Mathematical Foundations of Consciousness

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

Alfalfa Varieties for Ohio

PDF pages:

Does Long-Term Macrophyte Management in Lakes Affect Biotic Richness and Diversity?

We hypothesize that the richness and diversity of the biota in Lake Moraine (42°50’47”N, 75°31’39”W) in New York have been negatively impacted by 60 years of macrophyte and algae management to control Eurasian watermilfoil ( Myriophyllum spicatum L.) and associated noxious plants. To test this hypothesis we compare water quality characteristics, richness and selected indicators of plant diversity, zooplankton, benthic macroinvertebrates and fish in Lake Moraine with those in nearby Hatch Lake (42°50’06”N, 75°40’67”W). The latter is of similar size and would be expected to have similar biota, but has not been subjected to management. Measurements of temperature, pH, oxygen, conductivity, Secchi transparency, calcium, total phosphorus and nitrites + nitrates are comparable. Taxa richness and the diversity indices applied to the aquatic macrophytes are similar in both lakes. (PDF has 8 pages.

The Quest for Material

Symposium: The Writing of Judicial Biography American Political Science Association, Chicago, December 28-30, 194