Abstract This chapter examines the usability of Greenbergian implicational hierarchies (Greenberg 1966) in cross-linguistic research on language complexity. Recently an increasing number of linguists have started to question the conventional wisdom according to which all languages are equally complex. McWhorter (2001a) proposes a metric for measuring the overall complexity of grammars of languages. One of the criteria employed in the metric pays attention to the number of grammatically expressed semantic or pragmatic distinctions: for example, a language that has a singular, a plural, and a dual is more complex in this respect than a language where only two number categories, singular and plural, are found. McWhorter further argues (p. 160) that such complexity differences can be translated into implicational hierarchies. Thus, the existence of number categories is regulated by the implicational hierarchy in (1) (adapted from Greenberg 1963; Greenberg formulated his Universal 34 as follows: ‘‘No language has a trial number unless it has a dual. No language has a dual unless it has a plural.“).
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