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.

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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 <[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. > Checked by AVG Free Edition. > Version: 7.5.446 / Virus Database: 268.18.26/750 - Release Date: 4/6/2007 > 9:30 PM > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---