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Things which are true but not provable aren't paradoxes, they're simply unprovable.
by JulianWasTaken 4y ago
Things which are true but not provable aren't paradoxes, they're simply unprovable.
- Maursault 4y agoThis is a straw man. Truth values of paradoxes can not be determined, only postulated. It is a paradox because if it were proven true it would be false, and vice versa. In precisely the same way, "this phrase is false," is also a paradox, and whether or not the truth value can be determined (it can not) is not relevant to whether it is a paradox.
- JulianWasTaken 4y agoYes, truth values of paradoxes cannot be determined, but it's you who called it a paradox. On its face, it isn't a paradox. If we're being pedantic, which your initial response struck me as, there are again true statements with no proof, and this isn't a paradox, it's Gödel's first incompleteness theorem (which is specifically different from the liar's paradox you mentioned, precisely in the difference between what is true and what is provable).