Abstract
According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by the preceding numeral. We have previously argued, however, that the conclusion of this Induction does not distinguish the standard meaning of the integers from nonstandard meanings in which, for example, "ten" could mean set sizes of 10, 20, 30, ... elements. Margolis and Laurence [Margolis, E., & Laurence, S. (2008). How to learn the natural numbers: Inductive inference and the acquisition of number concepts. Cognition, 106, 924939] believe that our argument depends on attributing to children "radically indeterminate" concepts. We show, first, that our conclusion is compatible with perfectly determinate meanings for "one" through "three." Second, although the inductive inference is indeed indeterminate  which is why it is consistent with nonstandard meanings  making it determinate presupposes the constraints that the inference is supposed to produce.
Original language  English (US) 

Pages (fromto)  940951 
Number of pages  12 
Journal  Cognition 
Volume  106 
Issue number  2 
DOIs 

State  Published  Feb 2008 
Keywords
 Induction
 Integers
 Natural number
 Number concepts
 Number learning
 Numerical cognition
ASJC Scopus subject areas
 Experimental and Cognitive Psychology
 Language and Linguistics
 Developmental and Educational Psychology
 Linguistics and Language
 Cognitive Neuroscience