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 of. 15 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 meaningsfor example, that the integers stop after ten or loop from ten back to one.
Original language  English (US) 

Pages (fromto)  320330 
Number of pages  11 
Journal  Cognition 
Volume  128 
Issue number  3 
DOIs 

State  Published  Sep 1 2013 
Keywords
 Bayesian inference
 Bootstrapping
 Number knowledge
 Number learning
 Statistical learning
ASJC Scopus subject areas
 Experimental and Cognitive Psychology
 Language and Linguistics
 Developmental and Educational Psychology
 Linguistics and Language
 Cognitive Neuroscience