Mathematical Foundations of Consciousness
Willard L. Miranker
(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
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