Full Idea
Supervaluation seems to inherit the power of classical logic, ...but also enables it to be extended. It makes room for a new operator 'definitely' to express supertruth in the object-language.
Gist of Idea
Supervaluation adds a 'definitely' operator to classical logic
Source
Timothy Williamson (Vagueness [1994], 5.3)
Book Reference
Williamson,Timothy: 'Vagueness' [Routledge 1996], p.149
A Reaction
Once you mention higher-order vagueness you can see a regress looming over the horizon. 'He is definitely definitely definitely bald'. [p.164 he says 'definitely' has no analysis, and is an uninteresting primitive]