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.
...MoreBook De Risi, Vincenzo (2015) Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age.
Similar Citations
Book
Vinci, Thomas C.;
(2015)
Space, Geometry, and Kant's Transcendental Deduction of the Categories
(/isis/citation/CBB001500573/)
Chapter
Gerhard Heinzmann;
(2016)
Kant et l'intuition épistémique
(/isis/citation/CBB981942154/)
Article
Giovanelli, Marco;
(2010)
Urbild und Abbild: Leibniz, Kant und Hausdorff über das Raumproblem
(/isis/citation/CBB001230056/)
Article
Giovanelli, Marco;
(2008)
Kant, Helmholtz, Riemann und der Ursprung der geometrischen Axiome
(/isis/citation/CBB001034987/)
Thesis
Domski, Mary;
(2003)
Geometry and Experimental Method in Locke, Newton and Kant
(/isis/citation/CBB001561970/)
Chapter
Guicciardini, Niccolò;
(2002)
Geometry, the Calculus and the Use of Limits in Newton's Principia
(/isis/citation/CBB000201990/)
Chapter
Pulte, Helmut;
(2001)
Order of Nature and Orders of Science: On the Material Philosophy of Nature and Its Changing Concepts of Science from Newton and Euler to Lagrange and Kant
(/isis/citation/CBB000101471/)
Article
Andrea Reichenberger;
(2021)
Émilie Du Châtelet on Space and Time
(/isis/citation/CBB162504912/)
Article
Shabel, Lisa;
(2003)
Reflections on Kant's Concept (and Intuition) of Space
(/isis/citation/CBB000340870/)
Article
Jessica J. Williams;
(2018)
Kant on the Original Synthesis of Understanding and Sensibility
(/isis/citation/CBB065350682/)
Article
Hon, Giora;
(2005)
Kant vs. Legendre on Symmetry: Mirror Images in Philosophy and Mathematics
(/isis/citation/CBB000651418/)
Chapter
Friedman, Michael;
(2012)
Newton and Kant on Absolute Space: From Theology to Transcendental Philosophy
(/isis/citation/CBB001500351/)
Article
De Pierris, Graciela;
(2012)
Hume on Space, Geometry, and Diagrammatic Reasoning
(/isis/citation/CBB001211479/)
Chapter
Graciela De Pierris;
(2015)
Hume’s Skepticism and Inductivism Concerning Space and Geometry
(/isis/citation/CBB279081372/)
Article
Biagioli, Francesca;
(2014)
Hermann Cohen and Alois Riehl on Geometrical Empiricism
(/isis/citation/CBB001421705/)
Book
Klep, Paul M. M.;
Stamhuis, Ida H.;
(2002)
The Statistical Mind in a Prestatistical Era: The Netherlands, 1750-1850
(/isis/citation/CBB000302282/)
Article
Anna Longo;
Ben Woodward;
(2017)
Infinitely Generative Structure: Fichte, Schelling, and Modern Geometry
(/isis/citation/CBB205102574/)
Article
Wojcik, W.;
(2007)
Bernard Riemann's New Philosophy Project
(/isis/citation/CBB000931659/)
Article
Heinzmann, Gerhard;
(2001)
The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré
(/isis/citation/CBB000102562/)
Chapter
Sutherland, Daniel;
(2010)
Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant
(/isis/citation/CBB001033539/)
Be the first to comment!