Consider dream skepticism. Suppose I have, or think I have, empirical grounds for believing that dreams and waking life are difficult to tell apart. On those grounds, I think that my experience now, which I'd taken to be waking experience, might actually be dream experience. But if I might now be dreaming, then my current opinions (or seeming opinions) about the past all become suspect. I no longer have good grounds for thinking that dreams and waking life are difficult to tell apart. Boom!
(That was supposed to be the sound of a skeptical argument imploding.)
Stephen Maitzen has recently been advancing an argument of roughly that sort: that the skeptic "must attribute to us justified empirical beliefs of the very kind the argument must deny us" (p. 30). Similarly, G.E. Moore, in "Certainty", argues that dream skeptics assume that they know that dreams have occurred, and that if one is dreaming one does not know that dreams have occurred. (Boom.)
One problem with this self-defeat objection to dream skepticism is that it assumes that the skeptic is committed to saying she is justified in thinking (or knows) that this might well be a dream. The most radical skeptics (e.g., Sextus), might not be committed to this.
A more moderate skeptic (like my 1% skeptic) can't escape the argument that way, but another way is available. And that is to concede that whatever degree of credence she was initially inclined to assign to the possibility that she is dreaming, on the basis of her assumed empirical evidence and memories of the past, she probably should tweak that credence somewhat to take into account the fact that she can no longer be highly confident about the provenance of that seeming empirical evidence. But unless she somehow discovers new grounds for thinking that it's impossible or hugely unlikely that she is dreaming, this is only partial undercutting -- not grounds for 100% confidence that she is not dreaming. She can still maintain reasonable doubt: Previously she was very confident that she knew that dreams and waking life were hard to tell apart; now she could see going either way on that question.
Consider this case as an analogy. I have a very vivid and realistic seeming-memory of having been told ten minutes ago, by a powerful demon, that in five minutes this demon would flip a coin. If it comes up heads, she will give me a 50% mix of true and false memories about the half hour before and after the coin flip, including about that very conversation; if tails, she won't tamper with my memory. Then she'll walk away and leave me in my office.
Should I trust my seeming-memories of the past half hour, including of that conversation? If I trust those memories, that gives me reason not to trust them. If I don't trust those memories, well that seems hardly less skeptical. Either way, I'm left with substantial doubt. The doubt undercuts its own grounds to some extent, yes, but it doesn't seem epistemically justified to react to that self-undercutting by purging all doubt and resting in perfect confidence that my memories of that conversation are entirely veridical.
This is the heart of the empirical skeptic's dilemma: Either I confidently take my experience at face value or I don't. If I don't confidently take my experience at face value, I am already a skeptic. If I do confidently take my experience at face value, then I discover empirical reasons not to take it confidently at face value after all. Those reasons partly undercut themselves, but that partial undercutting does not then justify shifting back to high confidence as though there were no such grounds for doubt.