Monotonicity Revisited: Mass Nouns and Comparisons of Purity
Bibliographic record
Abstract
Abstract Comparatives with more plus mass noun, like John has more milk than Bill, are naturally analyzed as referencing measure functions, functions like volume or weight that map individuals to degrees. Although such measure functions vary with context as well as the choice of mass noun, there are well known grammatical limitations on this variation. In particular, Schwarzschild (2006) proposes that only monotonic measure functions can enter into the interpretation of comparatives with more plus mass noun. While this Monotonicity Constraint has strong empirical support, Bale & Barner (2009) have drawn attention to data that seemingly contradict it. For example, There is more gold in the ring than in the bracelet can be evaluated based on whether the ring is made from purer gold than the bracelet. This seems to suggest that comparatives with more plus mass noun can reference purity, yet purity is non-monotonic ( Schwarzschild 2006; Wellwood 2015). Building on Solt (2018) and Bale & Schwarz (2020), we show here that comparisons of purity can be credited to monotonic proportional measure functions, thereby reconciling Bale & Barner (2009)’s observation with the Monotonicity Constraint. We provide independent support for this proposal, establishing that reference to the relevant monotonic proportional measure functions, but not to purity, yields meanings that accurately track speakers’ truth value judgments. Our analysis commits us to the assumption that the main clause and the comparative clause can invoke different measure functions. We propose that this is made possible by Skolemization and binding. Specifically, we posit covert expressions denoting measure functions which contain variables bound by different expressions in the two clauses.
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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 | 0.007 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.005 | 0.019 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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".