I've been thinking about Chalmers' Constructing the World. It is absolutely crucial for Chalmers to have a distinction between what is a priori knowable and what is a posteriori knowable.
Now, imagine that we have evolved to believe that the number one has a successor (call this proposition "Two") as well as that many snakes are dangerous ("Snake"). In both cases, let us suppose, we evolved to believe the true claim because believing it conduced to our survival. (We may add that the reason belief in the claim conduced to our survival was explained by the truth of the claim, if we are worried about debunking arguments.) It now looks like Two and Snake are on par: either both beliefs are a priori or both beliefs are a posteriori. However, Chalmers cannot afford to say that Snake could be a priori—that will destroy much of his story.
So it seems that if Chalmers' story is to work, we will have to say that Snake and Two are a posteriori. However, it is also important for Chalmers to say that fundamental principles like Two are knowable a priori. The story doesn't destroy this: after all, something can be both a posteriori known and a priori knowable (say, a result of a calculation done with a calculator). Nonetheless, there is a problem here. It may well be that all fundamental principles like Two are known by us through something like this evolutionary mechanism (and "something like" includes the theistic variant where God instills this belief in us on account of its truth). And if so, then what reason do we have to think that they are a priori knowable, given that we don't know them a priori? One might have some conviction that some hypothetical or actual non-human reasoner knows them a priori, but it is difficult to see that conviction as justified.
However, I think there is a speculative non-naturalist story one could give that would help make the distinction. Suppose that all our knowledge is at base perceptual. However, sometimes what we perceive are abstracta and sometimes what we perceive are concreta. Knowledge that is grounded only in perception of abstracta is a priori, while knowledge that is grounded at least in part in perception of concreta is a posteriori. It may be that we can just see the number two as the successor of the number one. There is some phenomenological plausibility to this.
This would be really nice for Chalmers. For it is plausible that if any abstracta and their abstract relations are observable, they all are. If so, then all facts about the realm of abstracta are a priori knowable.
Granted, on this story knowledge of abstracta is observational and hence empirical. But while this does mean that the above use of "a priori" and "a posteriori" is idiosyncratic, the above use nonetheless may help recover at least some of Chalmers' story.
Some, but perhaps not the two-dimensionalism? For the account above is apt to make it a priori that wateriness is H2O-ness, since that seems to just be a fact about abstracta.