[[This is a slightly expanded version of comments in reply to Stephen Schiffer's "Mental Content and Epistemic Two-Dimensional Semantics" at the 2002 Pacific APA meeting, which was itself a response to my "The Foundations of Two-Dimensional Semantics".]]
Stephen gives a nice demonstration of the inadequacies of what he calls theory C. Theory C merely postulates a connection between its intensions and the epistemic domain, and gives no argument that intensions exist that satisfies the relevant postulates. Theory C corresponds roughly to the state of affairs at the end of Section 1 of my paper, at which 1-intensions that satisfy the Core Thesis had been postulated but not defended.
The account in the residue of my paper differs from theory C in a number of respects. Most important here is that does not just postulate the relevant intensions, but gives a specific method for associating intensions with sentences (and with thoughts). This account is constructed in epistemic terms from the start. And specific arguments are given that the relevant postulates are satisfied. These parts of the discussion, which are not addressed by Stephen, provide the materials to resist his criticism.
Stephen says that theory C is notationally equivalent to a certain Russellian account. Leaving theory C aside, I think that there are some deep connections between my view and Russell's, but the connections are not nearly as straightforward as Stephen suggests.
Most obviously, my account makes no mention of acquaintance. I do appeal to a notion of semantic neutrality (roughly, non-Twin-Earthability). But this is prima facie a different notion: semantically neutral concepts arguably include philosopher, computer, doctor (used nondeferentially), and all sorts of other concepts whose connection to acquaintance is at best unclear. Semantic neutrality only enters the account on the world-based account (it plays no role in the pure epistemic account). When it does, there is no requirement that concepts be composed of semantically neutral elements; at most, it is required that the worlds in the domain of the intension be described in semantically neutral terms. So there is no analog to the Russellian requirement that all concepts be composed from acquaintance-based concepts. For similar reasons, I have no need for theory C's principle that (roughly) every 1-proposition is the 1-proposition of some semantically neutral sentence in an idealized language.
Second, as Stephen notes, the Russellian theory does not appeal to possible worlds, but simply postulates associated uniqueness properties. On my account, possible worlds (or scenarios) play a crucial role in defining the associated intensions. In effect, the account gives a epistemic recipe for taking a given scenario, and delivering the associated extension. Maybe epistemic intensions are equivalent at some level to uniqueness properties (though really to uniqueness relations, and only on option 1 above). But in any case, the recipe plays a crucial role in defining these properties and relations, and so in answering questions about their existence. So possible worlds are not epiphenomenal here.
The recipe can straightforwardly be used to answer Stephen's existence worries. For Kripke cases, or Burge cases, or memory cases, is there a relevant intension? In each case, we simply apply the recipe. Take the Gödel/Schmidt scenario: Kripke's own intuitions suggest that if we hypothetically accept that this scenario is actual, we conclude that Gödel is the stealer, not the prover. This sort of intuition supports the existence of an epistemic intension rather than defeating it; at best, it suggests that the intension is not equivalent to a description.
Similarly in the Burge cases: in these cases of semantic deference, if the subject is given relevant information about the pattern of linguistic use in their community, they should rationally revise their judgments appropriately. Once again, this conditional epistemic role of the concept straightforwardly grounds an epistemic intension. The epistemic intension of a deferential concept arthritis functions roughly by picking out in a given scenario the referent of 'arthritis' in the community at the center of such a scenario. This intension will plausibly be the same between twins. Of course I have not argued today for the general claim that epistemic content is narrow, but I think that such argument can straightforwardly be given.
As for the memory case: the boy is presumably in a position to make judgments about extension, given relevant information about the world and rational reflection. The resulting intension may well have something to do with causal responsibility, but Stephen's objection that the boy may have no beliefs about causal responsibility is irrelevant here, since no such belief is required.
(In discussion Stephen objected that the boy may not even be able to make judgments about extension given relevant information. Maybe so, but what matters for the framework is not whether the boy (in his far-from-ideal cognitive state) can actually make the inferences in question, but whether idealized a priori reasoning with the boy's concepts would support them. This requires that the boy's inferences are subject to certain rational norms (so the relevant inferences might be justified if made), but not that the boy's reasoning actually meets those norms. In the extreme case of a creature that is not "in the space of reasons", the framework will not get a grip, and the epistemic contents may fail to exist. But in the case of an ordinary language-using child, it is plausible that the relevant epistemic structure is present.)
The point above about belief is relevant to the regress worry that Stephen raises. It is simply not required that if a concept C has an epistemic intension E, then the subject must have a belief of the form C is E', where E' is some privileged distinct concept with E as its content. Similarly, the subject is not required to have any belief to the effect the content of C is E'', where E'' is a privileged concept with E as its extension. It is not even required that such beliefs be available. The relevant intension E is part of the content of one's thought simply by thinking C: no further content or mode of presentation is required. Of course there may exist some distinct concepts or expressions that have E as their extension, but no regress will arise if these are not semantically neutral, since they are not doing any essential work in grounding the framework in the first place.
Finally, on intentionality: for reasons I have argued elsewhere, I think that the view that intentional properties are metaphysically but not epistemically necessitated by non-intentional properties is untenable: it involves a strong necessity of the sort that I have argued cannot exist. But this claim is not essential to the framework. If strong necessities exist, then we simply need to model epistemic contents using the epistemic construction of scenarios, which will then be more fine-grained than metaphysically possible worlds. So this point carries no weight against the general framework presented today.