Is Global Nihilism Self-Refuting?

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.


Comments

Is Global Nihilism Self-Refuting? — 10 Comments

  1. I don’t think he ever claimed (6). I think the inference we are supposed to make from (5) is that there’s no reason to prefer nihilism over the alternatives, and it’s just arbitrary. I agree, however, how bad that is depends on whether you believe in nihilism in the first place.

  2. Jonas, you are right that S-L does not explicitly claim (6). Also, your suggestion about the inference we are to make from (5) does make some sense of the claim he makes right after the quoted argument: “Since global nihilism cannot be true, it cannot serve as a plausible basis for anything, much less moral nihilism.” (p. 52) (Query: is this so? Not unless `basis’ is construed in a question-begging way, I think.) The best reason I can see for attributing (6) to S-L is that he concludes from his claim that all versions of global skepticism are self-refuting not simply that global skepticism is not true, but that it is false. (He says explicitly that the fact that they are self-refuting, though not directly self-refuting as global nihilism is, shows that global subjectivism and global relativism are “false” (pp. 52, 53) which suggests that he takes `false’ and `not true’ to be equivalent.) For unless he thinks he has shown the latter, he cannot legitimately infer that “[t]here must be some objective truth.” (p. 54) If propositions could be true, false, or neither, the fact that all versions of global skepticism are not true would not entail that objectivism is true. It could be true, false, or neither.

    Thank you very much for your comment. I had a nagging worry, not quite explicit, about attributing the inference from (5) to (6) to S-L and thinking about your comment has, I hoped, strengthened my interpretation.

  3. Andy, suppose we accept the following:
    1. a position is self-contradictory iff it is an instance of p&~p.
    2. a position is self-refuting iff the assumption of its truth entails that it is not true.
    On these understandings, S-L shouldn’t have said that global nihilism is self-contradictory. But he could have said that it is self-refuting, and your response to his actual argument endorses the same conclusion. Right? And that point will remain, I think, even if your imagined global nihilist is sophisticated enough to recognize the peril of claiming that the view is true, and so claims only that it, like everything else, has no truth value.

  4. Jon, On point (1): I think we should be a bit more inclusive about what it is for a position to be self-contradictory. I prefer this semantic account: a set of propositions is self-contradictory iff it is logically impossible that every member of the set is true. Any theory that is self-contradictory in this sense will, of course, entail every instance of P&~P, and everything else. Still, not all contradictions are syntactically explicit, thus not all self-contradictory theories will include instances of P & ~P (this one, for example: “All men are mortal,” “some men are not mortal”). On either understanding, S-L can show that GN is self-contradictory only if he assumes the law of excluded middle.

    On point (2): Yes, if a view is self-refuting if the assumption that it is true entails that it is not true, I agree that GN is self-refuting since I think the argument is ok (for the global nihilist) up to step (5). If this all S-L wants to claim, then we should just ask whether global nihilists should care if their view is self-refuting. Still, I think S-L needs the stronger claim–that GN is false–if he is to make the inference from the self-refuting nature of all versions of global skepticism to his conclusion that there are objective truths.

    Summary: S-L has shown that GN is self-refuting, in one sense, but the GN shouldn’t care (nor should anyone else with doubts about excluded middle) and this demonstration is not sufficient to support SL’s subsequent inference from the self-refuting character of skepticism to the existence of objective truths.

  5. Andy, on point 1, it doesn’t much matter which account one accepts. But lottery and preface paradoxes are best understood when we distinguish inconsistent belief sets from contradictory ones: inconsistent sets of beliefs can all be justified, but self-contradictory ones present more of a problem.

    On the self-refutation idea. Suppose there are either 3 truth values, or truth value gaps. If we suppose that global nihilism is true, we get a contradiction, from which it follows that it is false that there are no truths. If we suppose that gn is neither true nor false, then we can derive that it’s negation has no truth value either. But that’s an instance of the denial of excluded middle, and even people who don’t like excluded middle (intuitionists, for example) are committed to the theoremhood of its double negation. That is, even for intuitionists there can’t be counterexamples to excluded middle.

