Abstract
A position that has been called ‘classical indeterminism’ has recently been developed in order to model vagueness: this approach appeals to an object-language ‘determinately’ operator, the semantics of which are defined in such a way as to preserve the principle of bivalence. I suggest that a prominent argument against this strategy, which I call the Field–Williamson argument, fails. The classical indeterminist position in its general form was anticipated by the Aristotelian commentators in their discussions of Aristotle’s famous ‘sea battle’ passage concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds.
Highlights
An approach to the phenomenon of vagueness in natural language that Hartry Field has called ‘classical indeterminism’ (2008, p. 151) posits a objectlanguage operator, which I symbolize as ‘Δ’, meaning ‘definitely’ or ‘determinately’.1 This operator conforms to an analogue of the weak modal logic KT: that is, we maintain analogues of the meta-rule of necessitation, namely
By contrast, according to the classical indeterminists’ strategy for dealing with vagueness, supertruth is identified with determinate truth, not with truth simpliciter; in consequence classical logic and classical semantics can both be fully preserved
Classical indeterminists may continue to maintain the law of excluded middle and the principle of bivalence, so that a vague statement is either true or false, and determinately so; but one cannot ‘divide’, as the Aristotelian commentators put it, and say that it is either determinately true or determinately false
Summary
An approach to the phenomenon of vagueness in natural language that Hartry Field has called ‘classical indeterminism’ (2008, p. 151) posits a (perhaps tacit) objectlanguage operator, which I symbolize as ‘Δ’, meaning ‘definitely’ or ‘determinately’ (these adverbs here being taken to be synonymous, likewise with ‘indefinitely’ and ‘indeterminately’). This operator conforms to an analogue of the weak modal logic KT: that is, we maintain analogues of the meta-rule of necessitation, namely. He raised problems for it, and abandoned it for a non-classical strategy; Williamson advances similar arguments against classical indeterminism.12 Both Williamson and (the later) Field think that, if ⌜⊨ A ∨ ~ A⌝ holds—so that, given the analogue of necessitation, ⌜⊨ Δ(A ∨ ~ A)⌝ holds, but not, in general, ⌜⊨ ΔA ∨ Δ ~ A⌝—it ought to be reasonable in a vague case, and notwithstanding the failure of ⌜⊨ ΔA ∨ Δ ~ A⌝, to speculate which of ⌜A⌝ or ⌜ ~ A⌝ is true, seeing that one of them is true, and so to wonder which of ⌜A⌝ and ⌜ ~ A⌝ an omniscient (or a sufficiently superior) being would believe. See here esp. Wright (1994, 2003, pp. 87, 90, 2007, pp. 424–425), McGee and McLaughlin (1998, pp. 232–233, 2004, pp. 123–124), Schiffer (1999), Keefe (2000, Ch. 3)
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