From Russell's Paradox to a Theory of Consciouness

Gregg Zuckerman

Yale University

Brandeis University

Thursday, February 11, 2010

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: Russell's paradox in naive set theory suggests the definition of what we call the Russell operator: Rx = {y in x| y is not in y}. In Zermelo's axiomatic set theory, the Russell operator is well defined and is not paradoxical in nature. The key property of the Russell operator is that for any set A in the Zermelo universe, the set RA is not in A. If we drop the axiom of foundation, and substitute Aczel's axiom of antifoundation, the Russell operator becomes quite nontrivial, since now many sets are elements of themselves. Thus, the original scope of the Russell paradox in naive set theory gets transmuted to a rich and consistent theory of the Russell operator in nonwellfounded axiomatic set theory.

In joint work with Willard Miranker of Yale Computer Science, we have proposed a mathematical theory of consciousness based on a combination of the standard theory of neural networks and the emerging theory of nonwellfounded sets. The Russell operator and certain generalizations we call consciousness operators play a central role in our proposal. We will present many examples of nonwellfounded sets and consciousness operators, and thus make this lecture as self contained as possible.

Home Web page: Alexandru I. Suciu Posted: January 27, 2010
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