Wilfried Sieg. Hilbert's Programs and Beyond. Oxford: Oxford University Press, 2013. ISBN 978-0-19-537222-9 (hbk); 978-0-19-970715-7 (e-book). Pp. xii + 439
Bibliographic record
Abstract
This book is a collection of previously published papers by Wilfried Sieg (with minor corrections marked in footnotes), together with a newly written Introduction (in two parts), and brief, informative ‘guides’ at the start of each of the sections into which the book is divided. The unifying theme of the book is the foundational work of Hilbert and Bernays, and, to a lesser extent, that of closely related figures such as von Neumann, Gentzen, and Gödel, with certain chapters discussing proof theory and its philosophical significance more generally. The book opens with two introductions; the first offers, as its title indicates, a ‘perspective on Hilbert's Programs’; the plural form, which also figures in the title of the book, indicates Sieg's view that Hilbert's work on the foundations of mathematics is spread across different time periods, in which different goals are set and different means used. The second introductory essay is a summarized timeline of the various papers and lecture notes of which these ‘programs’ are composed. Especially worth noting here is Sieg's view regarding the main tasks for the philosophy of mathematics in the aftermath of the foundational and proof-theoretic work examined in the book: first, to investigate the rôle of abstract structures in mathematical practice and in mathematical understanding. Second, to analyze the function of accessibility notions in both technical and philosophical work on the foundations of mathematics.
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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.072 | 0.034 |
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".