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?
Truth is a queen who wins all the wars without any army.
You can guess it by reading a newspaper. But you can better guess it
by reading two independent newspaper, and still better by reading three independent
newspapers, etc.
What is a sentence?
An informal sentence is a ordered set of words having hopefully some meaning.
A formal sentence is the same but with a decidable grammar, and sometimes a
mathematical notion of meaning in the form of a mathematical structure satisfying
the sentence. This can be find in any textbook in logic.
What is arithmetical?
A sentence is arithmetical, roughly, if it bears on (natural) numbers.
As Stephen Paul King asked: How is truth resolved for a given sentence?
It is resolved partially by proof.
Why the down select re descriptions vs the All.
I don't understand.
How is the set of such sentences known to be consistent?
It is never known to be consistent. We can just hope it is.
(Smullyan makes a different case for arithmetical truth, but this would be in contradiction
with the comp hyp).
To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ...
Right. This indeed follows from Goedel's incompleteness.
...and where did all that info come from and why allow any in a base level system for worlds?
Concerning just natural numbers this is a mystery. With comp it is necessarily mysterious.
Best regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
