On 3 Apr, 20:08, Brent Meeker <meeke....domain.name.hidden> 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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Received on Sat Apr 07 2007 - 12:57:42 PDT