Bibliographic record
Abstract
To what extent is the compositional structure of quantity terms in natural language aligned with the structure of the quantity calculus commonly used in scientific practice, a calculus that critically relies on mathematical operations like division and the computation of quotients? In pioneering work, Coppock (2021) addresses this general question through a case study on the English preposition "per", as in "0.9 grams per milliliter". Coppock proposes that "per" expresses the operation of quantity division, an operation that forms quantities like 0.9g/mL by using ratios of measurements from different dimensions. Here we show that this “division theory” of "per" makes the wrong prediction with respect to statements about measures of density and concentration. We argue that these types of expressions call for an “anaphoric theory” ofper. On this analysis, anaphora allows for the composition to invoke multiple measurements in basic dimensions, creating the appearance of reference to complex quantities like 0.9g/mL, even though no such quantities are actually composed nor denoted in the formal semantics.
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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 | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.012 |
| Scholarly communication | 0.005 | 0.025 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".