To infinity and beyond: Children generalize the successor function to all possible numbers years after learning to count
Bibliographic record
Abstract
Recent accounts of number word learning posit that when children learn toaccurately count sets (i.e., become "cardinal principle" or "CP" knowers),they have a conceptual insight about how the count list implements thesuccessor function - i.e., that every natural number *n *has a successordefined as *n+1* (Carey, 2004, 2009; Sarnecka & Carey, 2008). However,recent studies suggest that knowledge of the successor function emergessometime after children learn to accurately count, though it remainsunknown when this occurs, and what causes this developmental transition. Wetested knowledge of the successor function in 100 children aged 4 through 7and asked how age and counting ability are related to: (1) children'sability to infer the successors of all numbers in their count list, and (2)knowledge that *all *numbers have a successor. We found that children donot acquire these two facets of the successor function until they are about5.5 or 6 years of age - roughly 2 years after they learn to accuratelycount sets and become CP-knowers. These findings show that acquisition ofthe successor function is highly protracted, providing the strongestevidence yet that it cannot drive the cardinal principle induction. Wesuggest that counting experience, as well as knowledge of recursivecounting structures, may instead drive the learning of the successorfunction.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".