[Note: All vagueness posts are archived HERE.]
Peter Simons' 1998 "Does the Sun Exist? The Problem of Vague Objects" blows my mind. The technical trick to accommodate two fuzzy logical intuitions is brilliant. My student and sometimes co-writer* Joshua Heller (who actually understands the calculus way better than me) is probably going to do some cool stuff with it in his thesis. Here I'm interested in this argument:
A decided disadvantage to the supervaluatitonal theory concerns identity. For while the sun exists (since all candidates do) nothing is definitely identical with the sun: since there is more than one candidate, none of them is determinately it. Hence if for no candidate c is it determinately true (or false) that it fulfills the propositional function x = s, then it follows that the proposition s = s has no truth-value. Yet since all candidates fulfill the propositional function x = x it would seem that s = s is true after all. If the sun exists in some sense we want to say it is definitely itself in the same sense. The problem is symptomatic of the havoc wreaked in our conceptual scheme by vague objects (p. 4)
When I first read this, I just glossed it as the Evans/Salmon argument,** but it's clear I was mistaken. I think Simons is actually saying something interesting about de dicto versus de re identity claims. The claim that it is de dicto determinately true that there exists an object identical to x can be formalized in this manner:
De Dicto- △∃x(x = s)
You get the corresponding de re claim by putting the determinacy operator inside of the existential quantifier:
De Re- ∃x△(x = s)
The first says that it is determinately the case that something is identical to s, while the second says that something is such that it is determinately the case that it is identical to s. Supervaluational as well as Barnes type (see here and here) approaches (if they treat identity like other two place predicates) make the de dicto claim true while rendering the de re claim either false or lacking truth value. At every acceptable precise model something will be equal to s, which renders the de dicto true (note: in my reconfigured version of Barnes which saves her view from my and Jessica Wilson's criticisms, the de dicto identity claim can come out false). But the de re claim can fail to be true if there isn't something in the original model that is such that it is identical to s in every possible precisification of the original vague model.