> On May 8, 4:22 pm, Brent Meeker <[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 

>According to the Tegmark paper just
> recently posted, math concepts map to physical concepts.  

We only know that some math concepts map to physical concepts and we dont' know 
that the mapping is perfect and in fact we have some reason to believe that it 
is not.

>We can infer
> that there must be some physical concept which can be indentified with
> an infinite set.  And the existence of this physical thing would be a
> violation of reductionism.  To escape from the conclusion we either
> have to deny that infinite sets are real, or else deny the one-to-one
> match between the mathematical and physical world.
>>> (2)  The Laws of Physics and (3) Quantum Wave
>>> Functions
>>> It is established that all of these concepts are indispensible to our
>>> explanations of reality and they are logically well defined and
>>> supported.  But none of these concepts can be reduced to any finite
>>> set of empirical facts.
>> That's because we invented them.
> 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.

>> QM isn't even a physical theory; it's just a set of principles for 
>> formulating physical theories; as classical mechanics was before it.
> Exactly so!  I agree.  QM is  really an abstract *high-level*
> explanation of reality.  This sounds strange, because the QM
> description is usually thought of as the *low level* (basement level)
> description fo reality, but it ain't.  It's true that QM may be the
> basement level in the sense of *accuracy* (best scientific model so
> far), but *not* in the ontological sense.  As you point out, in the
> *ontological* sense it's really a sort of high-level *reality shell* -
> an abstracted set of principles rather a complete physical principle
> in itself.
> 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

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