Two roads to the successor axiom

  title={Two roads to the successor axiom},
  author={Stefan Buijsman},
Most accounts of our knowledge of the successor axiom claim that this is based on the procedure of adding one. While they usually don’t claim to provide an account of how children actually acquire this knowledge, one may well think that this is how they get that knowledge. I argue that when we look at children’s responses in interviews, the time when they learn the successor axiom and the intermediate learning stages they find themselves in, that there is an empirically viable alternative. I… Expand
3 Citations
Is thirty-two three tens and two ones? The embedded structure of cardinal numbers
It is proposed that the syntax for building complex numerals, not the successor principle, represents a structural platform for numerical thinking in young children and regularity in numerical syntax facilitates the acquisition of generative properties of numbers. Expand
A Complete Bibliography of Publications in Synthese, 2020–2029
Abduction [336]. Abductive [11, 124]. ability [143]. Absence [188]. absences [233]. absurdity [154]. Acceptable [18]. accepting [120]. account [81, 169, 129, 13, 196, 168]. across [35]. Action [271,Expand


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  • M. Le Corre
  • Medicine
  • The British journal of developmental psychology
  • 2014
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Results show that acquisition of the successor function is highly protracted, providing the strongest evidence yet that it cannot drive the cardinal principle induction, and suggest that counting experience, as well as knowledge of recursive counting structures, may instead drive the learning of the predecessor function. Expand
Children acquire the later-greater principle after the cardinal principle.
Many have proposed that the acquisition of the cardinal principle is a result of the discovery of the numerical significance of the order of the number words in the count list. However, this need notExpand
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  • K. Wynn
  • Psychology
  • Cognitive Psychology
  • 1992
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Where Our Number Concepts Come From.
  • S. Carey
  • Psychology, Medicine
  • The journal of philosophy
  • 2009
In a recent book I present case studies of the acquisition of several important domains of conceptual representations, arguing that the details of the Acquisition process adjudicate among rival theories of concepts within cognitive science. Expand