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Plerosis and Atomic Gestalts

Jan Koenderink
  • Laboratory of Experimental Psychology, University of Leuven (K.U. Leuven), Tiensestraat 102 - Box 3711, Leuven B-3000, Belgium
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/ Andrea van Doorn
  • Faculteit Sociale Wetenschappen, Psychologische Functieleer, Universiteit Utrecht, Heidelberglaan 2, 3584 CS Utrecht, The Netherlands
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/ Baingio Pinna
Published Online: 2017-03-31 | DOI: https://doi.org/10.1515/gth-2017-0005


Franz Brentano, 1838–1917, introduced the intriguing concept of “plerosis” in order to account for aspects of the continuum that were “explained” by formal mathematics in ways that he considered absurd from the perspective of intuition, especially visual awareness and imagery. In doing this, he pointed in directions later developed by the Dutch mathematician Luitzen Brouwer. Brentano’s notion of plerosis involves distinct though coincident points, which one might call “atomic entities with parts”. This notion fits the modern concepts of “receptive field” in neurophysiology, “perceptive field” in psychology and “differential operator” in the formal theory of scale space. We identify Brentano’s boundary points as the primordial atomic Gestalts of visual imagery. The concept deserves to play a key role in Gestalt theory.

Keywords: Plerosis; continua; receptive fields; perceptive fields; atomic Gestalt; squares


  • Albertazzi, L. (2002). Towards a neo-Aristotelian theory of continua: Elements of an empirical geometry. In L. Albertazzi (Ed.), Unfolding perceptual continua (pp. 29–80; esp. pp. 44–52). Amsterdam, Netherlands: Benjamins.Google Scholar

  • Albertazzi, L. (2006). Immanent realism: An introduction to Brentano. (pp. 233–268; esp. pp. 248–267). Dordrecht, Netherlands: Springer.Google Scholar

  • Albertazzi, L. (2015). Spatial elements in visual awareness. Challenges for an intrinsic “Geometry” of the visible. Philosophia Scientiæ, 19(3), 95–125.Google Scholar

  • Attneave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61, 184–193.Google Scholar

  • Bakalis, N. (2005). Handbook of Greek philosophy: From Thales to the Stoics analysis and fragments. Victoria, BC, Canada: Trafford Publishing.Google Scholar

  • Bell, J. (2006). The continuous and the infinitesimal in mathematics and philosophy. Monza, Italy: Polimetrica.Google Scholar

  • Bell, J. (2009). Cohesiveness. Intellectica, 9(1), 51.Google Scholar

  • Bijl, P., Koenderink, J. J., & Toet, A. (1989). Visibility of blobs with a Gaussian luminance profile. Vision Research, 29(4), 447–456.CrossrefGoogle Scholar

  • Blum, M. (1967). A transformation for extracting new descriptors of shape. In W. Wathen-Dunn (Ed.), Models for the perception of speech and visual form (pp. 362–380). Cambridge, MA: MIT Press.Google Scholar

  • Boime, A. (1993). The art of the Macchia and the Risorgimento. Chicago and London: The University of Chicago Press.Google Scholar

  • Bouma, H. (1970). Interaction effects in parafoveal letter recognition. Nature, 226(241), 177–178.Google Scholar

  • Brentano, F. (1974, [1874]). Psychologie vom empirischen Standpunkt. Leipzig, Germany: Duncker und Humblot. (English quotations from: “Psychology from an Empirical Standpoint”. New York: Humanities Press).Google Scholar

  • Brentano, F. (1988). Philosophical investigations on space, time and the continuum (Smith, Trans.). London, England: Croom Helm.Google Scholar

  • Broude, N. (1987). The Macchiaioli: Italian painters of the nineteenth century. New Haven and London: Yale University Press.Google Scholar

  • Brouwer, L. E. J. (1918). Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Erster Teil, Allgemeine Mengenlehre. KNAW Verhandlungen, 5, 1–43.Google Scholar

  • Brown, J. W. (1977). Mind, brain and consciousness. New York, NY: Academic Press.Google Scholar

  • Cartan, É (1923). Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie). Annales Scientifiques de l’École Normale Supérieure, 40, 325–412.Google Scholar

  • Cateura, L. (1995). Oil painting secrets from a master. New York, NY: Watson & Guptill.Google Scholar

  • Chadwick, H. (1992). St. Augustine, Confessions. [orig. 397-400CE]. Oxford, England: Oxford University Press.Google Scholar

  • Dedekind, R. (1872). Stetigkeit und irrationale Zahlen. Braunschweig, Germany: Vieweg, p. 18.Google Scholar

