This paper has two primary aims. The first is to provide an introductory discussion of hyperset theory and its usefulness for modeling complex systems. The second aim is to provide a hyperset analysis of several perspectives on autonomy: Robert Rosen’s metabolism-repair systems and his claim that living things are closed to efficient cause, Maturana and Varela’s autopoietic systems, and Kauffman’s cataytically closed systems. Consequences of the hyperset models for Rosen’s claim that autonomous systems have non-computable models are discussed.

Key words: Autonomy, Autopoiesis, Catalytic closure, Francisco Varela, Hyperset, Robert Rose

Synaptic communication, nonsynaptic diffusion neurotransmission and glial activity each update the morphology of the other two. These interactions lead to an endogenous structure of causal entailment. It has internal ambiguities rendering it incomputable. The entailed effects are bizarre. These include abduction of novelty in response to conflicting cues, a resolution of the seeming conflict between freewill and determinism, and anticipatory behavior. Such inherent ambiguity of the causal entailment structure does not preclude the implementation of brain-like activities artificially. Although an algorithm is incapable of neuromimetically reproducing self-referential character of the brain, there is a currently-feasible strategy for wiring a “human in the loop” to use the cognitive powers of anticipation and unconscious integration to provide dramatic improvement in the operation of large engineered systems.

Key words: hyperset, endogenous system, bizarre system, recursion, impredicative, incomputable, anticipatory system, unconscious integration.