Pith. Sign in

RECORD

A footnote to The crisis in contemporary mathematics

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Boris Katz, Mikhail G. Katz, Sam Sanders

History and Overview · Submitted 8 Apr 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1804.02645 (version 1)
Pith IDDDBAQUWM, Pith's permanent record of this paper and its review
CitationBoris Katz, Mikhail G. Katz, Sam Sanders. "A footnote to The crisis in contemporary mathematics." arXiv:1804.02645 (2018). https://pith.science/paper/DDBAQUWM
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,329 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.07 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as 'a debasement of meaning.' The 'debasement' comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the 'debasement' comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle. Keywords: Constructive mathematics; Robinson's framework; infinitesimal analysis.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. contribution 0.93 0.74 0.04 asserted 0.98
s1 Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. result 0.46 0.10 0.16 asserted 1.00
s2 He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as 'a debasement of meaning.' The 'debasement' comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. result 0.84 0.67 0.14 asserted 0.75
s3 We elucidate the context of the 'debasement' comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle. contribution 1.00 0.87 0.14 asserted 0.95
s4 Keywords: Constructive mathematics; Robinson's framework; infinitesimal analysis. background 0.83 0.06 0.03 unclear 0.98

What kind of paper the classifier reports this is: position or commentary 0.95 · evidence from literature 0.85.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as 'a debasement of meaning.' The 'debasement' comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the 'debasement' comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle. Keywords: Constructive mathematics; Robinson's framework; infinitesimal analysis.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

What it cites · 5 sentences without a confident label

Cites as background 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.