On 05 Jan 2010, at 23:44, Brent Meeker wrote:

Nick Prince wrote:
OOps sorry I sent an empty post by accident.

I agree with you here.  But I am new to this field so I am uncertain
about so many things.  However, I don't understand why it is that  a
UD would know how to generate these law like sequences of states. It
may well generate all possible programs that generate all possible
universes (with different values for the physical constants say -
maybe even different laws) but I wonder why our conciousness defines
itself by "selecting" only those "consistent" extension among all the
states available that obey a certain set of  laws of physics.

I thought that a TOE should explain the laws of physics and Bruno
states in his SANE paper

" Conclusion: Physics is given by a measure on the consistent
computational histories, or
maximal consistent extensions as seen from some first person point of
view.

But consistent in what sense? We can't say "consistent with the laws of physics" because that's what we're trying to explain.

Laws of physics,
in particular, should be inferable from the true verifiable ‘‘atomic
sentences’’. Those are the
verifiable arithmetical sentences.

I understand true arithmetical sentences, but I'm not sure what 'verifiable' means? Does it mean computable, or provable? What's an atomic sentence? Is it just a finite statement, like "17 is prime"; so it excludes infinite statements like Goldbach's conjecture?


p is verifiable means that if p is true then p is provable.

 "p -> Bp" is true for those sentences p.

All statements of the shape "It exist a machine x which will access state y" are of that nature. We may run all machines, and never access state y, so that we remain ignorant, in case the statement is false, but if the statement is true we will know it, soon or later (in principle, or in platonia).

Typically, the Sigma_1 sentences. Those can be put in the shape ExP(x), with P decidable. If "ExP(x)' is true, we can find it by testing P(0), P(1), P(2) ... up to the P(k) witnessing the truth of "ExP(x)". If "ExP(x)" is false, we may never know, and this procedure will not decide the sentence.

The DU, implemented in arithmetic, flows through all true Sigma_1 sentences, but also on all proofs of the false one, this change the internal measure of the true one. Enough for a successful arithmetical renormalization? Open problem.

Bruno


http://iridia.ulb.ac.be/~marchal/



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