“This sentence is false”. Is that sentence true or false? If it’s true, then what it says must hold; but what it says is that it’s false, so it must be false. But if it’s false, then what it says must not hold; but what it says is that it’s false, so it must not be false. But if it’s not false, it must be true. So if the sentence is true, it is false, and if it is false, it is true. The sentence, therefore, seems to be both true and false, which seems absurd.
Philosopher and logician Stephen Read is one of the preeminent scholars on this “liar paradox”. He is known, in large part, for rediscovering and defending a long forgotten solution to the paradox first proposed by the medieval philosopher Thomas Bradwardine. In this first half of our conversation, Read covers the paradox’s rich and influential history. It was first discovered, in its full form, in the 4th century BCE by Eubulides (who also first set down the sorites paradox). It became a central problem in the 20th century via its association with Russell’s Paradox, a major problem in the foundations of mathematics. Later in the century, two thinkers – Alfred Tarski and Saul Kripke – proposed monumentally influential theories of language and truth motivated, largely, by the paradox. But even after their contributions, the consensus is that the paradox remains unsolved. Quite a few new solutions have been suggested in the decades since Kripke’s 1975 proposal. Among the more influential is Stephen Read’s revival of the Bradwardine solution, which will the subject of part 2 of this interview.
0:19 – Intro to Stephen Read
4:24 – What is the Liar Paradox?
6:33 – The Greeks on the Liar
11:06 – Frege, Cantor’s Paradox, and Russell’s Paradox
18:24 – Tarski’s solution
21:55 – Natural language, formal languages, semantics, and the T-schema
32:03 – Shortcomings of Tarski’s solution
36:12 – Kripke’s solution