Mackie argues that we cannot have any type of "objective value" without having some sort of non-natural property, which doesn't exist.
I know that I said that I would use the term "intrinsic prescriptivity" to describe the types of values Mackie was arguing against. This is because of a confusion often generated between two types of "objective" - intrinsic prescriptivity vs. objectively true statements about relationships between objects of evaluation and desires.
However, in this case, "intrinsic prescriptivity" is going to beg some questions against the argument at hand.
Michel Smith aims to show - and effectively does show - that it is possible for the statement, "we would each desire ourselves to maximize happiness and minimize suffering if we formed our desires in the list of full information and the requirements of rationality." (Smith, Michael, "Beyond the Error Theory," in A World Without Values: Essays on John Mackie's Moral Error Theory, (Richard Joyce and Simon Kirchin, eds.), 2010.)
I have already argued that rationality has nothing to say about desires-as-ends. It is only relevant when we look at desires-as-means and, there, only because desires-as-means includes beliefs that can be subject to rational evaluation.
Yet, that is exactly the point that Smith wants to draw from. His argument here is that it is at least possible that an agent - regardless of his ends, who considers the case in the light of full information, would come to see that they have an instrumental reason to maximize happiness and minimize suffering.
NOTE: Smith is only using the happiness principle as an illustrative example. A reader may object that this may well be false with respect to happiness, but may hold that it is true with respect to some other good such as health or education.
Let me repeat, this is not an argument that shows that happiness (or some other good) has "intrinsic prescriptivity". It is an argument that shows that a good may have a "instrumental prescriptivity" - be something that every person has instrumental reasons to promote - no matter what they desire. There can be no set of desires whereby promoting such a good would not have instrumental value.
However, Smith then asserts, there is no such good.
Unfortunately, however, the alleged empirical fact – the fact, given our simplifying assumption, that maximizing happiness and minimizing suffering is an all-purpose means to the satisfaction of whatever desires anyone happens to have – seems to be no empirical fact at all. . . . For whatever we are in fact obliged to do, it seems not to be an empirical fact that our doing that is an all-purpose means to the satisfaction of whatever desires we happen to have.In fact, for many of our obligations, we seem to have no trouble at all coming up with scenarios where doing what an agent has an obligation to do is not at all instrumentally useful - no matter what the agent's actual desires are.
As a result, no true real-world moral claim can claim that something is a universal means. It also remains the case, as Mackie explicitly argued, that no true real-world moral claim can claim that something has intrinsic prescriptivity. Consequently, Mackie's main conclusion - that all moral claims are false - would still hold up even if we consider universal means along with intrinsically prescriptive ends.
One final caveat before I go . . . I reject Mackie's claim that all moral statements are false. I reject it, not because I deny his view on intrinsic prescriptivity. I reject it because I deny that "intrinsic prescriptivity" is built into the meaning of each moral claim. And even if that happens to be true, it will turn out that - for reasons that Mackie himself provides - it is a relatively unimportant truth.