The Central APA author-meets-critics session on Scott Soames' book on two-dimensionalism took place a couple of days ago. Scott's response to my paper is not currently online (update: it's now online). I've put online a response in turn where I summarize a few of the things Scott said and respond.
The upshot of the discussion of Scott's critical arguments was that Scott agreed that a number of them don't apply to the epistemic two-dimensionalist view that I hold (though he thinks they apply to the view in The Conscious Mind). His view seems to be that since epistemic two-dimensional semantic values aren't "semantic" contents in his sense (roughly, built into the specification of a public language), he's less concerned to argue against them. My view is that they can play all the relevant explanatory and analytic roles that I want them to play whether they are "semantic" in this sense or not, so that the core of two-dimensionalism ends up being untouched.
As for the discussion of Scott's positive view, unsurprisingly he resisted the suggestion that it can be seen as a sort of two-dimensionalism. The central point of resistance is that he denies the analog in his system of the two-dimensionalist principle E5 from my paper: that a proposition is a priori iff it is true at all epistemically possible world-states. He thinks that the principle is usually true, but not in the key cases involving 'actually' that I raised in the paper: the proposition [P if actually P] is a priori but false in some epistemically possible world-states.
In discussion I said that I think this view is vulnerable to a criticism analogous to one that Scott raised for Bob Stalnaker. Bob's view holds that when someone believes that a given paperweight (one that is actually made of wood) is made of plastic, she really endorses epistemic possibilities where some other paperweight is made of wood. Arguing against Bob, Scott says this seems incorrect: surely she endorses epistemic possible (though metaphysically impossible) world-states with respect to which this paperweight is made of plastic. The principle seems to be that when one believes a proposition, one thereby endorses world-states where that very proposition is true, and excludes those where it is false. The same presumably goes for knowledge, and for a priori knowledge: when one knows a priori that P, one thereby rules out a priori world-states where P is false. But then it follows that if P is a priori knowable, any world-state where P is false can be ruled out a priori, so are not epistemically possible. So something like principle E5 follows. Scott needs to deny the thesis that when one believes/knows that P, one thereby excludes world-states in which ~P: although the thesis usually holds, it is false in the special case where P is of the form [Q iff actually Q], and perhaps in other related cases involving 'actually'. I think this leads to special pleading of the sort that Scott criticized in Bob's view, and undermines some of the coherence and power of the framework of epistemically possible worlds. The view also opens up a few other cans of worms, discussed in my response. So I think that a version of the view that accepts something like E5 is much better.
In any case, I note that attenuating the link between apriority and the first dimension by rejecting E5 in certain special cases doesn't suffice to undermine the interpretation of the view as a sort of two-dimensionalism. After all, most of the 2D systems of the 1970s (Kaplan, Stalnaker, Evans, Davies and Humberstone) have only an attenuated link here that holds in some cases but not others. So Soames' attenuation of E5 is consistent with seeing the view as at least as two-dimensionalist (in the broad sense) as these paradigmatic versions of the view. There's a lot more on issues in the vicinity in my response.