Residual puzzle: so then you're view is that 'This sentence is false' (call this sentence The Liar) is not false, but has no truth value. So you think the Liar is not false. So it's false to say that it's false. But what the Liar says *is* that it is false, so it's false after all. Where did this reasoning go wrong?
This sentence is false has no truth value. Thus, while it's false to say that what the liar says is false, it's also not true. It's sord've like the statement go over there--it's not propositional.
Yes, I understand that's your position: the Liar sentence has no truth value. But what I'm doing in my comment is trying to put pressure on that, or to highlight some unfinished business.
Namely, this seems puzzling: If I stand "outside" and say 'The Liar sentence is false', then what I've said -- given your view -- is simply false: the Liar isn't false (on your view).
But it seems that the Liar itself *says the same thing*, i.e. that it's false.
Thus, I feel that solutions like yours (which I've also been attracted to) face a puzzle here: how can there be two sentences which say the same thing, yet one is truth-valueless while the other is false?
But if you're right that the Liar sentence lacks a truth value, then it's simply not the case that it's false. And so if we say that it *is* false, it looks as though we've said something false about it. But you can't go along with that, and as far as I can tell you can't explain why it's not OK to go along with that.
Right, and that takes us back to the original puzzle. How can that be, if the Liar itself says the same thing and is not false?
To be clear, I'm not arguing that your position is wrong -- only that it does not constitute a fully satisfying solution to the paradox. That's what I've been trying to get you to see -- or perhaps 'feel' is the better term here.
Alternative Solution: Every statement of fact contains an implicit "It is true that" so the statement "The Sky is Blue" is equal to the phrase "It is true that the Sky is blue" and the phrase "It is false that the Sky is Blue" is equal to the phrase "It is true that it is false that the Sky is blue".
So we can say that the phrase "This sentence is false", as a sentence making an assertion of fact, is equal to "It is true that this sentence is false" - or alternatively "This sentence is true and false", which is obviously false.
That’s very good actually. If you know any mathematicians they could make this a formal proof.
Residual puzzle: so then you're view is that 'This sentence is false' (call this sentence The Liar) is not false, but has no truth value. So you think the Liar is not false. So it's false to say that it's false. But what the Liar says *is* that it is false, so it's false after all. Where did this reasoning go wrong?
This sentence is false has no truth value. Thus, while it's false to say that what the liar says is false, it's also not true. It's sord've like the statement go over there--it's not propositional.
Yes, I understand that's your position: the Liar sentence has no truth value. But what I'm doing in my comment is trying to put pressure on that, or to highlight some unfinished business.
Namely, this seems puzzling: If I stand "outside" and say 'The Liar sentence is false', then what I've said -- given your view -- is simply false: the Liar isn't false (on your view).
But it seems that the Liar itself *says the same thing*, i.e. that it's false.
Thus, I feel that solutions like yours (which I've also been attracted to) face a puzzle here: how can there be two sentences which say the same thing, yet one is truth-valueless while the other is false?
Saying the liar sentence is false would lack a truth value.
But if you're right that the Liar sentence lacks a truth value, then it's simply not the case that it's false. And so if we say that it *is* false, it looks as though we've said something false about it. But you can't go along with that, and as far as I can tell you can't explain why it's not OK to go along with that.
Or no, I guess the sentence the liar sentence is false would be false.
Right, and that takes us back to the original puzzle. How can that be, if the Liar itself says the same thing and is not false?
To be clear, I'm not arguing that your position is wrong -- only that it does not constitute a fully satisfying solution to the paradox. That's what I've been trying to get you to see -- or perhaps 'feel' is the better term here.
Alternative Solution: Every statement of fact contains an implicit "It is true that" so the statement "The Sky is Blue" is equal to the phrase "It is true that the Sky is blue" and the phrase "It is false that the Sky is Blue" is equal to the phrase "It is true that it is false that the Sky is blue".
So we can say that the phrase "This sentence is false", as a sentence making an assertion of fact, is equal to "It is true that this sentence is false" - or alternatively "This sentence is true and false", which is obviously false.
It is true that this sentence is false is not the same as this sentence is true and false.