The generative basis of natural number concepts.
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.
Leslie
Alan M
AM
Department of Psychology and Center for Cognitive Science, Rutgers University, 152 Frelinghuysen Road, Piscataway, NJ 08854, USA. aleslie@ruccs.rutgers.edu
Gelman
Rochel
R
Gallistel
C R
CR
D002648:Child; D002675:Child, Preschool; D003071:Cognition / Q000502:physiology*; D003210:Concept Formation / Q000502:physiology; D006801:Humans; D007223:Infant; D007858:Learning / Q000502:physiology*; D008433:Mathematics; D009323:Natural Language Processing; D013850:Thinking / Q000502:physiology*