  • Dunn, C. (1995). Conversations in paint, a notebook of fundamentals. New York, NY: Workman Publishing.Google Scholar

  • Ehrlich, P. (2006). The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes. Archive for History of Exact Sciences, 60(1), 1–121.CrossrefGoogle Scholar

  • Elkind, D. (1964). Studies in perceptual development II, part-whole. Child Development, 35(1), 81–90.CrossrefGoogle Scholar

  • Euclid. (1956, [fl. 300BCE]). The thirteen books of Euclid’s elements, (Translation and Commentaries by Heath, T. L.), Three volumes. New York, NY: Dover Publications.Google Scholar

  • Feynman, R. (1966). The character of physical law. Cambridge, MA: MIT Press.Google Scholar

  • Florack, L. (1997). Image structure. Dordrecht, Netherlands: Kluwer Academic.Google Scholar

  • Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: Harmony search. Simulation, 76(2), 60–68.CrossrefGoogle Scholar

  • Giordano, P. (2001). Nilpotent infinitesimals and synthetic differential geometry in classical logic. In P. Schuster, U. Berger, & H. Osswald (Eds.), Reuniting the antipodes–constructive and nonstandard views of the continuum (pp. 75–92). Dordrecht, Netherlands: Kluwer.Google Scholar

  • Gödel, K. (1960, [1947]). What is Cantor’s continuum problem? The American Mathematical Monthly, 54, 515–525. (originally published in 1947, Page references are to the reprinting of the expanded 1960 version in Benacerraf and Putnam 1983, pp. 420–485).Google Scholar

  • Hartline, H. K. (1938). The response of single optic nerve fibers of the vertebrate eye to illumination of the retina. The American Journal of Physiology, 121, 400–415.Google Scholar

  • Hilbert, D. (1980, [1899]). The foundations of geometry (2nd ed.). Chicago, IL: Open Court.Google Scholar

  • Hoffman, D. D. (2009). The interface theory of perception. In S. Dickinson, M. Tarr, A. Leonardis, & B. Schiele (Eds.), Object categorization: Computer and human vision perspectives (pp. 148–165). New York, NY: Cambridge University Press.Google Scholar

  • Hubel, D. H., & Wiesel, T. N. (1968). Receptive fields and functional architecture of monkey striate cortex. Journal of Neuroscience, 195, 215–243.Google Scholar

  • Husserl, E. (1991, [1893-1917]). On the phenomenology of the consciousness of internal time (1893-1917) (J. B. Brough, Trans.). Dordrecht, Netherlands: Kluwer.Google Scholar

  • Imbriano, V. (1868). La quinta promotrice 1878-1868: Appendici di Vittorio Imbriani. Napoli, Italy: Tipografia Napolitana.Google Scholar

  • Jacobs, T. S. (1986). Light for the Artist. NewYork, NY: Watson-Guptill.Google Scholar

  • Kandinsky, W. (1926). In W. Gropius & L. Moholy-Nagy (Eds.), Punkt und Linie zu Fläche. Bauhaus Bücher, Schriftleitung München, Germany: Verlag Albert Langen.Google Scholar

  • Kanizsa, G. (1980). Grammatica del vedere. Saggi su percezione e Gestalt. Bologna, Italy: IL Mulino.Google Scholar

  • Koenderink, J. J. (1984). The structure of images. Biological Cybernetics, 50, 363–370.CrossrefGoogle Scholar

  • Koenderink, J. J. (1988). Operational significance of receptive field assemblies. Biological Cybernetics, 58(3), 163–171.CrossrefGoogle Scholar

  • Koenderink, J. J. (1990). The brain a geometry engine. Psychological Research, 52(2–3), 122–127.Google Scholar

  • Koenderink, J. J. (1993). What is a “feature”? Journal of Intelligent Systems, 3(1), 49–82.Google Scholar

  • Koenderink, J. J. (2002). Continua in vision. In L. Albertazzi (Ed.), Unfolding perceptual continua, advances in consciousness research 41 (pp. 101–118). Amsterdam and Philadelphia: John Benjamins.Google Scholar

  • Koenderink, J. J. (2011). Vision as a user interface. In B. E. Rogowitz & T. N. Pappas (Eds.), Proceedings of SPIE-IS&T Electronic Imaging, SPIE, Vol. 7865: Human Vision and Electronic Imaging XVI (pp. 1–13). San Francisco: SPIE-IS&T.Google Scholar

  • Koenderink, J. J. (2014). The all seeing eye. Perception, 43, 1–6.CrossrefGoogle Scholar

