Re: Platonism

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 11/29/04

  • Next message: Stephen Harris: "Re: Turing Machines and Physical Computation" 
    Date: 28 Nov 2004 17:20:42 -0800

    "robert j. kolker" <nowhere@nowhere.net> wrote in message news:<30rk4eF33qrs4U1@uni-berlin.de>...
    > Mitch Harris wrote:
    > >
    > >
    > > I disagree ... sort of. "People" is a bit too broad. I was under the
    > > impression that mathematicians are naively platonistic, in that, without
    > > giving too much thought to it, they consider all the things they work
    > > with as real as anything a mechanical engineer works with.
    >
    > The do while they are doing the work. The mathematician, in effect,
    > plays an "as if" game. And why not? How much motivation would there be
    > for breaking one's head on proving a theorem or discovering some new
    > relationship if the major premis is that it is all vaporware and
    > therefore meaningless.

    I don't think mathematics is meaningless. That's my trouble!

    If I thought it was meaningless or merely fiction, then I'd have no
    problem with it. I'd simply say this is no science, and deal with it.

    That would be escapism, and I don't endorse it.

    > A mathematician has to make his conceptual world
    > real (or seem real) to work in it, just an an artist (particulary and
    > abstract artist) has to believe his paint is -about- something.

    Well, the conceptual world is always real in some sense. First and
    foremost, it's in your head, as some picture, and that picture is just
    as real as a glass of water. The challenge is in identifying real in
    what sense. If you try to make some metaphysical talk, possibly
    containing nonsense, the basis for *all* mathematics, then you only
    call for trouble, when what you wanted was just making it more stable
    and clear. (That is why Poincare says this Platonist set theory is
    like theology. It seems that way to some others, too. Why, was
    Poincare an idiot?)

    If you know, on the other hand, just which concepts are nomologically
    possible, that is compatible with what we know about *physics*, then
    you would want to assign these guys a priority. These are things that
    will probably come up in physical sciences! So, they would make a nice
    foundation not only for making it possible to get paid, but also for
    science in general. The rest is more metaphysical, you should be
    really careful if you want to incorporate them into the foundations,
    they will draw a lot of fire from physicalists. (But oh, God-fearing
    monkeys will love it! It would justify their habit of talking
    nonsense!)

    That is, we should have a different attitude to these matters when we
    are talking about foundations. I don't suggest that if you are doing
    arithmetic, you should think about how set theory defines integers, or
    reals, or anything like that. I'm suggesting that you shouldn't. You
    should go on and calculate, because you can understand arithmetic on
    its own. And arithmetic surely has nothing to do with Cantor's theorem
    or any of the nonsense we are talking about. As a matter of fact, very
    few courses that I took even mentioned the cardinality of c, and I
    imagine the same thing goes for many other engineering disciplines.
    Although we were taught that it made Turing undecidability clearer, I
    now see that is not the case, there is a much better, a complete
    physicalist route to showing Turing undecidability, it's just that
    Cantor's theory is not completely incommensurable with the currently
    known reality! That is so, because there are proofs that are
    *fundamentally* simpler, e.g. in the assumptions they make about the
    world! Was this comprehensible, or should I explain it?

    > Every working mathematician is a closet Platonist, at least part of the
    > time. He has to be, in order to function.

    I disagree. One can do mathematics thinking it's something else. It's
    misled to suggest there is only one "sane" philosophy of mathematics.

    Regards, 

    --
Eray Ozkural
  • Next message: Stephen Harris: "Re: Turing Machines and Physical Computation"

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