Journal of Philosophical Logic

, Volume 26, Issue 5, pp 477-500

First online:

A Theory of Truth that Prefers Falsehood

  • Melvin FittingAffiliated withDept. Mathematics and Computer Science, Lehman College (CUNY)Depts. Computer Science, Philosophy, Mathematics, Graduate Center (CUNY)

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We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to have many nice features. It is noted that a similar class of fixed points, preferring truth, can also be studied. The notion of intrinsic is shown to relativize to these two subclasses. The mathematical ideas presented here originated in investigations of so-called stable models in the semantics of logic programming.