  • Koenderink, J. J. (2015). Ontology of the mirror world. Gestalt Theory, 37(2), 119–140.Google Scholar

  • Koenderink, J. J., Albertazzi, L., van Doorn, A. J., van Ee, R., van de Grind, W. A., Kappers, A. M. L., … de Vries, S. (2010). Does monocular visual space contain planes? Acta Psychologica (Amst), 134(1), 40–47.Google Scholar

  • Koenderink, J. J., & Richards, W. A. (1988). Two-dimensional curvature operators. Journal of the Optical Society of America A, 5(7), 1136–1141.Google Scholar

  • Koenderink, J. J., & Van Doorn, A. J. (1990). Receptive field families. Biological Cybernetics, 63(4), 291–297.CrossrefGoogle Scholar

  • Koenderink, J. J., & Van Doorn, A. J. (1992a). Generic neighbourhood operators. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 597–605.CrossrefGoogle Scholar

  • Koenderink, J. J., & Van Doorn, A. J. (1992b). Receptive field assembly pattern specificity. Journal of Visual Communication and Image Representation, 3(1), 1–12.CrossrefGoogle Scholar

  • Koenderink, J. J., & van Doorn, A. J. (1997). Local image operators and iconic structure. In G. Sommer & J. J. Koenderink (Eds.), Proceedings of the AFPAC’97. Algebraic Frames for the Perception-Action Cycle (pp. 66–93). Berlin, Heidelberg: Springer.Google Scholar

  • Koenderink, J. J., van Doorn, A. J., & Pinna, B. (2015). Psychogenesis of Gestalt. Gestalt Theory, 37(3), 287–304.Google Scholar

  • Koenderink, J. J., van Doorn, A. J., Albertazzi, L., & Wagemans, J. (2015). Relief articulation techniques. Art & Perception, 3(2), 151–171.Google Scholar

  • Koenderink, J. J., van Doorn, A. J., Pinna, B., & Wagemans, J. (2016). Boundaries, transitions and passages. Art & Perception, 4(3), 185–204.Google Scholar

  • Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. New York, NY: Freeman.Google Scholar

  • Marr, D., & Hildreth, E. (1980). Theory of edge detection. Proceedings of Royal Society of London B, 207, 187–217.Google Scholar

  • Metzger, W. (1936). Gesetze des Sehens. Frankfurt am Main, Germany: W. Kramer & Co.Google Scholar

  • Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. San Francisco, CA: W. H. Freeman.Google Scholar

  • Panconi, T. (1999). Antologia dei Macchiaioli, La trasformazione sociale e artica nella Toscana di metà 800. Pisa, Italy: Pacini Editore.Google Scholar

  • Pasch, M. (1912). [first edition 1882], Vorlesungen uber neuere Geometrie (2nd ed.). Leipzig, Germany: B.G. Teubner, p. 21.Google Scholar

  • Photoshop. (2014). Adobe, Retrieved from http://www.adobe.com/mena_en/products/photoshop.html

  • Pinna, B. (2008). Watercolor illusion. Scholarpedia, 3(1), 5352.Google Scholar

  • Pinna, B. (2010). New Gestalt principles of perceptual organization: An extension from grouping to shape and meaning. Gestalt Theory, 32(1), 11–78.Google Scholar

  • Pinna, B. (2012). Perceptual organization of shape, color, shade and lighting in visual and pictorial objects. i-Perception, 3, 257–281.CrossrefGoogle Scholar

  • Pinna, B., & Albertazzi, L. (2011). From grouping to visual meanings: A new theory of perceptual organization. In L. Albertazzi, G. van Tonder, & D. Vishwanath (Eds.), Information in perception (pp. 288–344). Cambridge, MA: MIT Press.Google Scholar

  • Pinna, B., Brelstaff, G., & Spillmann, L. (2001). Surface color from boundaries: A new ‘watercolor’ illusion. Vision Research, 41, 2669–2676.CrossrefGoogle Scholar

  • Pinna, B., & Deiana, K. (2015). The syntax organization of shape and color and the laws of coloration in vision, art and biology. Art & Perception, 3(3), 319–345.Google Scholar

  • Pinna, B., & Grossberg, S. (2005). The watercolor illusion and neon color spreading: A unified analysis of new cases and neural mechanisms. Journal of the Optical Society of America A, 22, 2207–2221.Google Scholar

  • Pinna, B., & Reeves, A. (2006). Lighting, backlighting and watercolor illusions and the laws of figurality. Spatial Vision, 19, 341–373.Google Scholar

