J. L. Mackie, answered from the texts and cited to the page.
The argument has two parts, and they need to be kept separate because they do their work at different levels.1 The metaphysical part: if there were objective values, they would be entities or qualities or relations of a very strange sort, utterly different from anything else in the universe.1 The clearest way to see what is being demanded is to look at what Plato required.
The Form of the Good is such that knowledge of it provides the knower with both a direction and an overriding motive — something's being good both tells the person who knows this to pursue it and makes him pursue it.2 An objective good of that kind would be sought by anyone acquainted with it, not because of any contingent fact about what that person desires, but just because the end has to-be-pursuedness somehow built into it.2
Nothing else in our ontology works like that. The demand is real, and it is expensive. The epistemological part follows directly: if we were aware of such values, it would have to be by some special faculty of moral perception or intuition, utterly different from our ordinary ways of knowing everything else.1 None of our ordinary accounts — sensory perception, introspection, the framing of explanatory hypotheses, inference, logical construction, conceptual analysis, or any combination of them — will provide a satisfactory answer to how such awareness could work.3
A special sort of intuition is a lame answer, but it is the one to which the clearheaded objectivist is compelled to resort.3 There is a third pressure the argument exerts, which I think is underappreciated. Ask how the moral quality is linked to the natural features of an action. The wrongness of a piece of deliberate cruelty is not related to the natural facts by entailment — it is not a logical or semantic necessity.
Yet it is not merely a coincidence either; the wrongness is supposed to be consequential upon, or supervenient on, the natural features.4 But what in the world is signified by that "because"? Something must be postulated that can see at once the natural features, the wrongness, and the mysterious consequential link between them.4 How much simpler the situation would be if we replaced the moral quality with a subjective response causally related to the detection of those natural features.4
The best counter is Price's companions-in-guilt argument: empiricism struggles to account not just for moral knowledge but for our ideas of necessity, causation, identity, and much else besides, so why single out moral perception as peculiarly suspect?5 I take the point seriously. The only adequate reply is to show how, on empiricist foundations, satisfactory accounts of those other ideas can be given; and if some supposed metaphysical necessities resist that treatment, they too should be added to the targets of the argument, not used as cover for objective values.5
If there were objective values, then they would be entities or qualities or relations of a very strange sort, utterly different from anything else in the universe. Correspondingly, if we were aware of them, it would have to be by some special faculty of moral perception or intuition, utterly different from our ordinary ways of knowing everything else.Ethics, Inventing Right and Wrong, pp. 35–36
The Form of the Good is such that knowledge of it provides the knower with both a direction and an overriding motive; something's being good both tells the person who knows this to pursue it and makes him pursue it. An objective good would be sought by anyone who was acquainted with it, not because of any contingent fact that this person, or every person, is so constituted that he desires this end, but just because the end has to-be-pursuedness somehow built into it.Ethics, Inventing Right and Wrong, pp. 37–38
none of our ordinary accounts of sensory perception or introspection or the framing and confirming of explanatory hypotheses or inference or logical construction or conceptual analysis, or any combination of these, will provide a satisfactory answer; 'a special sort of intuition' is a lame answer, but it is the one to which the clearheaded objectivist is compelled to resort.Ethics, Inventing Right and Wrong, pp. 35–36
What is the connection between the natural fact that an action is a piece of deliberate cruelty - say, causing pain just for fun — and the moral fact that it is wrong? It cannot be an entailment, a logical or semantic necessity. Yet it is not merely that the two features occur together... something must be postulated which can see at once the natural features that constitute the cruelty, and the wrongness, and the mysterious consequential link between the two... How much simpler and more comprehensible the situation would be if we could replace the moral quality with some sort of subjective response which could be causally related to the detection of the natural features on which the supposed quality is said to be consequential.Ethics, Inventing Right and Wrong, p. 38
Richard Price argues that it is not moral knowledge alone that such an empiricism as those of Locke and Hume is unable to account for... If some supposed metaphysical necessities or essences resist such treatment, then they too should be included, along with objective values, among the targets of the argument from queerness.Ethics, Inventing Right and Wrong, pp. 36–37