The role of diagrams in mathematical arguments

Foundations of Science 14 (1-2):59-74 (2008)
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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.



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Citations of this work

Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
Diagrams and proofs in analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
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.

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