Hi Bruno and Jesse:
At 10:23 AM 12/18/2004, you wrote:
At 21:48 17/12/04 -0500, Hal Ruhl wrote:
Can a kernel of information be self inconsistent? From Bruno's last post
I think it is possible to impose this idea on the All.
I'm afraid I said the contrary (unless I misunderstand what you are
pointing at through the expression "kernel of information"). If you agree
that a kernel of information is like a theory or any finitely describable
machine, then only such a thing can be said inconsistent.
At this point I have talked myself into the position that since the All is
absent information then we have no way to describe it as consistent or
inconsistent in the usual logic meaning that I understand. It may contain
self inconsistent kernels or pair wise inconsistent kernels but this seems
to sum to a neutral position.
Pair wise [or better group wise] inconsistent kernels would differ in the
truth value assigned to the same internal component but sum to a neutral
position to maintain the overall nature of the All. I am not saying they
exist but allow for it.
The "All", I put it on the semantical side, I don't see how that can be
made inconsistent in any interesting way. It is *our* attempts to manage
the "All" which can lead to our inconsistencies. In case we discover some
of those inconsistencies we better should backtrack. I think. No?
I now agree with this as above.
Next post:
At 11:28 AM 12/18/2004, you wrote:
At 20:39 17/12/04 -0800, Pete Carlton wrote:
As usual when I ask a question like this, if the answer is available in a
text on logic or elsewhere, please just tell me where to look.
..I'm also interested in the implicit use of time, or sequence, in many
of the ideas discussed here.
For instance you might say that some of your Somethings are 'bitstrings'
that could make up one of Bruno's or Jürgen's worlds/observers.
Remember that comp, as I present it, make "worlds" non computable. It is a
consequence of
of the self-duplicability, when distinguishing 1 and 3 person points of view.
Do you mind then a little more non computability re the third person point
of view as per my dynamic?
Part of our idea of a string is the convention that one element comes
first, then the second, then the third, et cetera.
However, the information that accounts for that convention is not
contained in the string itself. 'Taking' a Something as a bitstring
involves some degree of external convention.
Indeed, it needs a universal machine, and even an infinity of them. But
all that exists and describes by the set of (sigma1) true arithmetical
propositions. See Podniek's page
http://www.ltn.lv/~podnieks/gt.html
I may not have time left for yet another schooling but I intend to take a
much closer look at your material after I resolve my issues with residual
information and the origin of the dynamic which this thread might accomplish.
So my question is, what do you mean when you say "a universe that has a
sequence of successive states that follow a set of fixed rules?" What
could make one state "give rise" to the "next" state?Citing
"causality" just gives a name the problem; it doesn't explain it.
I completely agree with you. The primitive "causality" of the comp
platonist is just the
"implication" of classical propositionnal logic. Most of the time (sorry
for the pun) time of a computation can be described using no more than the
axioms of Peano Arithmetic, including especially the induction axioms:
that if P(0) is true and if for all x (P(x) ->P(x+1) ) then for all x we
have P(x).
(Witten B(0) & Ax(B(x)->B(Sx)) -> AxB(x) in
http://www.ltn.lv/~podnieks/gt3.html#BM3
(S x) is x + 1
As I said in another post I think the idea of one state giving rise to the
next creates issues with accumulating algorithmic complexity. However, a
sequence in which each state is independent of any other state could look
causal for long strings of states.
And I don't think introducing a Turing machine helps with this basic
problem, since in any automaton you have rules that say e.g. state X at
time T begets state Y at time T+1, again placing a convention of sequence
(time, here) external to the system itself.
But that "time" can be substituted by natural numbers, enumerating for
exemple the states of some universal machine (itself described in arithmetic).
This sounds like kernels to me.
This question doesn't engage with your schema head-on; it's more of a
side detour I've thought of asking about many times on the list; I
thought it might get explained at some point. Well, now I'm asking.
Now, if you ask where natural numbers comes from, that's a real mystery.
But then I can explain you why no Lobian Machine can solve that mystery,
and why, if we want to talk about all the natural numbers, we are obliged
to postulate them at the start.
My kernels would be describable by natural numbers so are they actually
natural numbers?
Next post:
At 11:45 AM 12/18/2004, you wrote:
At 03:31 18/12/04 -0
