Self-reference and Chaos in Fuzzy Logic

IEEE Transactions on Fuzzy Systems 1:237-253 (1993)
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Abstract

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of mutually referential triples.

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Patrick Grim
University of Michigan, Ann Arbor

Citations of this work

Recent Developments in Computing and Philosophy.Anthony F. Beavers - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (2):385-397.

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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Truth and paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
A note on the entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.

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