At 17:15 03/12/04 -0500, Hal Ruhl wrote:
>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/
Received on Mon Dec 06 2004 - 08:17:43 PST