"What's innate about integer concepts?", David Barner (University of California, San Diego - Department of Psychology)
Tuesday, April 27, 2021, 01:00pm
Abstract: In 1978 Gelman and Gallistel proposed a powerful nativist thesis regarding the ontogenetic origin of integer concepts in human children, and argued for a series of five distinct "counting principles" which included one-to-one correspondence, stable order, and the cardinal principle. This proposal was met with several significant waves of responses from non-nativist psychologists, who argued that children's early counting behaviors do not respect the counting principles in various ways. Currently, the field has achieved a remarkable degree of consensus regarding the empirical facts of number word learning, but the questions set out by Gelman and Gallistel remain difficult to answer, and a clear synthesis is absent. In this talk I lay out these facts and suggest a new synthesis, according to which the core innate feature of number word learning is Hume's principle of one-to-one correspondence, somewhat akin to what Gelman & Gallistel argued. However, I also argue - against their thesis - that the format by which one-to-one is innately represented - i.e., some form of parallel enumeration - is not readily translated to the sequential algorithms of culturally constructed counting algorithms, explaining why children's early counting behaviors do not immediately express Hume's Principle. Second, compatible with Gelman & Gallistel, I argue that an innate (ostensibly linguistic) syntax is responsible for generating a stable count list that extends beyond the limits of human sequence learning. But contrary to them I argue that the procedures that are the output of this syntax precede the conceptual content that it represents - namely, a numerical successor function that generates an infinite number of numbers. Learning how to express one-to-one correspondence via a sequential algorithm, and how to extend this algorithm via a generative syntactic rule are the two key cultural innovations that form the basis of counting, and are also the key conceptual hurdles that children face when learning to count.
Carey, S., & Barner, D. (2019). Ontogenetic origins of human integer representations. Trends in Cognitive Sciences, 23(10), 823-835.