On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <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).

>> 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.


> 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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