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This reminds me of the highly complex explanations given for the observed movement of planets, stars, etc in the Ptolemaic system of the solar system. Elaborate and painstakingly correct within its own axioms. Problem was the basic concept was in error. An entire system, rationally self consistent and logically built upon a fundamental misconception. It endured for over a thousand years.
Are you a smart guy? If so, do yourself, and perhaps also maths, a favor, and just think about that for a while. Or would you rather just think we have got our fundamental conceptual understanding about math correct in the first place? After all, counting things..., separating objects, either physical or abstract, on some arbitrary parameters, that's just got to be right, doesn't it? Cant go wrong if we start from there.
