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‘A REMARKABLE ARTIFICE’: LAPLACE, POISSON AND MATHEMATICAL PURITY

Part of: History of mathematics and mathematicians Measure and integration Proof theory and constructive mathematics General and miscellaneous specific topics

Published online by Cambridge University Press:  24 July 2023

BRAM PEL
BRAM PEL*
Affiliation:
INDEPENDENT SCHOLAR
*
E-mail: brampel.pel@gmail.com
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Abstract

In the early nineteenth century, a series of articles by Laplace and Poisson discussed the importance of ‘directness’ in mathematical methodology. In this thesis, we argue that their conception of a ‘direct’ proof is similar to the more widely contemplated notion of a ‘pure’ proof. More rigorous definitions of mathematical purity were proposed in recent publications by Arana and Detlefsen, as well as by Kahle and Pulcini: we compare Laplace and Poisson’s writings with these modern definitions of purity and show how the modern definitions fail to grasp some more nuanced aspects.

Keywords

mathematical puritytopical purityoperational puritypurity of methodLaplacePoissoncomplex substitution

MSC classification

Primary: 00A30: Philosophy of mathematics 01A50: 18th century 01A55: 19th century 03F20: Complexity of proofs 28-03: Historical (must also be assigned at least one classification number from Section 01)
Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 37
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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