Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Special Article

Vol. 9 No. 4 (2006): Número Especial

EVERYDAY AND MATHEMATICAL LANGUAGE 100 YEARS AFTER THE PUBLICATION OF "ON DENOTING" BY BERTRAND RUSELL.

Submitted
October 28, 2024
Published
2006-12-30

Abstract

The article “On denoting” by B. Russell, published in 1905, is a milestone in philosophical reflection on language. In the present paper, we examine pupils’ reactions both to a sentence inspired by a celebrated example introduced by Russell and to a statement expressed in mathematical language. We move away from an interpretation of experimental data confined to the classical concepts of truth and rationality and propose instead some reflections that shift “the standard of epistemic objectivity from the private certainty of an experiencing subject to the public practice of justification within a communicative community” (J. Habermas). We conclude that language is a very important moment in which the meaning of an expression is fixed, but we keep in mind that “language, like any other semiotic system, functions inside a cultural network of significations” (L. Radford).

References

  1. Andronico, M. (2000). Giochi linguistici e forme di vita. In Marconi, D. (Ed.), Guida a Wittgenstein. Laterza, Roma-Bari, 241-288.
  2. Apel, K.-O. (1987). Fallibilismus, Konsenstheorie der Wahrheit und Letzbegründung. Forum f. Philosophie. Philosophie und begründung. Suhrkamp, Frankfurt a.M., 116-211.
  3. Bagni, G.T. (1997). Elementi di storia della logica formale. Pitagora, Bologna.
  4. Bocenski, J.M. (1956). Formale Logik. Verlag Karl Alber, Freiburg-München (page numbers refer to the Italian translation: La logica formale. Einaudi, Torino 1972).
  5. Bonomi, A. (1973). La struttura logica del linguaggio. Bompiani, Milano.
  6. Brandom, R. (1994). Making it Explicit. Harvard University Press, Cambridge MA.
  7. Brandom, R. (2000). Articulating Reasons. An Introduction to Inferentialism. Harvard University Press, Cambridge MA.
  8. Cassirer, E. (1958). Philosophie der symbolischen Formen. WBG, Darmstadt.
  9. Crombie, A.C. (1995). Commitments and styles of European scientific thinking. History of Sciences 33, 225-238.
  10. D’Amore, B. (2001a). Une contribution au débat sur les concepts et les objets mathématiques. Scientia Paedagogica Experimentalis XXXVIII, 1, 17-46.
  11. D’Amore, B. (2001b). Conceptualisation, registres de représentations sémiotiques et noétique: interactions constructivistes dans l’apprentissage des concepts mathématiques et hypothèse sur quelques facteurs inhibant la dévolution. Scientia Paedagogica Experimentalis XXXVIII, 2, 143-168.
  12. D’Amore, B. (2003a). La complexité de la noétique en mathématiques ou les raisons de la dévolution manqué. For the learning of mathematics, 23(1), 47-51.
  13. D’Amore, B. (2003b). The noetic in mathematics. Scientia Pedagogica Experimentalis XXXIX, 1, 75-82.
  14. Davidson, D. (1990). The Structure and Content of Truth. The Journal of Philosophy, 87, 279-328.
  15. Dummett, M. (1993). Language and Communication. In The Seas of Language. Oxford University Press, Oxford, 166-187.
  16. Duval, R. (1998). Signe et objet (I). Trois grandes étapes dans la problématique des rapports entre représentation et objet. Annales de Didactique et de Sciences Cognitives, 6, 139-163.
  17. Frege, G. (1892). Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100, 25-50 (Senso e riferimento. Senso, funzione e concetto, Laterza, Roma-Bari, 2001).
  18. Frege, G. (1923). Logische Untersuchungen, Dritter Teil: Gedankegefuge. Beitrage zur Philopsophie des Deutschen Idealismus, 3, 36-51 (page numbers refer to Italian translation: Ricerche logiche. Guerini, Milano 1992).
  19. Furinghetti, F. & Radford, L. (2002). Historical conceptual developments and the teaching of mathematics: from philogenesis and ontogenesis theory to classroom practice. In English L. (Ed.), Handbook of International Research in mathematics education. Erlbaum, Hillsdale, 631-654.
  20. Gadamer, H.G. (2005). Linguaggio. Laterza, Roma-Bari.
  21. Geymonat, L. (1970). Storia del pensiero filosofico e scientifico. Garzanti, Milano.
  22. Habermas, J. (1983). Moralbewusstsein und kommunikatives Handeln. Suhrkamp, Frankfurt a.M. (page numbers refer to Italian translation: Etica del discorso. Laterza, Roma-Bari 1985).
  23. Habermas, J. (1999). Wahrheit und Rechtfertigung. Philosophische Aufsätze. Suhrkamp, Frankfurt a.M. (page numbers refer to Italian translation: Verità e giustificazione. Laterza, Roma-Bari 2001).
  24. Ilyenkov, E. (1977). The concept of the ideal. In Philosophy in the USSR. Problems of Dialectical Materialism. Progress Publishers, Moskwa, 71-79.
  25. Kambartel, F. (1996). Universalität, richtig verstanden. Deutsche Zeitschrift für Philosophie, 44, 249.
  26. Kneale, W.C. (1962). Modality “De Dicto” and “De Re”. In Nagel, E., Suppes, P. & Tarsky, A. (Eds.), Logic, Methodology and Philosophy of Science, I. The University Press, Stanford, 622-633.
  27. Kneale, W.C. & Kneale, M. (1962). The Development of Logic. Clarendon Press, Oxford.
  28. Lakoff, G. & Johnson, M. (1980). Metaphors we live by. University of Chicago Press, Chicago (page numbers refer to Italian translation: Metafora e vita quotidiana. Bompiani, Milano 1998).
  29. Lolli, G. (2005). QED Fenomenologia della dimostrazione. Bollati Boringhieri, Torino.
  30. Lo Piparo, F. (2003). Aristotele e il linguaggio. