In my questions about truth etc I was not really looking for a response but was rather trying to demonstrate the need for additional information in your theory. Your responses made my point I think. It is this issue I struggle with. I seek a TOE that has no net information. Though its components individually may have any amount of information the sum of all the information in all the components is no information.
At 08:13 AM 12/6/2004, you wrote:
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
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.
My "theory" almost [However see below] includes yours as a sub component. My only spin is that my theory necessarily has all dynamics in it subject to external random input. Why down select to just your theory and as a result add all that extra required info?
How is the set of such sentences known to be consistent?
It is never known to be consistent. We can just hope it is.
That is what I thought.
(Smullyan makes a different case for arithmetical truth, but this would be in contradiction
with the comp hyp).
Please give me a URL or reference for his work.
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.
Here you appear to me to be saying that your theory is indeed subject to random external input.
"Random" because we do not know if the set of sentences is consistent in its current state and if incomplete it can be added to. How can it be added to in a manner that is consistent with the existing state? .
So it would seem that your theory is indeed a sub component of my theory so as I said why down select and be burdened with all that net info?
...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.
Perhaps it is mysterious because it is unnecessary.