On 05 Mar 2012, at 19:03, 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.


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.

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

What most mathematicians believe is that mathematics are the laws true in all physical universes. And physics is true in one physical universe. But with the mechanist hypothesis, we know better: the physical laws are invariant in all numbers' dreams, and physical universe are shared computations. This explains also (not directly) the non sharable truth, the contingent one, etc. The advantage is that we can explain both quanta and qualia, without postulating a physical, nor a mental realm, just by listening to the machine, and not taking them for zombie. It hurts our intuition, today, but science always do that, since its claim that the earth is not the center of reality. With comp we can even understand why science has to hurt machine's intuition.

So a physicalist has just to find non mechanist theory of mind, if we want the physical universe to be ontological (existing in some primary sense).



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