Qualitative mathematics for the social sciences: Mathematical models for research on cultural dynamics
In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics.
Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations.
The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.
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.