On May 9, 6:08 am, Brent Meeker <[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).  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).

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 ;)  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

> > 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

> > 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.  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.

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