Phenomenology and the Cognitive Sciences

, Volume 11, Issue 3, pp 335–366 | Cite as

Idealization and external symbolic storage: the epistemic and technical dimensions of theoretic cognition



This paper explores some of the constructive dimensions and specifics of human theoretic cognition, combining perspectives from (Husserlian) genetic phenomenology and distributed cognition approaches. I further consult recent psychological research concerning spatial and numerical cognition. The focus is on the nexus between the theoretic development of abstract, idealized geometrical and mathematical notions of space and the development and effective use of environmental cognitive support systems. In my discussion, I show that the evolution of the theoretic cognition of space apparently follows two opposing, but in truth, intrinsically aligned trajectories. On the epistemic plane, which is the main focus of Husserl’s genetic phenomenological investigations, theoretic conceptions of space are progressively constituted by way of an idealizing emancipation of spatial cognition from the concrete, embodied intentionality underlying the human organism’s perception of space. As a result of this emancipation, it ultimately becomes possible for the human mind to theoretically conceive of and posit space as an ideal entity that is universally geometrical and mathematical. At the same time, by synthesizing a range of literature on spatial and mathematical cognition, I illustrate that for the theoretic mind to undertake precisely this emancipating process successfully, and further, for an ideal and objective notion of geometrical and mathematical space to first of all become fully scientifically operative, the cognitive support provided by a range of specific symbolic technologies is central. These include lettered diagrams, notation systems, and more generally, the technique of formalization and require for their functioning various cognitively efficacious types of embodiment. Ultimately, this paper endeavors to understand the specific symbolic-technological dimensions that have been instrumental to major shifts in the development of idealized, scientific conceptions of space. The epistemic characteristics of these shifts have been previously discussed in genetic phenomenology, but without devoting sufficient attention to the constructive role of symbolic technologies. At the same time, this paper identifies some of the irreducible phenomenological and epistemic dimensions that characterize the functioning of the historically situated, embodied and distributed theoretic mind.


Theoretic cognition Spatial cognition Distributed cognition Genetic phenomenology Enculturation Formalization Idealization Symbolic technology Embodiment 


  1. Acredolo, L. (1978). The development of spatial orientation in infancy. Developmental Psychology, 14(3), 224–234.CrossRefGoogle Scholar
  2. Armstrong, D. F., & Wilcox, S. E. (2007). The gestural origin of language. Oxford: Oxford University Press.CrossRefGoogle Scholar
  3. Barton, D., & Hamilton, M. (1996). Social and cognitive factors in the historical elaboration of writing. In A. Lock & C. R. Peters (Eds.), Handbook of human symbolic evolution (pp. 793–858). Oxford: Clarendon.Google Scholar
  4. Brissiaud, R. (1992). A tool for number construction: finger symbol sets. In J. Bideaud, C. Meljac, & J.-P. Fischer (Eds.), Pathways to number: children’s developing numerical abilities (pp. 41–66). Hillsdale: Hillbaum.Google Scholar
  5. Butterworth, B. (1999). The mathematical brain. London: Macmillan.Google Scholar
  6. Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 3–18.CrossRefGoogle Scholar
  7. Butterworth, B., Reeve, R., Reynolds, F., & Lloyd, D. (2008). Numerical thought with and without words: evidence from indigenous Australian children. Proceedings of the National Academy of Sciences, 105(35), 13179–13184.CrossRefGoogle Scholar
  8. Cajori, F. (1952). A history of mathematical notations (2 vols.). Chicago: Open Court (Original work published 1929).Google Scholar
  9. Cassirer, E. (1998). Leibniz’ System in seinen wissenschaftlichen Grundlagen. Hamburg: Meiner.Google Scholar
  10. Corballis, M. C. (2002). From hand to mouth: the origins of language. Princeton: Princeton University Press.Google Scholar
