From: Ben Goertzel (ben@goertzel.org)
Date: Wed Jan 25 2006 - 19:22:39 MST
Marc,
Inconsistentism also seems to tie in with G. Spencer Brown's notion of
modeling the universe using "imaginary logic", in which contradiction
is treated as an extra truth value similar in status to true and
false.
See www.lawsofform.org
Francisco Varela and Louis Kauffmann extended Brown's approach to
include two different imaginary truth values I and J, basically
corresponding to the series
I = True, False, True, False,...
J = False, True, False, True,...
which are two "solutions" to the paradox
X = Not(X)
obtained by introducing the notion of time and rewriting the paradox as
X[t+1] = Not (X[t])
In Brownian philosophy, the universe may be viewed in two ways
* timeless and inconsistent
* time-ful and consistent
Tying this in with the subjective/objective distinction, we obtain the
interesting idea that time emerges from the feedback between
subjective and objective. That is, one may look at a paradox such as
creates(subjective reality, objective reality)
creates(objective reality, subjective reality)
creates(X,Y) --> ~ creates(Y,X)
and then a resolution such as
I = subjective, objective, subjective, objective,...
J = objective, subjective, objective, subjective,...
embodying the iteration
creates(subjective reality[t], objective reality[t+1])
creates(objective reality[t+1], subjective reality[t+2])
If this describes the universe then it would follow that the
subjective/objective distinction only introduces contradiction if one
ignores the existence of time.
Arguing in favor of this kind of iteration, however, is a very deep
matter that I don't have time to undertake at the moment!
-- Ben Goertzel
On 1/25/06, Maru Dubshinki <marudubshinki@gmail.com> wrote:
> 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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