Solutions to the Liar: It’s Meaningless (Part 2)

M.C. Escher’s “Drawing Hands”

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.…

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Solutions to the Liar: It’s Meaningless (Part 1)

“Print Gallery” by M.C. Escher

If you’re interested in solutions to the Liar, I assume you know what it is, so I’ll be quick with the explanation. “This sentence is false” – is that sentence true or false? If it’s true, then it’s false, and if it’s false, then it’s true. Whoa!

The Liar is a serious problem for logicians and philosophers because it calls classical logic into question. The Liar does not go away unless we make some changes, either to the way that we refer to things, the way we understand truth, or to some laws of classical logic, such as the law of excluded middle or the law of non-contradiction.

There have been many proposed solutions to the problem, and I’ll be doing a survey of them. I’ll begin with the most tempting and popular solution: the argument that the Liar is (or should be considered) meaningless.

The solution comes in a few basic flavors, but they all hinge on the idea that the Liar is only a problem if it is in fact saying something. If it isn’t – in other words, if it doesn’t express a proposition (philosophy talk for “statement”) – then it’s just a bunch of words put together, like “mafpol govohav,” or “the dog.” In order for a sentence to be meaningful, it must have a subject – a thing it is about – and a predicate – something being said of that subject. The Liar, so the argument goes, has no subject.…

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