Educational Studies in Mathematics

, Volume 61, Issue 1–2, pp 39–65 | Cite as

The Anthropology of Meaning

Some have concluded that, if meaning is negotiable, then it is no longer of any use in explaining the way we understand one another. (Eco, 1999, p. 271)
  • Luis RadfordEmail author


Meaning is one of the recent terms which have gained great currency in mathematics education. It is generally used as a correlate of individuals' intentions and considered a central element in contemporary accounts of knowledge formation. One important question that arises in this context is the following: if, in one way or another, knowledge rests on the intrinsically subjective intentions and deeds of the individual, how can the objectivity of conceptual mathematical entities be guaranteed? In the first part of this paper, both Peirce's and Husserl's theories of meaning are discussed in light of the aforementioned question. I examine their attempts to reconcile the subjective dimension of knowing with the alleged transcendental nature of mathematical objects. I argue that transcendentalism, either in Peirce's or Husserl's theory of meaning, leads to an irresolvable tension between subject and object. In the final part of the article, I sketch a notion of meaning and conceptual objects based on a semiotic-cultural approach to cognition and knowledge which gives up transcendentalism and instead conveys the notion of contextual objectivity.

Key Words

activity cultural semiotics epistemology Husserl mathematical objects meaning ontology Peirce subjectivity 


