Re: Tegmark's TOE & Cantor's Absolute Infinity

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Tue, 24 Sep 2002 11:05:19 +0200

At 21:36 -0400 21/09/2002, Vikee1.domain.name.hidden wrote:
>For those of you who are familiar with Max Tegmark's TOE, could someone tell
>me whether Georg Cantor's " Absolute Infinity, Absolute Maximum or Absolute
>Infinite Collections" represent "mathematical structures" and, therefore have
>"physical existence".


Hi Dave,

Cantor was aware that his "absolute infinity" was strictly speaking
inconsistent. I also deduce from letters Cantor wrote to bishops that
his absolute infinity was some sort of un-nameable "god". The class of all
sets (or of all mathematical structures) can play that role in axiomatic
set theory, but keep in mind that in those context the class of all set is
not a set, nor is the class of all mathematical structure a mathematical
structure. Formalization of this "impossibility" has lead to the "reflection
principle", the fact that if you find a nameable property of such universal
class, then you get a set (a mathematical structure) having that
property, and thus approximating the universal class in your universe
(= model of set theory).
Please read Rudy Rucker "infinity and the mind" which is the best and quasi
unique popular explanation of the reflection principle.

Now "physical existence" is another matter. With the comp hyp in the
cognitive science, physical existence is mathematical existence seen
from inside arithmetics. I agree with Tim and Hal Finney that mathematical
existence is more, and different, from the existence of formal description
of mathematical object. For example, arithmetical truth cannot be unified
in a sound and complete theory, and if comp is true, arithmetical truth
escape all possible consistent set theories even with very large cardinal
axioms. The "seen from inside", that is the 1-person/3-person" distinction
is the key ingredient missed by Schmidhuber and Tegmark (although Tegmark
is apparantly aware of the distinction in his interpretation of QM).
See also Rossler's papers or Svozil's one, for works by physicist who are
aware of that distinction (under the labels exo/endo-physics).

Bruno
Received on Tue Sep 24 2002 - 02:08:38 PDT