Abstract
One well known approach to the soritical paradoxes is epistemicism, the view that propositions involving vague notions have definite truth values, though it is impossible in principle to know what they are. Recently, Paul Horwich has extended this approach to the liar paradox, arguing that the liar proposition has a truth value, though it is impossible to know which one it is. The main virtue of the epistemicist approach is that it need not reject classical logic, and in particular the unrestricted acceptance of the principle of bivalence and law of excluded middle. Regardless of its success in solving the soritical paradoxes, the epistemicist approach faces a number of independent objections when it is applied to the liar paradox. I argue that the approach does not offer a satisfying, stable response to the paradoxes—not in general, and not for a minimalist about truth like Horwich.
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Notes
I use propositions as my principal truth bearer because they are the kind that Horwich embraces. The expression ‘\(<p>\)’ stands for ‘the proposition that \(p\)’.
Though he later adds the proviso that only propositions are true (1998b, p. 43).
This pairing is also the focus of Armour-Garb and Beall (2005).
See Simmons (1999) for independent worries about this proposal.
Further problem cases for Horwich include (1), \(<\)(1) is neither true nor false\(>\), and (2), \(<\)(2) is either true or false\(>\). Because of bivalence, we know that (1) is false and (2) is true, though they and their T-biconditionals are ungrounded. The T-biconditionals for (1) and (2) are provably true, given bivalence, so they too constitute a challenge to the integrity of Horwich’s criterion of groundedness. (They also show that Horwich cannot maintain that all ungrounded truth-theoretic propositions are unknowable).
This account of indeterminacy does seem to provide an account of (T)’s indeterminate status. So to reframe the objection from the previous paragraph, it would be odd if the explanation of (T)’s indeterminacy closely paralleled Horwich’s account of indeterminacy for vagueness, but resembled the indeterminacy of (L) not at all; here we have further (yet still defeasible) reason to think that Horwich’s explanation of (L)’s indeterminacy is ad hoc.
Most prominently, it invites the “strengthened” paradox due to (S), \(<\)(S) is not true\(>\), discussed below. If (L) is meaningless, so too is (S), in which case it’s not true, and so appears to be true after all.
Cf. Beall (2001), which argues that deflationists have independent reason to claim that liar sentences are meaningless, given their ineliminable use of ‘true’ and ‘false’.
Armour-Garb and Beall also consider a further objection to semantic epistemicism, namely, that it faces a revenge paradox via (K): \(<\)No one knows that (K) is true\(>\). Since it is epistemically indeterminate, (K) is a consequence of semantic epistemicism. And so, Armour-Garb and Beall claim, (K) is known by semantic epistemicists, resulting in contradiction. However, we cannot take as a premise that semantic epistemicists know that their theory is true, even if it is; they might fail to know either because the theory is false, or because their belief in it fails to achieve the status of knowledge. The most one can derive from (K) is that if semantic epistemicism is true, it cannot be known. This result is not contradictory; it just shows that those who go in for semantic epistemicism had better not take themselves to know the truth of their view. This response to Armour-Garb and Beall, however, provides little comfort to the epistemicist, as other revenge problems are available. Consider the similarly ungrounded (J): \(<\)It is known that (J) is false\(>\). Supposing (J), it is known that (J) is false, and so (J) is false. By reductio, (J) is false, and knowably so since it’s provably false. So (J) is known to be false, in which case (J) is true. Thanks go to a referee for identifying this further revenge problem.
Cf. Simmons (1999), pp. 463–464. To reply that propositions like (S) and (L) are “few and far between” (Horwich 1998b, p. 42, footnote 21) does little to assuage the objection. Liar propositions are not few in number: there are infinitely many of them. Even one truth-theoretic proposition that cannot be explained by minimalism is sufficient to serve as a counterexample to the minimalist’s claim of having accounted for all the facts about truth. As with much in philosophy, no tensions arise in normal cases; it’s the extraordinary cases that fuel philosophical interest, and that lead us to question the very principles that we think lie behind the ordinary cases. To say that truth works in the ordinary way in ordinary cases does little to remove the worries that arise from observing how the ordinary begins to act extraordinarily in extraordinary cases.
See Armstrong (2004) for an introduction to truthmaker theory.
Cf. Horgan (1997).
For example, supposing that (L) is true, one might posit the existence of an entity called “the fact that (L) is true”, which wouldn’t have existed had (L) been false. In this case, the “fact” can’t just be the true proposition itself, but rather some separate entity that makes (L) true. But what is this fact composed of? Do we have any reason to believe in its existence independently of a commitment to epistemicism? The challenge for the epistemicist is to offer a truthmaker that is sufficiently explanatory while not being an ad hoc ontological posit.
This turns out to be Sorensen’s stance with respect to (T), the truth-teller (Sorensen 2001). Sorensen is not an epistemicist with respect to (L), however, for he thinks that there are no liar propositions, let alone truth-valued ones (2001, p. 182). The objections raised in this section concerning (L) apply equally well to Sorensen’s view concerning (T).
For example, Lange (2009) posits the existence of brute counterfactual truths, but then puts them to work by showing how we can use them to give satisfying accounts of various notions important to the philosophy of science, such as the laws of nature.
Cf. the problem of “surprising determination facts” for epistemicists about vagueness (Eklund 2011, p. 357).
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Acknowledgments
My thanks go to the referees for the journal, Bradley Armour-Garb, Luke Elson, Thomas Hofweber, and especially Keith Simmons for their invaluable comments. A version of this paper was presented to the Pacific Division of the American Philosophical Association in April 2012 in Seattle. I thank Jeff Snapper for his very helpful commentary, and the audience for a productive exchange.
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Asay, J. Epistemicism and the liar. Synthese 192, 679–699 (2015). https://doi.org/10.1007/s11229-014-0596-x
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DOI: https://doi.org/10.1007/s11229-014-0596-x