Synthese (forthcoming)

Silvia De Toffoli
Princeton University
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 (or both). I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain (away) 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.
Keywords Mathematical Diagram  Visualization  Illustration  Mathematical Proof  Heuristic  Anschauung
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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.
The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
How Deep is the Distinction Between A Priori and A Posteriori Knowledge?Timothy Williamson - 2013 - In Albert Casullo & Joshua C. Thurow (eds.), The A Priori in Philosophy. Oxford University Press. pp. 291-312.

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