This is an interesting anthology. It covers relativism in two areas: general conceptual and epistemological relativism, and moral relativism. Lots of the papers here are of signal importance, and many of them have been extremely influential. Still, though, it is somewhat difficult to see a lot of connection between the two general topics. And the reader should note that this is not an anthology for the neophyte. For the most part, these are sophisticated articles written by professional philosophers and for professional philosophers
Krausz and Meiland begin with a general introduction that introduces the topic. (There are also short introductions to the paper that summarize their main claims and relate their contents to the contents of other essays.) The introduction says something about the significance of relativism in contemporary culture, and a little bit about the history of relativism in philosophy. It is, in effect, a general attempt to motivate the issues here by pointing the facts of conceptual and moral diversity, and explaining how relativism is one, albeit only one, of the possible responses to these facts about diversity. Basically, the relativist's response is to deny the reality of a single truth here. There is what is true-for-them and what is true-for-us, and that's all there is to it.
The first section of the anthology, the section on what the authors call "cognitive relativism," includes papers about a very radical and very general form of relativism. This is the sort of relativism according to which different groups (or individuals) possess different general conceptual schemes, different groups of concepts in which they think and speak. And, the relativist claims, there is no way to determine which is the one correct conceptual scheme. Indeed, they may think the suggestion that there is one privileged conceptual scheme doesn't even make sense. Why? Because they believe the truth and falsity apply to judgments only relative to a particular conceptual scheme. The facts are what they are only in some scheme or another, and there is no standpoint outside any framework from which we can determine which is the one correct conceptual scheme. This leads to a relativism about all our thought and talk about the world.
In the first reading of this section, Nelson Goodman defends a relativism of this variety. Then there are two papers attacking it: Maurice Mandelbaum argues that this sort of relativism leads to self-contradictions, and Donald Davidson, in an influential and typically difficult paper, attacks this form of relativism by denying that the idea of a conceptual scheme is a coherent one. This is followed by a paper by Chris Swoyer in which he attacks the concept of truth-for a particular group or individual, a concept relativists of this sort may need. Finally, there is a paper by Gerald Doppelt in which he draws on Kuhn's philosophy of science in order to defend a relativism of this sort.
The second half of the anthology focuses on the more narrow topic of relativism about morality. What is moral relativism? Here's a first pass. The basic idea of relativism is that the moral facts are somehow constituted by the moral attitudes, beliefs, conventions, standards, etc. of a group of people, and that the truth and falsity of particular moral claims depends upon the moral attitudes, beliefs, conventions, standards, etc. of a group of people. But, as David Lyons points out in his paper, there are two ways to understand this dependence, because there are two different groups that might matter here: the group of the person making a moral judgment and the group of the person whose action is being judged. I'll explain the distinction by focusing on what the two types of relativism tell us about the truth of a particular person's, b's, moral judgment that another person, a, ought not to commit murder. One way of understanding this dependence gives us agent relativism, a view according to which b's judgment that a person a ought not to commit murder is true if and only if people in a's group have a negative moral attitude towards committing murder, or believe that committing murder is wrong, or have a convention against committing murder, or have moral standards that rule out committing murder, or something similar. So, according to agent relativism, what matters is the group of the person being judged, the group of the person doing the action. The other way of understanding the dependence gives us appraiser relativism, a view according to which b's judgment that a person a ought not to commit murder is true if and only if people in b's group have a negative moral attitude towards committing murder, or believe that committing murder is wrong, or have a convention against committing murder, or have moral standards that rule out committing murder, or something similar. So, according to appraiser relativism, what matters is the group of the person doing the judging.
Now that we know what moral relativism is, I can tell you about the selections on moral relativism here. the. There are papers defending forms of relativism by Gilbert Harman, Philippa Foot, and Bernard Williams. Harman argues that a certain sort of agent relativism is the appropriate moral theory on the basis of certain views about when it is appropriate to claim that a person ought to do something. Foot argues that a sort of appraiser relativism can be defended for some moral judgments, but not for all of them. Bernard Williams is represented by two selections, one arguing that a crude form of relativism is incoherent and the other arguing that there may be something to a more sophisticated sort of relativism grounded in radically moral differences between groups. This is followed by papers critiquing moral relativism by David Lyons and by Geoffrey Harrison. Lyons formulates the distinction between agent and appraiser relativism, and he argues that appraiser relativism leads to endorsing contradictions. Harrison argues against the ordinary view that relativism supports tolerance of other people.