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The generative basis of natural number concepts
Alan M Leslie1, Rochel Gelman, C R Gallistel
1Department of Psychology and Center for Cognitive Science, Rutgers University, 152 Frelinghuysen Road, Piscataway, NJ 08854, USA. aleslie@ruccs.rutgers.edu
Abstract:
Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes.
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