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/
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