Husserl Studies

, Volume 20, Issue 3, pp 207–267 | Cite as

Questions Regarding Husserlian Geometry and Phenomenology. A Study of the Concept of Manifold and Spatial Perception

  • Luciano Boi


Spatial Perception 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. E.D. Adrian, The Physical Background of Perception (Clarendon Press, Oxford, 1967).Google Scholar
  2. R.B. Angel, “The Geometry of Visibles,” Noûs 8(2) (1974): 87–117.Google Scholar
  3. F. Atteneave, “Criteria for a Tenable Theory of Form Perception,” W. Wathen-Dunn (eds.), Models for the Perception of Speech and Visual Form (Cambridge, Mass.: MIT Press, 1967), pp. 56–67.Google Scholar
  4. A.M. Battro, “Riemannian Geometries of Variable Curvature in Visual Space: Visual Alleys, Horopters, and Triangles in Big Open Fields,” Perception 5(1976): 9–23.Google Scholar
  5. O. Becker, “Beiträge zur phänomenologischen Begründung der Geometrie und ihrer physikalischen Anwendung,” Jahrbuch für Philosophie und phänomenologische Forschung IV (1923).Google Scholar
  6. A. Berthoz, “Reference Frames for the Perception and Control of Movement,” in J. Paillard (ed.), Brain and Space (Oxford: Oxford University Press, 1991).Google Scholar
  7. A. Berthoz, Le sens du mouvement (Paris: Odile Jacob, 1996).Google Scholar
  8. H. Blum, “Biological Shape and Visual Science,” Journal of Theoretical Biology 38 (1973): 205–287.Google Scholar
  9. L. Boi, “Le concept de variété et la nouvelle géométrie de l’espace dans la pensée de Bernhard Riemann,” Archives Internationales d’Histoire des Sciences 134(45) (1995): 82–128.Google Scholar
  10. L. Boi, “Les géométries non euclidiennes, le problème philosophique de l’espace et la conception transcendantale; de Helmholtz et Kant, les néo-kantiens, Einstein, Poincaré et Mach,” Kant-Studien 87(3) (1996): 257–289.CrossRefGoogle Scholar
  11. L. Boi, “The Concepts of Connection and Group in the Perception Process,” Journal of Mathematical Psychology (2004), forthcoimg.Google Scholar
  12. L. Boi, Le problème mathématique de l’espace. Une quête de l’intelligible (Heidelberg, Berlin: Springer-Verlag, 1995).Google Scholar
  13. L. Boi, “The Role of Intuition and Formal Thinking in Kant, Husserl and in Modern Mathematics and Physics,” Mathesis (2004), forthcoming.Google Scholar
  14. L. Boi, Géométrie et Phénoménologie de la Perception. Modèles mathématiques et interprétations philosophiques de la perception spatiale (Paris, 2004) (forthcoming).Google Scholar
  15. L. Boi and L. Verner, “Sur quelques aspects phénoménologiques, géométriques et esthétiques de la perception et de la relation entre surface, forme et couleur,” VISIO, Special Issue “Cultural Cognition and Space Cognition” 6(2–3) (2001): 205–247.Google Scholar
  16. E.G. Boring, “Visual Perception as Invariance,” Psychological Review 59 (1952): 141–148.Google Scholar
  17. J. Bouveresse, Langage, perception et réalité, vol. 1 (Nîmes: J. Chambon, 1995).Google Scholar
  18. F. Brentano, Untersuchungen zur Sinnespsychologie (Hamburg: Meiner, 1979), first edition, 1907.Google Scholar
  19. F. Brentano, Psychology from an Empirical Standpoint, in O. Kraus (ed.) (English edition edited by L. L. McAlister, London: Routledge & Kegan Paul, 1973) (first German edition published in 1874).Google Scholar
  20. L.E.J. Brouwer, “Consciousness, Philosophy, and Mathematics”, in Collected Works, vol. 1: Philosophy and Foundations of Mathematics (Amsterdam: North-Holland, 1975).Google Scholar
  21. L.E.J. Brouwer, “Über die Abbildung von Mannigfaltigkeiten,” Mathematische Annalen 71 (1911): 97–115.Google Scholar
