Averaging dimensions severs the deterministic link between concept intension and empirical extension.

Evidence

One might ask about the mean aggregation class. As one might imagine, there is no clear automatic relationship between adding dimensions and extension. This is intuitively obvious by thinking about the average: if you add a new dimension the average might go up or might go down depending on the specific values for each observation. — Gary Goertz, Social Science Concepts and Measurement, 1376

Categorization

• SEED: Angle: ‘The arithmetic of concepts’ — a short essay on how the choice of aggregation rule (AND, OR, sum, mean) silently determines which countries count as democratic, developed, or failed.
• QUESTION: Does this hold for other non-linear aggregators (min, max, geometric mean), or is mean uniquely indeterminate? Worth testing against real democracy indices.