Full Idea
The principle of bivalence (that every statement is either true or false) has been rejected for vague languages. To reject bivalence is to reject classical logic or semantics.
Gist of Idea
When bivalence is rejected because of vagueness, we lose classical logic
Source
Timothy Williamson (Vagueness [1994], Intro)
Book Reference
Williamson,Timothy: 'Vagueness' [Routledge 1996], p.2
A Reaction
His example is specifying a moment when Rembrandt became 'old'. This is the number one reason why the problem of vagueness is seen as important. Is the rejection of classical logic a loss of our grip on the world?