The orthodox interpretation of G.E. Moore’s Open Question Argument (OQA) has it that Moore set out to show that no satisfactory definition of goodness (or other evaluative/deontic terms) could be given. To define goodness in terms of some other property was to commit the naturalistic fallacy. The reason why such definitions are impossible is because any competent user of the concepts being employed in the definition can sensibly ask if such and such is good. One example employed by Moore, from Bertrand Russell, is that goodness is that which we desire to desire. But any competent user of the concepts “desire” and “goodness” can sensibly ask if what we desire to desire is good, whereas we cannot sensibly ask if what we desire to desire is what we desire to desire. So, “goodness” does not mean “that which we desire to desire”. The same argument can be run in terms of pleasure, or what God wills (or anything).
What one should notice about this version of the argument is that it’s about meanings of words. The argument does not entail anything about property identities, which should provide reductionists about moral ontology some relief. A hedonist could claim that she isn’t in the business of giving analytic identity claims, but rather goodness being the same thing as pleasure is a synthetic identity claim. Synthetic identity claims carry no commitment to synonymy between the terms denoting the things that are identical. So, water is identical to H2O, but “water” doesn’t mean the same thing as “H2O”. It should be noted, however, that the proponent of the OQA explained above would take this as a concession, because the synthetic reductionist is granting her conclusion.
A more interesting kind of OQA can be formulated with Leibniz’s law. Roughly, Leibniz’s law says that it is necessarily true that for any A and any B, A is identical to B iff every property that A has, B also has. And any property that B has, A also has. It seems like a relatively uncontroversial principle, until we get into the quantum domain, which doesn’t concern us here. So, bracketing any quantum concerns, we can formulate the new OQA using this principle. Let’s take goodness and happiness. It seems like we could sensibly doubt whether happiness is good, but we cannot sensibly doubt whether goodness is good. So, happiness has a property that goodness lacks, which is that happiness is such that we can sensibly doubt whether it is good. By Leibniz’s law, goodness and happiness are not identical, because happiness has a property that goodness lacks. What’s interesting about this argument is it gets you a metaphysical conclusion, unlike the OQA discussed before, which gets you a semantic conclusion. The OQA employing Leibniz’s law is more worrisome for synthetic reductionists, as it has to do with properties rather than meanings.
The OQA employing Leibniz’s law is not obviously unsound, and figuring out where it goes wrong is challenging. Personally, I think it goes wrong somewhere, but it isn’t obvious to me where exactly that is.