Epistemic Possibility

I’m working on a paper about epistemic possibility, and I need some help. Can someone tell me what epistemic possibility is? (This is a trick question.) To show why this is puzzling, here is a ‘problem case’:

S, a person of ordinary mathematical abilities, performs a complex mathematical calculation, which leads to a certain mathematical claim, P. S and I then have the following dialogue:

S: P.
Me: That was a pretty difficult calculation, and you’ve made mistakes before. Could you be wrong about P?
S: Yes. I could be wrong in thinking that P.

S speaks wisely here. But, if P is true, it is necessary in (what is usually called) the strongest sense: logical necessity. So in what sense could S be wrong? Well, it’s epistemically possible that S is wrong: yes, but how is that to be interpreted, such that it yields a kind of possibility broader than logical possibility?


Comments

Epistemic Possibility — 49 Comments

  1. Michael, very interesting problem. If the issue were one concerning a metaphysically necessary claim, I would have gone for the usual idea of what is logically consistent with what you know. But since the claim is one that is logically necessary, this one won’t work.

    Given the dialogue, it appears that the issue is one of human fallibility. How about this idea? Count as your evidence all your sensory experiences plus all your seeming states, including the seeming states that occurred during the calculation in question. Then, the sense in which you might have made a mistake is that you could have all this evidence and still have made a mistake. That is, your evidence (in this restricted sense) does not guarantee that you are right.

    I bet you have reasons to reject this idea though?

  2. I am probably missing a subtle point here, but this question about the breadth of epistemic possibility seems to me predicated on a false assumption: that the breadth of logical possibility and the breadth of epistemic possibility are measures in the same “dimension”. (BTW, the notion of the breadth of any possibility is a curious one. But we can leave that aside for now.)

    Logical possibility (necessity) is an attribute of the claim P. Epistemic possibility (necessity) is an attribute of, at a minimum, S, P and S’s reasons for believing P. Why is it problematic at all that S could be wrong about P when P is logically necessary? I suppose that this would be a problem if one thought that every logically necessary claim is also self evident. Does anyone believe this anymore?

  3. Dave, the usual understanding of epistemic possibility is in terms of what is logically consistent with what you know to be true. For a logically necessary truth, however, it’s negation is not logically consistent, and hence not logically consistent with what you know to be true. So the usual understanding doesn’t help with Michael’s dialogue.

  4. My first approximation for “it is epistemically possible for S that ~p” is just “S doesn’t know that p”, and there doesn’t seem to be any problematic sense in that even when p is necessary. I take it, however, that the problem turns on an attempt to specify an (epistemically) possible world in which S is wrong about p.

    How about:

    A world w is “epistemically complete” for S iff (1) for every p that S knows, w contains p; and (2) for every proposition p, w contains either p or ~p.

    A world is “epistemically consistent” for S iff S doesnâ��t know of any contradictions present or derivable in w.

    Epistemically possible worlds for S are sets of propositions that are both epistemically complete and epistemically consistent for S.

  5. Heath, I think this account of epistemic consistency is too weak. The only way for this account to explain Michael’s example would be for S to fail to think that no contradiction was derivable from ~p, but it’s easy to adjust the case so that in calculating, say, that 2+2=4, S also thinks that identifying 2+2 with anything other than 4 will yield a contradiction. If S thinks this, then no ~p world will count as epistemically possible on your account.

    I also think your first definition of epistemic possibility shouldn’t be accepted. That account, in terms of not knowing, is not a modal notion at all, and whatever else we say about epistemic possibility, it is clearly a modal notion.

  6. I thought that one strategy for dealing with these sorts of cases was to move from p’s epistemic possibility being determined by its being _logically consistent with what you know_ to its being _obviously logically consistent with what you know_.

    This doesn’t help with Mike’s question though–after all, p is among the things that the person seems to know having done the proof (even though it is a difficult one) and I don’t think that knowledge of p is lost even if a concession of the sort that is offered is warranted.

    Maybe this kind of case gives us reason to rethink the standard account of epistemic possibility in terms of DKO that DeRose offers? It seems to me that Colin Radford’s cases also create difficulty for the DKO account as it stands (he offered them as counterexamples to K –> B, I think they can be read as counterexamples to the claim that Kp –> ~ < e > ~p [Note: ‘< e >‘ is a cute way of representing epistemic possibility]). In those cases, it seems we can ascribe knowledge while still recognizing that there is real sense in which the falsity of the relevant belief is an open epistemic possibility for them. Mike’s mathematician, or someone similarly situated, seems to be in a similar position.

    If we read S’s second assertion as a genuine expression of the open epistemic possibility that p is false, think that it is plausible to describe S or someone in S’s position as knowing p, and think that warranted assertion requires truth or knowledge, then we run into a difficulty if we accept DKO. If S’s concessive assertion is warranted and DKO is correct, S is ignorant. One possible remedy might be this. Knowledge doesn’t require psychological certainty but intuitively epistemic necessity does. If we think that ‘must’ is factive (as Hawthorne says it is), then ‘It must be that p’ entails p whereas ‘I’m certain that p’ doesn’t. There must be more to epistemic necessity than certainty and there must be more to epistemic necessity than knowledge–why not both? ‘It must be that p’ is true, as uttered by S, iff (i) ~p is obviously inconsistent with what S knows (ii) S is certain that p. ‘It might be that p’ is true, as uttered by S, iff either (i) or (ii) isn’t satisfied. Yes this account of the truth-conditions is ugly with its disjunctive account of ‘might’, but I think it accounts for a wider range of cases than DKO. For Mike’s mathematician, p will no longer be an open epistemic possibility not simply in virtue of adding more knowledge, but in the resolution of certain doubts as well (unintentional mention I swear).

  7. Note: for some reason my attempt to represent put a diamond in to represent epistemic possibility didn’t work. I was saying that Radford’s examples cause trouble for the claim that Kp entails that it is not the case that ~p is an epistemic possibility. I was not saying that they created difficulty for Kp –> ~~p.

  8. Jon,

    I’m not quite following. Is “2+2=4” supposed to supplement the presented case (i.e., is it in addition to Huemer’s p) or is it supposed to be a different example (i.e. it becomes p, in the new example)? In the former case, I don’t see how my definition fails; S still doesn’t see any contradictions in his beliefs. In the latter case, I would be willing to say that 2+2=5 (or anything other than 4) is not, in general, epistemically possible. Or maybe I am missing something?

