“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. …
In Part 1, I considered the argument that solves the Liar by calling it meaningless. I concluded that, ultimately, whether we consider the sentence meaningful has to be stipulated – we are not compelled one way or the other. I also claimed that, all things considered, the argument for stipulating it to be meaningful is significantly stronger.
In this second part, I’ll consider three additional reasons to call the Liar meaningful: the meaningfulness of other self-referential statements, Kripke’s Nixon/Jones example, and Quine’s paradox.
“This sentence has five words.”
Is that sentence true or false? Of course it’s true! Just count.
“This sentence is in Japanese.” How about that sentence? False.
Any argument that says that the Liar’s self-reference renders it meaningless will say of these sentences that they are meaningless as well. There is no way around it. This is a bullet that anyone arguing for meaningless based on self-reference must bite.
It’s possible to bite it by saying that everyday language is not perfect, and so makes it seem like these sentences are meaningful, even though they are not. But a rule that calls self-reference meaningless isn’t given to us, nor is it logically necessary – as noted in part 1, it has to be stipulated. Why stipulate such a rule? There’s only one good reason: to avoid the Liar paradox. This is incredibly ad-hoc, especially when it also means calling sentences meaningless that seem to be not only meaningful, but whose truth value seems to be obvious.…