And so on... : reasoning with infinite diagrams

Synthese 186 (1):371-386 (2012)
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Abstract

This paper presents examples of infinite diagrams whose use is more or less essential for understanding and accepting various proofs in higher mathematics. The significance of these is discussed with respect to the thesis that every proof can be formalized, and a “pre” form of this thesis that every proof can be presented in everyday statements-only form.

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10.1007/s11229-011-9985-6

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Citations of this work

What are mathematical diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
Who's Afraid of Mathematical Diagrams?Silvia De Toffoli - 2023 - Philosophers' Imprint 23 (1).
Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
Plans and planning in mathematical proofs.Yacin Hamami & Rebecca Lea Morris - 2020 - Review of Symbolic Logic 14 (4):1030-1065.

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References found in this work

Science and method.Henri Poincaré - 1914 - New York]: Dover Publications. Edited by Francis Maitland.
The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
Logical reasoning with diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - New York: Oxford University Press.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
In the Light of Logic.Solomon Feferman - 1998 - New York and Oxford: Oxford University Press.

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