    Re my first definition, since knowing plausibly involves ruling out alternative possibilities (dickering over this point is behind lots of Cartesian-style skeptical argumentation) I don’t think it is a non-modal definition in the relevant sense. But I said “first approximation” on purpose, too.

  9. Michael, one rather extravagant answer to your question would be to adopt the view (which is in fact adopted in a different context by my fellow FBCer Allan Hazlett) that there are impossible worlds. That would give you a span of worlds wider than the logically possible ones.

    Setting that aside, I’ve got a question. As the case is described, one needn’t advert to epistemic possibility in order to explain S’s concession. Couldn’t one go wrong in forming a belief without the belief being false? Despite the fact that one’s belief is true, if one’s belief isn’t appropriately based on good evidence, then one has in some sense gone wrong. One could have easily believed something false in proceeding as one did. Did you mean to rule this sort of thing out in the original case?

  10. Thanks to Jon for the clarification re epistemic possibility: P is epistemically possible for S iff P is logically consistent with what S knows. (I assume that everything that S knows or could know is true.) If X is necessary, then ~ X cannot be epistemically possible for S, by definition.

    If we look at the dialogue, the question is “So in what sense could S be wrong?”, if turns out that P is necessarily true. Isn’t it simply that S could be wrong in thinking that she knows P?

    Let K be everything that S knows, and let P be necessarily true. Then, by definition, ~ P cannot be in K, and thus P is epistemically possible for S. (It follows that every P that is necessarily true is epistemically possible for everyone. Generous, but probably ok.) However, this almost nothing about whether S knows P, since S’s reasons for believing the necessary truth P may not be “good enough”.

    So S cannot be wrong in thinking that P, just in thinking that she knows P.

    I look forward to learning why this won’t work.

  11. Dave, what Michael wants is an explanation of why ~p is epistemically possible, not why p is. And it doesn’t follow from p’s being epistemically possible that ~p is, so I don’t see yet how your proposal helps make sense of Michael’s dialogue.

    Heath, the 2+2=4 was supposed to be the value for p, one which is logically necessary. Michael’s case is one where we are supposed to admit that the negation is epistemically possible, so if you claim that the negation here isn’t epistemically possible, I’ll have to change the value to some other logical truth. If you deny all of them, then you should find Michael’s dialogue incoherent, at least to the extent that he claims to be presenting a dialogue that involves the notion of epistemic possibility. If, however, you’ll let one such example go through, where p is a logical truth, and ~p is epistemically possible, then you can substitute it into my earlier remarks to get a counterexample to your proposal, I think.

  12. Thanks again to Jon for helping me understand the issue. I’ll try to make my point one more time, and then I’ll desist.

    Jon wrote: “… what Michael wants is an explanation of why ~p is epistemically possible, not why p is.” Since p is assumed to be a true statement of mathematics, I have been assuming that ~p is necessarily false and therefore not epistemically possible. So the answer is just that ~p is NOT epistemically possible. This just follows from the fact that p is false.

    Perhaps the problem is the sentence from the dialogue:
    … itâ��s epistemically possible that S is wrong.

    This would seem to mean that it is epistemically possible that, despite what S believes, P is false, i.e., it is epistemically possible that ~ P. But I am now back to my original objection: it is a levels-mistake to talk about the epistemic possibility of a claim. Epistemic possibility is only well defined for a pair [person, claim]. If you tidy this up and ask whether it is epistemically possible [S, ~P], then the answer is just no (see above).

    Since this seems so easy for me, I must be missing the point of the debate, and as promised, will stop now.

  13. Dave, you’re right that what is epistemically possible or not should be person-relative, but I don’t think the right answer is that no necessary falsehoods can be epistemically possible for anyone. Let p range over propositions that are either necessarily true or necessarily false (logically). Some values for p are counterbalanced for us, in which case we should say that both p and ~p are possible in some sense related to the subject matter of epistemology: epistemically possible, for short.

    Whether this notion of epistemic possibility is the proper concept to use to clarify Michael’s example, which involves fallibility, is an open question, I think. But in both the above case and in the fallibility case, we don’t want the mere fact that a claim is logically true to preclude our being fallible about it or it’s negation being epistemically possible.

  14. Thank you all for your comments. Following are my responses to (most of?) them:

    1) Jon Kvanvig wrote:

    “the sense in which you might have made a mistake is that you could have all this evidence and still have made a mistake. That is, your evidence . . . does not guarantee that you are right.”

    This contains the modal terms “could” and “guarantee.” What sort of modality is involved? If it is epistemic, the account is circular. If it is logical or metaphysical, the account runs into the original problem: You couldn’t have all this evidence and P still be false, because P is necessary.

    But perhaps I’m misunderstanding: perhaps “you could have made a mistake” doesn’t mean that P, itself, might be false. Perhaps you meant either suggestion (2) or suggestion (3) below . . .

    2) John Turri:

    “Couldn’t one go wrong in forming a belief without the belief being false? Despite the fact that one’s belief is true, if one’s belief isn’t appropriately based on good evidence, then one has in some sense gone wrong”

    When S says, “I could be wrong in thinking P,” I think that means that, while I believe P, P might be false.

    One problem with your suggestion is that, if S’s proof is in fact correct (and let’s stipulate that it is), then every step in it is necessarily true, and every inference is necessarily valid, just as P is necessarily true. So even if “I could be wrong” could be plausibly interpreted as “There might be a mistake in this proof,” this wouldn’t avoid the original problem.

    Another problem is that if your suggestion is correct, then S should be recognizing the possibility that his proof contains an error, but not that P is false, and this would entail different behavior and attitudes than a recognition that P might be false. For instance, if someone else performs his own calculation and thereupon asserts ~P, S can confidently proclaim, “No, you’re wrong, because P.”

    Of course, S should recognize the possibility that his calculation contains a mistake; but upon doing so, he should then, consequently, recognize the possibility that P is mistaken.

    3) One might say (perhaps as an interpretation of Jon K) that a person could have the sort of evidence one has for P, for some (other) proposition, while that proposition was false. E.g., one can go through an apparent proof that seems just as compelling as the proof of P, but for a false conclusion. The “could” here is logical, let’s say. It seems a little odd that the (epistemic) possibility of one’s being wrong about P should be explained in terms of the (logical) possibility of one’s being wrong about other propositions. But perhaps this is acceptable nevertheless.

