True, False, Etc.

Abstract

How many truth-values are there? Although this appears to be a very simple question, in my opinion it defies any very simple answer. Some of us have trouble making up our minds. Frege, who invented the term “truth-value”, declared that apart from Truth and Falsity “there are no further truth-values”; and yet Frege, who introduced many of us to semantic presuppositions, acknowledged truth-value gaps. Now how many values would that be? On one way of counting, True, False and Gap make three. To be sure it's not Frege's way of counting; but it's defensible. And we are left with the historical puzzle that Frege, who founded his semantics on the insistence that functions be everywhere defined—without any gaps—has come to be known as the author of the doctrine of semantic presuppositions and truth-value gaps.