Who’s afraid of mathematical diagrams?

Philosophers' Imprint (forthcoming)
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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.

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Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

Citations of this work

What are mathematical diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.

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Languages of Art.Nelson Goodman - 1970 - Philosophy and Rhetoric 3 (1):62-63.
What metaphors mean.Donald Davidson - 2010 - In Darragh Byrne & Max Kölbel (eds.), Critical Inquiry. Routledge. pp. 31.
What Metaphors Mean.Donald Davidson - 1978 - Critical Inquiry 5 (1):31-47.
The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.

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