What are mathematical diagrams?

Synthese 200 (2):1-29 (2022)
  Copy   BIBTEX

Abstract

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading.

Similar books and articles

The role of diagrams in mathematical arguments.David Sherry - 2008 - Foundations of Science 14 (1-2):59-74.
Diagrams as sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.
Mathematical rigor and proof.Yacin Hamami - 2022 - Review of Symbolic Logic 15 (2):409-449.
Groundwork for a Fallibilist Account of Mathematics.Silvia De Toffoli - 2021 - Philosophical Quarterly 7 (4):823-844.
Proof: Its nature and significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 1.
Diagrams and proofs in analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.

Analytics

Added to PP
2021-12-25

Downloads
506 (#20,315)

6 months
210 (#2,470)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

Citations of this work

Add more citations

References found in this work

Languages of Art.Nelson Goodman - 1970 - Philosophy and Rhetoric 3 (1):62-63.
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.
Rigor and Structure.John P. Burgess - 2015 - Oxford, England: Oxford University Press UK.
Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.

View all 55 references / Add more references