The Perception of Spatial Depth in Kepler’s and Descartes’ Optics: A Study of an Epistemological Reversal

  • Delphine BellisEmail author
Part of the Studies in History and Philosophy of Science book series (AUST, volume 41)


This paper is devoted to the explanation of the location and distance of objects in three-dimensional space through vision in the work of two major opticians of the 17th century, namely Kepler and Descartes. I show that, in his Dioptrique, Descartes took up from Kepler’s Ad Vitellionem Paralipomena a psychological procedure involved in vision and consisting in a trigonometric operation. But, whereas Kepler had resorted to this procedure to account for the illusory, imaginary location of objects seen through reflection or refraction, Descartes applied it to the perception of distance in non-deceptive direct vision. This brings about a complete shift regarding the epistemological value of the psychological operations involved in vision. I indeed show that this displacement reveals that Descartes saw his natural geometry of vision as an epistemological foundation for the integration of sense perception into his physics.


Visible Object Visual Space Psychological Dimension Crystalline Lens Visual Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Research for this article was made possible by a postdoctoral fellowship from the Max Planck Institut für Wissenschaftsgeschichte zu Berlin, within Vincenzo De Risi’s research group ‘Modern Geometry and the Concept of Space’ and by a Rubicon grant (446-10-031) funded by NWO (the Netherlands Organisation for Scientific Research) and the Marie Curie Cofund Action. Several versions of this paper were presented during seminars and conferences and greatly benefited from the audience’s comments. I would like to thank the organizers for giving me the opportunity to present my research during those events: Vincenzo De Risi, organizer of the 2011 Max Planck summer colloquium on theories of space; Anouk Barberousse and Anne-Lise Rey, organizers of the seminar of the Centre d’Histoire des Sciences et d’Épistémologie, Université Lille I; Sébastien Maronne and David Rabouin, organizers of the seminar ‘Mathématiques à l’âge classique,’ SPHERE research group, Université Paris VII; Jonathan Regier and Koen Vermeir, organizers of the international conference ‘Space, Knots, and Bonds,’ held at the Université Paris VII in June 2012. I would like to thank Tawrin Baker, Philippe Hamou, and Lucien Vinciguerra for their useful suggestions on earlier versions of this article. Many thanks are also due to Jonathan Regier and Charles Wolfe for their emendations to my English text. All translations are the author’s except where otherwise noted.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Research Foundation Flanders (FWO). Center for the History of Philosophy and ScienceRadboud University NijmegenNijmegenThe Netherlands

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