From: Maru Dubshinki (marudubshinki@gmail.com)
Date: Wed Jan 25 2006 - 18:51:50 MST
On 1/25/06, Marc Geddes <m_j_geddes@yahoo.com.au> wrote:
...
> *A* particular formal system has to be consistent
> (because in an inconsistent system you can prove
> anything), but my suggestion was that a full
> description of reality may require *several*
> over-lapping formal systems. Each system *in itself*
> would be consistent, but the different systems would
> not be fully consistent *with each other*. An analogy
> here would be a 3-D movie. To get the 3-D effect two
> different versions of a scene are shot - each version
> is shifted slightly in space (one version for each
> eye). Each version of the scene is consistent in
> itself (left eye version or right eye version), but
> the two versions are not fully consistent with each
> other. (Consider the two versions to be analogous to
> several formal systems).
...
IANAM, but as I recall, Goedel's theorems put one on the horns of a dilemna:
you could either accept completeness and contradiction, or consistency and
incompleteness.
Why can't we take the former prong of the dilemna (and not the latter
as you suggest), and simply accept that there will be errors (read
"Contradictions")
in any map smaller than the territory?
~Maru
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