    This is what I was thinking for a while, and I was going to write my paper defending that. However, I am bothered by the fact that this does not tie epistemic possibility to “knowledge,” and as a result, it does not capture the context-sensitivity of epistemic possibility. (Anyone else think epistemic possibility is context-sensitive?)

    4) Heath White:

    “My first approximation for â??it is epistemically possible for S that ~p’ is just â??S doesn’t know that p’.”

    The problem here will be cases in which p obviously and directly follows from something S knows, although S hasn’t actually drawn that inference yet. I take it that we want to say that ~p is epistemically impossible for S, though S doesn’t know ~p (due to not believing it). This naturally leads to . . .

    5) Clayton:

    “… move from p’s epistemic possibility being determined by its being _logically consistent with what you know_ to its being _obviously logically consistent with what you know_.”

    This doesn’t account for my case, because in my case, S correctly says ~P is possible, but it is false that ~P is obviously logically consistent with what S knows. In fact, ~P is logically impossible, and so not consistent with what S knows.

    By the way, I think S does not know P in this situation, precisely because he correctly recognizes that he might be wrong. (But this does not make me an infallibilist or a skeptic: I think epistemic possibility is context-sensitive in the same way as knowledge.) (Another note: What is DKO?)

    6) Clayton again:

    “â??It must be that p’ is true, as uttered by S, iff (i) ~p is obviously inconsistent with what S knows [and] (ii) S is certain that p.”

    This seems to succumb again to the problem under (4). Now things that obviously follow from what S knows will not be epistemically necessary, provided S has not thought of them and so is not certain of them (I assume that S’s being certain of something requires having a belief about it). Example: S sees a table, under normal conditions, and knows it to be a table. S has never heard of the planet Rigel-7, so S has no attitudes about the latter. Is it epistemically possible for S that what he is seeing is actually Rigel-7? Can I correctly say: “For all S knows, that is Rigel-7.”?

    7) Heath again:

    “A world w is “epistemically complete” for S iff (1) for every p that S knows, w contains p; and (2) for every proposition p, w contains either p or ~p. A world is “epistemically consistent” for S iff S doesn’t know of any contradictions present or derivable in w. Epistemically possible worlds for S are sets of propositions that are both epistemically complete and epistemically consistent for S.”

    I don’t believe talk of â??possible worlds’ is useful here. Why not just talk directly about the epistemic possibility of propositions? (You’re using propositions to define “worlds” anyway.) Then I think your proposal comes to: p is epistemically possible for S iff: S doesn’t know of any contradiction between p and anything that S knows.

    I think this faces the problem in (4) and (6) again.

    8) Dave:

    “S cannot be wrong in thinking that P, just in thinking that she knows P.”

    I take it that it is intuitively correct of S to say he could be wrong about P, and not merely about whether he knows that P. Now, you might be requesting some further argument for this intuition.

    First, suppose we take your line. Tell me more about the possible worlds that S is alluding to, in which S doesn’t know P. Why does S not know P in these worlds? Consider some suggestions:
    i) Because S doesn’t believe P? No, because that would license S in saying, “It’s possible that I don’t believe P,” which is wrong. S definitely believes P; so he knows for certain he’s not in one of those worlds.
    ii) Because P isn’t true? No, P is necessary.
    iii) Because P isn’t justified? No, P is justified by the proof, and S knows for certain that he has that argument and that it renders his belief at least justified. He knows he’s not in one of the worlds where he didn’t construct an argument but instead consulted astrology, etc.
    iv) Because there is a mistake in the proof (even though P is true)? No–see suggestion (2) above.

    Second, it seems that the judgement of fallibility here is not only intuitive on its own, but useful and important in certain contexts. Suppose the result of the calculation S has just done is going to be used in directing critical equipment on the space shuttle. If the calculation is wrong, then the space shuttle will likely crash. (But if the calculation is correct but S doesn’t know it because of some Gettier business, the space shuttle will not crash.) The fact that S recognizes the possibility that his answer to the problem is false explains why he might do such things as checking over the proof, asking other experts, expending resources to make sure (where the amount of expenditure he’s willing to accept is proportional to the badness of the space shuttle catastrophe), and so on.

    I take it none of us would want to convict S of irrationality here. And I take it that nothing less than the possibility of ~P can explain this. (If there’s another explanation I haven’t thought of, someone please tell me.)

    —-

    Again, thank you all. I’ll probably use some of these ideas in my paper, attributing them to you all. Unfortunately, I don’t know Dave & Clayton’s last names (please help). Also let me know if you don’t want to be cited (though that would be odd).

  15. Mike,

    As for what you wrote in (5)–I agree with your response. I was just pointing out that I thought your case showed that we can’t just weaken an account under which ~p being epistemically possible by adding the notion of ‘obviousness’ works as it seemed to me (and still seems) that in the case (or at least in cases very similar to this) the mathematician knows p and there ain’t no entailment more obvious from p to p.

    I must say that I just don’t have the intuition at all that someone in the mathematician’s position couldn’t know the relevant proposition. In part, that’s because I think that the conditions under which you could be warranted in conceding the possibility of error are more expansive than the conditions under which you couldn’t know. I’m just curious, but in the Radford examples like Jean the Librarian, do you have the intuition that Jean knows when she correctly responds to the questions she’s asked? Would you take her concessions that she might well be wrong to be out of place? I say she knows but I also think her concessions are warranted and that’s why I’m sceptical of DKO.

    The proposal I wanted to offer was a revision of the DKO account of the truth-conditions for ‘might’ and ‘must’ which is something closely resembling the following account:

    As said by S, ‘It might be that ~p’ or ‘~p is epistemically possible’ is true iff S doesn’t know otherwise; ‘It must be that p’ or ‘p is epistemically necessary is true iff S knows p.

    My worry was that in cases of knowledge with uncertainty, perhaps cases in which S falsely believes she doesn’t know p, or perhaps Radford examples, it seems strained to say that p is epistemically necessary for the speaker. (I used to think it was impossible to falsely believe you don’t know but everyone beat up on me for how silly it was to think that so I have deferred to the wisdom of others and am now using this possibility freely).

    The dirty solution was to make the truth-conditions for ‘might’ disjunctive–‘It might be that ~p’ as said by S is true iff either (i) S doesn’t know otherwise or (ii) S is uncertain and the truth-conditions for ‘must’ conjunctive [I made a mistake in the previous post by omitting a tilde after a lengthy but failed attempt to add a diamond to my comments].

