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
