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TheOtherDave 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.
On your view, is there such a thing as a Nature against which models can be tested and which arbitrates among them?
Not mathematical models... These can be motivated by experiment, but they are not bound to make accurate predictions. If that's what you were asking...
Mathematical theories and constructs aren't bound by nature...but models? Models are there to model something, surely?