    So, what logic will they let you use? If the answer is “none”, and refutation requires using principles acceptable to one’s opponent to derive a contradiction, then they can’t be refuted. But then we should reject this account of refutation. Let’s say instead that a position has been refuted when a contradiction has been derived by truth-preserving rules of inferences from the position itself. That is, let’s distinguish the logical notion of refutation from the rhetorical notion of what would, or must, persuade one’s opponent to give up their view.

  6. First, I’m not sure who, if anyone, endorses global nihilism (Shaffer-Landau’s undergraduates?) I think this is relevant, because we have to know what the actual defenders of a position think and why they think it before we know what counts as a refutation. If the only reason anyone holds it is silly confusion, then S-L refutes the position as long as he says something that exposes said confusion.

    Second, a quibble: I take it that the Law of Excluded Middle is that for any proposition P, (P v ~P) (actually an axiom schema). The principle of Bivalence, on the other hand, is that for every sentence, S, that asserts something, either S is true or S is false. The distinction is that LEM is an object-level principle, whereas Bivalence is a metalinguisic statement. The truth of Bivalence thus depends on the actual meanings of “true” and “false,” whereas LEM does not say anything about truth or falsity.

    Now, on any reasonable dialectical criteria, if S-L shows that ~Nihilism–that is, that it is not the case that nothing is true–then the Global Nihilist is refuted and has to shut up. Without having read S-L’s book, I propose this reconstructed argument:

    1. There are no truths. (Assumption for RAA)
    2. It is not true that there are no truths. (From 1; universal instantiation)
    3. It is true that p iff p. (Premise)
    4. It is true that there are no truths. (From 1, 3)
    5. It is true that there are no truths, and it is not true that there are no truths. (From 2, 4)
    6. It is not the case that there are no truths. (From 1-5; RAA)

    The only premise of the argument is the analytic truth in (3), which is guaranteed trivially by our use of the word “true.”

    Does this refute Global Nihilism? If the GN’s are confused students who never noticed the fact that GN would have to apply to itself, then yes. If they are people who endorse intuitionistic logic and so reject RAA, then no. But then the argument might be able to be recast. Can someone who knows about intuitionistic logic tell me whether the following is acceptable:

    7. It is true that p iff p. (premise)
    8. If there are no truths, then it is not true that there are no truths. (premise)
    9. If there are no truths, then it is true that there are no truths. (From 7)
    10. If there are no truths, then it is true that there are no truths, and it is not true that there are no truths. (From 8, 9)
    11. It is not the case that it is true that there are no truths, and it is not true that there are no truths. (Law of non-contradiction)
    12. It is not the case that there are no truths. (From 10, 11; modus tollens)
    ?

  7. Jon, because I find these issues to be difficult and because I am slow, it is helpful for me to spell out your objections in somewhat laborious detail. Here is your first objection:

    “On the self-refutation idea. Suppose there are either 3 truth values, or truth value gaps. If we suppose that global nihilism is true, we get a contradiction, from which it follows that it is false that there are no truths.”

    I understand this objection to run as follows:

    1. Every proposition has one (and only one) of three truth values (True, False, or N). [assumption]
    2. (GN) There are no true propositions is true. [assumption for RAA]
    3. Either (GN) is F or N (but not both). [from (1) and (2)]
    4. (GN) is not true. [from (1) and (3)]
    5. (GN) is true and (GN) is not true. [from (2) and (4)]
    6. If (GN) is true, then (GN) is true and (GN) is not true. [(2)-(5) conditional proof]
    7. (GN) is not true. [from (6)]
    8. (GN) is false. [from (7)]

    An analogous argument can be given from the assumption that every proposition has one (and only one) of these properties: it is true, it is false, it is neither true nor false.

