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Geometry and Measurement in Otto Hölder's Epistemology

Abstract : The aim of the paper is to analyze Hölder’s understanding of ge- ometry and measurement presented in Intuition and Reasoning (1899), The Axioms of Quantity and the Theory of Measurement (1901) and The Mathematical Method (1924). The paper explores the relations between a) Hölder’s demar- cation of geometry from arithmetic based on the notion of given concepts, b) his philosophical stance towards Kantian apriorism and empiricism, and c) the choice of Dedekind’s continuity in the axiomatic formulation of the theory of magnitudes. The paper shows that the choices made at the axiomatic level reflect Hölder’s epistemological framework, and individuates the originality of his approach in the case by case analysis of deductive procedures.
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Submitted on : Thursday, August 30, 2012 - 3:07:28 PM
Last modification on : Monday, March 2, 2020 - 4:04:03 PM

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Paola Cantu. Geometry and Measurement in Otto Hölder's Epistemology. Philosophia Scientiae, Editions Kime, 2012, 17 (1), pp.131--164. ⟨10.4000/philosophiascientiae.832⟩. ⟨halshs-00726529⟩

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