How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts

Cognition 106 (2):924-939 (2008)
Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. Ó 2007 Elsevier B.V. All rights reserved
Keywords number concepts  bootstrapping  number module
Categories (categorize this paper)
DOI 10.1016/j.cognition.2007.03.003
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

View all 8 references / Add more references

Citations of this work BETA

View all 11 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

23 ( #128,632 of 1,726,249 )

Recent downloads (6 months)

10 ( #66,646 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.