 According to Field’s error-theory of arithmetic, the objects distinctive of arithmetic do not exist, and it is this which leads to the rejection of the existence dimension of arithmetical realism, at least as platonistically conceived (for a non-platonistic view of arithmetic which is at least potentially realist, see Benacerraf 1965; for incisive discussion, see Wright 1983, Ch.3). J. L. Mackie, on the other hand, proposes an error-theoretic account of morals, not because there are no objects or entities that could form the subject matter of ethics (it is no part of Mackie’s brief to deny the existence of persons and their actions and so on), but because it is implausible to suppose that the sorts of properties that moral properties would have to be are ever instantiated in the world (Mackie 1977, Ch.1). Like Field on arithmetic, then, Mackie’s central claim about the atomic, declarative sentences of ethics (such as ‘Napoleon was evil’) is that they are systematically and uniformly false. How might one argue for such a radical-sounding thesis? The clearest way to view Mackie’s argument for the error-theory is as a conjunction of a conceptual claim with an ontological claim (following Smith 1994, pp. 63–66). The conceptual claim is that moral facts are objective and categorically prescriptive facts, or, equivalently, that our concept of a moral property is a concept of an objective and categorically prescriptive quality (what Mackie means by this is explained below). The ontological claim is simply that there are no objective and categorically prescriptive facts, that objective and categorically prescriptive properties are nowhere instantiated. The conclusion is that there is nothing in the world answering to our moral concepts, no facts or properties which render the judgements formed via those moral concepts true. Our moral (atomic) moral judgements are systematically false. We can thus construe the argument for the error-theory as follows: