1 - Sets, set membership, and calibration

Summary

The notions of sets

Sets and concepts

The use of the term “set” is not very broadly diffused in social science methodology. However, a good part of our conceptual reasoning, as Mahoney (2010) shows, is at least based on an implicit idea of sets. According to Mahoney , there are two basic modes of looking at concepts: if we define concepts “as a mental representation of an empirical property” (Mahoney 2010:2), then we will measure cases “according to whether or the extent to which they are in possession of the represented property” (Mahoney 2010:2). Measurement theory provides us with many useful techniques for doing this. This ultimately results in the use of variables when defining a concept (Mahoney 2010: 13). If, however, we refer to concepts as sets, defined in terms of “boundaries that define zones of inclusion and exclusion” (Mahoney 2010: 7), then “[c]ases are measured according to their fit within the boundaries of a set” (Mahoney 2010: 2). Sets work as “data containers” (Sartori 1970: 1039). Although this seems to be a subtle and often overlooked differentiation, these two views of concepts are fundamentally different. When we measure a concept by means of traditional measurement theory, it represents a property or a group of properties. The set-theoretic view, instead, uses set membership in order to define whether a case can be described by a concept or not. Therefore, in the framework of set-theoretic methods , issues of concept formation have a somewhat different connotation than in traditional measurement theory, by focussing on whether a case belongs to a concept (i.e., a set) or not. This process of assigning set membership is also called “calibration” (see section 1.2).