On 2/17/2012 12:00 AM, meekerdb wrote:
On 2/16/2012 7:27 PM, Stephen P. King wrote:
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:
How can Brouwer's fixed point theorem be applied computers of REAs,
they don't form a manifold.
Hi Brent,
This is where my inability to express this idea in English puts me
in a very unpleasant situation. Honestly, you might as well count as
just wrong. I'll accept that. But I will bet that I'm right. :-) I just
don't know how to explain my idea any better at the moment. I will
predict one thing, there will be a paper published within the year that
will cover this idea by someone with the right skills. I will just be
happy to have come to understand it on my own.
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.
That's the crux of the disagreement. Bruno says 2 exists because it's
the successor of the successor of zero. I think it exists as a
concept because we invented it, along with counting (c.f. "The Origin
of Reason" by William S. Cooper). But I'm willing to take it's
existence, along with the rest of arithmetic, as an hypothesis just to
see where it leads.
You do realize that this gives a definition of "existence" that is
very different from that that almost all philosophers use. That's OK,
Bruno is not a philosopher although he does pretend to be one very well. :-)
Onward!
Stephen
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