Re: Platonism

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 12/09/04

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    Date: Thu, 09 Dec 2004 01:23:05 GMT

    Lester Zick wrote:
    > On Wed, 08 Dec 2004 19:48:55 GMT, patty <pattyNO@SPAMicyberspace.net>
    > in comp.ai.philosophy wrote:
    >
    >
    >>Lester Zick wrote:
    >>
    >>>On Wed, 08 Dec 2004 18:25:34 GMT, patty <pattyNO@SPAMicyberspace.net>
    >>>in comp.ai.philosophy wrote:
    >>>
    >>>
    >>>
    >>>>stephen@nomail.com wrote:
    >>>>
    >>>>
    >>>>
    >>>>>In sci.math patty <pattyNO@spamicyberspace.net> wrote:
    >>>>>: I think this is an interesting observation and one that i have
    >>>>>: independently come to. It turns out that there is no way to represent a
    >>>>>: set physically without ordering it; but we can represent it in whatever
    >>>>>: medium and then ignore the order.
    >>>>>
    >>>>>Below is a representation of a set of numbers
    >>>>>
    >>>>> 11 9 5
    >>>>> 2 28
    >>>>> 13 19 18
    >>>>>17
    >>>>> 3 10 29
    >>>>> 7
    >>>>>
    >>>>>What is the order?
    >>>>>
    >>>>
    >>>>There is a two dimensional order represented by which character and line
    >>>>position of each number.
    >>>>
    >>>>
    >>>>
    >>>>>: But i have always felt that an
    >>>>>: ordered set is a more fundamental object than a set because of this
    >>>>>: property.
    >>>>>
    >>>>>: patty
    >>>>>
    >>>>>Given that an ordered set consists of both the elements and
    >>>>>an ordering it seems strange to claim that it is more fundamental
    >>>>>than a set that just consists of the elements.
    >>>>
    >>>>But isn't it more fundamental to you just because you are so used to
    >>>>thinking of it that way? I think the orderelessness of a set is a
    >>>>mentalism that you have learned. It is just beauty in your eyes and the
    >>>>eyes of other mathematicians. Any objective procedure that actually
    >>>>operates on a set will operate in some particular order on that set.
    >>>>
    >>>>
    >>>>
    >>>>>People seem quite comfortable with representing information
    >>>>>as unordered sets. If you take a typical educated U.S. citizen
    >>>>>and ask them if X is one of the 50 states in the U.S.
    >>>>>they will answer quickly and correctly for any X. Ask someone
    >>>>>to list all 50 states and it is a different matter.
    >>>>
    >>>>Random access into a set does not exclude the fact that the set is
    >>>>represented as ordered.
    >>>
    >>>
    >>>I'm really impressed, patty. All of a sudden you begin to talk sense,
    >>>like someone just hit the ON switch.
    >>>
    >>>Regards - Lester
    >>
    >>Not at all, i still regard you as a linguistic pervert.
    >
    >
    > Good. I was afraid you might have become mentally competent.
    >
    >
    >> Just because we
    >>saw the same thing, is not a sign of a change over here. Actually that
    >>was something that i had an agenda to say in any case, you just gave me
    >>the opportunity to say it in context here. I had ~discovered~ it many
    >>years ago.
    >
    >
    > Yeah, and I'm sure you were just keeping it secret til the second
    > coming.
    >
    > Regards - Lester

    Well it's not really that profound. To a mathematician an ordered set
    has membership and ordering. One properties is more fundamental than
    two properties. But if you come from the bias of what can be
    represented in some physical medium, then the ordered set is more
    fundamental. I can well understand why a mathematician would reject
    that perspective.

    patty

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