paper-machine comments on The Dilemma: Science or Bayes? - Less Wrong
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Mathematicians do not test their models against Nature, the ultimate arbiter, only for self-consistency and validity within their own framework. Math will be the same in many different possible worlds. Of course, on their less-sane days they engage in philosophical debates about which axioms are right.
Nature sneaks in the back door from time to time. Math may be the same in different possible worlds, eventually, but the way it unfolds in history is going to change from world to world.