Counting & Infinity in English- and Hindi-Speaking Children

By around five and a half years of age, English-speaking children in the US claim that numbers never end. This belief has been linked to their knowledge of the successor function, i.e., every natural number n has a successor n + 1 (e.g., Cheung et al., 2017; Chu et al., 2020). Children’s knowledge of successor relations, in turn, is related to learning the productive linguistic rules that govern verbal counting. On one analysis of this pattern of results, children demonstrate an understanding of the successor function once they discover that when one item is added to an enumerated set, the syntax of counting provides the morphological rules to generate the next number, such that the next number in the count procedure describes the new set. For example, children learn that when one item is added to a set labeled ‘six’, then the new set is labeled ‘seven’ (Schneider et al., 2020; see also, Barner et al., 2017; Cheung et al., 2017). As a test of this hypothesis, Schneider et al. (2020) examined children’s acquisition of the successor function across five languages: three with relatively transparent count lists (Cantonese, Slovenian, and English) and two with relatively opaque count lists (Hindi and Gujarati), and found that more opaque languages were associated with lower performance on successor function tasks, relative to more transparent languages. Moreover, children who demonstrated knowledge of a productive counting rule showed significantly better successor knowledge in almost every language. Consistent with this evidence, Chu et al. (2020) found that English-speaking children who understand the productive rules governing counting (i.e., productive counters) are significantly more likely to believe that numbers are infinite, relative to children who have not yet acquired such a productive rule. Chu reasoned that noticing the base-10 structure of the count list provided the basis for learning the successor function and inferring that number words are unbounded. To further test this idea that children’s beliefs about the unbounded nature of the count routine are linked to (1) knowledge of successor function, and (2) understanding the productive rules of counting, the present study will examine how beliefs about infinity emerge across children who speak a language with a relatively transparent count list (i.e., English), and children who speak a language with a relatively opaque count list (i.e., Hindi). Like English, Hindi numbers are generated through a base-10 system. Unlike English, however, Hindi exhibits many irregularities, i.e., morphological and phonological variations (Berger, 1992; Bright, 1969). The high number of morphological and phonological irregularities in the Hindi count routine has led some to conclude that numbers 1 to 100 can only be learned in a rote manner (Bright, 1969; Comrie, 2011). Therefore, Hindi provides a natural test of the role of the rules governing counting and the knowledge that numbers are infinite, consistent with the data from Schneider et al. (2020). In particular, we asked whether children who acquire productive rules of counting later in development are also later to acquire the belief that numbers never end.