Set membership requires adjective-like concepts, not raw quantities.

Evidence

Sets and set labels almost always involve adjectives in some way. For example, it is possible to assess degree of membership in heavy; it is not possible to assess degree of membership in weight. This aspect of sets is fundamental to set-theoretic analysis. L&S [Lucas and Szatrowski] violate this principle by using mechanistic calibrations based on ranges. This issue is especially important for the calibration of temperature because the overarching engineering concern was for temperatures that were low, a unipolar concept. Thus, L&S should have calibrated degree of membership in low temperature, based at least in part on case knowledge. Instead, they tried to calibrate degree of membership in temperature, which is nonsensical. — Gary Goertz, Social Science Concepts and Measurement, 742

Categorization

• DEFINE: Distinguishes quantities (weight, temperature) from gradable concepts (heavy, low temperature) — the core semantic distinction of fuzzy-set calibration.
• XREF: Connects to the book’s earlier treatment of concept structure and three-valued logic, and to Ragin’s fuzzy-set methodology generally.