What reasons does Mackie argue for expressions of values being objective?
I think that his book A World without Values argues that values are objective, but that values cannot be objective (they would be too "queer").
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Actually, A World without Values isn't a book by J. L. Mackie, it's an anthology which is about his (meta-)ethical philosophy.
As a moral anti-realist, J. L. Mackie doesn't claim that “expressions of value” are objective. To the contrary, his view can be summarized as:
Values are subjective and
humans wrongly believe that their claims or judgments involving values are objective.
He supports his first claim with his argument from queerness, trying to show that moral values would be “qualities or relations of a very strange sort, utterly different from anything else in the universe” 1 – and so with all likelihood do not exist.
The second claim he supports, well, empirically: a “survey” of Western philosophers shows that they were predominantly and explicitly moral realists. Supposedly for ordinary people something similar holds:
The ordinary user of moral language means to say something about whatever it is that he characterizes morally, for example a possible action, as it is in itself, or would be if it were realized, and not about, or even simply expressive of, his, or anyone else’s, attitude or relation to it. 2
Finally, he argues, the emotional reaction we observe, when people accept the subjectivity of values, is evidence that they were pretty convinced of the objectivity of values:
The prevalence of this tendency to objectify values – and not only moral ones – is confirmed by a pattern of thinking that we find in existentialists and those influenced by them. The denial of objective values can carry with it an extreme emotional reaction, a feeling that nothing matters at all, that life has lost its purpose. Of course this does not follow; the lack of objective values is not a good reason for abandoning subjective concern or for ceasing to want anything.[nb: probably he's inconsistent here, it seems like he's making a value-judgment that really sounds like it should be understood objectively. If he thinks that all values are subjective, there's nothing really wrong with abandoning them because one found out they are not objective] But the abandonment of a belief in objective values can cause, at least temporarily, a decay of subjective concern and sense of purpose. That it does so is evidence that the people in whom this reaction occurs have been tending to objectify their concerns and purposes, have been giving them a fictitious external authority. A claim to objectivity has been so strongly associated with their subjective concerns and purposes that the collapse of the former seems to undermine the latter as well. 3
2 Ibid., p. 33
3 Ibid., p. 34