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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Received on Sat Apr 07 2007 - 18:48:36 PDT