Bibliographic record
Abstract
Principia Mathematica *38 introduces what it calls “Relations and Classes Derived from a Double Descriptive Function”. The notion of a relation-e (relation in extension) so derived is called an operation, and of course all dyadic relation-e theorems rely ultimately on the comprehension axiom schema for relations in intension given at *12.11. But in attempting to give a general pattern of definition, *38 uses the odd-looking “x?y ” which lends itself to the misconception that is itself an operation sign. The informal summary makes matters worse, writing “E!(x?y)” which is ungrammatical. This paper argues that with P, R and S as relation-e variables and ?, ?, and ? as class variables, operations are comprehended by wffs such as “ P=x?y”, “?=???” and “P=R?S”. Relying on triadic relations-e, I explain how the sign ? can be entirely avoided using comprehension. Along the way, puzzling cases such as ? and ? are resolved. [Greek and other symbols do not repoduce here. See the first page of the paper for the correct abstract.--Ed.]
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.027 | 0.011 |
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".