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.


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

It's a language game.

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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