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- Title
# Geometric diagrams as an effective notation

- Authors
## Mumma, John

- Abstract
## In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's ‘Why a diagram is (sometimes) worth 10,000 words’, between diagrammatic and sentential notations as a means for presenting geometric proofs. Wittgenstein takes up the question of mathematical notation and proof in Section III of Remarks on the Foundations of Mathematics. After discussing his observations on a proof's ‘characteristic visual shape’ in Section III with respect to arithmetical proofs, the paper shows how the notion of a characteristic visual shape illuminates the special effectiveness of diagrammatic notation in geometry.

- Publication
## Philosophical Investigations, 2024, Vol 47, Issue 4, p558

- ISSN
## 0190-0536

- DOI
## 10.1111/phin.12440