  • Pinna, B., Spillmann, L., & Werner, J. (2003). The watercolor effect: A new principle of grouping and figure-ground organization. Vision Research, 43, 43–52.CrossrefGoogle Scholar

  • Richards, W. R., & Bobick, A. (1988). Playing twenty questions with nature. In Z. W. Pylyshyn (Ed.), Computational processes in human vision: An interdisciplinary perspective (pp. 3–26). The Canadian Institute for Advanced Research Series in Artificial Intelligence. Norwood, NJ: Ablex Publishing.Google Scholar

  • Richards, W.R. (1982, December): How to play twenty questions with nature and win (M.I.T. A.I. Memo 660).Google Scholar

  • Riedl, R. (1975). Die Ordnung des Lebendigen. Systembedingungen der Evolution. Hamburg, Germany: Paul Parey.Google Scholar

  • Riemann, B. (2013). [Habilitationsvortrag 10. Juni 1854]. Über die Hypothesen, Welche der Geometrie zu Grunde Liegen. Berlin, Germany: Springer.Google Scholar

  • Roeper, P. (2006). The Aristotelian continuum. A formal characterization. Notre Dame Journal of Formal Logic, 47(2), 211–232.Google Scholar

  • Schrödinger, E. (1944). What is life?. Cambridge, UK: Cambridge University Press.Google Scholar

  • Spillmann, L. (1971). Foveal perceptive fields in the human visual system measured with simultaneous contrast in grids and bars. Pflügers Archiv, 326(4), 281–299.Google Scholar

  • Stevin, S. (1585). In A. J. E. M. Smeur (Ed.), De Thiende (p. 1965). Nieuwkoop, Netherlands: De Graaf.Google Scholar

  • Stoltz, O. (1883). Zur Geometrie der Alten, insbesondere über ein Axiom des Archimedes. Mathematische Annalen, 22, 504–519.CrossrefGoogle Scholar

  • ter Haar Romeny, B. M. (2003). Front-end vision and multi-scale image analysis. Dordrecht, Netherlands: Kluwer Academic.Google Scholar

  • Tinbergen, N. (1952). The curious behavior of the stickleback. Scientific American, 187(6), 22–26.Google Scholar

  • van Dalen, D. (1997). How connected is the intuitionistic continuum? The Journal of Symbolic Logic, 62(4), 1147–1150.CrossrefGoogle Scholar

  • Veronese, G. (1894). Grundzüge der Geometrie von mehreren Dimensionen und mehreren Arten gradliniger Einheiten in elementarer Form entwickelt (Uebersetzt von A. Schepp). Leipzig, Germany: B.G. Teubner.Google Scholar

  • von Uexküll, J. (1909). Umwelt und Innenwelt der Tiere. Berlin, Germany: Springer.Google Scholar

  • von Uexküll, J. (1920). Theoretische Biologie. Berlin, Germany: Springer.Google Scholar

  • Weber, E. H. (1846). Tastsinn und Gemeingefühl. In R. Wagner (Ed.), Handwörterbuch der Physiologie mit Rücksicht auf physiologische Pathologie (Band 3 ed., pp. 481–588). Braunschweig, Germany: Vieweg.Google Scholar

  • Wertheimer, M. (1922): Untersuchungen zur Lehre von der Gestalt, I: Prinzipielle Bemerkungen. Psychologische Forschung, 1, pp. 47–58. [Translated extract reprinted as “The general theoretical situation.” In W. D. Ellis (Ed.), (1938). A source book of Gestalt psychology (pp. 12–16). London, UK: Routledge & Kegan Paul Ltd.].Google Scholar

  • Wertheimer, M. (1923): Untersuchungen zur Lehre von der Gestalt, II. Psychologische Forschung, 4, pp. 301–350. [Translated as “Investigations on Gestalt principles, II. In L. Spillmann (Ed.), (2012). On motion and figure-ground organization (pp. 127–182). Cambridge, MA: M.I.T. Press].CrossrefGoogle Scholar

  • Weyl, H. (1925). On the current epistemological situation in mathematics [English translation of Die Heutige Erkenntnislage in der Mathematik, Symposion, 1, 1925–1927, 1–32.] In P. Mancosu (Ed.) (1998), pp. 123–142.Google Scholar

About the article

Published Online: 2017-03-31

Published in Print: 2017-03-01

Citation Information: Gestalt Theory, Volume 39, Issue 1, Pages 30–53, ISSN (Online) 2519-5808, DOI: https://doi.org/10.1515/gth-2017-0005.

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© 2017 Jan Koenderink et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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