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  1. Almeder, R.: 1983, ‘Peirce on meaning’, in E. Freeman (ed.), The Relevance of Charles Peirce, Monist Library of Philosophy, La Salle, pp. 328–347.Google Scholar
  2. Bakhtin, M.M.: 1986, Speech Genres and Other Late Essays, University of Texas Press, Austin.Google Scholar
  3. Bégout, B.: 2003, ‘L'ontologie dans les limites de la simple phénoménologie: Husserl et le primat de la théorie phénoménologique de la connaissance’, in D. Fisette and S. Lapointe (eds.), Aux origines de la phénoménologie, Paris, Vrin, pp. 149–178.Google Scholar
  4. Berger, P.L. and Luckmann, T.: 1967, The Social Construction of Reality, Anchor Book, New York.Google Scholar
  5. Brent, J.: 1998, Charles Sanders Peirce. A Life, revised and enlarged edition, Indiana University Press, Blomington.Google Scholar
  6. Cassirer, E.: 1957, The Philosophy of Symbolic Forms, Vol. 3, Oxford University Press, London.Google Scholar
  7. CP = Peirce, Ch. S.: 1931–1958, Collected Papers, Vols. I–VIII, Harvard University Press, Cambridge, Massachusetts.Google Scholar
  8. D'Amore, B.: 2001, ‘Une contribution au débat sur les concepts et les objets mathématiques: la position “naïve” dans une théorie “réaliste” contre le modèle “anthropologique” dans une théorie “pragmatique”, in A. Gagatsis (ed.), Learning in Mathematics and Science and Educational Technology, Vol. 1, pp. 131–162.Google Scholar
  9. Dewey, J.: 1946, ‘Peirce's theory of linguistic signs, thought, and meaning’, The Journal of Philosophy 43(4), 85–95.CrossRefGoogle Scholar
  10. Dörfler, W.: 2002, ‘Formation of mathematical objects as decision making’, Mathematical Thinking and Learning 4(4), 337–350.CrossRefGoogle Scholar
  11. Duval, R.: 1998, ‘Signe et objet, I et II’, Annales de didactique et de sciences cognitives, IREM de Strasbourg, Vol. 6, pp. 139–196.Google Scholar
  12. Eagleton, T.: 2003, After Theory, Penguin Books, London.Google Scholar
  13. Eco, U.: 1999, Kant and the Platypus. Essays on Language and Cognition, Harcourt, San Diego/New York/London.Google Scholar
  14. Floridi, L.: 1994, ‘Scepticism and the search for knowledge: A Peirceish answer to a Kantian doubt’, Transactions of the Charles S. Peirce Society 30(3), 543–573.Google Scholar
  15. Føllesdal, D.: 1969, ‘Husserl's notion of noema’, The Journal of Philosophy 66(20), 680–687.CrossRefGoogle Scholar
  16. Furinghetti, F.: 1997, ‘History of mathematics, mathematics education, school practice: Case studies in linking different domains’, For the Learning of Mathematics 17(1), 55– 61.Google Scholar
  17. Furinghetti, F. and Radford, L.: 2002, ‘Historical conceptual developments and the teaching of mathematics: From phylogenesis and ontogenesis theory to classroom practice’, in L. English (ed.), Handbook of International Research in Mathematics Education, Lawrence Erlbaum, New Jersey, pp. 631–654.Google Scholar
  18. Godino, J.D. and Batanero, C.: 1999, ‘The meaning of mathematical objects as analysis units for didactic of mathematics’, in I. Schwank (ed.), Proceedings of the First Conference of the European Society for Research in Mathematics Education, Scholar
  19. Husserl, E.: 1890–1908/1994, Early Writings in the Philosophy of Logic and Mathematics, Kluwer, Dordrecht.Google Scholar
  20. Husserl, E.: 1891/1972, Philosophie de l'arithmétique, translated by J. English, Presses Universitaires de France, Paris.Google Scholar
  21. Husserl, E.: 1900/1970, Logical Investigations, translated by J.N. Findlay, Routledge & Kegan Paul, London.Google Scholar
  22. Husserl, E.: 1913/1931, Ideas. General Introduction to Pure Phenomenology, translated by W.R. Boyce Gibson, Third Edition, 1958, The Macmillan Company, New York.Google Scholar
  23. Husserl, E.: 1935, Letter to Lucien Lévy-Bruhl, Husserl Archives, Leuven.Google Scholar
  24. Husserl, E.: 1973, Experience and Judgment, Northwestern University Press, Evanston.Google Scholar
  25. Husserl, E.: 1989, Origin of Geometry, Introduction by Jacques Derrida, translated by John P. Leavey, Jr., University of Nebraska Press, Lincoln and London.Google Scholar
  26. Husserl, E.: 2001, Sur l'intersubjectivité II, Presses Universitaires de France, Paris.Google Scholar
  27. Ilyenkov, E.: 1977a, ‘The concept of the ideal’, in Philosophy in the USSR: Problems of Dialectical Materialism, Progress Publishers, Moscow.Google Scholar
  28. Ilyenkov, E.V.: 1977b, Dialectical Logic, Progress Publishers, Moscow.Google Scholar
  29. Lektorsky, V.A.: 1984, Subject, Object, Cognition, Progress Publishers, Moscow.Google Scholar
  30. Leont'ev, A.N.: 1978, Activity, Consciousness, and Personality, Prentice-Hall, New Jersey.Google Scholar
  31. Luria, A.R.: 1984, Sensación y percepción, Ediciones Martínez Roca, Barcelona.Google Scholar
