Qualitative Mathematics for the Social Sciences
Mathematical Models for Research on Cultural Dynamics
Edited by Lee Rudolph
Series Editor: Jaan Valsiner
Routledge – 2013 – 492 pages
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.
Rudolph, Valsiner, Preface. Rudolph, Valsiner, Introduction: Mathematical Models and Social Representation. Part I: Logics of Modeling. Rudolph, Logic in Modeling, Logics as Models. Busemeyer, Introduction to Quantum Probability for Social and Behavioral Scientists. Dzhafarov, The Sorites Paradox: A Behavioral Approach. Tat Ng, On an Intensity Attribute—Loudness. Part II: Model Structures. Rudolph, Functions of Structure in Mathematics and Modeling. Diriwächter, Structure and Hierarchies in Ganzheitspsychologie. Kawauchi, Mind-Knots and Mind-Relations: Knot Theory Applied to Psychology. Neuman, A Novel Generic Conception of Structure: Solving Piaget's Riddle. Part III: Dynamic Models. Rudolph, The Varieties of Dynamic(al) Experience. Abraham, Friedman, Viotti, Complex Dynamical Systems and the Social Sciences. Poddiakov, Valsiner, Intransitivity Cycles and Their Transformations: How Dynamically Adapting Systems Function? Part IV: Conclusions. Rudolph, Modeling and Diagrammatic Reasoning.