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
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
Thesis
Domski, Mary;
(2003)
Geometry and Experimental Method in Locke, Newton and Kant
Chapter
Guicciardini, Niccolò;
(2002)
Geometry, the Calculus and the Use of Limits in Newton's Principia
Article
Giovanelli, Marco;
(2010)
Urbild und Abbild: Leibniz, Kant und Hausdorff über das Raumproblem
Chapter
Gerhard Heinzmann;
(2016)
Kant et l'intuition épistémique
Article
Giovanelli, Marco;
(2008)
Kant, Helmholtz, Riemann und der Ursprung der geometrischen Axiome
Article
Shabel, Lisa;
(2003)
Reflections on Kant's Concept (and Intuition) of Space
Article
Jessica J. Williams;
(2018)
Kant on the Original Synthesis of Understanding and Sensibility
Article
Andrea Reichenberger;
(2021)
Émilie Du Châtelet on Space and Time
Article
Hon, Giora;
(2005)
Kant vs. Legendre on Symmetry: Mirror Images in Philosophy and Mathematics
Chapter
Friedman, Michael;
(2012)
Newton and Kant on Absolute Space: From Theology to Transcendental Philosophy
Chapter
Graciela De Pierris;
(2015)
Hume’s Skepticism and Inductivism Concerning Space and Geometry
Article
De Pierris, Graciela;
(2012)
Hume on Space, Geometry, and Diagrammatic Reasoning
Article
Biagioli, Francesca;
(2014)
Hermann Cohen and Alois Riehl on Geometrical Empiricism
Article
Anna Longo;
Ben Woodward;
(2017)
Infinitely Generative Structure: Fichte, Schelling, and Modern Geometry
Article
Heinzmann, Gerhard;
(2001)
The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré
Article
Wojcik, W.;
(2007)
Bernard Riemann's New Philosophy Project
Article
Meschini, Diego;
Lehto, Markku;
Piilonen, Johanna;
(2005)
Geometry, Pregeometry and Beyond
Chapter
Giulio Ferroni;
(2019)
Il punto e il cerchio: geometria dantesca
Be the first to comment!