[EMAIL PROTECTED] wrote: > > > On May 9, 6:08 am, Brent Meeker <[EMAIL PROTECTED]> wrote: >> [EMAIL PROTECTED] wrote: >> >>> On May 8, 4:22 pm, Brent Meeker <[EMAIL PROTECTED]> wrote: >>>> [EMAIL PROTECTED] wrote: >>>>> I have now given three clear-cut exmaples of a failure of >>>>> reductionism. (1) Infinite Sets >>>> But there is no infinite set of anything. >>> Says who? The point is that infinite sets appear to be >>> indispensible to our explanations of reality. >> All measurements yield finite numbers. Infinite sets and >> infinitesimals are mathematical conveniences that avoid having to >> worry about how small is small enough and how big is too big. Do >> you ever use infinite sets in computer science? > > Infinite sets and infinitesimals are a lot more than 'mathematical > conveniences'. There are precise logical theories for these things > (As I mentioned before - Cantor worked out the theory of infinite > sets, Robinson/Conway worked out the theory of infinitesimals).

Being logically consistent and/or precise doesn't imply existence. There are consistent theories in which there is a cardinality between the integers and the reals. But there are also consistent theories which deny such a cardinality. Does that mean some set exists with that cardinality or not? > A dislike of infinities characterized the early Greeks and pre 20th > century mathematicians. It hindered the development of mathematics. > (Read the excellent books by Rudy Rucker). I've read'em. I don't dislike them - as I said calculus is a lot easier than finite differences. > It's true that infinite sets are not used in comptuer science (which > is all about discrete/finite math) but beware of making assumptions > about reality purely on the basis of what can be measured ;) If it can't be measured even indirectly, like an infinitesimal, then whether it is kept in your model of reality is mostly a matter of convenience. > It has never been established that space is discrete (a point Stephen > Hawking just recently was at pains to get across). The supposed > discreteness of space seems to be yet another dogma currently popular > with computer scientists. True, but neither is it clear that spacetime must be a continuum. > >>> No, it's because reductionism is false. We invented the >>> concepts, but (as I mentioned in the previous post) for concepts >>> which are useful there has to be at least a *partial* match >>> between the information content of the concepts and the >>> information content of reality. Therefore we can infer general >>> things about reality from knowledge of this information content. >>> Where informational content of our useful concepts is not >>> computable, this tells us that there do exist physical things >>> which also mimic this uncomputability (and hence reductionism is >>> false). >> Or that our mapping is faulty and there a mathematical concepts >> that don't map to anything physical - which I think would be >> obvious since it has been shown that a mathematical system will >> always include undecidable propositions and such propositions or >> their negation can be added to create new, mutually inconsistent >> mathematical systems. >> > > I don't see that uncomputability or undecidability has any bearing on > the issue of the mapping between the physical and mathematical. In > the multiverse view, all possible mathematical systems could be > physically real. 'Physical' does not have to mean 'finite' or > 'computable'. But the multiverse view is anything but precise and logical. Where are the multiverses? What does it mean for them to be "physically real" - but undetectable and immeasurable? > > > >>> My reality theory is a three-level model of reality (as I >>> mentioned earlier in the thread). And QM is actually at the >>> *highest* level of explanation! This is the complete reverse of >>> how QM is conventinally thought of. It makes more sense of you >>> think of the wave function of the whole universe. Then you can >>> how QM is actually the *highest level* (most abstract) >>> explanation of reality. Next level down are functional systems. >>> Then the lowest level is the particle level. All three of these >>> levels of description are equally valid. This is somewhat >>> similair to Bohm's two-level interpretation (wave function at one >>> level, particles the other level). Only I have inserted a third >>> level into the scheme. *Between* the QM wave level description >>> (high level) and the aprticle level description (low level) is >>> where I think the solution to the puzzle of consciousness may be >>> found. >> But QM assumes a fixed background spacetime, which is inconsistent >> with general relativity - so one of them (or more likely both) are >> wrong. >> >> Brent Meeker > > There are *degrees* of rightness/wrongness. Later successful > theories of reality will still have to have some of the same features > of the earlier theories in areas where the earlier theories were > empirically proven. But the earlier theories were NOT empirically proven - they were found to hold over the observable domain. Later they were disproven in a wider domain and replaced by another theory, e.g. thermodynamics was replaced by statistical mechanics. Where they overlapped they agreed on the observations, what could be measured, but they didn't agree on the ontology. So it is the facts, the observations, that are the aspects of reality that are preserved as theories change. Not the mathematics and not the ontology. >For instance it's been proven from the EPR > experiments that any theory that replaces current QM still has to > have some of the same general features such as a 'wave of > possibilities/sum over histories', non-locality or uncertainties and > so on. There are already at least three formulations of QM, Griffiths', Bohm's, and Everett's that are logically incompatible at the level of fundamental ontology - and yet they are described by exactly the same mathematics. Brent Meeker --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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