Eduardo Giovannini
University of Vienna
This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry. 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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DOI 10.1007/s00407-021-00278-z
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Proofs and Refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.

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