We ask whether the same idea explains why numeral systems appear as they do, from approximate to fully recursive form.įigure 1 illustrates these ideas. This idea has been supported by cross-language computational analyses in the domains of color (Regier, Kemp, & Kay, 2015 Zaslavsky, Kemp, Regier, & Tishby, 2018), kinship (Kemp & Regier, 2012), spatial relations (Khetarpal, Neveu, Majid, Michael, & Regier, 2013), names for containers (Xu, Regier, & Malt, 2016 Zaslavsky, Regier, Tishby, & Kemp, 2019), and names for seasons (Kemp, Gaby, & Regier, 2019). On this account, for any given semantic domain, the different categorical partitionings of that domain observed in the world’s languages represent different means to the same functional end of efficiency. Of direct relevance to numeral systems, it has been argued in particular that systems of word meanings across languages reflect such a need for efficient communication (Kemp, Xu, & Regier, 2018). It has long been argued (e.g., von der Gabelentz, 1901 Zipf, 1949) that languages are shaped by functional pressure for efficient communication-that is, pressure to communicate precisely yet with minimal cognitive effort-and this idea has attracted increasing attention recently (e.g., Fedzechkina, Jaeger, & Newport, 2012 Gibson et al., 2019 Haspelmath, 1999 Hopper & Traugott, 2003 Kanwal, Smith, Culbertson, & Kirby, 2017 Piantadosi, Tily, & Gibson, 2011 Smith, Tamariz, & Kirby, 2013). At the other extreme, the ability to judge exact high numerosity is not universal but appears instead to rely on the existence of a linguistic counting system that singles out such exact high numerosities (Gordon, 2004 Pica, Lemer, Izard, & Dehaene, 2004).Īn existing proposal has the potential to answer these questions. For example, approximate numeral systems may be grounded directly in the nonlinguistic approximate number system, a cognitive capacity for approximate numerosity that humans share with nonhuman animals (Dehaene, 2011). These different numeral systems are likely to be grounded in different cognitive capacities for judging numerosity. Some languages have numeral systems that express only approximate or inexact numerosity other languages have systems that express exact numerosity but only over a restricted range of relatively small numbers while yet other languages have fully recursive counting systems that express exact numerosity over a very large range.
Moreover, there are qualitatively distinct classes of such numeral systems. Number is a core element of human knowledge (e.g., Spelke & Kinzler, 2007) and languages vary widely in their numeral systems (Beller & Bender, 2008 Bender & Beller, 2014 Comrie, 2013 Greenberg, 1978 Hammarström, 2010).
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