Series: Penn State Logic Seminar Date: Tuesday, September 30, 2003 Time: 2:30 - 3:45 PM Place: 324 Sackett Building Speaker: Dale Jacquette, Penn State, Philosophy Title: Denying the Liar Abstract: The liar paradox as an informal semantic diagonalization has impressed philosophers and mathematicians as a challenge to the bivalence of propositional logic. A sentence that declares its own falsehood as a semantic self-non-application that appears to be true if and only if it is false has served as the model for similar kinds of paradoxes in the form of Grelling's heterology paradox, Russell's paradox in set theory with unrestricted descriptive comprehension, and even G"odel's incompleteness theorems. Efforts to solve or resolve the liar have produced Tarski's ascending hierarchy of object and infinitely iterated metalanguages, Kripke's transfinitely ramified theory of truth value gaps, and Hartry Field's variations on Kripke's proposal, among other interesting reactions. I identify and formalize three requirements for the liar paradox in the bivalence of classical logic, the Tarskian deflationary or disquotational truth convention, and the definability of the liar sentence, and argue that while the first liar horn goes through, beginning with the assumption that the liar sentence is true and proving that in that case it is false, the second horn, from the assumption that the liar sentence is false, fails. I diagnose the failure of the second liar paradox dilemma horn as resulting from the fact the the conditional needed to prove the truth of the liar from the assumption of its falsehood is contradicted by the three requirements that have generally been supposed to be sufficient to generate the liar. If the reasoning is correct, then there is no liar paradox to be solved.