Synthese (4):1-29 (2019)

Landon D. C. Elkind
Western Kentucky University
We examine the influence of word choices on mathematical practice, i.e. in developing definitions, theorems, and proofs. As a case study, we consider Euclid’s and Euler’s word choices in their influential developments of geometry and, in particular, their use of the term ‘polyhedron’. Then, jumping to the twentieth century, we look at word choices surrounding the use of the term ‘polyhedron’ in the work of Coxeter and of Grünbaum. We also consider a recent and explicit conflict of approach between Grünbaum and Shephard on the one hand and that of Hilton and Pedersen on the other, elucidating that the conflict was engendered by disagreement over the proper conceptualization, and so also the appropriate word choices, in the study of polyhedra.
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DOI 10.1007/s11229-019-02287-6
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References found in this work BETA

Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos (ed.) - 1976 - Cambridge and London: Cambridge University Press.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.
The Philosophy of Mathematical Practice.Paolo Mancosu - 2009 - Studia Logica 92 (1):137-141.
Proofs and Refutations: The Logic of Mathematical Discovery.I. Lakatos, John Worrall & Elie Zahar - 1977 - British Journal for the Philosophy of Science 28 (1):81-82.

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