This book, by Schneider and Wagemann, provides a comprehensive overview of the basic principles of set theory to model causality and applications of Qualitative Comparative Analysis (QCA), the most developed form of set-theoretic method, for research across the social sciences.
"Different mathematical sub-disciplines provide the underpinnings for the vast majority of social science methods and techniques. Most of the well-known and commonly applied statistical methods in the social sciences are applications of probability calculus or matrix algebra to social science data. While most of these mathematical sub-disciplines might be remembered from school, set theory is less familiar to most people. Although formal logic, a close relative of set theory, is a well-studied system of thought in disciplines such as philosophy and mathematics, it currently plays only a marginal role in school education and social science methods training in many parts of the world. This is unfortunate, because, as shown, set-theoretic notions are invoked in social science research more often than is usually recognized. The notion of sets and their relations is almost unavoidably invoked when forming concepts or when verbally formulating (causal) relations between social phenomena. This book is motivated by the belief that the study of set-theoretic relationships provides an important perspective on social science research problems, thus adding to the currently predominant correlational approaches. (Schneider & Wagemann 2012, p.1)."
- Part I. Set-Theoretic Methods: The Basics
- Sets, set membership, and calibration
- Notions and operations in set theory
- Set relations
- Truth tables
- Part II. Neat Formal Logic Meets Noisy Social Science Data
- Parameters of fit
- Limited diversity and logical remainders
- The truth table algorithm;
- Part III. Potential Pitfalls and Suggestions for Solutions
- Potential pitfalls in the standard analysis procedure and suggestions for improvement
- Potential pitfalls in the analysis of necessity and sufficiency and suggestions for avoiding them
- Part IV. Variants of QCA as a Technique Meet QCA as an Approach
- Variants of QCA
- Data analysis technique meets set-theoretic approach
- Looking back: looking ahead
Schneider, C. Q., & Wagemann, C. (2012). Set-theoretic methods for the social sciences: A guide to qualitative comparative analysis. Cambridge: Cambridge University Press.