Tobriand said:
Well, if your theory is inconsistent, then it can trivially proove anything. So apply any inconsistent theory and anything will indeed be possible.
I'm a bit fuzzy on the details, but didn't Gödel prove that any mathemmatical/logical system that is sufficiently advanced to prove number theory, must by definition be inconsistent or incomplete?
So I guess that means anything is possible in any theory that is sufficiently advanced...
Fairly close but not quite, at least as I understand it. Gödel proved incompleteness for consistent, "sufficiently rich", recursively axiomatizable theories, yes. He also proved that no such theory will be able to prove it's own consistency (although as I understand it, some other theory may be able to).
But: that still requires that the theory be consistent. So there will still be things that you can't prove with such a consistent theory, because if it did prove them it would be inconsistent. I think.
Anyway, this is way OT - back on track: Changing the processor is unlikely at best (unless you live in a world with a contradiction
)!