Concept logic and statistical measurement obey incompatible formal structures

Evidence

Much of this volume is a working out of this basic tension between the “logic” of concepts, which is frequently of a necessary and suf- ficient condition or family resemblance sort, and the “statistics” of quantitative measures. Fuzzy logic plays a key role in permitting us to give mathematical and formal representation of the ways in which most scholars have thought about concepts. Using the concept of substitutability permits us to contrast the mathematics of fuzzy logic with the mathematics of statistical measures. The substitutability continuum provides a method for comparing and contrasting different concept structures, be they drawn from logic or statistics. — Gary Goertz, Social Science Concepts, 302

Categorization

• DEFINE: Introduces the volume’s core distinction: the ‘logic’ of concepts (necessary/sufficient, family resemblance) versus the ‘statistics’ of quantitative measures, with substitutability as the bridge concept.
• XREF: Connects to the reader’s interest in measurement validity and construct definition — the same tension as treating ‘trust’ or ‘noise’ as either a scale score or a threshold concept.
• SEED: Article angle: why so many social-science concepts break when you switch from logical definition to regression variables — a piece on the quiet incommensurability of our two dominant formalisms.