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.

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
    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. :-)



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