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?
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?
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.