Survey on the Recent Studies of the Role of Diagrams in Mathematics from the Viewpoint of Philosophy of Mathematics

Kagaku Tetsugaku 47 (1):67-82 (2014)
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Abstract

In this paper, we would present an overview of the recent studies on the role of diagram in mathematics. Traditionally, mathematicians and philosophers had thought that diagram should not be used in mathematical proofs, because relying on diagram would cause to various types of fallacies. But recently, some logicians and philosophers try to show that diagram has a legitimate place in proving mathematical theorems. We would review such trends of studies and provide some perspective from viewpoint of philosophy of mathematics.

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Hiroyuki Inaoka
Kobe University

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References found in this work

The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
A Formal System for Euclid’s Elements.Jeremy Avigad, Edward Dean & John Mumma - 2009 - Review of Symbolic Logic 2 (4):700--768.
Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
Diagram-Based Geometric Practice.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 65--79.
The Withering Away of Formal Semantics?Neil Tennant - 1986 - Mind and Language 1 (4):302-318.

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