  22. V. Bruce, P. Green and M. Georgeson, Visual Perception. Physiology, Psychology, and Ecology, 3rd edn. (Sussex: Psychology Press, 1996).Google Scholar
  23. E.H. Carlton and R.N. Shepard, “Psychologically Simple Motions as Geosedic Paths. I. Asymmetric Objects,” Journal of Mathematical Psychology 34 (1990): 127–188.Google Scholar
  24. É. Cartan, “La géométrie des groupes de transformations,” Journal de Mathématiques Pures et Appliquées 6 (1927): 11–119.Google Scholar
  25. E.C. Carterette and M.P. Friedman, Handbook of Perception, vol. III: Biology of Perceptual Systems (New York: Academic Press, 1974).Google Scholar
  26. E. Cassirer, “The concept of Group and the Theory of Perception,” Philosophy and Phenomenological Research IV (1944).Google Scholar
  27. M. Cesa-Bianchi, A. Beretta and R. Luccio, La percezione (Milan: Franco Angeli Editore, 1977).Google Scholar
  28. K.C. Chen, “A Group-Theoretic Analysis of Mental Space Isometries in Form Recognition,” Journal of Mathematical Psychology 37(1993): 401–420.Google Scholar
  29. U. Claesges, Edmund Husserls Theorie der Raumkonstitution (The Hague: Martinus Nijhoff, 1964).Google Scholar
  30. W.K. Clifford, Lectures and Essays, vol. I (London: Macmillan, 1879).Google Scholar
  31. H. Conrad-Martius, “Zur Ontologie und Erscheinungslehre der realen Auβenwelt,” Jahrbuch für Philosophie und phänomenologische Forschung 3(1920): 345-396.Google Scholar
  32. Da Silva, “Husserl’s Phenomenology and Weyl’s Predicativism,” Synthese 110(2) (1997): 277–296.Google Scholar
  33. M. Delbrück, Mind from Matter? (Palo Alto, California: Blackwell Scientific Publishers, 1986).Google Scholar
  34. Ch. Ehrenfels, “Über Gestaltqualitäten,” Vierteljahrschrift für wissenschaftliche Philosophie XIV (1890): 249–292.Google Scholar
  35. W. D. Ellis (ed.), A Source Book of Gestalt Psychology (London: Routledge & Kegan Paul, 1967).Google Scholar
  36. F. Enriques, “Sulla spiegazione psicologica dei postulati della geometria,” Rivista di Filosofia IV(3) (1901): 171–195.Google Scholar
  37. D. F⊘llesdal, “Phenomenology,” in E.C. Carterette and M.P. Friedmann (eds.), Handbook of Perception (New York: Academic Press, 1974), pp. 377–386.Google Scholar
  38. J.J. Gibson, The Perception of the Visual World (Boston: Houghton Mifflin, 1950).Google Scholar
  39. J.J. Gibson, The Senses Considered as Perceptual System (Boston: Houghton Mifflin, 1966).Google Scholar
  40. R.L. Gregory, The Intelligent Eye (London: Weidenfeld and Nicolson, 1970).Google Scholar
  41. R.L. Gregory, Eye and Brain. The Psychology of Seeing, 5th edn. (Princeton: Princeton University Press, 1997).Google Scholar
  42. N.R. Hanson, Patterns of Discovery, An Inquiry into the Conceptual Foundations of Science (Cambridge: Cambridge University Press, 1958).Google Scholar
  43. C.W. Harvey, Husserl’s Phenomenology and the Foundations of Natural Science (Athens: Ohio University Press, 1989).Google Scholar
  44. S. Helgason, Differential Geometry, Lie Groups and Symmetric Space (New York: Academic Press, 1978).Google Scholar
  45. H. Helmholtz, Handbuch der physiologischen Optik, 3 vols. (Leipzig: J.A. Barth, 1867).Google Scholar
  46. H. Helmholtz, Wissenschaftliche Abhandlungen, vol. II (Leipzig: J.A. Barth, 1883).Google Scholar
  47. J.F. Herbart, Psychologie als Wissenschaft. Neu gegründet auf Erfahrung, Metaphysik und Mathematik (Königsberg, 1825).Google Scholar
  48. E. Hering, Grundzüge der Lehre vom Lichtsinn (Berlin: Springer-Verlag, 1905).Google Scholar
