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The role of diagrams in mathematical arguments
Foundations of Science 14 (1-2):59-74 (2008)
Abstract
Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs.Author's Profile
Reprint years
2009
DOI
10.1007/s10699-008-9147-6
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Citations of this work
Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (1):51-89.
Diagrams and proofs in analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
What Philosophy of Mathematical Practice Can Teach Argumentation Theory About Diagrams and Pictures.Brendan Larvor - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 239--253.
Mathematics as the art of abstraction.Richard L. Epstein - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 257--289.
References found in this work
Tractatus Logico-Philosophicus.Ludwig Wittgenstein, G. C. M. Colombo & Bertrand Russell - 2013 - New York: Routledge.
Tractatus Logico-Philosophicus.Ludwig Wittgenstein - 1956 - Revista Portuguesa de Filosofia 12 (1):109-110.
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