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Vagueness: Why Do We Believe in Tolerance?

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Abstract

The tolerance principle, the idea that vague predicates are insensitive to sufficiently small changes, remains the main bone of contention between theories of vagueness. In this paper I examine three sources behind our ordinary belief in the tolerance principle, to establish whether any of them might give us a good reason to revise classical logic. First, I compare our understanding of tolerance in the case of precise predicates and in the case of vague predicates. While tolerance in the case of precise predicates results from approximation, tolerance in the case of vague predicates appears to originate from two more specific sources: semantic indeterminacy on the one hand, and epistemic indiscriminability on the other. Both give us good and coherent grounds to revise classical logic. Epistemic indiscriminability, it is argued, may be more fundamental than semantic indeterminacy to justify the intuition that vague predicates are tolerant.

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Notes

  1. When those restrictions would fail, some of those accounts accept the Dummettian view that vague predicates are simply inconsistent, see [8] and [22, 32].

  2. Fara’s articulation of the epistemological question differs somewhat from the present one, but this does not bear on the main distinction at stake here.

  3. See [18, 21, 45] on the consideration of such examples.

  4. Regarding the French version of the proverb, we are certainly ready to concede that a given glass recipient has a determinate volume. The English version of the proverb is more interesting in a way, because there is arguably no absolutely determinate load that counts as the maximum load the camel can support. The fact remains, however, that whatever the finite range in which this maximum would fall, its upper bound can be outweighed by any small quantity.

  5. Standard rules differ, in that they round to the even round value, see [28]. The specificity of the rounding rule chosen does not matter however in what follows, we may even consider nonsymmetric approximation intervals, and adapt our analysis accordingly.

  6. The analysis may also be related to the central gap account of tolerance defended by Pagin in [32], where the tolerance principle is pragmatically restricted by the assumption that individuals in the domain do not fall within a central gap whose size is at least that of a tolerance level fixed by the context for each vague predicate.

  7. See [46]: “Fortunately, ‘thin’ is not governed by the tolerance principle; it is governed by the margin for error principle (!), which generates no sorites paradox”. Williamson’s margin of error principle implies that we cannot know where the cutoff lies. According to Williamson, it is a verificationist bias that urges us, from the impossibility to know P x and ¬P y of any x and y such that x∼ P y, to believe that there are no such x and y.

  8. See particularly [50] and [33] on permissible disagreement in borderline cases. The resulting notion of indeterminacy fits what Smith calls plurivaluationism, what [13] calls second level indeterminacy, or what [41] calls open-texture (in a sense compatible with but weaker than Waismann’s original sense), to characterize the compatibility of the meaning of an expression with a multiplicity of different verdicts. This notion of semantic indeterminacy is compatible with stronger notions, such as what Eklund calls first-order indeterminacy, for when a predicate is semantically gappy, but it is not mandated by it.

  9. The notion of indifference is sometimes judged even more fundamental than that of indiscriminability, for cases in which we are in a position to make a distinction, but in which the difference is judged practically irrelevant. Arguably, however, the notion of indiscriminability is more explanatory of the phenomenon of tolerance. [21] writes that a difference between 41 and 40 chimpanzees is as discriminable in principle as a difference between 5 and 6 chimpanzees, but practically less relevant when ascribing “large” to a community of chimpanzees. This is correct, but it would be less easily discriminable if presented perceptually. He also considers that “large” is not a perceptual predicate in that example, but this is controversial. Our mental representation of numerosities, relative to some given unit, and even for more clearly nonphenomenal predicates such as “rich” or “expensive”, may remain highly dependent on our perceptual ability to discriminate between quantities. See [20] and [16] for arguments in that direction.

  10. See in particular [3] for a defense of gap principles against D-introduction, and work in progress by P. Pagin opposing the same rule, based on the assumption that “determinately” operators behave as intensifiers. For a recent assessment of higher-order gap principles, see also [52].

  11. See among others [9, 10, 23, 29, 30, 51] or [37]. For example, [30] write: “One existential claim we surely do not want to make is this: there is an n such that the nth tile definitely looks red and the (n+1)st tile definitely does not look red. Such a claim would allege a justifiable distinction where there is no significant difference”. Likewise, [9] writes: “‘no single grain makes a difference between a heap and a non-heap’. If this means: no single grains makes a decisive difference – takes you from a clear heap to a clear non-heap – then it is true. If it means: no single grain at all makes any difference to heapdom, then it is false”. Even [42]’s defense of closeness, the idea that close cases should receive close semantic values, may be reanalyzed in terms of gaps, as the idea that the assignment of opposite semantic values to P a and P b implies that a and b should be sufficiently far. See [11] and [4] for further discussion.

  12. See particularly [52], [36] and [4] for a defense of this inferentialist conception.

  13. Incidentally, it would also fail in the trivalent reinterpretation of TCS presented for instance in [4], where closeness is defined directly in terms of distance between semantic values, rather than as a relation over objects proper. This feature is not essential to the trivalent account, however.

  14. Monotonicity is what [18] calls an internal penumbral connection. I take the term “monotonicity” from [31]. It is used by [21] in the same sense. [2] uses the term “scalarity”.

  15. Compare with [52]’s talk of the “good” semantic values a sentence can take.

  16. See particularly [33] and [41] for related views about tolerance and semantic competence.

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Acknowledgments

I would like to thank Frank Veltman and Jeff Horty for their invitation to contribute this paper. I am indebted to Heather Burnett, Pablo Cobreros, Laurence Goldstein, David Ripley, Robert van Rooij and Frank Veltman for comments and discussions, to Laurence Goldstein and his students for a memorable conversation in a caf´e in Paris in 2013, and to audiences and colleagues at seminars held in Paris and NYU. Thanks to the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013), to the project ‘Borderlineness and Tolerance’ (FFI2010-16984), Ministerio de Economia y Competitividad, Government of Spain, and to grants ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL*.

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  1. Institut Jean-Nicod, (CNRS, EHESS, ENS), Paris, France

    Paul Égré

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Correspondence to Paul Égré.

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I dedicate this paper to the memory of Laurence Goldstein (1947-2014).

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Égré, P. Vagueness: Why Do We Believe in Tolerance?. J Philos Logic 44, 663–679 (2015). https://doi.org/10.1007/s10992-015-9352-z

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