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by perl4ever
1790 days ago
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>"This proposition is false." What about "this proposition is true"? Does it have a truth value? If "this proposition is true" is true, then it's true. But if "this proposition is true" is false, then it's false. It's self consistent whether it's true or false, but there's no way to determine if it is true or false. I've been wondering what the formal name is for this kind of statement; surely it's not a paradox. Searching for "the opposite of a paradox" is apparently not the right query. I feel like there's something questionable going on with the word "is" in either statement. |
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I think it'll probably end up being neither true nor false too in most 'nice' systems (since general rules that could be used to prove or disprove it tend to set off things like Curry's paradox[0]), but unlike the other one it's (I think) dependent on the details of how you're defining things.
0: https://en.wikipedia.org/wiki/Curry's_paradox