    Your Rigel 7 case was damn clever. I’m at a loss as to what to say. Obviously I don’t want to say that for all S knows, this table is Rigel 7. So I’m tempted to say that it is not an open epistemic possibility that this table is Rigel 7. The problem is that if we say that this table’s distinctnes from Rigel 7 is epistemically necessary for Sam, we have to say that he knows it (on the standard account of epistemic necessity), which seems to require that he believes it, which is impossible given the case, which is bad. I’m going out on a limb here, but I’m wondering if we sometimes don’t deny that S doesn’t know p even under circumstances in which it is obvious that S has no belief one way or the other–provided that p is so completely obvious to the speakers that we can’t imagine some fool believing it to be false. ‘Sam doesn’t know that his fish aren’t speaking Mandarin chinese’ sounds really odd to me. If you asked ‘But isn’t it the case that Sam doesn’t know that his fish aren’t speaking Mandarin?’, I’d be inclined to say no. Again–I’m not inclined to say that his fish speaking Mandarin chinese is an open epistemic possibility for Sam, nor am I inclined to say that its falsity being epistemically necessary requires Sam to have a belief one way or the other. Since I’m not allowed by the rules of the house to try to introduce some condition to the effect that p is epistemically necessary for Sam if Sam only considered whether p he’d immediately know with certainty, I’ll just tip my hat.

  16. Michael, your worry is legitimate here, but I think if you approach the terms proof-theoretically, rather than semantically, you can avoid the problem. Take the evidence as premises and whatever proof theory is appropriate. Then construct the proof of p. Now ask two questions. First, is the conclusion derivable from the premises, and second, does the conclusion depend on the premises? If the answer to both is “yes”, then the premises guarantee the truth of the conclusion; if not, then they don’t. Might that avoid your concern?

  17. Can someone tell me what epistemic possibility is? (This is a trick question.)

    Well, itâ??s epistemically possible that S is wrong: yes, but how is that to be interpreted, such that it yields a kind of possibility broader than logical possibility?

    Hi, Michael.

    I’ve found it best to “epistemic possibility” to mean the kind of possibility that certain modal sentences — “It’s possible that P[ind]” (the subscript “ind” indicates that the embedded P is in the indicative mood) and some others — typically express. The sentences in question seem to express possibilities that have something to do with knowledge, hence the name “epistemic possibilities.”

    “DKO” is an abbreviation I used in a couple of recent papers (“Contextualism: An Explanation and Defense” and “Assertion, Knowledge and Context”; all of the papers of mine that I’m mentioning are available at: http://pantheon.yale.edu/~kd47/OLP.htm) for the “Don’t Know Otherwise” account of epistemic possibility, according to which P is ep. pos. for S iff S doesn’t know that ~p. So this is basically the notion Heath White mentions in comment 4, above, before Clayton used the “DKO” abbreviation for it in comment 6.

    DKO, if it were right, would satisfactorily answer the questions of your post. Since S can fail to know that ~p even where ~p is logically necessary, it’s easy to see how, given DKO, p can be ep. pos. for S even where p is logically impossible.

    But DKO isn’t right — as you point out, for instance, in your response to HW. In the papers I mention above, I say that DKO isn’t right as it stands — I’m only using it as an example of a theory that could be defended from a certain type of attack by means of a certain defensive maneuver. But I do think that DKO is “on the right track” — as oppposed to DKEW (“Don’t Know Either Way”) accounts, which are the wrong path, according to me.

    So, if DKO isn’t exactly right, what is the correct analysis of epistemic possibility? In the comments above, we get a couple of the usual proposals: P is consistent with what S knows; P isn’t obviously inconsistent with what S knows. I canvass some other proposals in my old “Epistemic Possibilities” paper (PHIL REVIEW, 1991). But no such inflexible proposals can be generally right because of….
    context-sensitivity (of course). So, when you write in your reply, “Anyone else think epistemic possibility is context-sensitive?”, the answer is definitely YES — because I do.

    The relevant modal statements shift in content as the standards for knowledge shift, with more and more becoming ep. pos. as the standards for knowledge go up. I ignored this context-sensitivity in “Epistemic Possibilities” (though it was in my dissertation earlier, and has since been aired in section 3 of my “Simple MIGHTs, Indicative Possibilties, and the Open Future,” PHIL QUARTERLY, 1998).

    What’s relevant for our current concerns is instead the context-sensitivity that I did go into in “Epistemic Possibilities.” There I argued against various inflexible proposals, and for the flexible account that P is ep. pos. for S (S’s assertion of “It’s possible that P[ind]” is true) iff (roughly: I’m doing this from memory)
    1. Nobody in the contextually relevant group of people knows that ~p AND
    2. There’s no contextually relevant way by which they can come to know that ~p.
    (The contextually relevant group will standardly include S.)

    Jon proposed the fairly common analysis of ep. pos. according to which p is ep. pos. for S iff p is consistent with what S knows. But this turns out to be just one special case of what can be meant by the relevant modal statements — it’s what results when the contextually relevant group of people consists entirely of S, and where the the contextually relevant way of coming to know that ~p is by ~p being logically implied by what S knows. We may well use epistemic modal statements to express such a thing, but there are many, many uses of the modal statements that we would surely want to classify as epistemic, but where they don’t express consistency with what’s known. Sometimes the contextually relevant way of coming to know is instead something like: can very easily find out. Sometimes not-so-easy ways of coming to know that ~p are relevant. See “Epistemic Possibilities” for cases that show different things that can be meant by the relevant statements; you can then construct lots more that demonstrate lots of other possibilities. It’s futile to try single out one inflexible meaning as THE analysis of “epistemic possibility.”

    You may be quite receptive to this, given your allegiance to the context-sensitivity of ep. pos.

  18. Keith, I really like this aspect of the blog, that I learn there’s stuff I need to read that I haven’t read yet! I think my own intuitions about “might” sentences of the sort you describe may be corrupted: I hear lots of ambiguity in such sentences, and so have a hard time hearing them as always, or even usually, having something to do with knowledge. But I don’t trust my intuitions here, since I came to think of epistemic ‘mights’ after thinking quite a bit about other kinds, and so may interpret things in a way that is infected with other modalities that ordinary folk wouldn’t intend and ordinary language doesn’t encode in the usual case. As a result, it’s often the case that where you see contextualist signs, I see ambiguity.

