Truth is a One-Player Game: A Defense of Monaletheism and Classical Logic

The Liar Paradox and related semantic antinomies seem to challenge our deepest intuitions about language, truth and logic. Many philosophers believe that to solve them, we must give up either classical logic, or the expressive resources of natural language, or even the “naïve theory of truth” (according to which "P" and “it is true that 'P'” always entail each other). A particularly extreme form of radical surgery is proposed by figures like Graham Priest, who argues for “dialetheism”—the position that some contradictions are actually true—on the basis of the paradoxes. While Priest’s willingness to dispense with the Law of Non-Contradiction may be unpopular in contemporary analytic philosophy, figures as significant as Saul Kripke and Hartry Field have argued that, in light of the paradoxes, we can only save Non-Contradiction at the expense of the Law of the Excluded Middle, abandoning classical logic in favor of a “paracomplete” alternative in which P and ~P can simultaneously fail to hold. I believe that we can do better than that, and I argue for a more conservative approach, which retains not only “monaletheism” (the orthodox position that no sentence, either in natural languages or other language, can have more than one truth-value at a time), but the full inferential resources of classical logic.