On 3/5/2012 4:57 PM, Jason Resch wrote:


On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

        On 05.03.2012 18:29 meekerdb said the following:

            On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

                The experiment takes an operational approach to what Pi means.
                During the initial stage of the experiment mathematicians prove 
the
                existence of Pi.


            When mathematicians 'prove the existence' of something they are just
            showing that something which satisfies a certain definition can be
            inferred from a certain set of axioms. In your example the
            mathematicians may define Pi as the ratio of the circumference to 
the
            diameter of a circle in Euclidean geometry. But what does that mean
            if geometry is not Euclidean; and we know it's not since these
            mathematicians are in the gravitational field of the Earth.
            Mathematics is about abstract propositions. Whether they apply to
            reality is a separate question.

            Brent



        I agree that this assumption might not be the best one. I will think it 
over.

        However, I do not completely understand you. How the geometry of 
physical space
        in which mathematicians reside influences the definition of Pi? 
Mathematicians
        will consider just Euclidean geometry, that's it. In my view, whether 
the
        physical space Euclidean or not, does not influence the work of 
mathematicians.


    Exactly. Hence mathematics =/= reality.


This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).

The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality; but that was what the bunker thought experiment was intended to test. You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.

Brent




        In any case, the problem remains. What is mathematics under the 
assumption of
        physicalism? Do you have any idea?


    It's a language game.


This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. Mathematical truth transcends the symbol manipulation game defined by any set of axioms.

Jason

    Brent
    A physicist goes off to a conference. After a week his suit’s gotten soiled 
and
    crumpled, so he goes out to look for a dry cleaner. Walking down the main 
street of
    town, he comes upon a store with a lot of signs out front. One of them says 
“Dry
    Cleaning.” So he goes in with his dirty suit and asks when he can come back 
to pick
    it up. The mathematician who owns the shop replies, “I’m terribly sorry, 
but we
    don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign 
outside
    says ‘Dry Cleaning’!” “We do not do anything here,” replies the 
mathematician. “We
    only sell signs!”
    --- Alain Connes, in Changeux



        Evgenii


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