Intransitivity Cycles and Their Transformations: How Dynamically Adapting Systems Function

In L. Rudolph (Ed.), Qualitative Mathematics for the Social Sciences: Mathematical Models for Research on Cultural Dynamics (pp. 343-391). Abingdon, NY: Routledge, 2013

52 Pages Posted: 16 Sep 2015

See all articles by Alexander N. Poddiakov

Alexander N. Poddiakov

National Research University Higher School of Economics

Jaan Valsiner

Aalborg University

Date Written: September 9, 2015

Abstract

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 beso 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.

Keywords: rationality, transitivity, intransitivity cycles, nontransitivity

Suggested Citation

Poddiakov, Alexander N. and Valsiner, Jaan, Intransitivity Cycles and Their Transformations: How Dynamically Adapting Systems Function (September 9, 2015). In L. Rudolph (Ed.), Qualitative Mathematics for the Social Sciences: Mathematical Models for Research on Cultural Dynamics (pp. 343-391). Abingdon, NY: Routledge, 2013. Available at SSRN: https://ssrn.com/abstract=2657942

Alexander N. Poddiakov

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

Jaan Valsiner (Contact Author)

Aalborg University ( email )

Fredrik Bajers Vej 7E
Aalborg, DK-9220
Denmark

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