Epistemic Roles of Diagrams in Short Proofs

Henrik Kragh Sørensen; Mikkel Willum Johansen

doi:10.1007/978-3-031-15146-0_20

Epistemic Roles of Diagrams in Short Proofs

Henrik Kragh Sørensen^*, Mikkel Willum Johansen

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

Recent case studies in the philosophy of mathematical practice have pointed out that certain types of diagrams play epistemic roles in mathematical proofs. To complement such case studies and provide a quantitative basis for further analysis and discussions, we undertake an empirical study based on a large and contemporary corpus of mathematical texts. Following an a priori assumption that diagrams in short proofs carry more epistemic warrant, we focus on 1- or 2-sentence proofs that refer to diagrams, and we build a corpus of such proofs from the arXiv. Based on this corpus we analyze and develop a typology of such proofs in order to conduct selected qualitative close-readings of diagrams in their argumentative contexts. This leads us to discuss tensions between visual and syntactical aspects of diagrams that suggest that hybrid diagrams play distinct roles in mathematical practice.

Original language	Danish
Title of host publication	Diagrammatic Representation and Inference
Number of pages	8
Publisher	Springer
Publication date	2022
Pages	235–242
Chapter	20
ISBN (Print)	978-3-031-15145-3
ISBN (Electronic)	978-3-031-15146-0
DOIs	https://doi.org/10.1007/978-3-031-15146-0_20
Publication status	Published - 2022
Event	Diagrams 2022: 13th International Conference on the Theory and Application of Diagrams - Sapienza Universita di Roma, Rome, Italy Duration: 13 Sep 2022 → 17 Sep 2022 http://www.diagrams-conference.org/2022/

Conference

Conference	Diagrams 2022
Location	Sapienza Universita di Roma
Country/Territory	Italy
City	Rome
Period	13/09/2022 → 17/09/2022
Internet address	http://www.diagrams-conference.org/2022/

Series	Lecture Notes in Computer Science
Volume	13462
ISSN	0302-9743

Access to Document

10.1007/978-3-031-15146-0_20

Cite this

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title = "Epistemic Roles of Diagrams in Short Proofs",

abstract = "Recent case studies in the philosophy of mathematical practice have pointed out that certain types of diagrams play epistemic roles in mathematical proofs. To complement such case studies and provide a quantitative basis for further analysis and discussions, we undertake an empirical study based on a large and contemporary corpus of mathematical texts. Following an a priori assumption that diagrams in short proofs carry more epistemic warrant, we focus on 1- or 2-sentence proofs that refer to diagrams, and we build a corpus of such proofs from the arXiv. Based on this corpus we analyze and develop a typology of such proofs in order to conduct selected qualitative close-readings of diagrams in their argumentative contexts. This leads us to discuss tensions between visual and syntactical aspects of diagrams that suggest that hybrid diagrams play distinct roles in mathematical practice.",

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AB - Recent case studies in the philosophy of mathematical practice have pointed out that certain types of diagrams play epistemic roles in mathematical proofs. To complement such case studies and provide a quantitative basis for further analysis and discussions, we undertake an empirical study based on a large and contemporary corpus of mathematical texts. Following an a priori assumption that diagrams in short proofs carry more epistemic warrant, we focus on 1- or 2-sentence proofs that refer to diagrams, and we build a corpus of such proofs from the arXiv. Based on this corpus we analyze and develop a typology of such proofs in order to conduct selected qualitative close-readings of diagrams in their argumentative contexts. This leads us to discuss tensions between visual and syntactical aspects of diagrams that suggest that hybrid diagrams play distinct roles in mathematical practice.

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