Mathematical Foundations of Consciousness
arXiv Preprint Archive October 23, 2008 Willard L. Miranker, Gregg J. Zuckerman
The Zermelo-Fraenkel axioms, especially the Anti-foundation Axiom instead of the standard Axiom of Foundation, allow sets that can contain themselves, supporting Platonic interpretations. Using graphs, decorations, and labelings, a syntax and semantics of operators acting on these non-well-founded sets is developed. This framework is extended with new axioms that treat experience and consciousness as primitives, introducing consciousness operators, with the Russell operator as a central example. Neural networks provide non-well-founded graphs whose decorations generate sets with Platonic aspects. Applying consciousness operators to these sets shows how consciousness can supervene on its neural correlates, framing a theory of consciousness.