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Abstract: We employ the Zermelo-Fraenkel Axioms that characterize sets as mathematicalprimitives. The Anti-foundation Axiom plays a significant role in ourdevelopment, since among other of its features, its replacement for the Axiomof Foundation in the Zermelo-Fraenkel Axioms motivates Platonicinterpretations. These interpretations also depend on such allied notions forsets as pictures, graphs, decorations, labelings and various mappings that weuse. A syntax and semantics of operators acting on sets is developed. Suchfeatures enable construction of a theory of non-well-founded sets that we useto frame mathematical foundations of consciousness. To do this we introduce asupplementary axiomatic system that characterizes experience and consciousnessas primitives. The new axioms proceed through characterization of so- calledconsciousness operators. The Russell operator plays a central role and is shownto be one example of a consciousness operator. Neural networks supply strikingexamples of non-well-founded graphs the decorations of which generateassociated sets, each with a Platonic aspect. Employing our foundations, weshow how the supervening of consciousness on its neural correlates in the brainenables the framing of a theory of consciousness by applying appropriateconsciousness operators to the generated sets in question.

Author: Willard L. Miranker, Gregg J. Zuckerman



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