A few years back I noted that 2-D semantics provides a straightforward refutation of synthetic metaethical naturalism (SEN): SEN implies that moral terms differ in their primary and secondary intensions, this is clearly false (moral terms are "semantically neutral", or exhibit 2-D symmetry, in that their application to a world does not vary depending on whether we consider it as actual or as counterfactual), and so SEN must be false.
As I've been developing this argument in my paper 'Moral Symmetry and Two Dimensional Semantics', it occurs to me that 2-D semantics enables an even broader argument against metaethical naturalism.
To address the Open Question Argument, naturalists are committed to a divergence between the intension of 'good' (and other moral terms) and its meaning or cognitive significance. Such divergences are commonplace so far as the secondary intension is concerned: 'water' and 'H2O' have different meanings, despite picking out just the same stuff across all possible worlds (considered counterfactually). The problem for the naturalist is that such divergences do not seem justified when it comes to primary intensions. What a term picks out across worlds considered as actual seems very closely connected to the cognitive significance or sense of a term.
(For example, if we use 'the watery stuff' as shorthand for whatever fills the functional role of water, and which thus picks out H2O in our world but XYZ in Twin Earth, then note that 'water' and 'the watery stuff' have the same primary intensions and cognitive significance, despite differing in their secondary intensions. "Water is the watery stuff" is cognitively trivial, whereas "Water is H2O" -- relating terms with distinct primary intensions -- is informative.)
The difficulty now for the naturalist is that there is no way to flesh out the primary intension of moral terms using purely naturalistic items in a way that does justice to the cognitive significance of moral terms. If you have 'good' super-rigidly (in both primary and secondary intensions) pick out (say) happiness, then you seem committed to holding that 'good' means the same (or at least has much the same cognitive significance) as 'happiness', when intuitively they don't even seem to be in the same ballpark.
Note that non-naturalists face no such problem. They can hold that 'good' super-rigidly picks out the sui generis property of goodness, which in turn supervenes on the natural things that are good -- a class of items that can only be identified through substantive moral insight, and not mere conceptual competence. Different moral communities may thus share this concept, picking out the same property of moral goodness, even as they disagree in their (implicit) theorizing about which natural items possess the moral property.