Mathematical Foundations of Consciousness
| dc.creator | Miranker, Willard L. | |
| dc.creator | Zuckerman, Gregg J. | |
| dc.date | 2008-10-23 | |
| dc.date.accessioned | 2026-07-07T10:12:58Z | |
| dc.date.available | 2026-07-07T10:12:58Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0810.4339 | |
| dc.identifier | http://arxiv.org/abs/0810.4339 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172367 | |
| dc.subject | Logic | |
| dc.title | Mathematical Foundations of Consciousness | |
| dc.type | text |