That assumption is discharged at step 5 — Kornelius
Ugh, the Liar is such a pain. I was about to slap my forehead and say you're absolutely right, but are you? I'm genuinely not sure now. — Srap Tasmaner
(Not sure which of the logical equivalences I used are intuitionist-safe, but I so don't care at the moment.) — Srap Tasmaner
Consider the following sentence (Li): (Li) is not true. — Kornelius
Beliefs can be true, propositions can be true, mathematical equations can be true...sentences themselves can't. It's like saying "This horse is true", I don't know what it would even mean? — Isaac
I agree that a hammer has a purpose to us in the here and now because we exist. But if thinking beings cease to exist, wouldn't the hammer cease to have a purpose, and be just a collection of atoms, subject only to purely mechanical forces of nature? — Ash Abadear
Maybe something analogous to "hammers are for hammering", "this coin is worth two cents", "this note is a middle-C". — bongo fury
speech act theory, which seems to have continued an anti-abstract trend away from positing of (as entities) propositions to only sentences to only statements on particular occasions. (Yay, tokens! ... utterances, inscriptions.) — bongo fury
The token is about the things it is about. The proposition is an unnecessary abstraction? — bongo fury
Ah, sorry, I get you. Yes, the token is about itself — bongo fury
So the first question is this: why should we think that the concept of Truth is inconsistent? — Kornelius
But sentences aren't the sorts of things which can be true either. — Isaac
Beliefs can be true — Isaac
It's like saying "This horse is true", I don't know what it would even mean? — Isaac
but perhaps more importantly incompleteness — 3017amen
Hmmm, I'm not seeing the immediate connection between the Liar Paradox and the incompleteness theorems, but maybe there is an interesting one. Could you elaborate? — Kornelius
Sentences are precisely the things that can be true or false. The truth predicate applies to sentences (or propositions). It does not apply to any other object. — Kornelius
by predicating 'not true' of itself, the Liar claims to be a member of the class of sentences that are true or false, and perhaps it is this claim that turns out to be false, making the conjunction of its claims false. — Srap Tasmaner
I'm not seeing the immediate connection between the Liar Paradox and the incompleteness theorems — Kornelius
But sentences aren't the sorts of things which can be true either. Beliefs can be true, propositions can be true, mathematical equations can be true...sentences themselves can't. It's like saying "This horse is true", I don't know what it would even mean? — Isaac
There's no real state of affairs it's referring to. That's why I thought it was strange to give it a truth value. — Isaac
the immediate connection between the Liar Paradox and the incompleteness theorems — Kornelius
"The present King of France is bald" is another statement to which we cannot (easily) allocate a truth value. — Banno
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