Jonathan Colvin wrote:
Well, I was elaborating on Bruno's statement that worlds ("maximal
consistent set of propositions") of a FS are not computable; that even given
infinite resources (ie. infinite time) it is not possible to generate a
"complete" world. This suggests to me that it is *not* the case that given
infinite time, eveything that can happen must happen. I must admit this is
not my area of expertise; but it seems to me that the only other option of
defining a world (identifying it with the FS itself) will, by Godel's
incompleteness theorem, necessitate that there exist unprovable true
propositions of world; the world will be incomplete, so again, not
everything that can happen will happen.
Godel's incompleteness theorem only applies in cases where the statements have a "meaning" in terms of our mathematical model of arithmetic (see my comments at http://www.escribe.com/science/theory/m4584.html ). If your statements are something like descriptions of the state of a cellular automaton, then I don't see them having any kind of external meaning in terms of describing arithmetical truths, so there's no sense in which there would be "unprovable but true" statements.
Jesse
