At 21:36 -0400 21/09/2002, [EMAIL PROTECTED] 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