From: Marc Geddes (marc_geddes@yahoo.co.nz)
Date: Tue Aug 17 2004 - 01:40:57 MDT
--- Simon Gordon <sim_dizzy@yahoo.com> wrote:
>
> However human intellect is sufficiently complex as
> to
> have the capability of understanding and abstractly
> manipulating things which are not even part of this
> universe and therefore not necessarily reducible to
> math. Examples of this are: parallel universes,
> qualia, software programs, memetics, possible
> sociopolitical orders, kilometers, set theory,
> infinity, fairytales, etc -the list is pretty much
> endless. Some of these are obviously math-based,
> some
> not so; but none of them are actually part of the
> physical hardware of this universe. Humans are not
> number crunchers; we dont understand all these
> abstractions via reduction to numerals and
> equations,
> we understand them via neighbouring concepts,
> associations, metaphors and analogues.
>
> Personally I believe that this kind of higher level
> reasoning doesnt correlate at all well to the
> mathematical underpinnings of our chemical/physical
> wetware and it might well be proven that some
> "neural
> knots" might be just implicitly too complex to
> untangle. In those cases language might have a
> better
> shot at actually translating what cannot be
> expressed
> in pure math. I can already think of several
> examples
> of concepts which havent got a hope in hell of being
> written down in mathematical notation, yet can be
> expressed with a single word...
>
> If someonone wants to tell me to shutup for 2
> months,
> i wont be offended. :-)
>
> Simon Gordon.
>
>
Mathematical reasoning doesn't have to be
reductionist. As I said in the paragraph I wrote
entitled 'Levels of Organization' in my platform,
simple new concepts can emerge from complex
arrangements of concepts from a lower-level. The
higher-level concepts won't be able to be *explained*
in terms of the concepts on the lower level (although
the higher level concepts could still be *described*
in terms of the lower level concepts). This does not
make the higher level concepts any less mathematical.
I don't see that an infinity of axioms (reality is
uncountable) is a problem. We are not limited to
axiomatic reasoning. Although higher level
mathematical axioms would not be derivable from lower
level mathetical axioms, we can still reason about and
*prove* the higher level axioms using probabilistic
reasoning.
=====
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