>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.
>
Jesse: >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.
I was asking the question in the context of Tegmark's UE (by which all and
only structures that exist mathematically exist physically), and whether it
has relevance to the existence of all possible things. Frankly I'm not sure
that Godel is relevant in that context; but then I'm not sure that it's
irrelevant either. In this context statements like the descriptions of the
states of cellular automata *can* be seen as describing arithmetical truths.
No?
Jonathan Colvin
Received on Mon Apr 18 2005 - 03:08:12 PDT