One brand of skepticism claims that we cannot have knowledge because there are no true statements. In Whatever Happened to Good and Evil? (Oxford, 2004), a very clear and stimulating defense of moral objectivism, Russ Shafer-Landau argues that this form of skepticism—global nihilism—is self-refuting: “If there are no truths at all, then nihilism itself cannot be true. If we correctly apply the theory, it turns around and bites its own tail. If global nihilism is true, then there is at least one truth, and that is contrary to the claim global nihilism makes. Being self-contradictory, it cannot be true.” (p. 52)
I understand this argument to run as follows:
(1) If global nihilism is true, then there are no truths. [by definition]
(2) Thus, if global nihilism is true, then global nihilism is not true. [from (1) by quantifier exchange and universal instantiation of the consequent]
(3) If global nihilism is not true, then global nihilism is not true. [tautology]
(4) Either global nihilism is true or global nihilism is not true. [logical truth]
(5) Therefore, global nihilism is not true. [from (2), (3), and (4) by constructive dilemma]
(6) Therefore, global nihilism is false. [from (5) by the law of excluded middle]
Unlike some other charges of self-referential inconsistency—well-known arguments against eliminative materialism, for example—this argument promises to show that the theory under attack is inconsistent simplicitur, not just that it is incompatible with some additional propositions about the theory that are claimed to be obvious. “There are no sentences in English” is self-consistent but is incompatible with a claim about itself that is obviously true once it is written down or spoken. It is consistent but self-refuting. The reason Shafer-Landau’s argument, as I understand it, is supposed to show that global nihilism is not only self-refuting but inconsistent is that it assumes only the characteristic thesis of global nihilism together with some basic principles of logic.
The problem with Shafer-Landau’s argument against global nihilism—as with many charges of self-refutation or self-referential inconsistency—is that it begs a crucial question. If I were a global nihilist, I would not object to the reasoning up to step (5), though I would, of course, not accept all of the bracketed commentary on that reasoning (which implies that there are logical truths). But the inference from (5) to (6) depends upon the law of excluded middle—that every proposition is either true or false—which the global nihilist should reject. The most powerful version of global nihilism is the view that no proposition is either true or false, at least not in any traditional sense. This implies that no proposition is true without implying that any proposition is false. The global nihilist ought to claim that in the conceptual space of propositions, there are at least three cubbyholes: one for propositions that are true, one for propositions that are false, and one for propositions that are neither. Furthermore, all propositions are in the last cubbyhole, even the characteristic thesis of global nihilism itself. I conclude that Shafer-Landau has not shown that the most powerful version of global nihilism is inconsistent or that it is subject to self-refutation.