Children acquire the later‐greater principle after the cardinal principle
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Many have proposed that the acquisition of the cardinal principle (CP) is a result of the discovery of the numerical significance of the order of the number words in the count list. However, this need not be the case. Indeed, the CP does not state anything about the numerical significance of the order of the number words. It only states that the last word of a correct count denotes the numerosity of the counted set. Here, we test whether the acquisition of the CP involves the discovery of the later-greater principle - that is, that the order of the number words corresponds to the relative size of the numerosities they denote. Specifically, we tested knowledge of verbal numerical comparisons (e.g., Is 'ten' more than 'six'?) in children who had recently learned the CP. We find that these children can compare number words between 'six' and 'ten' only if they have mapped them onto non-verbal representations of numerosity. We suggest that this means that the acquisition of the CP does not involve the discovery of the correspondence between the order of the number words and the relative size of the numerosities they denote.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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 it