Abstract
One natural thought to have about vagueness is that the indeterminacy or imprecision inherent in vague expressions is intimately tied to the meanings of these expressions. If this is right, then important tool for studying vague predicates will be meaning theories. There are three critical issues that must be addressed by any such theory: the incompatibility of vague predicates with the ‘governing view’ of semantic theorizing, the relation between the meanings of vague expressions and the use we make of them, and the fact that vague predicates are open textured. This chapter explores the prospects for dealing with each of these from the perspective of three approaches: contextualist theories, epistemicist theories, and indeterminist theories. We conclude by looking at a variation of the first problem that applies, not to meaning theories, but to formal logics for vagueness: the problem of inappropriate precision.
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Notes
- 1.
For the remainder of this chapter we shall simplify our discussion by restricting our attention to vague predicates. The reader should keep in mind, however, that the considerations below can be generalized to all vague expressions.
- 2.
Of course, there is also a large literature on the issue of vague objects and metaphysical vagueness more generally – that is, so-called ontic vagueness (see, e.g Evans (1978), Parsons (2000)). While the issues tied up with the existence, or not, of vague objects are interesting and important, they are rather orthogonal to the present topic.
- 3.
In point of fact, the epistemic conception of vagueness can be thought of as a particularly sophisticated variant of the semantic view: By epistemicist lights, vagueness is a phenomenon that occurs in language, but it occurs in a different portion of language than we might have originally thought (in particular, the indeterminacy occurs not in simple predications of a vague predicate (e.g. “Bob is bald”), but in epistemic claims about such predications (e.g. “We can know that Bob is bald”). For our purposes here, however, it will prove more convenient to treat the epistemic view as a separate position.
- 4.
If the target of this chapter was ‘solving’ the Sorites paradoxs and similar puzzles that arise due to vagueness, then (c) would undoubtably play the most prominent role in our discussion.
- 5.
Of course, if the theorist in question holds a Davidsonian-like view that equates a theory of meaning with a (possibly formal) account of the truth conditions of statements (see, e.g. Davidson (1967)), then this complaint is unfounded (Sainsbury (1990) suggests (with some reservations) such a Davidsonian approach to the meaning of vague expressions).
- 6.
The qualifier “simply” is required here in order to handle dialethic accounts, which do not allow for any semantic values other than truth and falsity, but which do allow statements to be both. In addition, we shall assume that accounts which allow statements to fail to receive a value (so-called ‘gappy’ logics) to count as indeterminist accounts, interpreting the lack of a semantic value as a third semantic ‘status’.
- 7.
- 8.
- 9.
In fact, the challenge to the epistemicist is even more serious, since (at least on Williamson’s development of the view) there will potentially be infinitely many different boundaries that must be accounted for – not just the boundary between instances of the predicate and non-instances, but between knowable instances (i.e. those instances that can be known to be instances) and non-knowable instances, between knowable non-knowable instances and non-knowable non-knowable instances, etc.
- 10.
It should be noted that Tye takes pains to stress that his logic is not, in fact, three-valued, but is instead a gappy logic, where statements take at most one of true and false, but might receive neither. From the technical perspective at issue here, however, the distinction between such gappy logics and three-valued logics makes no difference.
- 11.
I am cheerfully borrowing Stewart Shapiro’s favorite example here.
- 12.
The term is originally due to Friedrich Weismann (1968), where he suggested the term for expressions whose meanings do not provide for, or determine, every possible instance of application.
- 13.
- 14.
The reader should also consider R. M. Sainsbury’s comments, quoted in Section 4.3.3, in light of this problem.
- 15.
It is worth noting that a move to non-standard mathematical theories, such as constructive or intuitionistic mathematics, does not seem to help here, since although the structures studied in such non-standard mathematical settings are less determinate in the sense of, for example, failing to satisfy bivalence, they are nevertheless still mathematically precise in the relevant sense.
- 16.
It should be noted that Edgington did not herself use the term ‘logic-as-modeling’ – the term arose in later writings by Cook (e.g. (2002)) and Shapiro (e.g. (2006)) that attempted to further flesh out the import of her comments (and those of other writers) on this topic. The view finds it earliest substantial developments in Corcoran (1973).
- 17.
The logic-as-modeling approach has been criticized (notably, by Keefe (2000)) for merely hypothesizing an artifact/representor distinction without failing to adequately account for where, exactly, the line between artifact and representor lies, although Cook (2002) goes some ways towards assuaging this worry.
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Cook, R.T. (2011). Vagueness and Meaning. In: Ronzitti, G. (eds) Vagueness: A Guide. Logic, Epistemology, and the Unity of Science, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0375-9_4
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