Re: consciousness and self-awareness

From: Brian Tenneson <>
Date: Fri, 10 Jul 2009 10:36:05 -0700

Thanks GŁnther. I'll look into it.

I also came across this article and thought some people might want to
discuss it.

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.

On Sun, Feb 8, 2009 at 7:49 AM, GŁnther Greindl

> Brian,
> Tononi's information integration view of consciousness might fit your bill.
> Overview:
> Paper (open access):
> Cheers,
> GŁnther
> Brian Tenneson wrote:
> > Dear Everything List,
> >
> > Tegmark mentioned in an article the idea of self-aware structures, SAS.
> > He wrote that the search for such structures is ongoing, i.e., he
> > postulated the existence of such structures without giving examples.
> >
> > I'm wondering if consciousness and self-awareness has been
> > "mathematized" somewhere, preferably in documents I can download without
> > academic affiliation / subscription.
> >
> > I'm inclined to thing agents might be a pathway to this end, as well as
> > what David Wolpert is calling a device.
> >
> > Do any of the formalizations come close to being reflective of human
> > consciousness? In other words a mathematical model of human
> consciousness?
> >
> > Thank you.
> >
> > >
> >
> --
> GŁnther Greindl
> Department of Philosophy of Science
> University of Vienna
> Blog:
> Thesis:
> >

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Received on Fri Jul 10 2009 - 10:36:05 PDT

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