In an earlier post, I discuss one good reason to reject the solution to the Liar paradox that says that it’s meaningless: it means calling some other sentences, like “This sentence is in Japanese” and “This sentence has five words” meaningless, though they seem to be obviously meaningful.
Anyone who defends this solution has to bite the bullet on these sentences. It’s a tough bullet to bite, but at first it doesn’t seem implausible. Maybe those sentences only seem to be meaningful, though they aren’t really.
I came across three sentences today that convince me that rejecting all self-referential sentences is, in fact, utterly ridiculous. I found them in Tim Urban’s newest amazing article on Elon Musks’ newest mind-blowing venture, Neuralink. (By the way: go read it. Now. Elon Musk is turning humanity into the Starchild from the end of 2001 and you’re reading about loopy sentences? Get out of here!)
Here are the three sentences:
That’s why we still communicate using technology Bok invented, it’s why I’m typing this sentence at about a 20th of the speed that I’m thinking it, and it’s why brain-related ailments still leave so many lives badly impaired or lost altogether.
Right now, your eyes are making a specific set of horizontal movements that allow you to read this sentence.
None of this stuff will take any effort or thought—we’ll all get very good at it and it’ll feel as automatic and subconscious as moving your eyes to read this sentence does to you now.
There’s a debate in the philosophy of language about the meaning of “meaning.”
Specifically, it is about whether meaning is “intensional” or “extensional.” Intensional meaning is meaning as we normally understand it. If I say “beaver,” the meaning of that word is some kind of concept or sense, perhaps based on meeting certain criteria. It’s some idea in my mind. Extensional meaning is meaning based solely on reference. Thinking extensionally, the meaning of “beaver” is the collection of all things that are beavers.
The debate gets complicated and technical. Traditionally, meaning has been thought to be intensional (“internalism”). Influential arguments by Saul Kripke and Hilary Putnam, among others, have tilted the balance, such that contemporary philosophers of language tend to lean more toward “externalism”: an extensional view of meaning. In this post, I’ll quickly summarize Putnam’s argument. In a subsequent post, I’ll spell out possible objections to it.
Imagine a Twin Earth on a galaxy far, far away. Twin Earth is exactly like Earth. Everything that has ever happened on Earth has also happened on Twin Earth, down to the last detail. There is only one exception: on Twin Earth, water isn’t made of H2O. It’s made of a totally different compound, called XYZ. XYZ looks, smells, and tastes exactly like H2O. Although the chemical makeups of XYZ and H2O are distinct, there is no difference that is discernible without sophisticated equipment.
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.…