Horgan and Timmons (1992) suggest the following argument against metaethical naturalism: First, note that the naturalist is committed to there being some semantic story about how the reference of our moral terms gets fixed. For example, perhaps ‘right’ and ‘wrong’ refer to those natural properties of actions that causally regulate our practices of praise and blame. So, if the consequentialist property of maximizing happiness is what causally regulates our praising practices, then ‘right’ will refer to the natural property of an act’s being happiness-maximizing.
Second, Horgan and Timmons point out that we can imagine a "Moral Twin Earth" -- a society very similar to ours but where the features identified in the naturalist's moral semantics play out slightly differently, such that they end up picking out a different natural property. So, in our above example, we might imagine a world much like ours except that the deontological property of conforming to the categorical imperative is what causally regulates our counterparts’ practices of praise and blame. So, in that world, ‘right’ will refer to the property of conforming to the categorical imperative.
This naturalist theory then implies that we are talking past each other -- both speaking the truth in our own moral language -- when we affirm consequentialism and our Moral Twin Earth counterparts affirm Kantianism. This seems an unacceptable relativistic result, and violates our semantic intuition that the two parties are -– despite their different answers -– addressing the same moral question. Intuitively, we are disagreeing with our Kantian counterparts, not merely speaking past one another. (Contrast the standard case of water/H2O: In regular Twin Earth, we have no semantic intuition that speakers genuinely disagree when we say “water is H2O” and our twins say “water is not H2O”. The standard Kripke/Putnam intuition is that the two parties are talking about different substances. This difference strongly suggests that it would be a mistake to model our moral semantics on the semantics of natural kind terms.)
Horgan and Timmons further hypothesize that this result can be generalized to any semantic story the naturalist might offer about how the reference of our moral terms gets fixed. Whatever the details of the reference-fixing story, they argue that it will be possible to construct an alternative “Twin” world where the same reference-fixing story picks out a different property than it does in the actual world.
Perhaps the most promising way for naturalists to respond (following Merli 2002) is to preclude the possibility of divergent moral reference by way of the following two claims: (1) The right reference-fixing story appeals not just to our actual (possibly irrational) theories or practices, but rather to an idealized version thereof. (2) All possible agents, when suitably idealized, would converge on the same moral theories or practices.
But this raises the question of whether the appropriate idealization is substantive or merely procedural in nature, posing a dilemma for the naturalist. Any purely procedural process of idealization is too weak to secure moral convergence amongst all possible agents. There are surely multiple possible internally-coherent moral views, any one of which might be endorsed by agents engaging in wide reflective equilibrium, depending on their starting points.
The naturalist might instead turn to a more substantive idealization (appealing to the fitting rather than merely procedurally rational agent). But this begs the question of which internally coherent moral viewpoint is the substantively correct one. The whole problem for the naturalist is that they have no basis for claiming that any particular one of the competing, internally coherent moral theories is the one true moral theory. After all, given the natural (non-moral) parity between us and our Moral Twin Earth counterparts, what in the two worlds can the naturalist appeal to as the basis for a moral or rational asymmetry between us?