Central to the claim of Chalmers’ two dimensional semantics is the idea that there are two different ways of considering a possible world. We may consider it counter-factually in which case we hold the actual world fixed or we may consider as actual in which case the proposed possible world is thought of as being actual, with our world then a counter-factual world. Thus Twin Earth, considered as actual, is a world where water is not H20 but is rather XYZ. From their point of view it is a necessary truth that water=XYZ and so there would be no water here on Earth (considered counter-factually).
The problem with this line is that it assumes that we can tell a priori which possible worlds there are. Before we can consider a possible world as actual, we need to know whether it is possible or not. The two-dimensionalist simply asserts that some world is conceivable and then proposes to consider it as actual. But we have no non-question begging way of saying what is or is not really conceivable. Some claim that to be conceivable is simply to lack any contradiction in teh thing conceived. But just because there is no obvious contradiction in a proposed conceivable world does not mean that there is no contradiction in that coneption. Besides whihc, there are those who claim that contradictions are conceivable. Kripke famously proposed ‘non-normal’ worlds (sometimes called ‘impossible worlds’) these are worlds where contradiction are true or where standard laws of logic fail to apply (like the rule of necessitation). Are such worlds conceivable? Kripke seems to think so, others do not.
Until we resolve this issue two-dimensional semantics is hopelessly question begging. The only thing that we can consider as actual is, well, the actual world.
Richard Brown 
Is the problem really that obvious? Aside from Chalmers, you realize, there’s Lloyd Humberstone (much earlier), S. Schiffer, Frank Jackson, Martin Davies, Garcia-Carpintero & Macia, Bob Stalnaker and a host of other pretty high-powered thinkers who have defended 2D and who do managed to miss this. . . .:)
Well maybe it isn’t obvious, but does that mean it isn’t a problem?
Just a minor correction: there are no true contradictions at Kripkean non-normal worlds. These are simply worlds where all necessities are false and all possibilities are true. But they are, for all that, still maximally complete and consistent.
On a more substantive note, I’ve always wondered about this “considering as actual” business. Your challenge to epistemic 2Dism sounds compelling, but I’m so unclear on the whole thing that I just don’t know whether your complaint is right (e.g. that the 2Dist assumes that we can tell a priori which possible worlds there are.)
Hey Colin,
Yeah that was a slip up. I didn’t mean to imply that Kripkean non-normal worlds are ones where there are true contradictions…but I do take it that there is a wider use of the term –by Priest for instance– where a non-normal world is any possible world where the (standard) laws of logic fail to hold and so will include ones where there are true contradictions.
As for the more substantive point, read Chalmers’ paper on this