Chapter 5 is Blackburn's introduction to issues concerning language and realism, and Blackburn uses debates about moral realism as his example of an area where linguistic issues are appealed to as providing evidence for an against certain forms of realism and anti-realism. The chapter involves a brief introduction to the sort of noncognitivist expressivism he favors. According to Blackburn, we can best understand moral judgments as expressions of our attitudes. This sort of noncognitivism, he argues, provides us with the best account of the nature, which is not best understood as language used to respond to some moral aspect of reality (as language about ordinary physical objects is best understood as responding to things outside our minds and the properties they possess). To the extent that we can legitimately speak of a moral aspect of reality, of the moral properties of things, they are projections of our attitudes; they're "out there" in virtue of our spreading our attitudes onto the world.
Chapter 6 begins with a discussions of some benefits of a projective theory of moral judgments. Blackburn claims there are three such benefits his theory provides: (i) metaphysical and epistemological simplicity, in that projectivism allows us to understand moral discourse without appealing to special moral properties and a special faculty for knowing them, things which, it seems, wouldn't have a place in a respectable naturalistic account of the world and of human psychology; (ii) a explanation of the supervenience of the moral properties of things on their natural properties better than any explanation a realist can offer; and (iii) an explanation of the intimate connection between a person's moral judgments and her motivations to behave in accord with those judgments.
Having sketched the outlines of his projectivist theory of moral discourse and some reasons to prefer it to its rivals, Blackburn turns to an apparent dilemma facing the projectivist (and noncognitivists more generally). The dilemma is that the projectivist seems to be committed to either declaring that moral discourse is subject to a pervasive error or abandoning projectivism and accepting a form of realism. Why? In short, the reason is that the structure of moral discourse is realist in nature. When we say that something is morally right or wrong, it appears that we are talking about properties of things that are out there, irrespective of human attitudes. We speak of moral claims being true and false, and we claim that people's moral views are occasionally wrong. We talk about what the moral facts are. All of this makes it seem that we're talking about moral facts that exist independently of us. If you go simply by the way we talk about morality, we don't see any difference between such language and how we talk about everyday physical objects.
But the expressivist tells us that there is a major difference here: talk about morality, unlike talk about everyday physical objects, is a means of expressing attitudes and doesn't even purport to describe mind-independent facts. So it looks like the projectivist is stuck. If she defends moral discourse against accusations that it is predicated upon an error, she seems to be committed to realism (i.e. to the view that there are moral facts, and that our moral discourse describes them) and to its, perhaps implausible, metaphysical and epistemological commitments. If she repudiates the appearance of moral discourse, then it appears the projectivist is telling us that people are mistakenly committed to realism though their use of ordinary moral language. Through the things they normally say using moral language, it appears that people erroneously think that there's something out there for moral language to describe, that moral claims can be literally true and false, and that the truth and falsity of moral claims is independent of facts about their attitudes.
Blackburn wants to avoid both both realism and an error-theoretic account of morality, and his quasi-realist project is the project of attempting to show that a projectivist can do so. That is, quasi-realism is the project of explaining and justifying the realist-seeming structure of moral thought and discourse on projectivist grounds
Why, if projectivism is true, do we use language that is realist? And why should we do so? In the rest of chapter 6 and in chapter 7, Blackburn deals with these questions. He presents certain elements of moral thought and language that seem to conflict with his projective theory of moral thought and language, and he tries to account for them on projective grounds. He's especially concerned with three thing: (i) The Frege-Geach problem: that is, the problem of accounting for the appearance of moral sentences in unasserted contexts; (ii) the application of truth and falsity to moral sentences; and (iii) the mind-independence of moral truth and falsity.
By accounting for these aspects of moral thought and language with projectivist resources, he hopes to provide some evidence that the quasi-realist project will be wholly successful.