Hi Eric:
At 09:46 PM 11/15/2004, you wrote:
On Tue, 2004-11-16 at 10:13, Hal Ruhl wrote: > To respond to comments on consistency. > > I see no reason why components of the system need to be internally > consistent. And I have indicated that the All is not internally > consistent. Generally speaking evolving Somethings are also not > consistent. Actually evolving Somethings are a sequence of Somethings in > that each new "quantum" of information incorporated into a Something makes > it a new system. > > Arithmetic and any system that incorporates it can not prove its [their] > own consistency.
Not to be able to prove its consistency doesn't mean it's inconsistent, does it?
Going a little further Turing showed that there is in general no decision procedure. Godel's proof is a corollary of this. So if arithmetic ever became complete it would have to be inconsistent. The All contains all arithmetics including the complete and inconsistent one. So the All is internally inconsistent.
Also if you did add an axiom to arithmetic how could this be done so it was known to be consistent with the previous axioms?
I'm thinking about an inconsistent system as one that can prove both a statement and its negation.
That is right
What exactly do you mean by your All? All systems of representations, or All that 'exists'? If the latter, what does it mean 'to exist'? If the former, do these systems necessarily have a one-to-one correspondence to something that 'exists', and in what sense?
As I said in an earlier post the information within the All may have a separate "physical existence".
I left open for now what that might be. I do believe this to be in any way essential as part of the description of "worlds". The All since it contains all information sums to no net information. Concepts would be packets of associated information. All this points to the first of the above which is a position I have preferred for awhile.
I just can't grasp what you could possibly mean by an inconsistent All. And therefore I can't see what use this model could possibly have, and how can it possibly represent Anything. :)
See above. If our world is indeed subject to true noise as I state in my model it would be a sequence of new systems - how does "prove" which is a step by step "process" within a given system have any relevance?
Hal