  11. d’Errico, F. (1998). Palaeolithic origins of artificial memory systems: an evolutionary perspective. In C. Renfrew & C. Scarre (Eds.), Cognition and material culture: the archaeology of symbolic storage (pp. 19–50). Cambridge: McDonald Institute for Archaeological Research.Google Scholar
  12. Danzig, T. (1954). Number: the language of science. New York: Free Press.Google Scholar
  13. De Cruz, H. (2008). An extended mind perspective on natural number representation. Philosophical Psychology, 21(4), 475–490.CrossRefGoogle Scholar
  14. De Cruz, H. & De Smedt, J. (2010). Mathematical symbols as epistemic actions. Synthese, 1–17. doi:10.1007/s11229-010-9837-9
  15. Deacon, T. (1997). The symbolic species: the co-evolution of language and the brain. New York: Norton.Google Scholar
  16. Dehaene, S. (1997). The number sense: how the mind creates mathematics. Oxford: Oxford University Press.Google Scholar
  17. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396.CrossRefGoogle Scholar
  18. Descartes, R. (1988). The philosophical writings of Descartes. Volume II (J. Cottingham, R. Stoothoff & D. Murdoch, Trans.). Cambridge: Cambridge University Press.Google Scholar
  19. Domahs, F., Moeller, K., Huber, S., Willmes, K., & Nuerk, H. C. (2010). Embodied numerosity: implicit hand-based representations influence symbolic number processing across cultures. Cognition, 116(2), 251–266.CrossRefGoogle Scholar
  20. Donald, M. (1991). Origins of the modern mind: three stages in the evolution of culture and cognition. Cambridge: Harvard University Press.Google Scholar
  21. Donald, M. (2001). A mind so rare: the evolution of human consciousness. New York: Norton.Google Scholar
  22. Donald, M. (2010). The exographic revolution: neuropsychological sequelae. In L. Malafouris & C. Renfrew (Eds.), The cognitive life of things: recasting the boundaries of the mind (pp. 71–79). Cambridge: McDonald Institute for Archaeological Research.Google Scholar
  23. Euclid. (1956). The thirteen books of Euclid’s Elements. Volume I–III (T. L. Heath, Trans.). New York: Dover Publications.Google Scholar
  24. Fias, W., & Fischer, M. H. (2005). Spatial representation of numbers. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 43–54). New York: Psychology Press.Google Scholar
  25. Fischer, M. H. (2003). Spatial representations in number processing: evidence from a pointing task. Visual Cognition, 10(4), 493–508.CrossRefGoogle Scholar
  26. Frank, M. C., Everett, D. L., Fedorenko, E., & Gibson, E. (2008). Number as a cognitive technology: evidence from Pirahã language and cognition. Cognition, 108(3), 819–824.CrossRefGoogle Scholar
  27. Fuson, K. C., & Kwon, Y. (1992). Learning addition and subtraction: effects of number words and other cultural tools. In J. Bideaud, C. Meljac, & J. P. Fischer (Eds.), Pathways to number: children’s developing numerical abilities (pp. 283–306). Hillsdale: Erlbaum.Google Scholar
  28. Gentner, D. (2007). Spatial cognition in apes and humans. Trends in Cognitive Sciences, 11(5), 192–194.CrossRefGoogle Scholar
  29. Gibbs, R. W. (2006). Embodiment and cognitive science. New York: Cambridge University Press.Google Scholar
  30. Gillings, R. J. (1972). Mathematics in the time of the pharaohs. Cambridge: MIT Press.Google Scholar
  31. Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A. (2009). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267–272.CrossRefGoogle Scholar
  32. Goody, J. (1977). The domestication of the savage mind. Cambridge: Cambridge University Press.Google Scholar
  33. Goody, J. (1986). The logic of writing and the organization of society. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  34. Goody, J., & Watt, I. (1963). The consequences of literacy. Comparative Studies in Society and History, 5(3), 304–345.CrossRefGoogle Scholar
  35. Gordon, P. (2004). Numerical cognition without words: evidence from Amazonia. Science, 306(5695), 496–499.CrossRefGoogle Scholar
  36. Hatano, G., Miyake, Y., & Binks, M. G. (1977). Performance of expert abacus operators. Cognition, 5(1), 47–55.CrossRefGoogle Scholar
  37. Haun, D. B. M., Rapold, C. J., Call, J., Janzen, G., & Levinson, S. C. (2006). Cognitive cladistics and cultural override in Hominid spatial cognition. Proceedings of the National Academy of Sciences of the United States of America, 103(46), 17568–17573.CrossRefGoogle Scholar
  38. Havelock, E. A. (1963). Preface to Plato. Cambridge: Harvard University Press.Google Scholar
