Glass Houses: Greenberg, Ringe, and the Mathematics of Comparative Linguistics

In a recent exchange, Ringe accused Greenberg of innumeracy on the basis of a mathematical illustration that Greenberg has used repeatedly. Ringe then argued that mathematical considerations show the method of binary comparison between languages to be superior to the method of multilateral comparison favored by Greenberg. We show that Ringe's charge of innumeracy rests on an elementary mathematical misunderstanding, and that the mathematics cited by Ringe undermines his own methodological conclusions. However, although Ringe's arguments are fallacious, his conclusions are not completely off the mark: Greenberg's attempts to justify his methodology mathematically are subject to some serious difficulties.