Abstract
I argue, pace Timothy Williamson, that one cannot provide an adequate account of what it is for a case to be borderline by appealing to facts about our inability to discriminate our actual situation from nearby counterfactual situations in which our language use differs in subtle ways. I consider the two most natural ways of using such resources to provide an account of what it is for a case to be borderline and argue that both face crippling defects. I argue that the problems faced by these two accounts point to more general reasons to be skeptical of the claim that facts about semantic indiscriminability provide sufficient resources for an analysis of what it is for a case to be borderline.
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Notes
Truth-value gaps are postulated by standard supervaluationist and standard degree theories of vagueness. There are, however, other versions of semantic theories of vagueness, e.g., that proposed by Vann McGee and Brian McLaughlin, that do not clearly fit this mould.
For the full development of this idea see chapter 8 in Williamson (1994).
But see Kearnes and Magidor (2008) for some worries about whether metalinguistic safety is in fact necessary for a judgment to count as knowledge.
Two points. First, the formal framework employed by a supervaluationist will not be exactly the same as that employed by an epistemicist. Of particular note is the fact that truth for the supervaluationist will be identified with truth at all points in the model, whereas for the epistemicist there will be a designated point that will represent the correct interpretation of the language. Second, it’s worth noting that Williamson in the appendix actually develops two models. The second is more complex than the first. Instead of a single accessibility relation over a set of points, it employs a set of such relations. Such added complexities will not matter for the problems that I will be raising, and so I will ignore them.
It is somewhat unclear to me which of these Williamson had in mind as a way of interpreting the model-theory he suggests. Since I think neither of these work I won’t be too concerned to sort out which Williamson intended. For the record, the second analysis that I will develop seems to me the one most naturally suggested by the above quote, since it is formally closest to standard supervaluationism. But the evidence here is far from unequivocal.
N.B. This way of using a classical semantic assignment to determine truth at a point differs from that employed by the supervaluationist. The latter uses a classical assignment σ to determine the truth value of ϕ at a point by evaluating what truth value ϕ has under σ at the actual world. In the next section I’ll consider an epistemicist account that parallels the supervaluationist in this respect.
Thanks here to Cian Dorr for helpful discussion.
Obviously this is true for claims of the form: It is borderline whether ϕ, only so long a ϕ does not contain modal vocabulary. I’ll take this restriction as implicit here and in what follows.
And in general, whether a case is borderline in w depends on how things are in w. It is, I suggest, because it is how things are in a world w that matters for the assessment of borderline claims at w that we can assess for an arbitrary world whether it is borderline whether ϕ at w despite there not being worlds related to w as the worlds in W @ are related to the actual world.
Both of these assumptions could be altered in certain ways to accommodate alternative semantic frameworks. It wouldn’t matter if the semantic value of ‘refers’ were simply something which determined an intension of the kind in question, but was perhaps more fine-grained. Nor would it matter if the semantic value of ‘Everest’ were simply something which rigidly picked out an object, but was not identified with the object itself.
Two points. First, note that the notion of word-type being employed here is one according to which a word-type may have different semantic values at different possible worlds. Assuming such a conception of word-type is fine in this context since this is the notion of word-type that is required to frame the epistemicist account. See Williamson (1994) chapter 8, footnote 12 for an explicit endorsement of this notion of word-type. Second, if you are worried that there may be some minor vagueness in this term, note that the arguments that follow could be reframed using the weaker and altogether plausible assumption that there are some nearby worlds in which the term ‘‘Everest’’ refers to the same word-type as it does given our actual use of language, but in which that word-type has a different semantic value than its actual semantic value.
See Hawthorne (2006) for an argument that the intension of ‘refers’ as used in all nearby possible worlds is the same as the actual intension of this term. Hawthorne uses this to argue that the conditions imposed by (B*)—which he takes to be the conditions proposed by Williamson—are not, in fact, necessary for a case to be borderline. In what follows, I use weaker assumptions to argue that these conditions are not, in fact, sufficient.
Note that even if one were inclined to give up the claim that knowledge that ϕ is precluded by it being borderline whether ϕ (see e.g., Dorr (2003)), one may at least allow that it being borderline whether ϕ precludes it being definite that one knows that ϕ. But it seems that we definitely know that ‘Everest’ refers to Everest, and so one who is attracted to this weaker constraint should also find (B*) inadequate.
References
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Hawthorne, J. (2006). Epistemicism and semantic plasticity. In Metaphysical essays (pp. 185–210). Oxford: Oxford University Press.
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Acknowledgments
Thanks to Fabrizio Cariani, Cian Dorr, John MacFarlane, Mike Martin and Mike Rieppel for helpful comments on an earlier version of this paper.
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Caie, M. Vagueness and semantic indiscriminability. Philos Stud 160, 365–377 (2012). https://doi.org/10.1007/s11098-011-9723-4
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DOI: https://doi.org/10.1007/s11098-011-9723-4