= 27d567bc2d48d9f40e9ccc20ea370b15)
The sentence/statement, "This sentence is false." has no content, no "aboutness", and thus can't participate in the true-false game. It's like a bishop on a chessboard. Why is this explanation wrong?
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The sentence/statement, "This sentence is false." has no content, no "aboutness", and thus can't participate in the true-false game. It's like a bishop on a chessboard. Why is this explanation wrong?
One can easily add some content and get something easily deducible to be true, yet which has clearly absurd implications. For example, "Either this sentence is false or you should give me all your money."
In more formal terms, if for every sentence Q there a sentence P such that P is equivalent to "either P is false or Q is true", then every Q is provable and the system is inconsistent.
So, what's the "content" in your example? I don't see that the example sentence has any content and so I don't see how it's relevant. If one were to say, "It is false." the natural response would be, "Huh?" or "What's the 'it'." There's nothing there that can be false. it's the same with the sentence, "This sentence is false." (Or, for that matter, "This sentence is true.") In order for something to be true or false, there need be something referred to.
I understand the stakes here and the ultimate conclusions that Godel came to with a related inquiry, but I can't get past the fact that there needs to be some content for the sentence to be admitted to the true or false game.