  39. Havelock, E. A. (1982). The literate revolution in Greece and its cultural consequences. Princeton: Princeton University Press.Google Scholar
  40. Heath, T. L. (1981). A history of Greek mathematics: from Thales to Euclid (Vol. 1). Mineola: Dover.Google Scholar
  41. Hockett, C. F. (1960). The origin of speech. Scientific American, 203, 89–97.CrossRefGoogle Scholar
  42. Husserl, E. (1970). The crisis of European sciences and transcendental phenomenology: an introduction to phenomenological philosophy (D. Carr, Trans.). Evanston, Ill.: Northwestern University Press. (Original work published 1954).Google Scholar
  43. Husserl, E. (1989). Ideas pertaining to a pure phenomenology and to a phenomenological philosophy. Second book: studies in the phenomenology of constitution (R. Rojcewicz and A. Schuwer, Trans.). Dordrecht: Kluwer. (Original work published 1952).Google Scholar
  44. Husserl, E. (1997). Thing and space: Lectures of 1907 (R. Rojcewicz, Trans). Dordrecht: Kluwer. (Original work published 1973).Google Scholar
  45. Hutchins, E. (1995). Cognition in the wild. Cambridge: MIT Press.Google Scholar
  46. Hutchins, E. (2010). Cognitive ecology. Topics in Cognitive Science, 2(4), 7-5–715.CrossRefGoogle Scholar
  47. Joseph, G. G. (2011). The crest of the peacock: non-European roots of mathematics (3rd ed.). Princeton: Princeton University Press.Google Scholar
  48. Kirsh, D. (1995). The intelligent use of space. Artifical Intelligence, 73(1–2), 31–68.CrossRefGoogle Scholar
  49. Kirsh, D. (2006). Distributed cognition: a methodological note. Pragmatics and Cognition, 14(2), 249–262.CrossRefGoogle Scholar
  50. Kirshner, D., & Awtry, Y. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35(4), 224–257.CrossRefGoogle Scholar
  51. Klein, J. (1968). Greek mathematical thought and the origin of algebra (E. Brann, Trans.). Cambridge, MA: MIT Press. (Original work published 1934 and 1936).Google Scholar
  52. Klein, J. (1985). Modern rationalism. In R. B. Williamson & E. Zuckerman (Eds.), Jacob Klein: lectures and essays (pp. 53–64). Annapolis: St. John’s College Press.Google Scholar
  53. Kline, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.Google Scholar
  54. Koyré, A. (1957). From the closed world to the infinite universe. Baltimore: Johns Hopkins Press.Google Scholar
  55. Krämer, S. (1988). Symbolische Maschinen. Die Idee der Formalisierung in geschichtlichem Abriß. Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
  56. Krämer, S. (1989). Algebra und Geometrie in Descartes Geometrié. Philosophia Naturalis, 26(1), 19–40.Google Scholar
  57. Kula, W. (1986). In R. Szreter (Ed.), Measures and man. Princeton: Princeton University Press.Google Scholar
  58. Kusukawa, S. (2001). A manual computer for reckoning time. In C. R. Sherman (Ed.), Writing on hands: memory and knowledge in early modern Europe (pp. 28–34). Seattle: University of Washington Press.Google Scholar
  59. Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: how the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  60. Landy, D., & Goldstone, R. L. (2007). Formal notations are diagrams: evidence from a production task. Memory and Cognition, 35(8), 2033–2040.CrossRefGoogle Scholar
  61. Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11(1), 65–99.CrossRefGoogle Scholar
  62. Leroi-Gourhan, A. (1993). Gesture and speech (A. Bostock Berger, Trans.). Cambridge, MA: MIT Press. (Original work published 1964 and 1965).Google Scholar
  63. Levinson, S. C. (2003). Space in language and cognition: explorations in cognitive diversity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  64. Menninger, K. (1969). Number words and number symbols. acultural history of numbers (P. Broneer, Trans.). Cambridge, MA: MIT Press. (Original work published in 1958).Google Scholar
  65. Merleau-Ponty, M. (1962). Phenomenology of perception (C. Smith, Trans). London: Routledge & Kegan Paul. (Original work published 1945).Google Scholar
  66. Netz, R. (1998). Greek mathematical diagrams: their use and their meaning. For the Learning of Mathematics, 18(3), 33–39.Google Scholar
  67. Netz, R. (1999). The shaping of deduction in Greek mathematics: a study in cognitive history. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  68. Noël, M. P. (2005). Finger gnosia: a predictor of numerical abilities in children? Child Neuropsychology, 11(5), 413–430.CrossRefGoogle Scholar
  69. Norman, D. A. (1991). Cognitive artifacts. In J. M. Carroll (Ed.), Designing interaction: psychology at the human–computer interface (pp. 17–38). Cambridge: Cambridge University Press.Google Scholar
  70. Piaget, J., & Inhelder, B. (1956). The child’s conception of space (F. J. Langdon & J. L. Lunzer, Trans.). London: Routledge & Kegan Paul. (Original work published 1948).Google Scholar
  71. Plato (1997). Plato: complete works (J. M. Cooper & D. S.Hutchinson, Eds.). Indianapolis: Hackett.Google Scholar
  72. Ritter, J. (1995). Measure for measure: mathematics in Egypt and Mesopotamia. In M. Serres (Ed.), History of scientific thought: elements of a history of science (pp. 44–72). Oxford: Blackwell.Google Scholar
  73. Savage-Rumbaugh, S., & Lewin, R. (1994). Kanzi: the ape at the brink of the human mind. New York: Wiley.Google Scholar
  74. Schmandt-Besserat, D. (1996). How writing came about. Austin: University of Texas Press.Google Scholar
  75. Sinha, C., & Jensen de López, K. (2000). Language, culture and the embodiment of spatial cognition. Cognitive Linguistics, 11(1/2), 17–41.Google Scholar
  76. Sonesson, G. (2007). The extensions of man revisited. From primary to tertiary embodiment. In J. M. Krois, M. Rosengren, A. Steidele, & D. Westerkamp (Eds.), Embodiment in cognition and culture (pp. 27–53). Amsterdam: John Benjamins.Google Scholar
  77. Stigler, J. W. (1984). Mental abacus: the effect of abacus training on Chinese children’s mental calculation. Cognitive Psychology, 16(2), 145–176.CrossRefGoogle Scholar
  78. Ströker, E. (1987). Investigations in philosophy of space (A. Mickunas, Trans). Athens, Ohio: Ohio University Press. (Original work published in 1965).Google Scholar
  79. Sutton, J. (2006). Distributed cognition: domains and dimensions. Pragmatics and Cognition, 14(2), 235–247.CrossRefGoogle Scholar
  80. Sutton, J. (2010). Exograms and interdisciplinarity: history, the extended mind and the civilizing process. In R. Menary (Ed.), The extended mind (pp. 189–225). Cambridge: MIT Press.Google Scholar
  81. Tieszen, R. L. (1989). Mathematical intuition: phenomenology and mathematical knowledge. Dordrecht: Kluwer.CrossRefGoogle Scholar
  82. Tomasello, M. (2008). Origins of human communication. Cambridge: MIT Press.Google Scholar
  83. Toretti, R. (1978). Philosophy of geometry from Riemann to Poincaré. Dordrecht: Reidel.CrossRefGoogle Scholar
  84. van der Waerden, B. L. (1961). Science awakening. Groningen: Noordhoff.Google Scholar
  85. Voorhees, B. (2004). Embodied mathematics: comments on Lakoff & Núñez. Journal of Consciousness Studies, 11(9), 83–88.Google Scholar
  86. Vygotsky, L. S. (1993). Studies on the history of behavior: Ape, primitive, and child (V. I. Golod & J. E. Knox, Eds. & Trans.). Hillsdale, NJ: Lawrence Erlbaum. (Original work published 1930).Google Scholar
  87. Williams, B. P., & Williams, R. S. (1995). Finger numbers in the Greco-Roman world and the early Middle Ages. Isis, 86(4), 587–608.CrossRefGoogle Scholar
  88. Wynn, K. (1990). Children’s understanding of counting. Cognition, 36(2), 155–193.CrossRefGoogle Scholar
  89. Zebian, S. (2005). Linkages between number concepts, spatial thinking, and directionality of writing: the SNARC effect and the REVERSE SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. Journal of Cognition and Culture, 5(1–2), 165–190.CrossRefGoogle Scholar
  90. Zhang, J. (1993). External representation: an issue for cognition (review of the book Origins of the Modern Mind). The Behavioral and Brain Sciences, 16(4), 774–775.CrossRefGoogle Scholar
  91. Zhang, J., & Norman, D. A. (1995). A representational analysis of numeration systems. Cognition, 57(3), 271–295.CrossRefGoogle Scholar
  92. Zhang, J., & Wang, H. (2005). The effect of external representations on numeric tasks. Quarterly Journal of Experimental Psychology, 58A(5), 817–838.Google Scholar
  93. Zlatev, J. (2008). The co-evolution of intersubjectivity and bodily mimesis. In J. Zlatev, T. P. Racine, C. Sinha, & E. Itkonen (Eds.), The shared mind: perspectives on intersubjectivity (pp. 215–244). Amsterdam: John Benjamins.Google Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Melbourne Graduate School of EducationUniversity of MelbourneParkvilleAustralia

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