Grounding Concepts: an Empirical Basis for Arithmetical Knowledge - C.S. Jenkins
Bibliographic record
Abstract
Grounding Concepts and The Origin of Concepts are two new and important books. The first is by Carrie Jenkins, a philosopher of mathematics very much in the analytic tradition; the second is by Susan Carey, a psychologist who is well connected to philosophy. Both are deeply concerned with how we acquire our arithmetical concepts, and both are empiricist‐minded (perhaps naturalist‐minded is a better description of Carey). Yet their approaches are strikingly different. Jenkins aims to reconcile three conflicting beliefs: (i) our knowledge of arithmetic is a priori; (ii) the facts of arithmetic are objectively true (realism, which she characterizes as mathematics being independent of our mental lives); (iii) sensory input is the only source of knowledge. Her solution, in brief, is to say that we acquire arithmetic concepts through empirical experience, but we learn mathematical truths through the analysis of those concepts.
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How this classification was reachedexpand
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 | 0.002 | 0.003 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
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".