And so on...: reasoning with infinite diagrams

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

Abstract
This paper presents examples of infinite diagrams (as well as infinite limits of finite 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
Keywords Diagrammatic reasoning  Infinite diagrams  Formalizability thesis
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DOI 10.1007/s11229-011-9985-6
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References found in this work BETA

The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
A Shorter Model Theory.Wilfrid Hodges - 2000 - Studia Logica 64 (1):133-134.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
A Formal System for Euclid’s Elements.Jeremy Avigad, Edward Dean & John Mumma - 2009 - Review of Symbolic Logic 2 (4):700--768.
The Derivation-Indicator View of Mathematical Practice.Jody Azzouni - 2004 - Philosophia Mathematica 12 (2):81-106.

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Citations of this work BETA

Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
Mathematical Inference and Logical Inference.Yacin Hamami - 2018 - Review of Symbolic Logic 11 (4):665-704.
Diagrams in Mathematics.Carlo Cellucci - 2019 - Foundations of Science 24 (3):583-604.

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