Juergen Schmidhuber wrote: > Which are the logically possible universes? Max Tegmark mentioned > a somewhat vaguely defined set of "self-consistent mathematical > structures'' implying provability of some sort. The postings of Bruno > Marchal and George Levy and Hal Ruhl also focus on what's provable > and what's not. > Is provability really relevant? Philosophers and physicists find > it sexy for its Goedelian limits. But what does this have to do with > the set of possible universes?
Many people think that if a formal statement is neither provable nor refutable, then it should be considered neither true, nor false. But it is not that way that we - normally - use the term "true". Somebody wrote: "Suppose that I have a steel safe that nobody knows the combination to. If I tell you that the safe contains 100 dollars - and it really does contain 100 dollars - then I'm telling the truth, whether or not anyone can prove it. And if it doesn't contain 100 dollars, then I'm telling a falsehood, whether or not anyone can prove it." (A multi-valued logics can deal with statements that are either definitely true or definitely false, but whose actual truth value may, or may not, be known, or even be knowable.). - scerir