math (was Re: Van Till's Ultimate Gap)

From: George Murphy (
Date: Thu Sep 04 2003 - 08:26:04 EDT

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    It seems to me that some of the discussion about whether math is created or
    discovered &c misses the forest for the trees, especially as the questions have to do
    with the relevance of math for descriptions of the physical world. Einstein, e.g.,
    starting from a few basic pieces of knowledge about the world, writes down a highly
    non-trivial system of equations which are supposed to describe certain important aspects
    of the world. These equations, while constrained somewhat by the data then available
    (1915), are highly _under_determined_ by that data. For the next ~90 years then it's
    found that all relevant observations that go beyond those of 1915 are in agreement with
    Einstein's equations.
            I am unable to see this as anything other than the ability of a human mind to
    _discover_ an approximation to a pattern that exists in the world independently of human
    minds. It certainly is not (as the positivists imagined) simply a matter of organizing
    observational data because the data didn't exist when the equations were first written.
     & certainly Einstin's mind didn't _create_ the regularities which were later found.
            Note that I said discover an "approximation." To make the sort of claim that I
    have made by no means requires that one believe the Einstein equations (or whatever) to
    be the ultimate truth about the world. & in fact we may never discover the true
    ultimate math pattern of the world. But we can get better & better approximations to

    George L. Murphy

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