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Learning the Natural Numbers as a Child
Author(s) -
Buijsman Stefan
Publication year - 2019
Publication title -
noûs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.574
H-Index - 66
eISSN - 1468-0068
pISSN - 0029-4624
DOI - 10.1111/nous.12219
Subject(s) - peano axioms , natural (archaeology) , axiom , natural number , epistemology , consistency (knowledge bases) , basis (linear algebra) , dedekind cut , process (computing) , computer science , mathematics , artificial intelligence , philosophy , pure mathematics , discrete mathematics , algorithm , geometry , archaeology , history , operating system
How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the initial segment of the natural numbers on the basis of the Fregean definitions, but do not learn the natural number structure as a whole on the basis of Hume's principle. Therefore, we need to account for some of the consistency of our number concepts with the Dedekind‐Peano axioms in other terms.