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Semantic defectiveness and the liar

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Abstract

In this paper, we do two things. First, we provide some support for adopting a version of the meaningless strategy with respect to the liar paradox, and, second, we extend that strategy, by providing, albeit tentatively, a solution to that paradox—one that is semantic, rather than logical.

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Notes

  1. Although we shall not be arguing for the set of principles of generation that we prefer, for the sake of completeness, we list them here:

    1. (i)

      It is to be pretended that expressions like ‘is true’ and ‘is false’ function predicatively to describe objects as having or lacking properties (called, not surprisingly, ‘truth’ and ‘falsity’).

    2. (ii)

      The pretenses displayed in an utterance of \( \ulcorner \langle {\text{p}} \rangle \,{\text{is}} \,{\text{true}} \urcorner \) are prescribed iff p.

    3. (iii)

      The pretenses displayed in an utterance of \( \ulcorner \langle{\text{p}} \rangle\, {\text{is}}\,{\text{ false}} \urcorner \) are prescribed iff ~p.

    4. (iv)

      If S1 and S2 are sentences that are alike except that (in some transparent context), one has as a subsentence \( \ulcorner {\text{p}} \urcorner \) where the other has \( \ulcorner \langle {\text{p}} \rangle\, {\text{is}}\,{\text{ true}} \urcorner \), then one can directly infer S1 from S2 and vice versa.

    For more on these principles, see Woodbridge (2005) and Armour-Garb and Woodbridge (2010).

  2. The same goes for wide-scope negation liar sentences, e.g.,

    • (L*) It is not the case that (L*) is true.

    The pretense never determines prescriptive M-conditions for these sentences either.

  3. For slightly different reasons, a similar diagnosis will apply to the following case, suggested by an anonymous referee:

    • (O) The M-conditions of (O) do not obtain.

    The self-referential aspect of this case creates a (slightly different) kind of looping, one that would require (O) to have M-conditions already, in order for any M-conditions to be determined for it. But this kind of semantic bootstrapping is impossible, so (O) fails to specify any M-conditions as well. Thanks to the referee, for the helpful suggestion.

  4. This diagnosis, and the treatment we offer below, also applies to truth-teller sentences, such as

    • (K) (K) is true,

    which appear to manifest indeterminate semantic pathology.

  5. As an aside, we should note that perhaps the main objection here arises as a consequence of so-called “contingent liars”. Since the points that we will make here clearly apply to contingent liars, we will not address them directly in this paper. For more on contingent liars, see Armour-Garb (2001).

  6. This allows for a possible contrast between ‘This is a fine red one’ and Chomsky’s (1957) sentence, viz., ‘Colorless green ideas sleep furiously’. The latter sentence is not even understood2, if we insist that to understand2 a sentence, we need how that sentence could be used to make a true assertion.

    We should note that, although we are inclined to accept this condition, we need not insist on it, for the points in this paper to go through.

  7. See Woodbridge (2005), p. 171, note 45.

  8. Some discussion at the Seventh Barcelona Workshop on Issues in the Theory of Reference: Paradoxes of Truth and Denotation suggested that this requirement might be a bit strong, but even if that is so, something in the neighborhood will still be required.

  9. Cf. Parsons (1984), Tappenden (1993), Richard (2008).

  10. An anonymous referee noted that one might object to our assumption of compositionality. The referee is right that one might object to this assumption (one can always object to such assumptions). But it bears noting that we are assuming a very minimal assumption of compositionality; indeed, one that is generally taken to be uncontroversial, viz., that, in extensional contexts, the meaning of a complex formula—in particular, a conjunction, disjunction, etc.—is a function from the meanings of its parts. Since this assumption is generally thought to be uncontroversial and since, anyway, one who resists this assumption will be faced with a rather difficult task, we will not address objections to this (minimal) assumption here.

  11. A tokenist (e.g., Goldstein 2009) might try to argue that that the token (D) can also consistently be s-defective (and without yielding expressive incompleteness), which, given the possibility of its falsity, would present a problem of indeterminacy for us regarding (D)’s semantic status. We think that this gambit is unlikely to succeed, given (familiar) revenge problems for tokenists, but we shall not make this case here. For worries about tokenist solutions to the liar paradox, see Armour-Garb (2012b).

  12. Similar (or: dual) reasoning applies in the case of the sentence,

    • (D′) (D′) is not s-defective,

    which we claim turns out to be true, as does the sentence,

    • (M′) (M′) is not meaningless.

