I have gone back to Tegmark's paper, which is discussed informally
at http://www.hep.upenn.edu/~max/toe.html and linked from
http://arXiv.org/abs/gr-qc/9704009.

I see that Russell is right, and that Tegmark does identify mathematical
structures with formal systems.  His chart at the first link above shows
"Formal Systems" as the foundation for all mathematical structures.
And the discussion in his paper is entirely in terms of formal systems
and their properties.  He does not seem to consider the implications if
any of Godel's theorem.

I still think it is an interesting question whether this is the only
possible perspective, or whether one could meaningfully think of an
ensemble theory built on mathematical structures considered in a more
intuitionist and Platonic model, where they have existence that is more
fundamental than what we capture in our axioms.  Even if this is not
what Tegmark had in mind, it is an alternative ensemble theory that is
worth considering.

Hal Finney

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