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How to learn the natural numbers: Inductive inference and the acquisition of number concepts

Authors
Publisher
Elsevier B.V.
Publication Date
Volume
106
Issue
2
Identifiers
DOI: 10.1016/j.cognition.2007.03.003
Keywords
  • Number Concept
  • Induction
  • Bootstrapping
  • Number Module
  • Concept Acquisition
Disciplines
  • Logic

Abstract

Abstract 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.

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