• alcontali
    82
    Yet, mathematical physics is one of the most successful sciences. Your theory can't explain this success. On it, what mathematical physicists do is completely unjustifiable.Dfpolis

    Mathematical physics is still physics. It is not axiomatic. It will ultimately still be experimentally tested. The amount of mathematics used by physics does not change its fundamental nature. It certainly does not turn physics into mathematics. It just makes sure that it is incredibly consistent. It is its consistency that explains its success.

    The difference between physics and mathematics is not that one is about nature and the other notDfpolis

    That is exactly the difference.

    Math is about nature as quantifiableDfpolis

    Mathematics is not number theory. Most mathematical theorems are not about numbers or quantities.

    The reason for Russell's paradox is not some formal problem that requires a theory of types (though a theory of types avoids the problem). The reason for it is that there is nothing in reality from which we can abstract the concept of the set of all sets that do not include themselves, just as there is nothing in reality from which we can abstract the parallel postulate or the axiom of choice.Dfpolis

    You can represent a set by its membership functions and disregard what elements it contains. From there on, the paradox becomes a problem with these membership functions. The function will not manage to return a result, simply because it never stops running. That is how the problem appears when it is modeled in software. The way automated systems behave, is unrelated to physical-world problems that they would mirror, because they often don't, and in this case, they certainly don't.

    All you're doing is ruling out obvious nonsense, leaving open the possibility that all mathematics may be obscure nonsense,Dfpolis

    Only category theory is termed general abstract nonsense.

    In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, “abstract nonsense” may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself.

    Not all mathematics is abstract nonsense, but the very best stuff certainly is.
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