I haven't read Max's latest epistle yet, but I feel the need to
respond to your points here.

On Fri, Sep 21, 2007 at 05:50:12AM -0000, [EMAIL PROTECTED] wrote:
> 
> It appears to me that to attempt to reduce everything to pure math
> runs the risk of a lapse into pure Idealism, the idea that reality is
> 'mind created'.  Since math is all about knowledge, a successful
> attempt to derive physics from math would appear to mean that there's
> nothing external to 'mind' itself.  As I said, there seems to be a
> slippery slipe into solipsism/idealism here."
> 

The Anthropic Principle prevents the slide into solipsism of an
idealist theory. The argument is a little subtle, but I'll try to
recap. Basically observed reality cannot be completely arbitrary, as
it must be consistent with the observer being embedded in the observed
reality. Quite why this should be so in an idealist setting is a
little mysterious, but is presumably a requirement of consciousness.

> ---
> 
> Another major problem is this idea of pure 'baggage free' description
> that Max talks about (the removal of all references to obervables ,
> leaving only abstract relations).  The problem with this , is that, by
> definition, it cannot possibly explain any observables we actually
> see.  Notions of space and agency (fundamental to our empirical
> descriptions), cannot be derived from pure mathematics, since these
> notions involve attaching additional 'non-mathematical' notions to the
> pure mathematics.  As I pointed out in another recent thread on this
> thread, the distinctions required for physical and teleological
> explanations of the world appear to be incommensurable with
> mathematical notions.  We cannot possibly explain anything about the
> empirical reality we actually observe without attaching additional
> *non-mathematical* notions to the mathematics.
> 

I suspect this comes from limitations in one's imagination of
mathematical structures. For me, maths is all about compression,
detecting regularities in systems. I think this leads onto your point below
about considering OO systems to be mathematical.

> 
> ---
> 
> There are yet more problems with Max's ideas.  For instance, he says
> in the New Scientist article that: 'mathematical relations, are by
> definition eternal and outside space and time'.  Certainly, there have
> to be *some* mathematical notions that are indeed eternal and platonic
> (if one believes in arthematical realism), but it also makes sense to
> talk about some kinds of mathematical objects that exist *inside*
> space-time and are not static.  As I pointed out in another thread
> here, implemented algoithms (instantiated computations) are equivalent
> to *dynamic* mathematical objects which exist *inside* space-time:
> 

Indeed, how the "inside view" of a mathematical structure relates to
the external view of the structure is unclear. There is a bit of the
same problem with Bruno's AUDA too. But there must be such a relationship...

> "Let us now apply a unique new perspective on mathematics - we shall
> now attempt to view mathematics through the lens of the object
> oriented framework.  That is to say, consider mathematics as we would
> try to model it using object oriented programming - what the classes,
> methods and objects of math?  This is a rather un-usual way of
> looking
> at math.  Mathematical entities, if they are considered in this way
> at
> all, are not regarded as 'Objects' (things with state, identity and
> behaviours) but merely as static class properties.  For instance the
> math classes in the Java libraries consist of static (class)
> variables
> and class methods.
> 

See above..


...
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A/Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         [EMAIL PROTECTED]
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