What is a Truth Value And How Many Are There?

摘要

Truth values are, properly understood, merely proxies for the various rela-tions that can hold between language and the world. Once truth values are understoodin this way, consideration of the Liar paradox and the revenge problem shows that ourlanguage is indefinitely extensible, as is the class of truth values that statements of ourlanguage can take - in short, there is a proper class of such truth values. As a result,important and unexpected connections emerge between the semantic paradoxes and theset-theoretic paradoxes.