Dear oh dear.

AI Researcher Yudkowsky is continuing to perpetuate the same old
reductionist mistakes on 'Overcoming Bias':
http://www.overcomingbias.com/2008/09/excluding-the-s.html#more

This is the reason I've long since given up on the poor fellow.  He
writes:

"different levels of organization can have separate representations in
human maps, but the territory itself is a single unified low-level
mathematical object."

He thinks the territory is:  "a single unified low-level mathematical
object".

Nice one.  I've love to hear what Bruno thinks of that silly notion.
Of course, as other readers in the thread pointed out, mathematical
objects themselves cannot be located at any particular location or
time in space or time ; if mathematical objects objectively exist  (as
Yudkowsky himself implies in his sentence), then, their very
existence  would represent a stark failure of reductionism.  Neither
inifinite sets nor uncomputable numbers can be identified with any
computable physical processes:

http://plato.stanford.edu/entries/platonism/

Of course, the reason mathematicians have to keep coming up with new
original concepts is precisely because no single-level mathematical
description is sufficient to encompass mathematical truth - as Godel
himself proved.  Mathematics itself operates on many levels of
abstraction.

Yudkowsky asks:

"What experimental observations would you expect to make, if you found
yourself in such a universe?" (where reductionism is false)

But we *are* in just such as universe!

What do you think Set Theory or Category Theory is?  IT IS THE
UNIVERSE MAPPING ITSELF

It is an 'inner model' or 'map' of mathematics.  If the Platonist/
Tegmark view is correct, then the universe itself contains a plethora
of mathematical objects at different levels of abstraction, and
objectively existing interfaces between them are required,  if the
consistency of reality is to be maintained.  Sets and Categories are
objectively existing high-level maps of lower-level level mathematical
objects


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