These days I am revising this paper, once again :-(! There I argue against the so-called ‘supervaluationist’ solution to the problem of the many, which is often the one favored by fellow defenders of the view of vagueness as semantic indecision.
In a nutshell, I claim that the feature of precisifications that such a solution requires—selecting just one of the many candidate-mountains in the vicinity of paradigmatic mountain Kilimanjaro—render them inadmissible. In my paper I focus on the penumbral truth that if something is a paradigmatic mountain, and something else is very similar to the former in that which is required for something to be a mountain, then the latter is also a mountain. One other main difficulty, emphasized by McGee 1998, is that such precisifications fail to preserve clear cases of application of the predicate, in that there is no entity that is determinately a mountain—at least, on standard ways of characterizing what it is for something to satisfy a 'determinately'-involving matrix.
In Williams 2006, Robbie claims that, in virtue of nothing determinately satisfying ‘is a mountain,’ the solution undermines the explanation offered by defenders of the view of vagueness as semantic indecision such as Keefe 2000 of the persuasiveness that the (false) sorites premise certainly has. According to her,
“Our belief that there is no true instance of the quantification gets confused with a belief that the quantified statement is not true. … The confusion … is a confusion of scope, according to whether the truth predicate appears inside or outside the existential quantifier” (Keefe 2000, 185).
Insofar as I can see, however, the difference in scope in truth- (or determinate-) involving existential statements appealed to here is compatible with nothing determinately satisfying ‘is a mountain’—disturbing as the latter might be for other reasons, of course.