the science of Linguistics uses truth-conditional semantics for natural languages. Since liar sentences can be formed in natural languages, then the linguist must provide a semantics for these sentences (on the assumption they are meaningful). But we cannot give such a semantics for such sentences, despite their being meaningful. — Kornelius
It seems grammatical, and its constituent terms are all meaningful. Intuitively, if I say "That sentence is false", referring to some other sentence P, then I know precisely what that means. If I say "This sentence contains five words" this is perfectly meaningful (and true). So the problem is not self-reference. So if the issue isn't grammar, the meaning of constituent terms or self-reference, why think the sentence isn't meaningful? — Kornelius
If you refer to some other sentence P, then there is the assumption that P can be either true, or false. For it to have that possibility, it must make a claim against reality. If you say, "That sentence is false," and "that" sentence is, "This sentence is false", its still just nonsense. — Philosophim
This sentence is false, does not make any sense. False in what way? — Philosophim
What is the mistake in this inference? — Kornelius
I was arguing without using a specific criterion of meaning. This is just to say that I was arguing by referencing speakers' intuitions and was anticipating with the other side may say to argue it is meaningless (i.e. ungrammatical, issue with self-reference). I think that (Li) is intuitively meaningful in this sense. Most competent speakers of English will not react to (Li) as they would to the sentence "the runner runs runningly run running". — Kornelius
We can say no to that one, even if we accept that there is a lot of nonsense around. — Kornelius
What you have here is in the form of a proof but of course it is not a proof because we're not talking about a formal system -- Tarski told us long ago that you just don't include predicates like '... is true' and '... is a proposition' in your language and you're fine. If you want them, they have to be in the next language up, the meta- to this object. What to do when it comes to natural languages -- there's the rub.
And while I sympathize with your approach, what happens with this sentence?
(L') 'This is not a proposition.'
If it's true, then it can't be true because it can't take a truth value. If it's false, then it can take a truth value and so assigning it "false" in all models is fine. So it looks like the predicate '... is a proposition' should be fine and L' is necessarily false. Cool.
But then what about this one?
(L'') 'This sentence is not true or is not a proposition.'
If it's true, it's either not true or it's not a proposition, so it's not a proposition, so it can't be true. If it's not true, it's true and a proposition.
This is the revenge paradox, and you could do the same thing with '... is meaningful' in my post above. In a sense, even formalizing truth the minimum amount that Scharp describes blocks you from formalizing other semantic predicates like '... is meaningful' or '... is a proposition' on pain of revenge. That would leave you with a formalized truth predicate you can't actually use in a formalized way. On the other hand, if you decide to give up on bivalence and roll the other semantic predicate you want into "truth", so you have three values, then you just get revenge immediately. This is the point Kornelius is making here.
The Liar always argues its way out of any argumentative box you try to put it in. To deal with it once and for all you have to give up on formalizing your semantics even a little, formalize it differently from the way we have so far (and there are always such proposals around, some of which are nice), or protect the old semantics from having to deal with it in some other way. (Whether this last is even an option is unclear, and it's the approach I was suggesting be explored, just for funsies.) — Srap Tasmaner
But there's no need for anything meta, right? — TheMadFool
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