  49. D. Hilbert and S. Cohn-Vossen, Anschauliche Geometrie (Berlin: Springer-Verlag, 1932).Google Scholar
  50. W.C. Hoffman, “The Lie Algebra of Visual Perception,” Journal of Mathematical Psychology 3 (1966): 65–98.Google Scholar
  51. J. Hopking, “Visual Geometry,” The Philosophical Review 82(1) (1973): 3–34.Google Scholar
  52. I.P. Howard, “Orientation and Motion in Space,” in Handbook of Perception, vol. III: Biology of Perceptual Systems (New York; Academic Press, 1974).Google Scholar
  53. E. Husserl, Logische Untersuchungen, vols. I–III (Tü bingen: Max Niemeyer, 1980) (Logical Investigations, English edition translated by J. N. Findlay, London: Routledge & Kegan Paul, 1973).Google Scholar
  54. E. Husserl, The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy (translated by D. Carr, Evanston, Ill.: Northwestern University Press, 1970).Google Scholar
  55. E. Husserl, Formal and Transcendental Logic (translated by D. Cairns, The Hague: Nijhoff, 1969).Google Scholar
  56. E. Husserl, Ding und Raum, Vorlesungen 1907 (herausgegeben von U. Claesges, The Hague: Martinus Nijhoff, 1973) (english translation by R. Rojcewicz, Thing and SpaceLectures of 1907, Dordrecht: Kluwer Academic Publishers, 1997).Google Scholar
  57. E. Husserl, in I. Strohmeyer (ed.), Husserliana – Gesammelte Werke, vol. XXI: Studien zur Arithmetik und Geometrie (The Hague: Nijhoff, 1983), texts from 1886–1901.Google Scholar
  58. E. Husserl, Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy. First book: General Introduction to a Pure Phenomenology (translated by F. Kersten, The Hague: Martinus Nijhoff, 1982).Google Scholar
  59. E. Husserl, Ideas Pertaining to a Pure Phenomenology of Constitution. Second book: Studies in the Phenomenology of Constitution (translated by R. Rojcewicz and A. Schuwer, Dordrecht: Kluwer Academic Publishers, 1989).Google Scholar
  60. P. Hut, “Turning ‘The Hard Problem’ Upside Down and Sideways,’ Journal of Consciousness Studies 3(4) (1996): 313–329.Google Scholar
  61. P. Hut, “Structuring Reality: The Role of Limits,” in J.L. Casti and A. Karlqvist (eds.), Boundaries and Barriers. On the Limits to Scientific Knowledge (Reading, MA: Addison-Wesley, 1996), pp. 148–187.Google Scholar
  62. M. Imbert, “La vision,” in Ch. Kayser (ed.), Traité de physiologie, tome II (Paris: Flammarion, 1976), pp. 1083–1191.Google Scholar
  63. W. James, “The Perception of Space. (I) and (II),” Mind 45 (1887): 1–30; 47 (1887): 183–211.Google Scholar
  64. W. James, The Principles of Psychology, vol. I (Cambridge, MA: Harvard University Press, 1981).Google Scholar
  65. G. Kanizsa, Organization in Vision (New York: Praeger, 1979).Google Scholar
  66. I. Kant, Kritik der reinen Vernunft (1781–1787) (Hamburg: Felix Meiner Verlag, 1990).Google Scholar
  67. P. Kerszberg, “Of Exact and Inexact Essences in Modern Physical Science,” in L. Hardy and L. Embree (eds.), Phenomenology of Natural Science (Amsterdam: Kluwer Academic Publishers, 1992).Google Scholar
  68. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, vols. I and II (New York: Interscience Publishers, 1963).Google Scholar
  69. K. Koffka, Principles of Gestalt Psychology (New York: Harcourt, 1935).Google Scholar
  70. W. Köhler, Die physischen Gestalten in Ruhe und in stationärem Zustand (Erlangen: Verlag der Philosophischen Akademie, 1924).Google Scholar
  71. W. Köhler, Gestalt Phychology (New York: H. Liveright, 1929).Google Scholar
  72. D. Lohmar, Phänomenologie der Mathematik, in Phænomenologica (Dordrecht: Kluwer Academic Publishers, 1989).Google Scholar
