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Record W4385763597 · doi:10.1353/rss.2023.a904086

Squaring the Circles: a Genealogy of Principia ’s Dot Notation

2023· article· en· W4385763597 on OpenAlexvenueno aff
Landon D. C. Elkind

Bibliographic record

VenueRussell the Journal of Bertrand Russell Studies · 2023
Typearticle
Languageen
FieldMathematics
TopicHistory and Theory of Mathematics
Canadian institutionsnot available
Fundersnot available
KeywordsPeano axiomsNotationSquare (algebra)Conjunction (astronomy)Scope (computer science)TRACE (psycholinguistics)MathematicsPhilosophyCalculus (dental)Computer scienceLinguisticsDiscrete mathematicsArithmeticPhysicsGeometryProgramming language

Abstract

fetched live from OpenAlex

Abstract: Russell derived many of his logical symbols from the pioneering notation of Giuseppe Peano. Principia Mathematica (1910–13) made these “Peanese” symbols (and others) famous. Here I focus on one of the more peculiar notational derivatives from Peano, namely, Principia ’s dual use of a squared dot or dots for both conjunction and scope. As Dirk Schlimm has noted, Peano always had circular dots and only used them to symbolize scope distinctions. In contrast, Principia has squared dots and conventions such that some dots mark scope distinctions while others symbolize conjunction. How did this come to pass? In this paper I trace a genealogy of Principia ’s square dots back to Russell’s appropriation of Peano’s use of circular dots. Russell never explicitly justifies appropriating Peano’s notations to symbolize two distinct notions, but below I explain why Russell deployed Peano’s dot notations in this manner. Further, I argue that it was Cambridge University Press who squared the circular dots.

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)0.003
metaresearch head score (Gemma)0.007
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: Empirical · Consensus signal: none
Teacher disagreement score0.005
Threshold uncertainty score0.017

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0030.007
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0030.015
Scholarly communication0.0050.007
Open science0.0010.002
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0040.001

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 head0.088
GPT teacher head0.335
Teacher spread0.247 · 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
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
Published2023
Admission routes1
Has abstractyes

Explore more

Same venueRussell the Journal of Bertrand Russell StudiesSame topicHistory and Theory of MathematicsFrench-language works237,207