  19. (1) Clayton–
    Actually, your suggestion at the end is good, and I think it’s close to being right. I’m not sure why you said you were not allowed to introduce “some condition to the effect that p is epistemically necessary for Sam if Sam only considered whether p he’d immediately know with certainty”. A grad student of mine said the same thing–roughly, that p is ep. nec. iff, if S were to consider whether P, then S would know that P. Of course, there are the usual sort of problems that you have when you analyze something using counterfactuals: we can come up with cases in which S would know that P, but in an unexpected and irrelevant way. (For instance, the analysis implies that, for every P, it’s always epistemically necessary that I’m considering P, because if I were to consider whether I was considering P, I would know that I was considering P. (This is using “consider” liberally, but you get the idea.)) But I don’t care much about those sorts of problems, and I think I can fix them. (Roughly, I want to build into the counterfactual a condition that excludes acquisition of new evidence relevant to P. Clearly that has to be in there.)

    (2) Jon–
    Yes, that’s a good point in response to my response to you. Whenever I make use of the “a necessary truth follows from anything” principle, I feel guilty. However, there’s a way to make my point (or something like it) without relying on that principle.
    First, take the axioms of mathematics (assume we’re talking about really simple, self-evident ones, which S clearly knows). Are they epistemically necessary, on your proposed account? If not, that’s an objection to the account. If they are, then anything that can be proven from them is epistemically necessary, so the P in my original example is ep. necessary.

    (3) Keith–
    Thanks very much. I was looking for more references on this subject.
    When you say, “But no such inflexible proposals can be generally right because of . . . context- sensitivity”, I don’t quite get this. DKO, for instance, makes ep. pos. context-sensitive, as long as knowledge is (as you recognize in the paragraph following that quotation). What I was hoping was that the context-sensitivity of “might” could just piggy back on that of “know”–that we wouldn’t need an extra contextualist element. I’m still hoping that that’s the case. It looks like the extra context-sensitive elements you want to include are
    a) What the relevant group of people is, and
    b) What the relevant “ways” of knowing are.

    I’m going to have to just read your paper to see what I think of that. I need to see the case for (b) varying with attributor context. Likely, I just haven’t heard the right examples yet.

  20. Michael, this may be completely wrongheaded, but I suspect there is a variety of notions properly classified as epistemic possibilities. One, for sure, has to do with knowledge and it’s lack, but when i read your example, it didn’t strike me as a case of that sort. In the comments, you claim that S doesn’t know because of S’s admission, but the case just didn’t look like that to me when I first read it. The reason is that if asked about the possibility of being wrong, anyone who understands their own fallibility will always grant such a possibility, but I don’t think the concept of fallible knowledge is incoherent.

    So when I read your example, I took it to be one involving a sense of epistemic possibility connected with our fallibility, and given the view I just expressed, that leaves open the question of whether or not S knows. If that is a possible reading of your dialogue, then we shouldn’t want to say that anything, including the simple axioms of arithmetic is epistemically necessary, since that would imply infallibility about them. Maybe the cogito is epistemically necessary in this sense, though I have some doubts there as well, but even if we grant that point, hardly anything else is.

    But suppose there is a natural reading of your dialogue on which it implies that S doesn’t know. Maybe there is, but that might still be pragmatically rather than semantically based. Given the infallibilist tradition in epistemology, it’s very easy to read the story as involving an admission or implication that S doesn’t know, since our pre-philosophical conception of knowledge includes that tradition (and I intend to separate what knowledge itself is from that pre-philosophical conception).

    One way to see whether there is this alternative, fallibilist sense of epistemic possibility is to imagine the dialogue as occurring between two unrepentant and thorough-going fallibilists whom one knows well enough to interpret properly. For me, I imagine Foley and Lehrer. Lehrer does a complicated proof and reports the result to Foley. Foley says, “that’s a pretty complicated proof, and you’ve made mistakes before, right?” Lehrer says, “Of course I have, that’s part of what it is to be human.” Foley says, “So you could be wrong?”, to which Lehrer says, “Yes, of course I could be wrong; as I said, that part of what it is to be human, but do you have any reason to be suspicious of my proof?”

    Here I’m not at all inclined to think that Lehrer has implied that he lacks knowledge.

  21. Jon–

    Maybe we have a difference of intuitions. I think explicit statements of fallibilism sound counter- intuitive, linguistically. E.g., “I know it’s raining, but it might not be.” Or, “I could be wrong, but I know that P.” (I mean that I don’t see any natural reading of those that makes them okay.) Those don’t sound wrong to you?

    Of course, I understand the motivation for fallibilism–we don’t want to give in to skepticism, but it seems that the arguments for our fallibility about almost everything are pretty irresistible. I sympathize with those motivations. But I propose, tentatively at least, that all three of these things can be accommodated by sufficient contextualism–
    1) “I know that P, but P might be false” is contradictory.
    2) Most ordinary knowledge ascriptions are true. (As when I say I know where my shoes are.)
    3) Arguments for fallibility are sound.

    We just say that the standards for “might” shift with context along with those for “know.” Thus, the arguments for our fallibility succeed partly by raising the standards for epistemic necessity. Consider two examples to support this context-sensitivity of epistemic modals:

    Ex. 1: You’ve just finished discussing Descartes’ 1st Meditation with students. You say, “So, is it possible that there’s no table here?” The students correctly answer, “Yes.”

    Ex. 2: You’re making a visit to Boulder to give a talk, and I’m supposed to pick you up at the airport, but you’re a little late. I call you on your cell phone and say…
    Me: “Where are you, Jon?”
    You: “I’m at the airport. We’ve just landed.”
    Me: “Is it possible that you’re still in the air?”
    You: “No, it isn’t. What do you think I am, stupid? I can see out the window, and we’re on the ground. Sheesh.”

    Notice that the student in Ex. 1 cannot appropriately say, “No, it’s not. What do you think I am, stupid? I can see the table right in front of me. I know what a table looks like. Sheesh.”

    About your Foley-Lehrer dialogue, I’m not sure what to say. But there’s some funny business going on, because you’ve stipulated that the characters in the dialogue have the very view about the analysis of “know” that’s in dispute. If they have a false or confused view about the meaning of “know” and “possible,” can we use judgements about what they are implying when they use these words as guides to what the words really (normally) mean? Compare: suppose U, a typical undergraduate, thinks that knowledge = strong belief. Then when U says, “In 1600, everybody knew that the sun went around the earth,” is U implying that in 1600, the sun went around the earth?

    (P.S. Who is the Dave who posted earlier [last name?])

