Bibliographic record
Abstract
At several points we have had occasion to note the fact that logic in smooth worlds differs in certain subtle respects from the classical logic with which we are familiar. These differences have not been obtrusive, and in developing the calculus and its applications in a smooth world it has not been necessary to pay particular attention to them. Nevertheless, it is a matter of logical interest to examine these differences a little more closely, and also to formulate an explicit description of the logical system which underpins reasoning in smooth worlds. As explained in the Introduction, any smooth world may be taken to be a certain type of category called a topos , which may be thought of as a model for mathematical concepts and operations in much the same way as the universe of set theory serves as such a model. In particular, will contain an object, which we shall denote by Ω, playing the role of the set of truth values. In set theory, Ω is the set 2 consisting of two distinct individuals true and false ; we assume that, in, Ω contains at least two such distinct individuals. Now the key property of Ω in any topos is that (just as in set theory) maps from any given object X to Ω correspond exactly to parts of X , the map with constant value true corresponding to X itself, and the map with constant value false corresponding to the empty part of X .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gpt | no category Domain: not available · Genre: Methods About the Canadian research system: no · About a Canadian topic: no | Theoretical or conceptual | high |
| grok | no category Domain: not available · Genre: Other About the Canadian research system: no · About a Canadian topic: no | Theoretical or conceptual | medium |
| opus | no category Domain: not available · Genre: Other About the Canadian research system: no · About a Canadian topic: no | Theoretical or conceptual | medium |
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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, unvalidatedLabeled directly by 3 models reading the full record.
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".