The Faculty of Language Integrates the Two Core Systems of Number - Hiraiwa, Ken (Frontiers in Psychology, 2017)
Only humans possess the faculty of language that allows an infinite array of hierarchically structured expressions (Hauser et al. 2002, Berwick and Chomsky 2015). Similarly, humans have a capacity for infinite natural numbers, while all other species seem to lack such a capacity (Gelman and Gallistel 1978, Dehaene 1997). Thus, the origin of this numerical capacity and its relation to language have been of much interdisciplinary interest, in developmental and behavioral psychology, cognitive neuroscience, and linguistics (Dehaene 1997, Hauser et al. 2002, Pica et al. 2004). Hauser et al. (2002) and Chomsky (2008) hypothesize that a recursive generative operation that is central to the computational system of language (called Merge) can give rise to the successor function in a set-theoretic fashion, from which capacities for discretely infinite natural numbers may be derived. However, a careful look at two domains in language, grammatical number and numerals, reveals no trace of the successor function. Following behavioral and neuropsychological evidence that there are two core systems of number cognition innately available, a core system of representation of large, approximate numerical magnitudes and a core system of precise representation of distinct small numbers (Feigenson et al. 2004), I argue that grammatical number reflects the core system of precise representation of distinct small numbers alone. In contrast, numeral systems arise from integrating the pre-existing two core systems of number and the human language faculty.