For much of the 20th century, the Liar paradox has stood as an elusive and stubborn puzzle. The main solutions to it have significant drawbacks, such as blocking meaningful cases of self-reference or abandoning bivalence (the principle that all propositions are either true or false and not both). In recent decades, Stephen Read has rediscovered and defended a solution by the medieval thinker Thomas Bradwardine. If Bradwardine’s argument is correct, the liar sentence is simply false. When properly examined, its falsity does not imply its truth. Bradwardine shows this with a clever argument that does not require us to abandon classical logic or block self-reference. It does rely on a controversial principle, “closure”: any statement implicitly says (or means) everything that follows from what it says. Arguably, whether the Bradwardine solution succeeds or fails to conclusively solve the Liar depends on whether one accepts closure. In this interview, Stephen Read runs through Bradwardine’s argument in some detail, then defends it against a few objections.
Bradwardine’s argument is rather subtle and abstract and can be hard to follow verbally. Here’s a short written version of Bradwardine’s argument, with minimum symbolism, that shows each step and notes where logical principles are invoked.
Be sure to listen to the first half of this interview, where Stephen explains the Liar and its significance and solutions in the 20th century.
Next week: Jason Lee Byas: Against Criminal Justice
Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.…