Georges Ifrah, Lucien Gerschel, and four as the limit of small number systems

In his popular book Universal History of Number Georges Ifrah gives several examples of small number systems. Ifrah uses them as evidence of the idea that small number systems have a limit of four and count: one, two, two-one, two-two, many. The sources and origins of Ifrah’s hypothesis and examples are examined in detail, particularly the number systems of the Aranda, Western Torres Strait Islanders, Murray Islanders, Botocudos, Puri, Bakairi, ‘Bushmen’, Zulus, Fuegians (Yaghans), Kamilaroi and the Veddas. The author argues that Ifrah’s use of citations is misleading and criticizes Ifrah’s handling of these number systems.