Family resemblance and necessary-condition concepts are two ends of one m-of-n spectrum.

Evidence

Classic family resemblance is an “m-of-n” concept structure: possessing m of the n total features is sufficient to be a member of the family (i.e., extension). This means substitutability for each individual dimension. It is worth noting that the m-of-n rule means at least m-of-n, so (m+1)-of-n counts, e.g., for a 2-of-3 rule, cases of 3-of-3 are included. The clearest example linking the m-of-n rule to the best shot is the 1-of-n rule: if one of the dimensions is present then it is a member of the family. The presence of one substitutes for the absence of all the others. At the other end of the spectrum, to require n-of-n means that each is necessary. Philosophers focused on the family resemblance as involving no necessary conditions. This means looking at the m-of-n structure toward the weakest link end. — Gary Goertz, Social Science Concepts and Measurement, 1356

Categorization

• DEFINE: Defines m-of-n, 1-of-n, and n-of-n as a single continuum spanning Wittgensteinian family resemblance and Aristotelian essentialism.
• XREF: Links to the aggregation classes (AND, OR, sum, mean, minimum) developed earlier in the volume.