NDLI: The Original and the Copy. Leibniz, Kant and Hausdorff on the Problem of Space

Content Provider	Springer Nature Link
Author	Giovanelli, Marco
Copyright Year	2010
Abstract	The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz’s and Kant’s philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff’s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz’s or Poincaré’s thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff’s philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant’s infamous appeal to “intuition” can be judged by more appropriate standards.
Starting Page	283
Ending Page	313
Page Count	31
File Format	PDF
ISSN	09254560
Journal	Journal for General Philosophy of Science
Volume Number	41
Issue Number	2
e-ISSN	15728587
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-12-02
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ähnlichkeit Hausdorff Inkongruente Gegenstücke Kant Kongruenz Leibniz Nicht-Euklidische Geometrie Congruence Incongruent counterparts Non-Euclidean geometry Similarity Social Sciences Methodology of the Social Sciences Philosophy of Education History Philosophy of Science
Content Type	Text
Resource Type	Article
Subject	Philosophy Social Sciences History and Philosophy of Science

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