The Faculty of Language Integrates the Two Core Systems of Number

Abstract

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. To the extent that my arguments are correct, linguistic representations of number, grammatical number, and numerals do not incorporate anything like the successor function.

Complex Cardinal Numerals and the Strong Minimalist Thesis

“…Both and and of share properties, as evidenced in English by the fact that and is also found in multiplicative complexes such as hundreds and thousands to express emphatically large but vague numerosity. The fact that they occur between the numerals in both additive and multiplicative complexes and do not precede or follow the numerals, see (20), (21), brings independent support to (19b). This regularity is also observed with simple coordinate NP/DPs.…”

“…A closer look at the properties of numerals in natural languages however reveals no trace of the successor function (Hiraiwa 2017) [21]. The hypothesis that unbounded Merge yields arithmetic is abandoned in Chomsky (2018).…”

The singularity of indeterminates: Number specification without classifiers

“…First, it follows that Japanese does have a category of grammatical number, supporting Watanabe (2010Watanabe ( , 2017. Its existence is naturally expected, if Hiraiwa's (2017a) claim that grammatical number (singular-dual-plural) is founded on the Approximate Number System (ANS) and hence universally available to the human language faculty (see Feigenson, Dehaene, and Spelke 2004 for the ANS and Hiraiwa 2017a for a hypothesis about how capacities for natural numbers could arise from integrating the two cognitive systems of number and Merge in Chomsky 2008).…”

Emergent Communication for Numerical Concepts Generalization

“…According to linguistics and cognitive psychology, this ability is considered foundational for human abstract reasoning (Gelman and Gallistel 1986;Wiese 2003). Natural language possesses a comprehensive numerical system that allows humans to describe the number of objects accurately, concisely, and efficiently (Hiraiwa 2017). Furthermore, humans can perform more complex mathematical operations based on numerical concepts and digits, constructing a complete arithmetic system (Dehaene 2011).…”