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Record W7117291707 · doi:10.21071/refime.v32i2.17849

Arithmetic and the Reality of Numbers in the Late Latin Middle Ages

2025· article· en· W7117291707 on OpenAlexaff
Kamil Majcherek

Bibliographic record

VenueRevista Española de Filosofía Medieval · 2025
Typearticle
Languageen
FieldArts and Humanities
TopicHistorical Philosophy and Science
Canadian institutionsTrinity College
Fundersnot available
KeywordsMiddle AgesObject (grammar)Division (mathematics)MetaphysicsRealism

Abstract

fetched live from OpenAlex

The late Middle Ages (ca. 1270-1400) in the Latin West witnessed an extraordinary rise of interest in the metaphysical status of numbers. This paper is a case study of one of the most popular arguments in favour of realism about numbers: the view according to which numbers are extramental entities distinct from the things that they number. Part one is a reconstruction of the realist argument, which is based on the commonly accepted division of sciences into real sciences and rational sciences. It is an equally commonly accepted claim that arithmetic is one of the real sciences. On the realist interpretation, for a science to be real, its object must be real. Thus, since the object of arithmetic is number, numbers must have extramental reality. Part two is an analysis of several most interesting anti-realist rebuttals of the above argument.

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 distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation 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: Empirical · Consensus signal: Empirical
Teacher disagreement score0.638
Threshold uncertainty score0.429

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.049
GPT teacher head0.259
Teacher spread0.210 · 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 teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
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

Citations0
Published2025
Admission routes1
Has abstractyes

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