The role of diagrams in mathematical arguments

Foundations of Science 14 (1-2):59-74 (2009)
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.
Keywords Diagram  Proof  Anti-platonism  Mathematical reasoning
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    References found in this work BETA
    James Robert Brown (1997). Proofs and Pictures. British Journal for the Philosophy of Science 48 (2):161-180.
    Marcus Giaquinto (1993). Diagrams: Socrates and Meno's Slave. International Journal of Philosophical Studies 1 (1):81 – 97.
    Marcus Giaquinto (1994). Epistemology of Visual Thinking in Elementary Real Analysis. British Journal for the Philosophy of Science 45 (3):789-813.

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    Citations of this work BETA
    Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
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