Hi Dave, welcome to the list!
At 0:31 -0400 3/09/2002, [EMAIL PROTECTED] wrote:
>In other words, does Cantor's Absolute Infinity not only have
>Mathematical Existence; but, does it also have Physical Existence in terms of
>the total number of universes?
Cantor referred himself to his absolute infinity in term of inconsistency.
The whole of mathematics cannot be defined mathematically, unless you
work with esoteric theories like the (totally unknown) Church set theory
or with version of NF (Quine *New Foundation*).
This is the major problem for Tegmark-like approaches, the whole of
math is more a mythical object than a well defined notion.
Some brilliant ideas here are not excluded of course ..., but even the
category of all categories will failed to describe all possible
coherent ideas by machines ...
Physical existence is still less well defined. At least I have shown
that the notion of physical existence has just no meaning whatsoever when
you postulate the mechanist hypothesis in the cognitive science (see my URL
for more, including posts to this list).
In a nutshell I would say that natural numbers exists and no more
(like Pythagoreans!) ... all the rest are layers of internal dreams with
different degrees of sharability (coherence) between number-theoretical
defined machine. Dreams = computational histories averaged by the machines.
The hard thing is to take account of the fact that those machine
are embedded in those histories. I use modal logic and self-reference
to handle that difficulty.
My approach is closer to Schmidhuber than Tegmark for the ontology,
and closer to Tegmark than Schmidhuber for the epistemology (the
taking into account of the embedding).