Bruno Marchal wrote:
> Hi Tim
> Le 03-avr.-07, à 12:03, Tim Boykett wrote (in part):
>>    One of the recurring ideas here is that of "mathematicalism" - an
>> idea
>> that I understand to be that we perceive things as physical that have
>> a certain
>> mathematical structure. One of the "everything" ideas that results is
>> that
>> only certain of the all-possible universes have the right stuff to be
>> perceivable, the right mathematical structure. We are in one such
>> universe,
>> and there are others.
> We can come back on this if you are really interested, but shortly: 
> once we assume the computationalist hypothesis (in the cognitive 
> science/theology), then the picture you give is most probably wrong. 
> Physics keeps a better role in the sense that physics emerges from the 
> "whole of arithmetic/mathematic". If you want, the physical world is 
> not a special mathematical world as seen from inside, but the physical 
> world somehow is the sum of all possible mathematical world where you 
> are.

That brings up an issue which has troubled me.  Why arithmetic?  Mathematical 
physics commonly uses continua.  Most speculate that this is an approximation 
to a more discrete structure at the Planck scale - but I don't believe there 
has ever been any rigorous proof that this kind of approximation can work.  

If we are to suppose that arithmetic "exists" because statements like "2+2=4" 
are true independent of the physical world, then it seems that calculus and 
analysis and geometry and topology should also "exist".

I initially thought the idea of using arithmetic as the foundational ur-stuff 
was attractive because I assumed that infinities could be avoided, i.e. 
allowing only "potential infinities" as in intuitionist mathematics.  But it 
appears that diagonalization arguments are essential to Bruno's program and 
those require realized infinities.

Brent Meeker

> "we" are not *in* a mathematical structure, we are distributed in an 
> infinity of mathematical structures, and physicality emerges from the 
> interference of them.
> Why a wavy interference? Open problem.
> Bruno
> > 

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