Hi Hal,
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.
I don't have a theory. Just an argument showing that if we are machine then eventually physics is derivable from machine psychology/computer science.
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.
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.
I deduce this from many readings of Smullyan. But I think Smullyan is just afraid that people takes Godel's second incompleteness theorem as an argument showing that Peano Arithmetic cannot been known to be consistent. And I agree with Smullyan on that point. But with comp I cannot know my own consistency and I can only show (to myself) that IF I am consistent then Peano Arithmetic is consistent. Look at the "Forever Undecided" book (on the net or in the list archive).
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.
Not the theory, but the possible observers described by theory. This is just a consequence of comp: we "belongs' to an uncountable infinity of (infinite) computations. Cf our talk on the white rabbits. We don't need to inject randomness: a priori we have too much (first person) randomness. With comp it is the *lack* of randomness which is in need to be explained.
"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?
This is not relevant. See Jesse's post.
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?
But which theory? COMP ? COMP is mainly the hope that it is possible to survive some treatment in a hospital.
...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.
But then you should explain why we believe in natural numbers. (You did give plenty evidence that you believe in natural numbers).
Bruno
http://iridia.ulb.ac.be/~marchal/
