Hello,
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.
Regards,
Quentin
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 <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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>
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Received on Sun Apr 08 2007 - 17:48:47 PDT