  22. Branden–
    Thanks very much. Those papers show me that the analysis of epistemic modality is a much deeper and more exasperating issue than I realized. I’m afraid I’m unsympathetic to the idea of messing around with the notion of truth in the way MacFarlane is doing, just to account for epistemic modals (though I know he is independently motivated to do the messing around in question). I’m very conservative when it comes to “truth”. But without going into that, I see a prima facie problem with his analysis. He says:

    â??It might be the case that p’ is true as uttered by S at t0 and assessed by A at t1 iff at t1 A does not know that ~p.

    He also imagines an example in which, referring to a very complex propositional logic formula, two people have the following dialogue:

    Anne: This formula might be a tautology, and it might not be.
    Jim: But it’s decidable whether a formula of propositional calculus is a tautology.
    Anne: Right. In principle, we could find out the answer, and I hope we will find it soon. But all we know now is that it might be a tautology, and it might not be.

    Now suppose that Jim subscribes to MacFarlane’s analysis of “might”, while Anne is a normal speaker. They set to work on the truth tables, and finally verify that the formula is tautological. The dialogue continues:

    Anne: Well, I see that the formula is a tautology.
    Jim: That’s right. So you see, you were wrong.
    Anne: What are you talking about? I didn’t say it wasn’t a tautology! In fact, I admitted that it might be one.
    Jim: Yes, but you also said it might not be a tautology. But now we know it is one. Why can’t you just admit you were wrong?
    Anne: Look, of course now we know it is a tautology. But at the time, I was right in what I said: for all we knew then, it might have turned out not to be tautological.
    Jim: Stop changing the subject. We know it’s not a tautology, so it’s false that it might not be one. You said it might be one. So you were wrong.

    To me, Jim’s statements sound absurd; Anne is clearly right. (Disclaimer: I’ve only skimmed through the paper and need to read it more carefully. But this is my initial objection.)

  23. The last line of the dialogue was supposed to be:

    Jim: Stop changing the subject. We know itâ??s a tautology, so itâ??s false that it might not be one. You said it might not be one. So you were wrong.

  24. Mike,

    If I may jump in one last time, can I press you a little about explicit statements of fallibility? I think Patrick Rysiew (apologies for spelling) calls statements such as these ‘concessive knowledge attributions’:

    (CKA) I know p but I might be wrong.

    These sound really, really bad. But, is there badness (or their bad soundingness) due to their being overt contradictions or something else?

    Compare CKA to overt contradictions such as:

    (1) I know that this is the turn for San Jose but I don’t believe it.
    (2) While there are no angels I know that there are.

    Also, (1) and (2) sound really, really bad and we can account for this in terms of the fact that they are overt contradictions. Suppose we embed them, qualifying them as follows:

    (1e) I believe that: I know that this is the turn for San Jose but I don’t believe it.
    (2e) I think: while there are no angels I know that there are.

    By embedding these, the sin isn’t washed away. Apparent lesson to be taken from this–epistemic qualification doesn’t wash away the sin of overt contradiction. Now, suppose you and I are cheating on a pop quiz, I’ve answered the second question with a ‘b’, and you raise a sceptical eyebrow. I whisper:

    (CKAe) I think I know that the answer is ‘b’ but I might be wrong, it might be ‘c’.

    This doesn’t sound odd to me in the slightest, but as embedding within the epistemic qualifier shouldn’t clean up an overt contradiction, isn’t that some reason to think that the oddity of (CKA) lies elsewhere?

    [[Note: if (CKA) can expresse a true proposition, ‘might’ expresses open epistemic possibility, knowledge doesn’t always close open epistemic possibilities. In this sort of case, clearly inspired by Radford examples, I don’t think we have to say if the answer really is ‘b’ that I didn’t know that the answer was ‘b’.]].

  25. Michael, great examples, especially the Boulder one–you’ve understood my emotional character exactly right!

    I agree with you about the tendentious character of the Foley/Lehrer case, but I don’t think it’s because of the particular analyses of knowledge that they hold. In fact, Foley has no such analysis, and their fallibilism about knowledge is independent of any particular analysis that might be proposed. But I agree with you that the contextualist approach here is very attractive.

    Clayton, this is a very nice argument about embedding the problematic assertions inside belief operators. I’m not sympathetic to the Radford line, but the embedding argument is important evidence that CKA need not be contradictory. Gives me something more to think about!

  26. Oh, one more thing, Michael. I read the McFarlane paper yesterday, and had the same reaction you did, plus some worries about the strategy of relying on Assertion-2 and Assertion-3 for his argument. I’m going to post tomorrow about the norm of assertion issue, and given the level of interest in epistemic possibility, it might be worth talking more about these relativistic approaches (though I cringe at the suggestion that truth should be understood this way, even if only locally…).

    Oh, and Dave is David MacCallum of Carleton College.

  27. Michael and Jon,

    Yeah, I first cringed at John’s stuff, too. But, now that I’m talking to him about it on a regular basis (and reading lots of deeper stuff of his on semantics that are not yet published but will appear in his book on relative truth), I no longer cringe. I think he’s really onto something, and his book will explain how you can do relative truth rigorously (and how useful relative truth is in many applications).

    Of course, this is all consistent with one not needing it for epistemic modals in particular. But, I think the case is actually rather strong here. Egan has a new manuscript on this, which goes in a similar direction to John (and which gets more into the nature of assertion, which Jon rightly notes is central):

    http://www.geocities.com/eganamit/might.doc

    I wonder why, exactly, you think Jim is right in the dialogue. Can you explain?

    -Branden

  28. I think explicit statements of fallibilism sound counter-intuitive, linguistically. E.g., “I know it’s raining, but it might not be.” Or, “I could be wrong, but I know that P.” (I mean that I don’t see any natural reading of those that makes them okay.) Those donâ??t sound wrong to you?

    Mike: I think it’s a good idea to distinguish between those two examples. The first certainly does “clash.” In the end, I think it is a genuine contradiction. (This is argued in the second-to-last section of “Epistemic Possibilities”; well, I’m there dealing with “I know that P, but it’s possible that not-P[ind]”, but the arg. would be the same for your “might” version of the same conjunction. The best reason for doubting that these are genuine contradictions is that “P, but it’s possible that not-P[ind]” (same as the above, but dropping the “I know that” from the first conjunct) also clashes, though it is clearly consistent, and one can worry that the clash of the sentences we’re dealing with may derive from this clash, and so might not be genuine contradictions, either. In the end, though, this worry doesn’t pan out.)

