Revisiting Greenberg’s “Generalizations about Numeral Systems” (1978)*

Abstract

This article examines seven of the 54 generalizations on numeral systems presented by Greenberg in 1978 either as absolute universals or as universal tendencies. Five of the generalizations deal with details of the arithmetic structure of numeral systems, with particular reference to the order of elements in the numeral expression and to the use of subtraction and related phenomena in numeral expressions. It is shown that the details of these generalizations need to be revised in light of new data, and argued that even the formulation of universal tendencies is problematic given the rarity of some of the phenomena at issue and the resulting difficulty of establishing statistically valid inferences. Two of the generalizations discuss fundamental properties of natural language numeral systems, namely whether they are necessarily finite, and whether they allow gaps. It is argued, contra Greenberg, that there are both natural number series that are infinite and those with gaps. Throughout, it is emphasized that only the careful formulation of the original generalizations by Greenberg has enabled us to progress in our understanding of these aspects of numeral systems in natural languages.