Two roads to the successor axiom
Bibliographic Data
| ID | 10814520 |
|---|---|
| Authors | Stefan Buijsman (0000-0002-0004-0681, Stockholm University, corresponding author) |
| Year | 2020 |
| Volume | 197 |
| Issue | 3 |
| Pages | 1241-1261 |
| Publication date | 2020-03-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Synthese (JOURNAL) |
| Journal identifiers | ISSN: 0039-7857 • E-ISSN: 1573-0964 |
| Publisher | Springer Science and Business Media LLC (PUBLISHER) |
| DOI | 10.1007/s11229-018-1752-5 |
| OpenAlex | W2789953504 |
| Language | EN |
| Citations received | 4 |
| References cited | 32 |
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 argue that they could also learn it on the basis of a method that has to do with the structure of the numeral system. Specifically, that they (1) use the syntactic structure of the numeral system and (2) attend to the leftmost digits, the one with the highest place-value. Children can learn that this is a reliable method of forming larger numbers by combining two elements. First, a grasp of the syntactic structure of the numeral system. That way they know that the leftmost digit receives the highest value. Second, an interpretation of numerals as designating cardinal values, so that they also realise that increasing or adding digits on the lefthand side of a numeral produces a larger number. There are thus two, currently equally well-supported, ways in which children might learn that there are infinitely many natural numbers
Arithmetic · Axiom · Epistemology · Interpretation (philosophy) · Linguistics · Mathematical economics · Numeral system · Statistics · Successor cardinal · Value (mathematics) · Artificial Intelligence · Cognitive and developmental aspects of mathematical skills · Computer Science · History and Theory of Mathematics · Mathematics · Mathematics Education and Teaching Techniques · Philosophy
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Re-establishing the distinction between numerosity, numerousness, and number in numerical cognition
Building blocks for a cognitive science-led epistemology of arithmetic
Arithmetic thinking as the basis of children's generative number concepts
Children’s Counting and Concepts of Number
Time required for Judgements of Numerical Inequality
Children's acquisition of the number words and the counting system
Children's understanding of counting
How counting represents number
Learning to represent exact numbers
Three processes underlying the carry effect in addition - Evidence from eye tracking
| Citations per year | 0.67 |
|---|---|
| Citation span | 2020 - 2023 (4) |
| Highly cited | No |