    But your second conjunction — “I could be wrong, but I know that P” — does have a natural reading on which it’s OK. “I could be wrong” could be read as saying that the speaker admitting that s/he could be wrong about whether s/he knows that P, rather than that she could be wrong about P. The same ambiguity comes up in Clayton’s “I think I know that the answer is â??bâ?? but I might be wrong” — indeed, since the “might” claim there follows the claim to know, it’s even more natural there to read the latter as an admission that the speaker might be wrong about their knowing. I think that explains why Clayton’s conjunction sounds fine to him. Eliminate that ambiguity, making it clear that the possibilty being admitted is the ep. pos. of not-P, as in “The correct answer might be ‘b’, but I think I know that it isn’t ‘b'”, and it no longer sounds so good.

    Re your exchange with Brandon, my advice is: DON’T STOP CRINGING.

  29. Oops — mistake above. Your “I could be wrong, but I know that P,” does have the ambiguity I mention above, but should clash on either reading (though it would be genuinely inconsistent on only one of the two readings), if “could” works like “might”. (I’ve got nothing on “could”; I’ve obsessed over “might”.)

    In virtue of the “I think” in it, Clayton’s “I think I know that the answer is ‘b’ but I might be wrong” should still have a very natural reading where it’s fine.

  30. Keith, this looks right about Clayton’s argument, and I agree as well that talk of fallibilistic knowledge sounds counterintuitive. One explanation is, of course, semantic, but there is also the mistaken theory explanation as well. If the entrenched folk theory of knowledge is infallibilistic, then we should expect such statements to sound counterintuituve. What’s hard is to figure out is which of these (or other) competing explanations should be given…

  31. Obviously I’m biased here (I cherish my intuitions), but I personally don’t find Keith’s rephrasals all that odd. For what it is worth, when I first started working on a paper on concessive knowledge attributions, I started out with the unadorned:

    (i) I think I know that p but I might be wrong.

    I recall some responded saying that this sounded like a general concession of fallibility rather than a concession that one might be wrong about p. In the next draft, I just made it explicit that it was p that was at issue:

    (ii) I think I know that p but I might be wrong, it might be that q (where q is obviously contradictory with p).

    Generally people I spoke to and wrote to didn’t find this all that odd, but what was interesting was that someone once suggested as a perfectly natural example of a concessive knowledge attribution:

    (iii) I might be mistaken in thinking the answer is ‘b’, but all the same I think I know that the answer is ‘b’
    (iv) The answer might not be ‘b’, but I think that I know it is.

    Anyway, I don’t think either (iii) or (iv) sound all that bad. So far, the reactions to these have been predictable. People already convinced of contextualism or subject sensitive invariantism thinking these are odd and those not committed, many of who don’t do epistemology, thinking that they aren’t objectionable. (Jon might be an exception).

    Of course I agree that these explicit concessions of fallibility coupled with a knowledge ascription of the unembedded variety ‘sound’ bad and ‘sound’ contradictory, but the thing is that this might be due to something other than their expressing contradictions and instead being unassertable for other reasons. It may be that the unembedded concessive knowledge attribution sounds odd to assert because the proposition it expresses isn’t a possible object of knowledge. Appeal to an account on which what isn’t known or what isn’t epistemically necessary oughtn’t be asserted would explain the oddity of the assertion while remaining neutral on the question as to whether a CKA could express a truth.

  32. Michael (and Clayton),
    Re your note 22 — I have a paper coming out in Analysis, “Fallibilism and
    Concessive Knowledge Attributions”, that makes exactly the point you’re making. Basically, the paper is a section of a longer paper I have on my website (“Context, Interest-Relativity, and Knowledge”). I don’t take these points to be so radical, in the sense that anyone who thinks about the topic hard will come up with the same conclusions (e.g. Keith made some of the points in his 1991 paper, but didn’t obviously apply them to a defense of fallibilism), but I thought it would be worth at least publishing a short paper putting to rest any Lewisian thought that concessive knowledge attributions raise a problem for fallibilism.

  33. I’m a little confused. Just what idea is epistemic possibility supposed to capture?

    Clayton: Now you can beat up on me for being silly: How can one falsely believe that one doesn’t know?

    Keith Brian Johnson

  34. It’s the sense of possibility used in contexts like this: “I’ve lost my keys. Where could they be? Hm, they might be in the car.” “Could they be at Sara’s house?” “No, I know I didn’t leave them there.”

    I don’t remember how falsely believing one doesn’t know came up, but perhaps a skeptic is an example of that.

  35. I don’t think a skeptic falsely thinks he doesn’t know; I think there are different senses of the word ‘know’. In the sense used by the skeptic, in which the mere conceivability of being wrong defeats knowledge, I’m a skeptic about just about everything except my own present mentally phenomenalizing. In the sense in which non-skeptics seem to be using the word, I’m an empiricist.

    I don’t think the skeptic thinks he doesn’t know in the empiricist’s sense of ‘know’; I think he thinks he doesn’t know in the Cartesian method-of-doubt sense of the word ‘know’.

    Keith Brian Johnson

  36. Trying to head back toward the original problem, I note that “I know that p but I might be wrong” might sound funny, but “I think that p but I might be wrong” or “I’m pretty sure that p but I might be wrong” doesn’t sound funny. Is the sense of epistemic possibility to be captured then simply that p is epistemically possible for S whenever S doesn’t feel sure of ~p?

    It’s true that S might be certain of some statement q that logically implies ~p without being certain of ~p, since he might not yet have performed the deduction; however, even in such a case I’d want to say that p is epistemically possible for S. But as I indicated, I’m not quite sure what idea is supposed to be captured by epistemic possibility. I’d want to say that anything that S could accept at time t without saying, “Wait a minute–that contradicts *this*!” is epistemically possible for S at time t; if he already accepts q, which logically implies ~p, then if he (mistakenly) thinks he’s proven p before he performs the deduction from q to ~p, isn’t he going to accept p? Isn’t p epistemically possible for him? Doesn’t p become epistemically impossible for S only after he has performed the deduction from q to ~p and then, for whatever reason, decided that the mistake lay in accepting p rather than in accepting q? (And while he’s busy making up his mind where the mistake lies, don’t both p and ~p remain live options for him and therefore remain epistemically possible for him?)

