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.
Saul Kripke proposes the following scenario:
Jones: “The majority of what Nixon says about Watergate is false.”
Nixon: “Everything Jones says about Watergate is true.”
Suppose that, besides his statement about Jones, the statements Nixon has made about Watergate split evenly between true and false. Also grant that Jones has never said anything else about Watergate. We’re left with a slightly more complicated version of the familiar Liar situation: if Nixon’s statement is true, Jones’s is true, and if Jones’s is true, then Nixon’s is false; if Nixon’s statement is false, then Jones’s is false, and if Jones’s is false, then Nixon’s is true. The truth values of the statements made by Jones and Nixon seem to really be contradictory.
This scenario, even if unlikely and rather contrived, is obviously possible. And there’s clearly nothing meaningless about Jones’s or Nixon’s statements. Tell Jones or Nixon that what they’re saying is gibberish, and they could very easily sit you down and explain precisely what they meant when they said what they said.
“Yields falsehood when preceded by its quotation” yields falsehood when preceded by its quotation.
Can you believe that people get paid to come up with this stuff? Like, a lot of money.
Anyway. Why does Quine’s extra convoluted version matter? Let’s recall the argument that wants to call the Liar meaningless. The subject of the Liar is referred to via an indexical: the word “this.” If the Liar has a subject, so the argument goes, then we should be able to specify what “this” refers to. It refers to “This sentence is false.” But that also has an indexical. When we specify that indexical, we’re led to another indexical, and so on. The subject-specification hunt never ends.
The reason Quine’s paradox matters is that it’s a version of the familiar Liar, but where the subject is not pointed to by an indexical. The subject – “Yields falsehood when preceded by its quotation” – is right there in the sentence. Note also that unlike the Liar’s subject, the subject of Quine’s sentence is not itself a sentence. It’s just a collection of words. This means that there’s no need to go hunting for a subject within it. It’s just a regular old concrete subject, like “the dog” – it’s not supposed to be meaningful on its own. The sentence it is a subject of, however, is perfectly meaningful.
So, even if we accept the argument for the Liar being meaningless, that argument doesn’t apply to Quine’s paradox. And Quine’s paradox is obviously just another form of the Liar. This means that the move to call the Liar meaningless isn’t only ad-hoc and implausible – it also doesn’t do the job of actually solving all versions of the paradox.