Hi Folks,


 Mathematical Foundations of Consciousness

Willard L. Miranker <http://arxiv.org/find/math/1/au:+Miranker_W/0/1/0/all/0/1>,Gregg J. Zuckerman <http://arxiv.org/find/math/1/au:+Zuckerman_G/0/1/0/all/0/1>
(Submitted on 23 Oct 2008)

   We employ the Zermelo-Fraenkel Axioms that characterize sets as
   mathematical primitives. The Anti-foundation Axiom plays a
   significant role in our development, since among other of its
   features, its replacement for the Axiom of Foundation in the
   Zermelo-Fraenkel Axioms motivates Platonic interpretations. These
   interpretations also depend on such allied notions for sets as
   pictures, graphs, decorations, labelings and various mappings that
   we use. A syntax and semantics of operators acting on sets is
   developed. Such features enable construction of a theory of
   non-well-founded sets that we use to frame mathematical foundations
   of consciousness. To do this we introduce a supplementary axiomatic
   system that characterizes experience and consciousness as
   primitives. The new axioms proceed through characterization of so-
   called consciousness operators. The Russell operator plays a central
   role and is shown to be one example of a consciousness operator.
   Neural networks supply striking examples of non-well-founded graphs
   the decorations of which generate associated sets, each with a
   Platonic aspect. Employing our foundations, we show how the
   supervening of consciousness on its neural correlates in the brain
   enables the framing of a theory of consciousness by applying
   appropriate consciousness operators to the generated sets in question.

This is part of what I have been assuming form the beginning of my conversation with Bruno so many moons ago. Its nice to see its independent discovery.



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