    Keith Brian Johnson

  37. Skeptics may well be introducing a different sense of “know” from that which most of us use in ordinary life. But I think they are also claiming that they are not introducing a new sense of “know” but are using the standard English sense. It is this that enables them plausibly to be described as mistakenly thinking they don’t know.

  38. Michael: You may well be right–it certainly seems to me that my skeptical use of the word ‘know’ is within the bounds of standard English, and I just have to take it on your and Jon’s word that it isn’t! (It strikes me as a standard use precisely because people *do* ask, “Yes, but do you really *know*?”–seeming to imply somehow that it isn’t knowledge if you don’t have [epistemic] certitude. And if you say you know something and then turn out to be wrong, we say you didn’t really know it, but only thought it.) Perhaps there’s a skeptic’s sense and an empiricist’s sense, and the empiricist’s sense is the usual one (I grant that the empiricist sense is the one used in everyday life, but limiting standard English to just that use seems odd to me). However, I will point out that it is not then plausible to say that the skeptic wrongly thinks he doesn’t know, except as an equivocation on the word ‘know’, since he correctly thinks he doesn’t skeptic-know but doesn’t incorrectly think he doesn’t empiricist-know.

    Keith Brian Johnson

  39. I’m still unclear on the concept the term ‘epistemic possibility’ is supposed to capture. I guess one question I have is why a logical impossibility is being assumed to be epistemically impossible. Certainly one can believe a logical impossibility. One might even rationally believe a logical impossibility–for example, if he mistakenly thinks he’s proven it. Is it simply by definition that a logical impossibility cannot be epistemically possible?

    Keith Brian Johnson

  40. Keith, there’s a paper now by Michael that you should take a look at, as well as papers by DeRose and others on the subject. As far as I know, nobody has said that a logical impossibility is epistemically impossible; and if they did, they shouldn’t have said it.

  41. Conceivability is sometimes a proposed test of epistemic possiblity. But suppose someone suggests that he knows that p and it is epistemically possible that ~p. Is he suggesting that he knows that p and it is conceivable that ~p? On a narrow scope reading of conceivability that seems true, since even if I know p I can conceive of my not knowing p, and ~p. But suppose the test ought to be the wide-scope reading: it is conceivable that I know p, and ~p. Is that false? One thing is sure, I can conceive that ‘I know p and ~p’ is true. But isn’t it also true that, for some S, S can conceive that S knows that p and it is false that p (i.e., C(Ksp & ~p))? Maybe S’s concept of knowledge is not perfectly clear, but that does not mean that he cannot conceive (Ksp & ~p). Many people managed to conceive that Fermat’s last theorem was false. But then their concept did not include the implications of that theorem. Why not similarly for the concept of knowledge? The (maybe) strange news is that it would be epistemically possible that I know p, and ~p.

  42. Keith,
    In my initial example, a logical impossibility is epistemically possible. The puzzle arises for definitions of epistemic possibility along the lines of, “P is epistemically possible if it is consistent with everything S knows.” This would (incorrectly!) make all logical impossibilities epistemically impossible as well. But that might otherwise be a tempting definition.

  43. Mike H:

    This is a long thread and you might have addressed this already. You say above: “Anne: Look, of course now we know it is a tautology. But at the time, I was right in what I said: for all we knew then, it might have turned out not to be tautological.
    Jim: Stop changing the subject. We know it’s not a tautology, so it’s false that it might not be one. You said it might be one. So you were wrong.
    To me, Jim’s statements sound absurd; Anne is clearly right”.

    But no doubt Anne could not have discovered that the tautology T was not one. Even given what she knew, she could not have discovered that T was not a tautology. There is no possiblity of that discovery. But (1)-(3) do seem possible.
    1. Anne believes that she will discover that T is not a tautology.
    2. Anne believes that she could discover that T is not a tautology.
    3. Anne believes that she could justifiably believe that T is not a tautology.

    Here’s my question. Suppose Anne realizes (as well as any reasonably informed person knows) that (1)-(3) are perfectly consistent with T being a tautology. How could it (still) be epistemically possible that ~T given any one of (1)-(3)? I can’t see how. More generally, for any conditions on epistemic possiblity C, any reasonaby informed person S will realize that C is consistent with it being logically impossible to discover that ~T. S should therefore conclude that, for any set of conditions C, C is not sufficient to conclude that ~T is epistemically possible.

  44. Jon: I thought your post #3 was saying that logical impossibilities were epistemic impossibilities (see Michael Huemer’s post #44). Sorry.

    Mike: It seems to me that ~T is epistemically consistent with all three of

    1. Anne believes that she will discover that T is not a tautology.
    2. Anne believes that she could discover that T is not a tautology.
    3. Anne believes that she could justifiably believe that T is not a tautology.

    If she believes she’ll discover T isn’t a tautology, then she believes that T is only logically possible rather than logically necessary, so she believes that ~T might be true. Similarly for (2). Similarly for (3). Was there a misprint there, or am I missing something?

    It also looks as though C is insufficient to conclude that ~T is logically possible, but as long as C isn’t sufficient to conclude that ~T is logically *impossible*, isn’t ~T epistemically possible? C is consistent with T’s being a tautology–T might be tautologous–so ~T might be logically undiscoverable–so ~T can’t be logically concluded–but how does that make ~T epistemically impossible?

    Keith Brian Johnson

  45. Here’s a simpler way to put it.

    1. If I believe that p is impossible, then I believe that I could not discover that p.
    2. If I believe that I could not discover that p, then I believe it is not epistemically possible that p.

    Suppose I believe that p might be impossible.

    In that case I believe it might be impossible to discover that p. So I believe that it might not be epistemically possible that p. But then I don’t know that p is epistemically possible.

    Anne seems to believe that ~T might be impossible. But then she does not know that ~T is epistemically possible.

  46. I’ll buy (2) if “discover” means something like “find sufficient justification for belief for.”

    “Anne seems to believe that ~T might be impossible. But then she does not know that ~T is epistemically possible.”

    I agree with that. However, I’ll point out that the sense of “know” being used seems to be the skeptic’s sense, since the sense of impossibility in Anne’s belief that ~T might be impossible seems to be conceivability that T might be tautologous. Anne might find it overwhelmingly likely that ~T is possible; she might find the likelihood that ~T is impossible to be vanishingly small (but nonzero). She can conceive of ~T’s impossibility, so she doesn’t skeptic-know that ~T is epistemically possible–whatever belief she might have that it is epistemically possible can’t be held beyond all conceivable doubt.

    Keith Brian Johnson

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