Godel, Escher, Bach

So when you ask for unproveable truths, maybe you're not asking for an unproveable statement which is true in some interpreation, maybe you're asking for an unproveable statement which is true in the one true interpretation. That is, you want a statement which is true about the actual integers, the real out-in-the-world number system that we're trying to model, but unproveable. I don't know of any "naturally occurring" statements like that off the top of my head (though some people think that the Goldbach conjecture might be one).

Godel, Escher, Bach

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