Yes, but it is also in its infancy. With Aczel's work not 30 years old, and this admittedly weak analogy to consciousness only a few years old, which Aczel does not seem to be following up on himself:
http://www.cs.man.ac.uk/~petera/papers.html My point is, this is very young, what's young is always messy and will hopefully tidy itself up, and I can feel some funky aspect, specifically the observer aspect of a non-well-founded set defining a Russell operator, hinting at quantum physics perhaps in the future. It should be called the Cantor operator, but as Zuckerman notes: "the importance of PR and publishing makes the difference." So, knowing this, why doesn't he call it the Cantor operator... m On Sat, Oct 6, 2012 at 9:12 AM, Bruno Marchal <[email protected]> wrote: > > 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<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. > > > > 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 > > > > -- > Onward! > > Stephen > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
