Vagueness: A Minimal Theory
Greenough (Patrick)
Source: Mind - 112/446 (April 2003)
Paper - Abstract

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Author’s Abstract

  1. Vagueness is given a philosophically neutral definition in terms of an epistemic notion of tolerance. Such a notion is intended to capture the thesis that vague terms draw no known boundary across their range of signification and contrasts sharply with the semantic notion of tolerance given by Wright (1975, 1976).
  2. This allows us to distinguish vagueness from superficially similar but distinct phenomena such as semantic incompleteness.
  3. Two proofs are given which show that vagueness qua epistemic tolerance and vagueness qua borderline cases (when properly construed to exclude terms which are stipulated to give rise to borderline cases) are in fact conceptually equivalent dimensions of vagueness, contrary to what might initially be expected.
    It is also argued that the common confusion of tolerance and epistemic tolerance has skewed the vagueness debate in favour of indeterminist over epistemic conceptions of vagueness. Clearing up that confusion provides an indirect argument in favour of epistemicism.
  4. Finally, given the equation of vagueness with epistemic tolerance, it is shown that there must be radical higher-order vagueness, contrary to what many authors have argued.

Author’s Overview
  1. The broad aim of this paper is to give a rigorous characterisation of vagueness from a perspective which is as neutral as possible on matters both logical and philosophical. In so doing, the foundation is laid for what may be called a minimal theory of vagueness. One key merit of this theory is that it promises to ensure that the dialectic of the vagueness debate can at least begin at a mutually agreed point-this theory can at least ensure that we are all taking about the same thing from the outset in our inquiry into the nature and source of vagueness. In setting forth this minimal theory, three related dimensions of vagueness are distinguished: vagueness qua sorites-susceptibility, vagueness qua borderline cases, and vagueness qua tolerance. Hitherto, the relationship between these dimensions has remained somewhat unclear. The minimal theory of vagueness is equipped to remove much of that unclarity. Of perhaps greater interest, is that this theory entails that there must be radical higher-order vagueness-a subject about which there has been vigorous dispute. So while the axioms of this minimal theory are uncontroversial in the first instance, some of its theorems turn out to be decidedly controversial.
  2. As a preliminary to such investigations, it is necessary to inquire as to what we might reasonably expect or demand from a minimal theory of vagueness. Can this theory solve the sorites paradox? Can it isolate the source of linguistic vagueness? Can this theory successfully rehabilitate the so-called characteristic sentence approach to defining vagueness? These are the sorts of questions addressed in §2.
  3. In §3, it is found that vagueness defined as sorites-susceptibility offers the least controversial characterisation of vagueness. However, this characterisation proves to be too insubstantial for the promises of the minimal theory to be properly satisfied.
  4. On what is perhaps the most prevalent conception, vagueness is the phenomenon of borderline cases (Sorenson 1985; Williamson 1994; Sainsbury 1995; Tye 1995). Whether or not it is plausible to give an uncontroversial definition by reference to such a phenomenon is the key issue of §4 through to §6. A number of non-epistemic and epistemic accounts of what it is to be a borderline case are scrutinised. For the purpose of finding a neutral definition of vagueness, none of these proves entirely satisfactory. The particular bug-bear proves to be the possibility of terms which we can stipulate to give rise to borderline cases but which draw sharp and clearly identifiable divisions across their associated dimension of comparison. Prima facie, it is far more plausible to minimally define vagueness by reference to an epistemic notion of tolerance. Such a notion is intended to capture the thesis that vague terms draw no clear or known boundary across their range of signification and contrasts sharply with the semantic notion of tolerance given by Wright (1975, 1976.)
  5. In §6, the identification of vagueness with epistemic tolerance is exploited so as to give a rigorous but nonetheless neutral definition of 'is vague'. This definition allows us to distinguish vagueness from superficially similar but distinct phenomena such as semantic incompleteness.
  6. In §8, two proofs are given which show that vagueness qua borderline cases (when properly construed to exclude terms we are stipulated to give rise to borderline cases) and vagueness qua epistemic tolerance are in fact conceptually equivalent, contrary to what might initially be expected.
  7. In §9, it is argued that the common confusion of tolerance and epistemic tolerance has skewed the vagueness debate in favour of indeterminist over epistemic conceptions of vagueness. Clearing up that confusion provides an indirect argument in favour of epistemicism.
  8. Finally, in §10, given the equation of vagueness with epistemic tolerance, it is shown that there must be radical higher-order vagueness, contrary to what many authors (e.g. Burgess 1990, 1998; Wright 1987, 1992b; Koons 1994) have argued. Radical higher-order vagueness is a fact of life for everyone.

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  1. Blue: Text by me; © Theo Todman, 2018
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



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