Some philosophers, including C.S. Peirce, have argued that the Liar is demonstrably false and not true. The argument is based on the premise that all statements implicitly assert their own truth.
At first glance, this seems plausible. If I tell someone, “I did your laundry,” it carries with it an implied “it is true that I did your laundry.” This would seem to hold for all assertions. So, Peirce argues, the Liar is really saying: “It is true that this sentence is false,” which essentially comes down to saying “this sentence is true and false.” This is no longer a paradox, but a plain contradiction, and so false. It is like saying, “I’m a cat owner that doesn’t own a cat.” That’s not a mystery, just a lie. What makes the Liar a paradox is that what it says is, on the surface of it, coherent. If it just asserts a flat-out contradiction, then it poses no problem.
That a proposition automatically asserts its own truth is an interesting notion, and it is not easy to say whether it is accurate or not. Peirce later in life argued that it was incorrect. Luckily, it is not necessary to determine whether it is accurate or not because, even if it is, it does not resolve the Liar.
It is not true that, if a proposition automatically asserts its own truth, then the Liar really says: “It is true that this sentence is false.” In that sentence, “this sentence” refers to that whole sentence.…
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.…
Debates over what a term “is” are always amusing. They’re arguments over definitions. Definitions are stipulated. There’s nothing more to what a term “is” than what people agree to have it mean. I can say that the colloquial name for the species felis catus is “parlock,” and so long as you agree with me, we can have a perfectly meaningful conversation about parlock whiskers. Now imagine someone comes along and says to us, “what are you guys talking about? Parlocks don’t have whiskers, they have 88 black and white keys and are used to make music.” We wouldn’t get into a debate with this person; we would simply let them know that we use the word differently. If the person were to respond, “no, it’s not a matter of use. Parlocks are a type of musical instrument,” we’d quickly come to the conclusion that this person doesn’t understand how language works.
With this point in mind, a question: what do you think logic is?
I’m willing to bet your answer is something like “the fundamental laws governing the universe,” “the laws of existence,” or “the laws of rationality.”
None of those is right. You might want to argue with me. But if you do, you’ll be arguing that a word doesn’t mean what people have historically taken it to mean. You can use the sound and letter-combo “logic” in whatever way you like. But the word has a definition, a history, and a way that it is used by philosophers and logicians.…