  73. G. Longo, “The Mathematical Continuum: From Intuition to Logic,” (Paris: Ecole Normale Supérieure), Preprint, LIENS 97/12, pp. 3–29.Google Scholar
  74. Z.K. Lorenz, The Role of Gestalt Perception in Animal and Human Behaviour, in L.L. Whyte (ed.), Aspects of Form (New York: Elsevier Publishing Company, 1968).Google Scholar
  75. E. Mach, Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung (Leipzig: J.A. Barth, 1906).Google Scholar
  76. K. Mulligan, “Perception,” in B. Smith and D.W. Smith (eds.), The Cambridge Companion to Husserl (Cambridge: Cambridge University Press, 1995), pp. 168–238.Google Scholar
  77. F. Nef, L’objet quleconque (Paris: Vrin, 1998).Google Scholar
  78. N. O’Connor and B. Hermelin, Seeing and Hearing and Space and Time (London: Academic Press, 1978).Google Scholar
  79. J. Paillard, “Motor and Representational Framing of Space,” in J. Paillard (ed.), Brain and Space (Oxford; Oxford University Press, 1991).Google Scholar
  80. S.E. Palmer, “The Role of Symmetry in Shape Perception,” Acta Psychologica 59 (1985): 67–90.Google Scholar
  81. S.E. Palmer, “Modern Theories of Gestalt Perception,” in G.W. Humphreys (ed.), Understanding vision (Oxford: Blackwell, 1992).Google Scholar
  82. R. Penrose, The Emperor’s New Mind. Concerning Computers, Minds, and The Laws of Physics (Oxford: Oxford University Press, 1989).Google Scholar
  83. C.S. Peskin, Lectures on Mathematical Aspects of Physiology, in F.C. Hoppensteadt (ed.), Lectures in Applied Mathematics, vol. 19 (Providence, Rhode Island: American Mathematical Society, 1981).Google Scholar
  84. J. Petitot, “Structuralisme et phénoménologie,” in J. Petitot (ed.), Logos et Théorie des Catastrophes, Actes du Colloque de Cerisy en l’honneur de René Thom (Genève: Ed. Patiño, 1989), pp. 345–376.Google Scholar
  85. J. Petitot, “Le physique, le morphologique, le symbolique: remarques sur la vision,” Revue de Synthèse (1–2) (1990): 139–183.Google Scholar
  86. J. Petitot, Physique du Sens, Editions du CNRS, Paris, 1992.Google Scholar
  87. H. Poincaré, “L’espace et la géométrie,” in La Science et l’Hypothèse, Flammarion, Paris, 1902.Google Scholar
  88. H. Poincaré, “The Foundation of Geometry,” The Monist IX(1) (1898): 1–43.Google Scholar
  89. L.S. Pontryagin, Topological Groups (first Russian edition, 1938, New York: Gordon & Breach, 1966).Google Scholar
  90. N. Rashevsky, “Physico-Mathematical Aspects of the Gestalt Problem,” Philosophy of Science 1 (1934): 409–419.Google Scholar
  91. Reinhardt-Rutland, A.H., “Perceiving the orientation-in-depth of triangular surfaces: static-monocular, moving-monocular, and static-binocular viewing”, The Journal of General Psychology, Vol. 123, No. 1, 1996, pp. 19–28.CrossRefGoogle Scholar
  92. W. Richards, “Visual Space Perception,” in E.C. Cartarette and M.P. Friedman (eds.), Handbook of Perception, vol. V: Seeing (New York: Academic Press, 1975), pp. 351–386.Google Scholar
  93. B. Riemann, in R. Narasimhan (ed.), Gesammelte mathematische Werke, wissenschaftlicher Nachlaβ und Nachträge/Collected Papers (Berlin: Springer-Verlag, 1990).Google Scholar
  94. I. Rock, Orientation and Form (New York: Academic Press, 1973).Google Scholar
  95. D. Rolfsen, Knots and Links (Berkeley, CA: Publish or Perish Press, 1979).Google Scholar
  96. W. Schapp, Beiträge zur Phänomenologie der Wahrnehmung (Wiesbaden: Heymann, 1976).Google Scholar
  97. R.N. Schepard, “The Circumplex and Related Topological Manifolds in the Study of Perception,” in S. Shye (ed.), Theory Construction and Data Analysis in the Behavioral Sciences (San Francisco: Jossey-Bass, 1978).Google Scholar
