Addition and correlation cannot formalize necessary-and-sufficient concept structures.

Evidence

In fact there are two structural questions: (1) how to combine indicators to form the secondary-level dimensions and (2) how to combine secondary-level dimensions to get the basic-level concept. The key issue in the context of this introduction is that almost all scholars use the necessary and sufficient condition structure to combine secondary-level dimensions into the final democracy concept. All of the quantitative measures use either addition or correlation. However, none of these is the appropriate mathematical formalization of the necessary and sufficient condition structure. — Gary Goertz, Social Science Concepts, 116

Categorization

• QUESTION: What mathematics does correctly formalize necessary-and-sufficient conditions, and how would that change existing composite indices?