Bibliographic record
Abstract
Abstract There are two problems in Alcuin’s Propositiones, numbers 11 and 14, that fall under the rubric of what today would be called recreational logic. The problems are original to Alcuin, since no earlier versions are known, and may thus be considered to be the founding ones of this puzzle genre. This chapter deals with the implications that these two problems have had not only for recreational logic, but also for studying the relationship between logic and mathematics—an area that has produced an abundance of fascinating ideas, including those by Charles Peirce, Lewis Carroll, Bertrand Russell, and Kurt Gödel, among others. Prominent in bringing out the linkage between logic and mathematical method is the ancient Liar Paradox, which has led to ideas such as the unprovability of certain propositions within systems of logic. What Alcuin seemed to be conveying by including two logic problems in his text, therefore, is that they entail fundamental mathematical thinking, at the same time that they are intellectually entertaining.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.042 | 0.007 |
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".