[**Note: All vagueness posts are archived HERE.] **

I've been reading J. Robert G. Williams' excellent 2008 *Philosophy Compas* (763-88) piece, "Ontic Vagueness and Metaphysical Indeterminacy" and a strange thought occurred to me. Here is the infamous Evans/Salmon argument against the metaphysical indeterminacy of identity. Let "Ind" stand for the usual "it is indeterminate whether" upside down triangle, "L" stand for the lambda, and "#" be the absurdity constant. Then, when fully expressed in a natural deduction system, the argument is:

- Ind(a = b) assumption
- Lx[Ind(x = b)]a 1, lambda abstraction
- ~Ind(b = b) premise
- | a = b assumptio for ~ introduction
- | | Lx[Ind(x = b)]b assumption for ~ introduction
- | | Ind(b = b) 5, lambda cancellation
- | | # 3,6 ~ elimination
- | ~Lx[Ind(x = b)]b 5-7 ~ introduction
- | Lx[Ind(x = b)]b 2.4 = elimination
- | # 8,9 ~ elimnation
- ~(a = b) 4-10 ~ introduction

According to Williams, Evans just sort of assumed the absurdity of affirming that it is indeterminate whether a equals b while simultaneously denying that a equals b. Modulo classical logic, this would be an instance of the more general policy that for any P, it is absurd to affirm P and that it is indeterminate whether not P.

I think certain views of vagueness might actually motivate seeing the Evansian tension as Moorean. In an old paper by Diana Raffman (I forget what it is, I think she's since changed her view), I remember her talking about the phenomenology of color sorities series. As you go up the, for example, orange to red series you never perceive a patch as being indeterminate. Rather, there is a point where your perception kind of makes a jump. Weirdly, when you do that, then the stuff just prior to that now looks red.

Why not say that the patchs that can look red or orange at a given time are in reality both red and orange (glut semantics)? The patches that are both will be, for example, orange yet indeterminately orange (alternately not red yet indeterminately red). But, given the Raffman phenomena, you are never in a position to perceive this. So there is at least a canonical context (when you are looking at the patch) where it would be absurd to affirm P and that it is indeterminate whether not P. The color phenomenology always forces it to seem that way.

This doesn't answer the whole problem, especially with respect to cases of metaphysical indeterminacy that don't involve sorites series, such as the indeterminate future. Consider that the Evans/Salmon argument can be turned into an explicit contradiction if you accept that there are cases where it is determinate that it is indeterminate that a given identity holds. Of course, as far as color phenomenology goes, there won't be such cases. But in cases such as the indeterminate future, there are classes of the principle.

Still, it's an interesting thought.

[Note:

*One of my better papers is how Moore's Paradox yields a notion of Moorean Validity that is a challenge to Heyting Semantics. The solution to the problem still seems to me to be on the right track. Joe Bob says check it out.

**In the paper cited above I motivate a proof theoretic restriction that stops this kind of inference (which initially seems reasonable on Heyting Semantics). The coolest thing about the paper is that once the restriction is in place, Berkeley's master argument and Davidson's argument about the impossibility of an untranslatable language are shown to be invalid.]