In two previous papers I explained why I believe that a certain sort of argument that seems to support skepticism about self-knowledge is actually self-undermining, in the sense that no one can justifiably accept all of its premises at once. Anthony Brueckner has recently tried to show that even if the central premises of my explanation are true, the skeptical argument in question is not self-undermining. He has also suggested that even if the skeptical argument is self-undermining, it can still (...) serve as a _reductio ad absurdum of the assumption that we have self-knowledge. My goal in this paper is to explain why I think neither of these responses is successful. (shrink)