# Who’s afraid of mathematical diagrams?

*Philosophers' Imprint*(forthcoming)

# 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.# Author's Profile

# DOI

10.3998/phimp.1348

# Analytics

**Added to PP**

2021-12-30

**Downloads**

436 (#19,349)

**6 months**

174 (#2,757)

**Historical graph of downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.*