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
Received on Sun Apr 17 2005 - 21:40:31 PDT