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Intransitivity cycles and their transformations: How dynamically adapting systems function

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A most interesting area in transitivity / intransitivity relations consists of relations like dominance / subordination, superiority / inferiority, preferences, etc. If A dominates B and B dominates C, must it be so that A dominates C? If A is superior to B, and B is superior to C, must it be so that A is superior to C? What happens if superiority/inferiority (dominance /subordination, etc.) relations form a cycle, an intransitive loop? Human rationality is often assumed to be based on the logical relation of transitivity. Yet, although transitivity fits relationships between physical objects or human decisions about targets that are independent of one another, it fails to fit the phenomena of systemic and developmental organization. Intransitivity has been shown to be present in various kinds of systems, ranging from the brain to society. In cyclical systems transitivity constitutes a special case of intransitivity. In this chapter, we examine different forms of emergence of intransitivity cycles, fixation of transitive parts in these cycles, and the organization of different levels of reflexivity within the systems. We conclude that reflexivity of cognitive processes— rather than transitivity in specific forms of thought—is the defining criterion of rationality.
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