Zeroing a defining dimension can shrink or expand a concept’s extension unpredictably.

Evidence

To see how this can work in practice, I continue with the Democracy–Dictatorship group view of democracy. Figure 9.4 illustrates what happens to extension when we fix the value of some of the defining dimensions as 0. One can see that, depending on which dimension one makes 0, the result can be fewer or more cases than the number of democracies. The number of cases and the extension can vary dramatically when one of the defining dimensions has value 0. This illustrates very clearly that there is no principle about the relationship between 0 on a given dimension and extension. — Gary Goertz, Social Science Concepts and Measurement, 1484

Categorization

• DEEPTHINKING: Undercuts the intuition that dropping an attribute straightforwardly narrows what counts as a member — extension can move either way, which unsettles casual uses of ‘subtype’ and ‘ideal type’.