Interesting Esoterica

Who's Afraid of Mathematical Diagrams?

Article by Silvia De Toffoli
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Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear.

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journal
Philosophers

BibTeX entry

@article{WhosAfraidofMathematicalDiagrams,
	title = {Who's Afraid of Mathematical Diagrams?},
	abstract = {Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. },
	url = {https://philpapers.org/rec/DETWAO https://philpapers.org/archive/DETWAO.pdf},
	year = {forthcoming},
	author = {Silvia De Toffoli},
	comment = {},
	urldate = {2022-05-13},
	doi = {},
	journal = {Philosophers},
	volume = 0,
	issue = {},
	collections = {attention-grabbing-titles,the-act-of-doing-maths}
}