Article ID: CBB044087153

David Hilbert and the foundations of the theory of plane area (2021)

unapi

This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry (1899). On the one hand, we offer a precise contextualization of this theory by considering it against its nineteenth-century geometrical background. Specifically, we examine some crucial steps in the emergence of the modern theory of geometrical equivalence. On the other hand, we analyze from a more conceptual perspective the significance of Hilbert’s theory of area for the foundational program pursued in Foundations. We argue that this theory played a fundamental role in the general attempt to provide a new independent basis for Euclidean geometry. Furthermore, we contend that our examination proves relevant for understanding the requirement of “purity of the method” in the tradition of modern synthetic geometry.

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https://data.isiscb.org/isis/citation/CBB044087153/

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Authors & Contributors
Hallett, Michael
Gambetta, Emanuele
Lorenat, Jemma
Wojcik, W.
Toepell, M.-M.
Stillwell, John
Concepts
Geometry
Philosophy of mathematics
Mathematics
Philosophy
Logic
Philosophy of science
Time Periods
19th century
20th century, early
20th century
18th century
Places
Italy
Europe
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