International Studies in the Philosophy of Science 24 (1):1 – 14 (2010)
This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept formation as well as representations of proofs. In addition we note that 'visualization' is used in two different ways. In the first sense 'visualization' denotes our inner mental pictures, which enable us to see that a certain fact holds, whereas in the other sense 'visualization' denotes a diagram or representation of something
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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.
The Role of Diagrams in Mathematical Arguments.David Sherry - 2009 - Foundations of Science 14 (1-2):59-74.
Representation and Productive Ambiguity in Mathematics and the Sciences.Emily Grosholz - 2007 - Oxford University Press.
Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.James Robert Brown - 1999 - Routledge.
Citations of this work BETA
Conceptual Metaphors and Mathematical Practice: On Cognitive Studies of Historical Developments in Mathematics.Dirk Schlimm - 2013 - Topics in Cognitive Science 5 (2):283-298.
Handling Mathematical Objects: Representations and Context.Jessica Carter - 2013 - Synthese 190 (17):3983-3999.
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