title: Can statistical learning bootstrap the integers?
abstract: This paper examines Piantadosi, Tenenbaum, and Goodman's (2012) model for how children learn the relation between number words ("one" through "ten") and cardinalities (sizes of sets with one through ten elements). This model shows how statistical learning can induce this relation, reorganizing its procedures as it does so in roughly the way children do. We question, however, Piantadosi et al.'s claim that the model performs "Quinian bootstrapping," in the sense of Carey (2009). Unlike bootstrapping, the concept it learns is not discontinuous with the concepts it starts with. Instead, the model learns by recombining its primitives into hypotheses and confirming them statistically. As such, it accords better with earlier claims (Fodor, 1975, 1981) that learning does not increase expressive power. We also question the relevance of the simulation for children's learning. The model starts with a preselected set of15 primitives, and the procedure it learns differs from children's method. Finally, the partial knowledge of the positive integers that the model attains is consistent with an infinite number of nonstandard meanings-for example, that the integers stop after ten or loop from ten back to one.
authors.affiliation: Psychology Department, Northwestern University, 2029 Sheridan Road, Evanston, IL 60208, USA. rips@northwestern.edu
authors.forename: Lance J
authors.initials: LJ
authors.lastname: Rips
authors.forename: Jennifer
authors.initials: J
authors.lastname: Asmuth
authors.forename: Amber
authors.initials: A
authors.lastname: Bloomfield
mesh_terms: D002648:Child; D006801:Humans; D019359:Knowledge; D007802:Language; D007858:Learning; D008960:Models, Psychological
keywords: Bayesian inference; Bootstrapping; Number knowledge; Number learning; Statistical learning