This chapter examines Saul Kripke's mathematically rigorous, paradox-free treatment of truth for certain formal languages. Kripke adds hints about how his formal construction might model some features of natural language, but his hints steer a path between an inconsistency view and a vindicationist one. The chapter first compares Kripke's notion of truth with that of Alfred Tarski before discussing what Kripke calls the minimum fixed point, the first level where no new sentences get classified as true that were not already so classified at some earlier level. It also considers the ungroundedness of a sentence, along with the concepts of transfinite construction, revision theories, and axiomatic theories of truth.
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