On 24 Aug 2009, at 18:58, Brent Meeker wrote:

>> There is no other definition of computation.
>> Quantum computation are Turing emulable, and beyond this physicists
>> have not defined or addressed the notion of computation. The Church-
>> Turing definition is very large. And the Church-Turing thesis is the
>> thesis which defines computation by Church Lambda Calculus, or Turing
>> machine, etc.
> The theory of computation with real numbers, i.e. geometry,
> differential equations, etc. is not so well defined but it is enough
> to show that CT does not encompass everythiing.  In fact that is a
> criticism of Tegmark's idea on which we agree - it tries to include to
> much.

CT is usually used for extending the notion of computation on diverse  
objects. It does not criticize the role of CT for digital  
combinatorial processes or computations.
Tegmark takes the whole of math, and is unclear between the difference  
between epistemology and ontology. The difference between the frog's  
and bird's view is more a difference of scaling than a difference  
between sharable objectivity and unsharable subjectivity I would say.

>> But you see Brent, here you confirm that materialist are religious in
>> the way they try to explain, or explain away the mind body problem. I
>> can imagine that your consciousness supervene on something
>> uncomputable in the universe. But we have not find anything
>> uncomputable in the universe, except the quantum indeterminacy, but
>> this is the kind of uncomputability predicted by the comp theory (and
>> AUDA suggested it is exactly the uncomputable aspect of the universe
>> predicted by comp).
> How do you know we haven't found anything uncomputable?  What would it
> look like?

If comp is true, the observation of something uncomputable has to be a  
purely empirical guess, or be derived some a theory (like QM+comp, or  
comp alone).

> Physics proceeds all the time assuming real numbers.  Even
> the idea of quantum multiverses arises from assuming that the
> probability measures are real numbers.  I think it can be done with
> rational numbers, but that is not the worked out theory.

Comp entails that the first person self-multiplication has to be  
managed through the use of real numbers too.
Think just about the infinite iteration of self-duplication, it  
justify already the use of a gaussian like e^(-x^2).
Comp entails that "real life" occurs on the border between the  
computable and the uncomputable, and that most things when observed  
are uncomputable, not enumerable, infinite, etc. (cf the white  
rabbits). The ontology is a tiny part of arithmetic, but the internal  
epistemology, the first person plenitude, is bigger than Cantor  

>> But thanks for that move, it makes me realize that "matter-of-the-
>> gaps" could be used to provide some genuine way to characterize a  
>> "God-
>> of-the-gaps" use of matter for explaining the mind-body problem away.
>> Primitive matter is a speculation which satisfies the need of
>> physicalism, but I don't know any other function it could have.
> It's not so much physicalism but rather explaining why *this* happens
> and *that* doesn't.  I'm not convinced by the Born rule has been
> justified in spite of many attempts to derive it from simpler axioms.

Perhaps. I do think that Gleason theorem provides the main explanation  
in the quantum physical (or physicalist) realm.
Everett, or even Paulette FĂ©vrier 20 years before, provide another big  
part of the explanation.
Comp is far well behind on this point: no doubt. But the  
incompleteness theorem, and the intensional variant of self-reference,  
provides structure where we did not suspect it before. It saves comp  
from an apparent easy refutation.
We already know that the "physics of universal machine" is non trivial.

>  I hope that your "argument" may provide such a justification - in
> which case I will be impressed and become much less dubious of AR.

AUDA provides the needed mathematical theology. It is far less  
advanced than physics, for matter, but much more advanced with respect  
of explaining where person and consciousness come from. And that's the  
main goal.

I am not sure if you know that AR is just the acceptation of the use  
of classical logic in elementary arithmetic. I will illustrate this  
when I will explain Church thesis, which is meaningless without AR,  
but I have to prove Cantor theorem before. Cantor theorem is based on  
a far more stronger form of mathematical realism. As such it is not  
used in comp, but Cantor theorem prepares well to Kleene theorem,  
which can be seen as an "arithmetical-realist-only" reformulation of  
Cantor theorem.



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