Chapter ID: CBB679809730

Kant on Geometry and Experience (2015)

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Towards the end of the eighteenth century, at the height of the German Enlightenment, Immanuel Kant developed a revolutionary theory of space and geometry that aimed to explain the distinctive relation of the mathematical science of geometry to our experience of the world around us—both our ordinary perceptual experience of the world in space and the more refined empirical knowledge of this same world afforded by the new mathematical science of nature. From the perspective of our contemporary conception of space and geometry, as it was first developed in the late nineteenth century by such thinkers as Helmholtz, Mach, and Poincaré, Kant’s earlier conception thereby involves a conflation of what we now distinguish as mathematical, perceptual, and physical space. According to this contemporary conception, mathematical space is the object of pure geometry, perceptual space is that within which empirical objects are first given to our senses, and physical space results from applying the propositions of pure geometry to the objects of the (empirical) science of physics—which, first and foremost, studies the motions of such objects in (physical) space. Yet it is essential to Kant’s conception that the three types of space (mathematical, perceptual, and physical) among which we now sharply distinguish are necessarily identical with one another, for it is in precisely this way, for Kant, that a priori knowledge of the empirical world around us is possible.

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Authors & Contributors
Heinzmann, Gerhard
Giovanelli, Marco
De Pierris, Graciela
Woodward, Ben
Reichenberger, Andrea
Longo, Anna
Journals
Azimuth
Synthese
Studies in History and Philosophy of Science
Science in Context
Revue d'Histoire des Sciences
Philosophia Naturalis
Publishers
Oxford University Press
Aksant Academic Publishers
Indiana University
Concepts
Outer space
Geometry
Mathematics
Philosophy of mathematics
Philosophy
Philosophy of science
People
Kant, Immanuel
Newton, Isaac
Riemann, Georg Friedrich Bernhard
Poincaré, Jules Henri
Leibniz, Gottfried Wilhelm von
Helmholtz, Hermann Ludwig Ferdinand von
Time Periods
18th century
19th century
17th century
Places
Europe
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