On 7 Apr, 18:47, "John M" <[EMAIL PROTECTED]> 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...
What makes mathematics true is not the point. Bruno is claiming that
numbers exist, and to make
his claim persuasive he focusses on the least contentious numbers.
> 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?)
Then numbers don't exist, they are fictions too.
> 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.
Brunoism relies on Platonism as well as computationalism.
Computationalism can be as true as tue can be, but so long as
Platonism is false, so long as a computer needs a physical instantion,
Brunoism does not follow. Brunoism doesn't follow from physicalism,
it is in oppostion to it.
> 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.
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