(untitled) (Rivista Italiana di Filosofia Analitica Junior, 2016)
A new model for the language of arithmetic enhanced by the unary truth predicate T is presented, which extends Kripke’s minimal fixed point. The latter, it will be argued, does not adequately model the truth predicate, since no difference between Liars and Truth-tellers can be made. The new model, which contains an extension of Kripke’s in- terpretation of T along with a new 4-valued logic, overcomes this inadequacy. The gist of my proposal is that ’paradoxical’ ought to be treated as a truth value: Liar sentences, unlike Truth-teller sentences, do not simply lack a truth value. They do posses one: they are paradoxical.