On 3 Apr, 20:08, Brent Meeker <[EMAIL PROTECTED]> wrote:
> Bruno Marchal wrote:

> That brings up an issue which has troubled me.  Why arithmetic?

It's widely agreed on. Otherwise there would e problems about the
existence of those platonic objects which can only be
defined with certain, disputable axioms, such as the AoC.

> 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".

Tell that to an intuitionist!

> 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
> >http://iridia.ulb.ac.be/~marchal/

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