Hi Bruno:
I assume your theory is intended to give the range of descriptions of worlds.
The All in my model contains - well - ALL so it includes systems to which Godel's theorem applies.
Your theory has problems for me.
What is truth? What is a sentence? What is arithmetical? As Stephen Paul King asked: How is truth resolved for a given sentence? Why the down select re descriptions vs the All. How is the set of such sentences known to be consistent?
To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - and where did all that info come from and why allow any in a base level system for worlds?
Yours
Hal
At 08:03 AM 12/3/2004, you wrote:
At 15:49 01/12/04 -0500, Hal Ruhl wrote:the All is internally inconsistent since it is complete.
I have a counter-example: take the following theory: All true arithmetical sentences. This is complete and yet consistent. Gödel's theorem applies only on axiomatizable (or mechanically generable) theory.
Bruno
http://iridia.ulb.ac.be/~marchal/
