With AND aggregation, adding necessary defining features can only shrink a concept’s extension.

Evidence

With the mathematical logic approach to concepts there is a clear relationship between concept structure and extension, which is the weakest link aggregation class: As one increases intension in the sense of increasing the number of necessary defining characteristics, the extension—number of empirical cases—must stay the same or go down. This is a mathematical fact linked to the use of necessary conditions. Once one moves to other methods of aggregation it no longer applies. Adding new secondary-level dimensions may result empirically in more or fewer cases. — Gary Goertz, Social Science Concepts and Measurement, 1356

Categorization

• XREF: Connects to Sartori’s ladder of abstraction and the traveling/stretching vocabulary already logged from earlier chapters.
• DEFINE: Intension = definition; extension = number of cases with nonzero membership — the load-bearing pair for the whole chapter.