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I am wondering whether Gödel believe ain the existence of his rotating universe since he is a mathematical Platonist. I am also wondering in what entities believe mathematical platonists. For example: do they believe only in "basic" mathematical entities like sets, numbers etc.? Or also in mathematical theories in their entirety? To clarify, if I have Gödel's rotating universe and I am a mathematical platonist, am I supposed to believe that the rotating universe exists since it is mathematical? Or I am supposed to believe only in the existence of all the singular entities that constitute the rotating universe (e.g. numbers) but not in the theory in its entirety? I am sure that there are a lot of mistakes in my reasoning and I am sorry for that but I do not know almost anything about that, I heed some help.

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    I'd have to do more research for an answer, but my understanding is that Godel was using the existence of closed timelike curves (causal loops) in a rotating universe to argue against the reality of "time" in the sense of presentism or McTaggart's A series. And I seem to remember he argued that even if our universe is not rotating, the fact that our universe is governed by laws of physics which allow for possible universes that disallow A-series time is enough to rule out A-series time.
    – Hypnosifl
    Nov 6 '20 at 19:32
  • If you merely mean mathematical existence, then yes, he believed in it platonistically, like in any other structure that one can build from set theory. But that's not really what the phrase "existence of rotating universe" suggests. I doubt he definitively believed that closed timelike curves actually occur in our physical universe, it is still an open question, and an empirical one.
    – Conifold
    Nov 6 '20 at 21:52
  • BTW, on my last comment about how he thought the laws of physics allowing rotating universes was sufficient to rule out A-series time, I found a reference on this: the book Godel Meets Einstein: Time Travel in the Godel Universe, starting p. 44, which says Godel was making a modal argument where "the mere mathematical possibility of an R-universe, in which time would be ideal, shows that in our actual universe time is ideal" (some more discussion in the preface on p. ix and later response to counter-arguments starting p. 96)
    – Hypnosifl
    Nov 6 '20 at 22:12
  • Thanks to both of you. Very clarifying replies. Thus, Am I right to believe that Gödel definitely believe in the existence of his rotating universe in the "mathematical dimension"? Gödel talks about the fact that we discover matheamtical entities through intuition, is it right to think that, according to his line of reasoning he "discovered" the rotating universe that is nothing but a mathematical reality? Thanks again!
    – W.V.O.
    Nov 7 '20 at 11:20
  • Even if general relativity proved to be wrong as a theory of physics in our universe, a rotating universe obeying GR's equations would still exist in the mathematical dimension, but as I understand his argument, that wouldn't be enough for Godel to conclude that time is ideal in our world. His argument seems to have specifically turned on the idea that the correct laws of physics for describing our real universe also have a solution involving a rotating universe with closed timelike curves--that solution may only exist in the math dimensions but the laws governing it are the real ones.
    – Hypnosifl
    Nov 7 '20 at 15:45

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