On 2/16/2012 7:09 PM, acw wrote:
Do you understand at all the stuff about material and idea monism that I
have mentioned previously? We are exploring the implications of a very
sophisticate form of Ideal Monism that I am very much interested in, as
it has, among other wonderful things, an unassailable proof that
material monism is WRONG. What I am trying to discuss is how this is a
good thing but the ontological theory as a whole that it is embedded in
has a problem that is being either a) misunderstood, b) ignored or both.
To be fair, I still have trouble understanding your objections to UDA
8/MGA, and this discussion has been going on for quite some time now,
maybe I'm just incapable of seeing the subtle distinction that you're
trying to draw. Bruno postulates arithmetic or combinators, but if you
want a different ontological foundation, you can formulate it and see
how it fits within COMP (in case you assume it) and how that changes
predictions and/or explanations.
Hi ACW,
My objection to UDA 8/MGA is that it assumes something that is is
deeply problematic. There is a difference between Computational
universality, in the sense of any given recursively enumerable algorithm
is universal if it does not depend for its functional properties on a
particular physical implementation of it, and the ideas that Recursively
Enumerable Algorithms (REA) have properties and "run" completely
independent of the possibility of implementation in physical hardware.
My proof is mathematical but may be very poorly explained because I
have a very hard time translating my thoughts into words and for this I
apologize. I am hoping that you can see past the words and "grok" the
meaning.
I am identifying the invariant aspect of a REA with a fixed point
in a manifold of transformations where the "points" that make up the
manifold represent the physical systems capable of implementing the REA
and then applying Brouwer's Fixed point theorem:
here is an example for Wiki.
In the plane <http://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem>
"Every continuous
<http://en.wikipedia.org/wiki/Continuous_function_%28topology%29>
function /f/ from a closed <http://en.wikipedia.org/wiki/Closed_set>
disk <http://en.wikipedia.org/wiki/Disk_%28mathematics%29> to itself
has at least one fixed point."
Think about this: Does the fixed point continue to exist if the
collection of points making up that closed disc or the continuous
transformations that are the functions where to vanish? Answer: No. The
same way a computation is no longer a computation in the sense of
universality when there is no "universe" for it.
The point is that unless it is possible for a physical system to
implement a REA, there is no such thing as an REA. So all the talk of
computations or whatever is taken as equivalent vanishes into
meaninglessness when and if we jump to the conclusion that USA/MGA
"proves" that the physical world is just a epiphenomenon of numbers.
That is the problem.
Onward!
Stephen
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