  98. E. Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen” (1920), in Gesammelte Abhandlungen, vol. 4 (Wien: Verlag der Österreichischen Akademie der Wissenschaften, 1984).Google Scholar
  99. A.V. Shubnikov and V.A. Koptsik, Symmetry in Science and Art (New York: Plenum Press, 1974).Google Scholar
  100. C. Sinigaglia, La seduzione dello spazio, Geometria e filosofia nel primo Husserl (Milan: Edizioni Unicopli, 2000).Google Scholar
  101. B. Smith and D.W. Smith, “Introduction,” in B. Smith and D.W. Smith (eds.), The Cambridge Companion to Husserl (Cambridge: Cambridge University Press, 1995), pp. 1–44.Google Scholar
  102. G. Sperling, “Mathematical Models of Binocular Vision,” in S. Grossberg (ed.), Mathematical Psychology and Psychophysiology, SIAM/AMS Proceedings, vol. 13 (Providence: American Mathematical Society, 1981).Google Scholar
  103. N. Steenrod, The Topology of Fibre Bundles (Princeton: Princeton University Press, 1951).Google Scholar
  104. C. Stumpf, Erekenntnislehre, vol. 1 (Leipzig: Verlag von J.A. Barth, 1939).Google Scholar
  105. C. Stumpf, Über den psychologischen Ursprung der Raumvorstellung (Leipzig, 1873).Google Scholar
  106. P. Suppes, “Is Visual Space Euclidean?,” Synthese 35 (1977): 397–421.Google Scholar
  107. R. Thom, Apologie du logos (Paris: Hachette, 1990).Google Scholar
  108. R. Thom, Esquisse d’une Sémiophysique (Paris: InterEditions, 1991).Google Scholar
  109. D’Arcy Thompson, On Growth and Form (Cambridge: Cambridge University Press, 1917).Google Scholar
  110. W.R. Uttal, Visual Form Detection in 3-Dimensional Space (New Jersey: Lawrence Erlbaum Associates, 1983).Google Scholar
  111. M. Wagner, “The Metric of Visual Space,” Perception and Psychophysics 38(6) (1985): 483–495.Google Scholar
  112. R. Walk and H. L. Pick Jr. (eds.), Intersensory Perception and Sensory Integration (New York: Plenum Press, 1981).Google Scholar
  113. M. Wertheimer, “Untersuchungen zur Lehre von der Gestalt. II,” Psychologische Forschung 4 (1923): 301–350.Google Scholar
  114. H. Weyl, Das Kontinuum. Kritische Untersuchungen über die Grundlagen der Analysis (Leipzig: Veit, 1918) (The Continuum. A Critical Examination of the Foundation of Analysis (english edition translated by S. Pollard and Th. Bole, Kirksville, Missouri: The Thomas Jefferson University Press, 1987), Dover edition, 1994.Google Scholar
  115. H. Weyl, Mathematische Analyse des Raumproblems (Berlin: Springer, 1923).Google Scholar
  116. H. Weyl, Mind and Nature (Philadelphia: University of Pennsylvania Press, 1934).Google Scholar
  117. H. Weyl, Philosophy of Mathematics and Natural Science (Princeton: Princeton University Press, 1949).Google Scholar
  118. H. Weyl, Symmetry (Princeton: Princeton University Press, 1952).Google Scholar
  119. F.R.S. Zeeman, “Brain Modeling,” in Structural Stability, The Theory of Catastrophes, and Applications in the Sciences 525 (1976): 367–372.Google Scholar
  120. S. Zeki, A Vision of the Brain (London: Blackwell Scientific Publishers, 1993).Google Scholar
  121. D.W. Zimmerman, “Could Extended Objects be Made Out of Simple Parts? An Argument for ‘Atomless Gunk’,” Philosophy and Phenomenology Research 56(1) (1996): 1–29.Google Scholar
  122. L. Zusne, Visual Perception of Form (New York: Academic Press, 1970).Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Luciano Boi
    • 1
  1. 1.Ecole des Hautes Etudes en Sciences SocialesCentre de MathématiquesParisFrance

Personalised recommendations