Adding family resemblance dimensions can increase, not shrink, the extension of a concept.

Evidence

Assume that the cases follow the binomial theorem, e.g., one can toss four or six coins to decide if the country has a welfare state or not. According to the binomial formula the percentage of welfare states increases from 31 percent of the total with four dimensions to 34 percent with six. — Gary Goertz, Social Science Concepts, 498

Categorization

• DEEPTHINKING: This overturns the Sartori/vagueness trade-off baked into most comparative-methods textbooks — intensional growth driving extensional growth is genuinely counterintuitive.
• SEED: Angle: ‘The Ladder of Generality Is a Lie’ — a short essay on why the extension/intension trade-off is a necessary-and-sufficient artifact, not a law of concepts.