative parameter of knowing is not so deeply hidden as Stephen implies.
    I think DeRose is right that few would reject the directed question asked of the opera fan.  (It's a completely empirical issue, of course, so what I and DeRose or Stephen think without having made a sociological study doesn't really signify, but here goes.)  As I said some weeks ago, the standards for knowing seem to vary with the gravity of the consequences of being wrong, though no doubt there are other factors too.

         "You say you know that Placido Domingo is scheduled to sing at the Met this season."
         "Yes, I saw it in the paper a few days ago."
         "Would you bet $20 on it?"
         "Sure."
         "How about $100?"
         "Um, yeah."
         "$1,000?"
         "Well, I'm not sure about that much."
         "Notice that I have a gun pointed at your baby daughter's head."

    There isn't a particularly good way of expressing the gravity-of-consequences parameter in ordinary English.  For want of better, I speak of knowing "for purposes of" this or that.  (Same for "flat": flat for the purpose of playing soccer on it vs. flat for the purpose of playing billiards on it.)  The opera fan knows for the purpose of winning a modest amount of money but not for the purpose of preserving his daughter's life.
    As DeRose says, people's usage conforms to that picture ("What ordinary speakers are happy to call knowledge in easier contexts, they will deny is knowledge in tougher contexts" (p. 2)).  And if there were a good colloquial way to phrase the directed question, I'm pretty sure they would be able to cough up such answers as "I meant for the purpose of winning a modest amount of money."  But, again, it's an empirical issue, so my defense of DeRose is itself only a bet.