Bibliographic record
Abstract
As its subtitle indicates, David Bostock’s Philosophy of Mathematics is an introductory work. It is significantly different from other recent books in being highly historical. There are extended discussions of Plato, Aristotle, the medievals, Kant, Mill, and so on. If, like me, you consider logicism, formalism, and intuitionism—whose heyday was a century ago—to be largely historical topics, then Bostock’s book is a very historical work indeed. This is its strength; it is also its weakness, though I do not mean this to be a criticism. Inevitably, by keeping the book within a reasonable limit of 300-odd pages, Bostock has given rather little time to current topics. That may trouble some, but I will return to this point below. The book covers a lot of ground. Some of the topics are well discussed; others may be a bit too quick. The discussion of real numbers, calculus, and the infinitesimals of Newton and Leibniz is sufficient for those familiar with the topics, but I dare say not for novices. On the other hand, some of the expositions are quite good. The chapter on logicism presents the usual material on Frege and Russell as well as Bostock’s own work on type theory. It ends with a discussion of non-standard models of arithmetic, which is very well done. His point is to address the question: what is logic? First-order logic allows such non-standard models; second-order does not. Bostock outlines some of the pros and cons of each, expressing a preference (rightly, I think) for second-order logic’s being genuine logic.
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
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.058 | 0.038 |
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".