Some years back I learned that when epistemologists talk about the "problem of scepticism", they are thinking about theses that deny that we have much knowledge about, say, the external world. When I found out this, I was disappointed. I thought that the problem that epistemologists were dealing with was the problem whether we can be reasonable in believing things about the external world. I care about that, not about whether we know. Suppose it were to turn out that knowledge has to be infallible, and so indeed we know nothing empirical about the external world. This would hardly bother me. It's too bad that I couldn't say that I know that I have two hands, but my rational confidence that I have two hands would be just as high as it ever was.
We sell the scepticism at the beginning of Descartes' Meditations and throughout Sextus Empiricus far short if we think about it as simply a denial of knowledge. If we take seriously Descartes' invocation of the possibility of dreaming or of a deceitful demon, that not only has a tendency to undercut the claim that we know, but even the claim that we are rational in being confident in ordinary empirical beliefs, and maybe even the claim that it is rational to hold such beliefs to be more likely true than not. This is the more radical and more interesting scepticism: it questions whether we have any non-circular reason to think we aren't being deceived. (And in the end I think Descartes' answer to it is pretty good.)