Structuralism and Mathematical Practice in Felix Klein’s Work on Non-Euclidean Geometry†

Philosophia Mathematica 28 (3):360-384 (2020)
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Abstract

It is well known that Felix Klein took a decisive step in investigating the invariants of transformation groups. However, less attention has been given to Klein’s considerations on the epistemological implications of his work on geometry. This paper proposes an interpretation of Klein’s view as a form of mathematical structuralism, according to which the study of mathematical structures provides the basis for a better understanding of how mathematical research and practice develop.

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Citations of this work

Pasch's empiricism as methodological structuralism.Dirk Schlimm - 2020 - In Erich H. Reck & Georg Schiemer, The Pre-History of Mathematical Structuralism. Oxford: Oxford University Press. pp. 80-105.

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References found in this work

Scientific Representation: Paradoxes of Perspective.Bas C. Van Fraassen - 2008 - Oxford, GB: Oxford University Press UK.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Representation and Invariance of Scientific Structures.Patrick Suppes - 2002 - CSLI Publications (distributed by Chicago University Press).

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