Comparing Fixed-Point and Revision Theories of Truth

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. (Martin and Woodruff independently developed this semantics, but not to the same extent as Kripke.) Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay of the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the companion paper to this one.