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Record W2569613525 · doi:10.1086/714814

Mathematical Structure and Empirical Content

2021· article· en· W2569613525 on OpenAlexaff
M. Miller

Bibliographic record

VenueThe British Journal for the Philosophy of Science · 2021
Typearticle
Languageen
FieldArts and Humanities
TopicPhilosophy and History of Science
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsObservableMeaning (existential)Interpretation (philosophy)EpistemologySemantics (computer science)Content (measure theory)Empirical researchMathematicsMathematical economicsComputer sciencePhilosophyPhysicsQuantum mechanics

Abstract

fetched live from OpenAlex

Approaches to the interpretation of physical theories provide accounts of how physical meaning accrues to the mathematical structure of a theory. According to many standard approaches to interpretation, meaning relations are captured by maps from the mathematical structure of the theory to statements expressing its empirical content. In this article I argue that while such accounts adequately address meaning relations when exact models are available or perturbation theory converges, they do not fare as well for models that give rise to divergent perturbative expansions. Since truncations of divergent perturbative expansions often play a critical role in establishing the empirical adequacy of a theory, this is a serious deficiency. I show how to augment state-space semantics, a view developed by Beth and van Fraassen, to capture perturbatively evaluated observables even in cases where perturbation theory is divergent. This new semantics establishes a sense in which the calculations that underwrite the empirical adequacy of a theory are both meaningful and true, but requires departure from the assumption that physical meaning is captured entirely by the exact models of a theory.

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)0.011
metaresearch head score (Gemma)0.033
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesScience and technology studies
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.997
Threshold uncertainty score0.057

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0110.033
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0050.002
Science and technology studies0.0030.033
Scholarly communication0.0070.021
Open science0.0030.006
Research integrity0.0030.005
Insufficient payload (model declined to judge)0.0060.001

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 head0.141
GPT teacher head0.289
Teacher spread0.147 · 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.

Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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

Citations13
Published2021
Admission routes1
Has abstractyes

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