© 2011, James Finley
The Liar’s paradox stands as one of the longest standing and most discussed problems in philosophical history. In this paper, I first briefly set up the requirements on a language needed for that language to have the expressive power to construct a Liar sentence and show how the Liar sentence leads to the inconsistency and triviality of said language (if it is a logically classical language). I will then quickly set up and reject responses to the Liar that keep a classical logic as the model logic for natural language (which I will take to be English here), and argue for a dialetheist response to the Liar which endorses a three-valued, para-consistent logic. A dialetheist view claims that some pairs of sentences and the negation of that very same sentence are true, and a para-consistent logic is any logic in which ex contradictione quodlibet (The inference from P and ~P to anything) fails. Such a solution, I think, provides a viable route to defusing the Liar and keeping the expressive power of natural language.
Finley, James (2011) "Defending a Dialetheist Response to the Liar's Paradox," Res Cogitans: Vol. 2: Iss. 1, Article 16.