Kant and non-euclidean geometry

Kant Studien 99 (1):80-98 (2008)
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Abstract

It is occasionally claimed that the important work of philosophers, physicists, and mathematicians in the nineteenth and in the early twentieth centuries made Kant’s critical philosophy of geometry look somewhat unattractive. Indeed, from the wider perspective of the discovery of non-Euclidean geometries, the replacement of Newtonian physics with Einstein’s theories of relativity, and the rise of quantificational logic, Kant’s philosophy seems “quaint at best and silly at worst”.1 While there is no doubt that Kant’s transcendental project involves his own conceptions of Newtonian physics, Euclidean geometry and Aristotelian logic, the issue at stake is whether the replacement of these conceptions collapses Kant’s philosophy into an unfortunate embarrassment.2 Thus, in evaluating the debate over the contemporary relevance of Kant’s philosophical project one is faced with the following two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics? Within this broad context, this paper aims to evaluate the Kantian project vis à vis the discovery and application of non-Euclidean geometries. Many important philosophers have evaluated Kant’s philosophy of geometry throughout the last century,3 but opinions with regard to the impact of non-Euclidean geometries on it diverge. In the beginning of the century there was a consensus that the Euclidean character of space should be considered as a consequence of the Kantian project, i.e., of the metaphysical view of space and of the synthetic a priori character of geometry. The impact of non-Euclidean geometries was then thought as undermining the Kantian project since it implied, according to positivists such..

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Amit Hagar
Indiana University, Bloomington

Citations of this work

Kant-Bibliographie 2008.Margit Ruffing - 2010 - Kant Studien 101 (4):487-538.
Maimon's Post-Kantian Skepticism.Emily Fitton - 2017 - Dissertation, University of Essex

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References found in this work

Essays on the Intellectual Powers of Man.Thomas Reid - 1785 - University Park, Pa.: Cambridge University Press. Edited by Derek R. Brookes & Knud Haakonssen.
Kant and the exact sciences.Michael Friedman - 1992 - Cambridge, Mass.: Harvard University Press.
Metaphysical Foundations of Natural Science.Immanuel Kant - 1970 - New York: Cambridge University Press. Edited by Michael Friedman.
An Inquiry Into the Human Mind.Thomas Reid - 1813 - Chicago: University of Chicago Press.

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