Looking back: the main topics of this book

This book started off from the general observation that claims about set relations are pervasive in the social sciences. Set-theoretical methods are thus an important addition to the correlational approach. We have defined set-theoretic methods as those approaches to examining social reality that operate on sets, not variables; model relations between phenomena in terms of set relations rather than covariations; and that put emphasis on sufficient and necessary conditions and their derivates INUS and SUIN conditions, thus unraveling causally complex patterns in terms of equifinal, conjunctural, and asymmetric causation. Within the family of set-theoretic methods, QCA can be distinguished by its explicit use of truth tables; the application of the principle of logical minimization; and its interest in a causal interpretation of its results. We have focused on csQCA and fsQCA as the two main variants of QCA, with csQCA being a special case of fsQCA. mvQCA and tQCA are among the extensions of the main QCA variants.

In Chapter 1, we showed how sets are defined and how set membership is calibrated. Chapter 2 laid the basics for the analysis by introducing the main principles of set theory, Boolean algebra, and the logic of propositions – the three underpinnings on which QCA is built. In Chapter 3, we clarified in great detail the basic notions of sufficiency and necessity, which are at the core of any set-theoretic analysis. A major insight in this chapter was that necessity and sufficiency both denote subset relations, which apply in both crisp and fuzzy sets. Furthermore, we showed that those who stipulate the presence of necessary and/or sufficient conditions unavoidably embrace causal complexity, which in set-theoretic methods is defined in terms of equifinality, conjunctural causation, and asymmetric causality. In Chapter 4, we explained that three steps are needed in order to construct a truth table based on a set membership data matrix: first, the truth table rows (i.e., the logically possible combinations of the conditions) have to be defined; second, cases have to be assigned to the single truth table row to which they best belong; and, third, for each truth table row the outcome value has to be determined by testing whether it is a subset of the outcome of interest. Rows that pass this test represent sufficient conditions. Subsequently, a QCA proceeds with the logical minimization of a truth table. The result of this procedure yields the sufficiency solution formula, one important goal of any QCA.