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Record W2755652180 · doi:10.1057/978-1-137-40808-2_11

The History of Algebra’s Impact on the Philosophy of Mathematics

2017· book-chapter· en· W2755652180 on OpenAlexaff
Audrey Yap

Bibliographic record

VenuePalgrave Macmillan UK eBooks · 2017
Typebook-chapter
Languageen
FieldMathematics
TopicHistory and Theory of Mathematics
Canadian institutionsUniversity of Victoria
Fundersnot available
KeywordsIdeal (ethics)Philosophy of mathematicsRange (aeronautics)EpistemologyDedekind cutMathematicsNatural (archaeology)Algebra over a fieldMathematics educationPure mathematicsPhilosophyHistoryEngineering

Abstract

fetched live from OpenAlex

StructuralismStructuralism in the philosophy of mathematics encompasses a range of views, many of which see structures, such as the natural numbers, as the proper objects of mathematics, rather than objects like individual numbers. This position is relatively recent—many see a paper by Paul Benacerraf in 1965 as one of its earliest articulations, though others have written about Richard DedekindDedekind, Richard as an earlier precursor. This paper will consider how Emmy NoetherNoether, Emmy , extending Dedekind’sDedekind, Richard work and general approach, contributed to a transition in mathematics enabling a fuller range of structuralist positions. Her work in ideal theory is a perfect illustration of the kind of conceptual step that permits seeing structures themselves as objects, which is required for certain contemporary views even to make sense.

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)0.002
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: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.011
Threshold uncertainty score0.058

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0020.002
Science and technology studies0.0030.013
Scholarly communication0.0050.007
Open science0.0010.002
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0110.002

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 head0.063
GPT teacher head0.276
Teacher spread0.213 · 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 designNot applicable
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

Citations2
Published2017
Admission routes1
Has abstractyes

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