    I see no way to get from (7) to (8) without simply assuming that every proposition that is not true must be false, a question-begging assumption in this instance. I see no reason why global nihilists need to object to the reasoning from (1) to (7). The reasoning is truth-preserving up to step (7).

    Your second objection is this:

    “If we suppose that gn is neither true nor false, then we can derive that it’s negation has no truth value either. But that’s an instance of the denial of excluded middle, and even people who don’t like excluded middle (intuitionists, for example) are committed to the theoremhood of its double negation. That is, even for intuitionists there can’t be counterexamples to excluded middle.”

    I understand this objection to run as follows:

    1. (GN) There are no true propositions is neither true nor false. [assumption]
    2. If a proposition is neither true nor false, then its negation is neither true nor false. [assumption]
    3. ~(GN) is neither true nor false. [from (1) and (2)]
    4. It is false that [(GN) or ~(GN)] [from (1) and (3)]
    5. If (GN) is neither true nor false, then it is false that [(GN) or ~(GN)]. [(1)-(4) conditional proof.]
    6. (GN) is either true or false. [from (5)]

    Once we have (6), it is easy to show that (GN) must be false because it will be self-refuting. (We could reject the assumption that propositions cannot be true and false, but Iâ??d need to call a Priest for help.)

    It seems to me global nihilists might resist the inference to (4) and claim that what follows from (1) and (3) is not that [(GN) or ~(GN)] is false, but that it is not true. (As an aside, it seems to me that (2) can be contested: it seems at least as plausible to say that if a proposition is neither true nor false, then its negation is true as to say that it must be neither true nor false. Much turns on whether `not’ means `it is false that’ or only `it is not true that.’)

    It seems to me that global nihilists and their opponents can agree on a substantial fragment of classical logic: all of it that does not assume bivalence and the (normally) corresponding law of excluded middle (thanks to Mike Huemer for noting my conflation of semantic and syntactic/proof-theoretic matters).

    Let me be clear: I think that global nihilism is both intellectually and morally dangerous. My claim is only that Shafer-Landau has not shown it to be self-refuting or self-contradictory. If there is a logical problem with global nihilism, this is because the logical principles that show this make substantial metaphysical assumptions that need to be defended.

    I shall have to wait until a later date to respond to Mike Huemer’ s interesting objections.

  8. I think the worry about Schafer-Landau’s argument is that it relies on the very assumptions denied by the global skeptic and is thus open to charges of weak circularity. There is a way to avoid this, and I’ll use the helpful cubbyhole metaphor to show how. The global nihilist is committed to all three of the following:

    1. All propositions are in the nil cubbyhole (the one in which props are neither true nor false).
    2. So, the prop “all props are in the nil cubbyhole” is in the nil cubbyhole.
    3. So, the prop “all props are in the nil cubbyhole” is neither true nor false.

    The weakly circular response runs as follows. Is (3) true? If so, then not all props are in the nil cubbyhole, and so (1) is false. This would involve the global nihilist in a contradiction: (3) is in the “true” cubbyhole and no propositions are in the “true” cubbyhole. The global nihilist can balk at this by refusing to say that (3) is true and by protesting that he is not working on the assumption that any prop is true (or false). Hence, he is not contradicting himself.

    But here’s the rub: if (1), (2), and (3) are neither true nor false, what is the point of asserting them? How can anyone endorse them? And if they can’t be endorsed, then there isn’t any position here at all, i.e., there isn’t even a position here we can call global nihilism. This is the self-defeating nature of global nihilism that Schafer-Landau is trying to bring out.

    This is akin to Aristotle’s argument in the Metaphysics (Bk. 4, Ch. 4) vis-à-vis the principle of non-contradiction. One can consistently deny the principle only by remaining silent, but this is tantamount to being a plant.

  9. Bill, welcome, and thanks for the comments. I think the argument you give creates worse problems than you suggest for gn. The gn-er has to deny that 3 follows from 1 and 2; as Andy pointed out in his original post, there can’t be any truth-preserving rules of inference for a gn-er. And I think the species is turnip, but I may be misremembering!

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