There are many anti-sceptical arguments which claim that the sceptic - of whatever kind - must assume and take as true certain things before he can offer us his sceptical possibilities or conclusions. Wittgenstein talked about the ‘hinges’ on which all discourse must turn - even sceptical discourse. Hume and Strawson believed that we must accept the existence of objects, other minds and even the existence of the ‘external’ world. Similarly, the premises on which both sceptical and paradoxical conclusions are built must be taken as true or even certain by the sceptic or paradox merchant.
John Searle talks specifically about the "presupposition of an independently existing" (185). He calls this 'a background presupposition". He says:
"It’s not something that’s up for grabs in the way that whether or not the human genome project will have such and such an effect is... I point out that it plays a certain role in our background presupposition, because it’s what we take for granted when we engage in discourse." (186)
This must mean that Searle thinks that even the global sceptic will take the existence of the world "for granted when [he] engages in discourse" (186). It seems, according to Searle, that he wouldn't even be able to say anything, or, more strongly, claim anything, if he didn't presuppose, perhaps tacitly, that the world actually existed. Perhaps he doesn't even know that he's doing this when he's doing it.
The very structure of language itself may include certain presuppositions as to the existence of the ‘external’ world. However, as I said about the meaning and the propositional attitude sceptic, the external world sceptic can't help but use the only language which he has. He has no choice but to do so. Perhaps the existence of God and Superman (as philosophers have argued) is written into our ‘ordinary’ and even our philosophical grammar. That doesn't mean that we are automatically committed to the existence of either God or Superman. It's simply a fact about our language and how it's structured.
Searle gives us a rather mundane example of a case of the presupposition that the world really exists:
"You and I made an arrangement to meet at a certain place at a certain time. We couldn’t make that and we couldn’t have our normal understanding of that unless we assume there is a place in space and in time that is independent of us and we can meet at that particular place. That is external realism." (186)
I don’t see immediately how it follows that because you and I arrange to meet at a place and a time that they must be ‘independent of us’. After all, I may be - or both of us may be - brains in vats fed by the same simulations.
Alternatively, on an idealist reading of Searle’s scenario, we can say that what he says happens could still happen if what the idealists claim is true. This place and time may just be mental ideas in our minds. Alternatively, they may be false sensory simulations given to us by an evil demon or a malicious scientist. According to the sceptic, the sceptical version would be identical to the non-sceptical scenario as far as our actual experiences are concerned.
So there doesn't seem to be any direct or automatic ‘presupposition’ of a mind-independent world here. In any case, not many people talk of - or even think at all about - the world’s mind-independence or its mind-dependence – that isn't the way people look at or think about the world.
So there needn't be either epistemological or ontological presuppositions involved when you or I arrange to meet somewhere at a place and a time.
Alternatively, if we arrange to meet at a particular building and unknown to us that building is just a facade from a film set, we still wouldn't assume that it's not a facade or, indeed, that it is a facade. Though it could be a facade. That wouldn't affect our meeting and what we thought about the meeting. (The street could also be a facade as well as having artificial traffic and human-like robots walking up and down it.)
Similarly, we could meet at this building at 6 O’ clock even thought it's 7 O’ clock when we actually meet. However, the clock on the building says it is 6 O’ clock and we think it is 6 O’clock because it says so. Not even that: it may well be 6 O’ clock when the clock says 6’ clock; though unknown to us that clock stopped three months ago and it's just a happy coincidence that it stopped at that time.
Again, none of this means that we need to assume the existence of the world and none of this has any impact on its existence or our knowledge of its existence.