Here’s a puzzle that Joan Weiner raises for supervaluationism from a recent PPQ paper. The basic idea is that supervaluationism is alleged to be in tension with perfectly acceptable scientific methodology. Here’s a quote from the paper that summarizes the point.

This much is certainly true; we want to know whether minoxidil (Rogaine) can prevent or reverse baldness; whether bald people are at increased risk of heart disease; whether thin people have a lower risk of heart disease; whether rich people are healthier than poor people. It may be an inalienable part of our understanding of the term ‘bald’ that anyone with no hairs growing out of her/his head is bald. But it is surely no part of our understanding that it is not possible to address the issue of whether or not minoxidil can prevent or reverse baldness. If it were, the text of Rogaine commericials would make no sense. There would be something wrong with an account of vagueness or the semantics of vague predicates that tells us that we cannot address questions about baldness via empirical research. (page. 356)

Weiner notes that this is not supposed to be an argument against supervaluationism. (page 371) A modest interpretation is that this is supposed to highlight a tension.

I’m going to formulate it as an argument against supervaluationism. I think it will be easier to discuss, and will do no injustice to Weiner’s presentation of the puzzle.

The Rogaine Argument Against Supervaluationism

1. If supervaluationism is true, then it is not possible to address the question of whether Rogaine can treat baldness via empirical research.
2. It is possible to address the question of whether Rogaine can treat baldness via empirical research.
3. Therefore, supervaluationism is not true.

Motivation for Premise (1)
There are three main camps as far as theories of vagueness go – epistemic, ontic, and semantic. Supervaluationism falls in the semantic camp. Consider Carl who has a few hairs on his head, but is far from a full head of hair. Now, consider the following sentence:

(A) Carl is bald.

The supervaluationist will hold that since “is bald” is vague it fails to pick out a determinate property. Strictly, speaking (A) does not have a truth value.

However, if sentences that refer to people like Carl that contain vague predicates like “is bald” lack determinate truth value, then the sorts of sentences that the scientists are in the business of confirming or disconfirming also lack truth values.

I’m not positive that this is the best way to reconstruct the argument. I’ll come back to this, but I thought it would be good to construct the argument first. Feel free to post thoughts.