While Peter did not answer your question about AoC... AoC means, I think, 
Axiom of Choice see http://en.wikipedia.org/wiki/Axiom_of_choice .
The correct "sigle" (in french this is the word, don't know the correct term 
in english) is AC.


On Sunday 08 April 2007 00:47:41 John M wrote:
> IZ wrote:
> >"...arithmetic?
> It's widely agreed on...."<
> In my oppinion scientific argumentation is not a democratic vote.
> Scientists overwhelmingly agreed in the Flat Earth. THEN: science changed
> and the general vote went for heliocentrism. THEN...
> IZ continued:
> >"... Otherwise there would (b)e problems about the
> existence of those platonic objects which can only be
> defined with certain, disputable axioms, such as the AoC."<
> Axioms in my wording are fictions necessary to prove OUR theory. (They may
> be true?) (What is AoC?)
> IZ also refers to Brent's 'continua'. In my nat. sci. views a discontinuum
> is an abrupt change in CERTAIN data. Can be a 'is' or 'is not', but could
> be only an aspect in which WE find an abrupt change, while in other aspects
> there is continuum. Now 'what we call it' (abrupt or slow - even monotonous
> change) is scale-dependent, depends on the magnitude of our applied
> measuring system. Measure it in parsecs, all our terrestrial items are
> homogenous. Measure in nanometers, a 'glass' is a heterogenous system. I
> find the 'Planck' measure just a domain in human (physical?) aspects, not
> providing a bottom-size for nature. (I.e. for Our thinking only. )
>  As I explained the origination of the biochemicals certain (outside?)
> factors in the material 'mass' ('mess?) disproportionated certain
> components into diverse (localised) agglomerations and a concentration
> potential- difference arose between certain domains. Such "potential
> gradients" (in the still homogenous = continuous mass) acted as
> transport-barriers, turned into hypothetical (and later: veritable)
> 'membranes' for a discontinuum. From the material-transport view the same
> substrate became discontinuous. (Hence: cell-walls etc.) Otherwise it was
> considerable as a homogenous (continuous?) biomass.
> Similar 'domain'related' arguments can work in "human consciousness as
> originated from (Platonic?) math (numbers) - or vice versa. I appreciate
> Bruno's inadvertent "if we accept UD/comp" etc.etc. formula. Hard to beat,
> especially since so far there is NO successfully applicable (not even a
> dreamed-up) alternative developed sufficiently into a hopeful replacement
> for the many millennia evolved 'physical view' of our reductionist
> conventional science. Even the new ways start from there if not in
> veritable sci-fi.
> John M
>   ----- Original Message -----
>   From: 1Z
>   To: Everything List
>   Sent: Saturday, April 07, 2007 12:57 PM
>   Subject: Re: Speaking about "Mathematicalism"
>   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/
>   --
>   No virus found in this incoming message.
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> 9:30 PM

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