The Joseph Greenberg problem: combinatorics and comparative linguistics

TL;DR

This paper corrects a historical combinatorial enumeration related to Greenberg's language classification method, providing insights into the number of language families and supporting the plausibility of alternative classifications.

Contribution

It rectifies Greenberg's 1957 enumeration and links combinatorics to linguistic classification, offering a new perspective on the number of language families.

Findings

Greenberg's enumeration matches Bell number B(25)

Supports the plausibility of classifications with over 100 language families

Provides a combinatorial estimate for language family counts

Abstract

We correct a 1957 combinatorial enumeration by the linguist J. Greenberg. The desired count, the Bell number B(25), supported using his Mass Comparison method for language classification. In 1987, he used this method to classify indigenous languages of the Americas into three families. Actually, the same combinatorics provides a back-of-the-envelope estimate for the number of families. This suggests that alternative classifications with over a hundred families possess the right order of magnitude.