Jeff writes that Rosen states:
>"Most, if not all, (of) the known paradoxes arise from an attempt to divide a
>universe into two parts on the basis of satisfying some property or not (e.g.,
a
>property like objectivity). Trouble arises whenever this property can be
>turned back on itself; in particular, when we try to put some consequent of the
>property back into one or the other class defined by the property."
This is *precisely* the kind of problems hyper-set theory solves with ease. In
ordinary set theory, sets are not allowed to turn back on themselves exactly
because this leads to paradoxes and infinite regresses. Hyperset theory solves
this by using a _relational_ definition of sets. For each set there is a
corresponding graph. (graph of relations) The question then is: do hypersets hav
e
a corresponding finite graph? The answer is yes. Although it is possible to
unfold an infinite regress in the hyperset, there are a finite set of
relations. It also strikes me that the discussion I've heard on Rosen has been
concerned with relations. It could very well be that hyperset theory is the
mathematics underlying Rosen's concepts of complexity. Hyperset theory is in any
case highly useful in theories involving self-reference and feedback. I've
applied it with success in reflective systems (the mirrorhouse). And its
application is obvious in such problems as self-awareness, self-reflection
(the hologram) and self-production (autopoiesis).
Onar.