JEAN-PIERRE MARQUIS. From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory
Bibliographic record
Abstract
Jean-Pierre Marquis has written a number of interesting and original papers on the philosophical issues related to category theory (e.g., [Marquis 1995; Marquis 1998; Landry and Marquis 2005; Marquis 2006]). His recent book incorporates a number of themes that he has previously examined, but considered from a more definite perspective: in this book his principal objective is to establish the claim that category theory is a generalization of Felix Klein’s Erlangen program. The central tenet he urges here is that category theory should be thought of in essentially geometric terms. The philosophically precise and innovative way in which he develops this thesis makes the book relevant to all those with some interest in category theory, logic, the foundations of mathematics, and more particularly the interplay among them. Readers should include all members of Marquis’ intended audience—mathematicians, philosophers and historians alike. Although Marquis’ writing is clear and accessible, this book is primarily for those with some familiarity with the subject matter. Readers lacking sufficient background in logic, geometry, algebra, and category theory should expect to do some supplemental reading in order to assimilate the arguments; but it would surely be a worthwhile endeavour for anyone interested in the history and philosophy of category theory and its relation to the more general body of mathematics. This review will provide a summary of the main philosophical points developed by Marquis.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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".