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The mathematician and mathematical physicist Alain Connes has expressed in many occasions that he is a Platonist and he thinks that mathematics itself does exist in the same level (or even in a "stronger" level) as physical reality.

This is very similar to Max Tegmark's hypothesis of the Mathematical Universe (MUH), which basically says that every mathematically possible structure exists as its own universe.

Since both approaches are almost identical, I was wondering if Connes has ever commented anything on Tegmark's views. I cannot find anything on the Internet, but since both ways of thinking are almost the same, it seems strange to me that Connes has never said anything about it. Does anyone know if Connes has commented anything on this?

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  • Suggested links and tag.
    – J D
    Dec 13, 2021 at 17:22
  • MUH is incoherent, and it's really obvious based on mathematical logic. Connes' views seem to be too vague rather than incoherent. You should read up about reverse mathematics. Mathematicians generally do not naturally come up with mathematical constructions beyond a certain proof-theoretic strength, roughly around bounded ZFC, but there is no evidence for platonic reality of mathematical entities beyond ATR0, which is in turn way stronger than what is needed for real-world applications of mathematics (roughly ACA).
    – user21820
    Dec 14, 2021 at 19:24
  • @user21820 Been I while since I read it, but MUH is based on the assertion nothing beyond mathematical objects are needed to describe/predict/experience all empirical facts. I would not call that mathematical logic unless you accept the MUH. A "person" is making that metaphysical judgment; it is not a proof arrived at after mathematical axioms and deductions. Now given MUH, a "person" is just a mathematical object, which would make everything mathematical logic. But you deny the MUH, so you can't have your cake and eat it too; MUH is not mathematical logic to the non-MUH'er.
    – J Kusin
    Dec 14, 2021 at 20:28
  • @JKusin: Sorry, but your comment is as incoherent as MUH. There is simply no such thing as a coherent definition of "mathematical object" or "mathematical structure" that does not depend on a fixed foundational system.
    – user21820
    Dec 14, 2021 at 20:40

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I've thought of Tegmark as a neo-Pythagorean but I've recently come to reject that that characterisation. Both Platonism and Pythagoreanism and their variants are quite clear that the cosmos has a moral dimension. This is conspicuously lacking in Tegmark's theory.

He's more akin to mathematical Platonism which as a severely truncated form of Platonism is not Platonism at all. Hence it's better described as mathematical realism. Mazur, a mathematician, has described Conne's as a definite mathematical realist. Although I haven't come across any remarks of Conne's on Tegmark's theories, I think it's fair to say that Tegmark is also a mathematical realist on the basis of his theories.

Of course this says nothing about how Connes views Tegmark's theories. There is nothing that I can see on the net. As the book has been well publicised and that we know Conne's is interested in mathematical physics, I think the safe answer would be - not very much.

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