Dialetheism:Vagueness

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Vagueness

Andrew ( @andrewjrad on twitter ) makes the point that this site doesn't mention vagueness. This page is here to address that lacuna.

In particular, the Stanford Encyclopaedia of Philosophy has this to say:

" (3) Borderline cases of vague predicates. With the exception of the so-called epistemicist solutions, the main approaches to vagueness (such as the ones based on many-valued logics, or supervaluations) require some under-determinacy of reference, and/or the rejection of Bivalence: if an adolescent, m, is a borderline case of adultness, A, then A(m) may turn out to have an intermediate truth value between truth and falsity, or no truth value at all. But it may be conjectured that a borderline object like m, instead of satisfying neither a vague predicate nor its negation, satisfies them both: an adolescent both is and is not an adult. Given the obvious dualities between the LEM and the Law of Bivalence on the one side, and (respectively, syntactic and semantic formulations of) the LNC on the other, it is not too difficult to envisage a ‘sub-valuational’ semantic approach, dual to the supervaluation strategy. Sub-valuational paraconsistent semantics have been proposed by Hyde, 1997, and Varzi, 1997. Other ‘glutty’ approaches to vagueness have recently been proposed by Colyvan, 2009, Weber, 2010a, Priest, 2010, and Ripley, 2012a. To be sure, it is an open option to assume that the inconsistencies due to vague predicates and borderline objects are, as a matter of fact, only de dicto, due to merely semantic under- and over- determination of ordinary language. But if the aforementioned phenomena have a de re reading, then actually inconsistent objects are admitted, together with vague objects. And this spreads inconsistency all over the empirical world: if borderline cases can be inconsistent, inconsistent objects are more or less everywhere, given how pervasive the phenomenon of vagueness notoriously is: adolescents, borderline bald men, etc. It is fair to say, though, that there is a certain schism in the dialetheic community on the issue whether vagueness ought to be given a dialetheic treatment: JC Beall has argued against the approach in Ch. 5 of Beall, 2009, and in Beall (forthcoming). " - Stanford Encyclopaedia of Philosophy

A Dielethic treatment of vagueness

The argument for including a discussion of vagueness is that, if there is ontic vagueness, if there is actually metaphysical indeterminacy, this might be a form of dialetheism. That is, an object may have type X, or it may have type Y, but it may also, because of vagueness, have a type somewhere between X and Y. In this case you could have it that:

if X, ~Y if Y, ~X but ∃ O ∈ {entic objects} s.t. O(X) ⋀ O(Y)

This does look like a dielethia because O(Y) -> ~O(X) so we'd have O(X) ⋀ ~O(X).

This is persuasive, to some extent, but, in a sorites paradox, there are a range of objects, x with property X, for which this is true - they may both be viewed as a heap, and as not a heap.

Taking the step from that range of views to the metaphysical statement that there are a range of x that are 'actually' in this paradoxical state, may be a step too far. The situation seems more a consequence of linguistics than of metaphysics.

If you have blue and green, then something bluish-geen would be in this category, but if we call that range of colours, 'marine', the paradox disappears.