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Sam TH scripsit: > > An example of what *might* be a Goedel sentence: nobody knows for sure. > > If it is unprovable, it has to be true, because if it were false, > > there'd be a counterexample, which would mean it wasn't unprovable. > > Still, lots of people thought Fermat's Last Theorem was unprovable too. > > That's only true in those cases where the idea of a counterexample > makes sense. For example, the continuum hypothesis [1], that the size > of the set of real numbers is the smallest number larger than the size > of the integers, is undecideable. Yet Cohen, who proved the > undecidability, believes the hypothesis to be false. Quite so. But Goldbach, if it is going to be false, has to be false by reason of some specific even number that is not expressible as the sum of two primes. It can't be the case that it is false even though no counterexample exists! -- John Cowan cowan@c... One art/there is/no less/no more/All things/to do/with sparks/galore --Douglas Hofstadter
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