Proceedings of the Annual Meeting of the Cognitive Science Society

Conceptual development, both in childhood and across the history of science, is marked by moments of discontinuity: landmark events after which previously inexpressible thoughts and theories, incommensurable with the initial cognitive or scientific repertoire, become accessible. Despite longstanding interest, a computational account of these transitions that answers the deepest Fodorian nativist objections remains elusive. Here we present such an explanation by revisiting Carey's Quinian bootstrapping. Building upon models based on program induction, we develop an enriched paradigm in which discontinuous conceptual change becomes the invention of a new type system, related by structural analogy to the previous representation system, but also, crucially, generalizing beyond it. We instantiate our method in the classic domain of children's early mathematical development, modeling the acquisition of both natural and rational number. We find our model captures several previously unmodeled phenomena, and provides more parsimonious explanations for cross-linguistic universals and intervention effects in number learning.