  13. We would like to thank Graham Priest both for raising this objection and for discussing the proposed response with Armour-Garb.

  14. Similar reasoning leads us to make the same evaluation of another case, suggested by an anonymous referee:

    • (E′) (E′) cannot be (correctly) assigned a truth-value.

    No contradiction arises if we assign (E′) the value ‘false’—if (E′) is false, then, assuming double-negation elimination and a little tinkering, it follows that (E′) can be correctly assigned a truth-value, which, given what (E′) says, would make it false. Hence, because (E′) can (consistently) be false, it follows that (E′) is false. Hence, (E′) is false.

    A further related case that the anonymous referee suggested is the sentence,

    • (E″) (E″) has no alethic evaluation.

    While this case differs from both (E) and (E′) in eliminating the modal element, like both of them, it still ends up specifying M-conditions (since it suffers from no apparent breakdown on that front), and thus has a correct aletheic evaluation. However, since (E″) says that it has no aletheic evaluation, that makes the value ‘false’ the correct evaluation for (E″).

    Thanks to an anonymous referee, for bringing (E′) and (E″) to our attention.

  15. Cf. Armour-Garb (2008).

  16. Without (P1) and (P2), one might conclude that (R) is aletheically indeterminate. But, actually, that would not be correct. Rather, without those principles (or ones like them), it would not be clear what the conditions are for the application of the truth-predicate to a sentence, in which case it would be underdetermined—that is, not currently known—what status (R) can or should have.

  17. For a recent discussion of deflationary accounts of truth, see Armour-Garb (2012a, 2012c).

References

  • Armour-Garb, B. (2001). Deflationism and the meaningless strategy. Analysis, 61(4), 280–289.

    Google Scholar 

  • Armour-Garb, B. (2008). Read and indirect revenge. In S. Rahman, T. Tulenheimo, & E. Genot, Emmanuel (Eds.), Unity, truth and the liar: The modern relevance of medieval solutions to the liar paradox (pp. 19–40). Springer.

  • Armour-Garb, B. (2012a). Challenges to deflationary theories of truth. Philosophical Compass.

  • Armour-Garb, B. (2012b). No consistent way with paradox. Analysis, 72(1), 66–75.

    Article  Google Scholar 

  • Armour-Garb, B. (2012c). Deflationism (about theories of truth). Philosophical Compass.

  • Armour-Garb, B., & Woodbridge, J. (2010). Why deflationists should be pretense theorists (and perhaps already are). In C. Wright & N. Pedersen (Eds.), New waves in truth (pp. 59–77). Basingstoke: Palgrave Macmillan.

    Google Scholar 

  • Chomsky, N. (1957). Syntactic structures. The Hague: Mouton de Gruyter.

    Google Scholar 

  • Field, H. (1994). Deflationary views of meaning and content. Mind, 103, 249–285.

    Article  Google Scholar 

  • Field, H. (2001). Truth and the absence of fact. Oxford: Clarendon Press.

    Book  Google Scholar 

  • Field, H. (2008). Saving truth from paradox. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Goldstein, L. (2009). A consistent way with paradox. Philosophical Studies, 144(3), 377–389.

    Article  Google Scholar 

  • Parsons, T. (1984). Assertion, denial and the liar paradox. Journal of Philosophical Logic, 13(1984), 137–152.

    Article  Google Scholar 

  • Richard, M. (2008). When truth gives out. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Strawson, P. (1950). On referring. Mind, 59, 320–344.

    Article  Google Scholar 

  • Tappenden, J. (1993). The liar and sorites paradoxes: Towards a unified treatment. Journal of Philosophy, 90, 551–577.

    Article  Google Scholar 

  • Woodbridge, J. (2005). Truth as a pretense. In M. Kalderon (Ed.), Fictionalism in metaphysics (pp. 134–177). Oxford: Oxford University Press.

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Acknowledgments

Thanks to Graham Priest, the audience at the Seventh Barcelona Workshop on Issues in the Theory of Reference: Paradoxes of Truth and Denotation, Barcelona, Spain, June 2011 and an anonymous referee, for helpful comments.

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Correspondence to Bradley Armour-Garb.

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Armour-Garb, B., Woodbridge, J.A. Semantic defectiveness and the liar. Philos Stud 164, 845–863 (2013). https://doi.org/10.1007/s11098-012-9915-6

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