On 06 Oct 2012, at 02:37, Stephen P. King wrote:

Hi Folks,



 http://arxiv.org/ftp/arxiv/papers/0810/0810.4339.pdf

Mathematical Foundations of Consciousness

Willard L. Miranker, Gregg J. Zuckerman
(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.


As the cow-boy guessed right this is assuming too much, both for the formalism used (which is OK), and the ontology, so it uses implicitly non-comp hypothesis, which is less OK, as comp is also assumed implicitly. IT is not uninteresting for possible progress, but it is unaware that matter as to be explained by statistics on computations "seen from inside". The role of "Russell operator" is played by the Kleene second recursion theorem, which encapsulates the "non foundation" well enough.

Bruno



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Onward!

Stephen

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http://iridia.ulb.ac.be/~marchal/



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