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Record W2122791911 · doi:10.1093/philmat/nkp016

DAVID BOSTOCK. Philosophy of Mathematics: An Introduction

2009· article· en· W2122791911 on OpenAlexaffabout
James Robert Brown

Bibliographic record

VenuePhilosophia Mathematica · 2009
Typearticle
Languageen
FieldPsychology
TopicPhilosophy and Theoretical Science
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsPhilosophy of mathematicsPhilosophyArt historySociologyEpistemologyArt

Abstract

fetched live from OpenAlex

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 imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: none
Teacher disagreement score0.058
Threshold uncertainty score0.193

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0050.005
Science and technology studies0.0010.003
Scholarly communication0.0030.007
Open science0.0010.002
Research integrity0.0030.005
Insufficient payload (model declined to judge)0.0580.038

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.

Opus teacher head0.038
GPT teacher head0.321
Teacher spread0.283 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreOther

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".

Quick stats

Citations0
Published2009
Admission routes2
Has abstractyes

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