Sider, Theodore & Braun, David [2003?] 'Vague, So Untrue', (in progress) , pp. .

According to an old and attractive view, vagueness must be eliminated before semantic notions — truth, implication, and so on — may be applied. This view was accepted by Frege, but is rarely defended nowadays. This recent neglect is unjustified: the thorny nest of problems surrounding vagueness is best untangled by accepting something like the old Fregean view. If semantic notions such as truth apply only to completely precise sentences, they do not apply to English or any other natural language. Thus, almost no English sentences are true (or false). We defend this seemingly nihilistic and self-refuting conclusion by arguing that it is usually harmless to ignore vagueness, since most of what we ordinarily say is in a sense approximately true. Our notion of approximate truth is, in essence, the notion of supertruth. But unlike supervaluationists, we do not identify supertruth with truth. Our theory is thus able to retain the virtues of supervaluationism while avoiding its vices. Moreover, though we do not attribute truth to English sentences, we do endorse bivalence for propositions, and we propose a theory of validity for English arguments that can agree with classical logic. Section one develops our theory, and section two compares it with supervaluationism.