A New Approach to Vagueness

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Author: Kit Fine
Source: UnpublishedUnpublished, 2007
Keywords: vagueness, truth, logic [edit]

@article{fine2007a,
    author = "Fine, Kit",
    title = {A New Approach to Vagueness},
    journal = "Unpublished",
    year = "2007"}

Synopsis

In a talk given to the Arché and CSMN Graduate Conference on 4th November 2007, Kit Fine outlined a new approach to problem of vagueness involving a modified Kripkean intuitionist semantics and corresponding non-classical logic. This approach begins with a definition of vagueness as involving predicates to which no complete set of truth values can be assigned. Fine diagnoses the problem of vagueness, and the appeal of the sorites paradox, as due to the illegitimate use of a 'transcendent concept' of truth (supertruth), over and above ordinary truth, which renders classical reasoning invalid.

Fine's new approach rejects the idea that we should deny LEM for vague predicates in individual cases, thus avoiding the contradictions inherent in such an approach (e.g. Williamson's reductio argument) in favour of denying conjunctions of multiple instances of LEM for comparable statements; e.g. 'a is bald' and 'b is bald'. According to the modified semantics, ~((P ∨ ~P) & (Q ∨ ~Q)) may be true even though the two conjuncts are false. This amounts to a denial that there are individual (definite) cases of borderline vagueness in favour of statements about sets of sentences whose truth values may be undefined, in accordance with Fine's logical definition of vagueness.

This approach also addresses the issue of higher order vagueness since it cannot be indeterminate whether a given statement is indeterminate — I(I(P)) — but only whether there is indeterminacy within a set of statements — e.g. I(I(P), I(Q)) — making vagueness 'self-undermining', although not infinitely recursive.