Intransitivity cycles and their transformations: How dynamically adapting systems function

Ch. 12. P. 343–391.

Alexander Poddiakov, Valsiner J.

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.

Keywords: рефлексия, rationality, рациональность, transitivity, intransitivity, complex dynamical systems, reflexivity, транзитивность, нетранзитивность, сложные динамические системы

In book

Qualitative mathematics for the social sciences: Mathematical models for research on cultural dynamics

NY, Abingdon: Routledge, 2013.