  32. McIntyre, R. and Smith, D.W.: 1976, ‘Husserl's equation of meaning and noema’, The Monist 59, 115–132.Google Scholar
  33. Marx, K. and Engels, F.: 1968, Theses on Feuerbach, Selected Works, International Publishers, New York, pp. 28–30.Google Scholar
  34. Merleau-Ponty, M.: 1960, Signes, Gallimard, Paris.Google Scholar
  35. Nabonnand, P.: 2004, ‘Applications des mathématiques au début du vingtième siècle’, in Coray, D., et al. (eds.), One Hundred Years of L'Enseignement Mathématique, L'Enseignement Mathématique, Monographie No. 39, pp. 229–249.Google Scholar
  36. Nesher, D.: 1997, ‘Peircean realism: Truth as the meaning of cognitive signs representing external reality’, Transactions of the Charles S. Peirce Society 33(1), 201–257.Google Scholar
  37. Otte, M.: 2003, Meaning and Mathematics. Pre-print. Institut für Didaktik der Mathematik, Universität Bielefeld.Google Scholar
  38. Otte, M.: forthcoming, ‘Does mathematics have objects? In what sense?’ Synthese.Google Scholar
  39. Parker, K.: 1994, ‘Peirce's semeiotic and ontology’, Transactions of the Charles S. Peirce Society 30(1), 51–75.Google Scholar
  40. Pea, R.D.: 1993, ‘Practices of distributed intelligence and designs for education’, in G. Salomon (ed.), Distributed Cognitions, Cambridge University Press, Cambridge, pp. 47–87.Google Scholar
  41. Piaget, J.: 1953, The Origin of Intelligence in the Child, Routledge & Kegan Paul, London.Google Scholar
  42. Radford, L.: 2000, ‘Signs and meanings in students' emergent algebraic thinking: A semiotic analysis’, Educational Studies in Mathematics 42(3), 237–268.CrossRefGoogle Scholar
  43. Radford, L.: 2002a, ‘The object of representations: Between wisdom and certainty’, in F. Hitt (ed.), Representations and Mathematics Visualization, Departamento de matemática educativa Cinvestav-IPN, Mexico, pp. 219–240.Google Scholar
  44. Radford, L.: 2002b, ‘The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge’, For the Learning of Mathematics 22(2), 14–23.Google Scholar
  45. Radford, L.: 2003a, ‘On culture and mind. A post-Vygotskian semiotic perspective, with an example from Greek mathematical thought’, in M. Anderson, A. Sáenz-Ludlow, S. Zellweger and V. Cifarelli (eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing, Legas Publishing, Ottawa, pp. 49–79.Google Scholar
  46. Radford, L.: 2003b, ‘Gestures, speech, and the sprouting of signs’, Mathematical Thinking and Learning 5(1), 37–70.CrossRefGoogle Scholar
  47. Radford, L.: 2003c, ‘On the epistemological limits of language. Mathematical knowledge and social practice during the Renaissance’, Educational Studies in Mathematics 52(2), 123–150.CrossRefGoogle Scholar
  48. Radford, L.: 2004, Cose sensibili, essenze, oggetti matematici ed altre ambiguità [Sensible Things, Essences, Mathematical Objects and other ambiguities], La Matematica e la sua didattica, No. 1, 4–23. (An English version is available at: Scholar
  49. Ricoeur, P.: 1996, A Key to Edmund Husserl's Ideas I, Marquette University Press, Milwaukee, WI.Google Scholar
  50. Rosenthal, S.: 1983, ‘Meaning as habit: Some systematic implications of Peirce's pragmatism’, in E. Freeman (ed.), The Relevance of Charles Peirce, Monist Library of Philosophy, La Salle, pp. 312–326.Google Scholar
  51. Sapir, E.: 1949, Selected Writings in Language, Culture and Personality, D.G. Mandelbaum (ed.), 5th printing, 1968, University of California Press, Berkeley and Los Angeles.Google Scholar
  52. Sfard, A.: 2000, ‘Symbolizing mathematical reality into being – or how mathematical discourse and mathematical objects create each other’, in P. Cobb et al. (eds.), Symbolizing and Communicating in Mathematics Classrooms, Lawrence Erlbaum, Mahwah, New Jersey and London, pp. 37–98.Google Scholar
  53. Sierpinska, A.: 1998, ‘Three epistemologies, three views of classroom communication: Constructivism, sociocultural approaches, interactionism’, in H. Steinbring, M. Bartolini Bussi and A. Sierpinska (eds.), Language et Communication in the Mathematics Classroom, The National Council of Teachers of Mathematics, Reston, Virginia, pp. 30–62.Google Scholar
  54. Smith, J.: 1983, ‘Community and reality’, in E. Freeman (ed.), The Relevance of Charles Peirce, Monist Library of Philosophy, La Salle, pp. 38–58.Google Scholar
  55. Vološinov, V.N.: 1976, Freudianism: A Critical Sketch. Translated by I. R. Titunik, Indiana University Press, Bloomington and Indianapolis.Google Scholar
  56. Wartofsky, M.: 1979, Models, Representation and the Scientific Understanding, D. Reidel, Dordrecht.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.École des sciences de l'éducationUniversité LaurentienneSudburyCanada

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