While he acknowledges that he only knows things because "in the past, I have known to be true other propositions which were evidence for them...and I certainly do not know exactly what the evidence was", he says that the fact that he doesn't have a never-ending chain of evidence isn't reason to doubting his knowledge of a "common-sense" truth. In fact, he seems to feel it is impossible to achieve a foundation of truth, and so any attempt to do so is a waste of time.
So, given that [according to Moore] the sceptics are arguing from a shaky position, and that [according to Moore] it is reasonable to accept the "common-sense", we can [according to Moore] disregard the arguments made by sceptics.
This seems such an extraordinarily weak argument that I feel I must be missing something (which I hope will become blindingly obvious in the forthcoming seminar: I would really like to feel that the sceptic has been convincingly defeated).
The sceptic argues, for example:
Granted, this sounds like a daft, non-commonsensical argument, but it's hard to see what's logically wrong with it, and to attack it by saying "your premises implicitly concede my existence and that of a real world" seems to be more an observation about the way that we habitually use language than an undermining of the argument's foundation.
It may be difficult to articulate a sceptical position without reference to objects whose existence is being denied, and it may be that the sceptic doesn't act in a way that is consistent with that position (a point made by Descartes) but the meaning of the sceptic's argument seems plain enough, and I fear that Moore does not succeed in refuting the sceptic.