According to the principle of armchair access:
AA: If p is included in my evidence it is possible to know from the armchair (i.e., on the basis of reflection or introspection) that p is part of my evidence.
Objection: AA leads to a kind of sceptical result. AA leads to the result I know from the armchair that I have no non-inferential knowledge of contingent propositions about the external world.
(1) My evidence is limited to propositions I can know-armchair belong to my evidence. [Assumption of armchair access]
(2) If p is part of my evidence (a) p is the case [ET].
(3) If I non-inferentially know that p, p is part of my evidence [NIK].
(4) If my evidence includes the proposition that I have hands, I have hands and I know-armchair that I have hands [(1), (2), (3)].
(4) But, it's absurd to think I know-armchair that I have hands.
(5) If my evidence cannot include the proposition that I have hands, either I'm handless or I cannot know non-inferentially that I have hands [(2), (3)].
(6) My evidence cannot include the proposition that I have hands [(2), (3), (4)].
(7) Either I'm handless or I cannot know non-inferentially that I have hands [(5), (6)]
(8) If I have hands, I cannot know non-inferentially that I do [(7)].
(9) Thus, whether I have hands or not, I cannot know non-inferentially that I do [(8) and factivity of 'knows'].
This doesn't rule out having knowledge of the external world. It only rules out having such knowledge without inferring it from propositions about matters known to you via introspection or reflection. That rules out a lot, I think. Now, the move from (1) to (4) might seem dodgy since it is mediated by an assumption about evidence (i.e., that evidence consists of truths) and knowledge (non-inferential knowledge suffices for a proposition's inclusion in your evidence). But, I don't see that these assumptions could be responsible for generating any untoward sceptical consequences. When NIK does, in effect, is say that the acquisition of evidence is cheap. ET is, so far as I can see, supported by solid linguistic evidence and I can't see how we are better positioned to respond to sceptical arguments by saying that our evidence is just the same even if everything we believe is mistaken and everything we seem to experience an illusion. Maybe that's just me. Anyway, it's late but I thought I should jot this down before I forget it. Let's hope there are no glaring mistakes.