Center Calendar
"What's innate about integer concepts?", David Barner (University of California, San Diego - Department of Psychology)
Tuesday, April 27, 2021, 01:00pm
via Zoom EST: Email Jason Geller at
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.
Reading:
Carey, S., & Barner, D. (2019). Ontogenetic origins of human integer representations. Trends in Cognitive Sciences, 23(10), 823-835.
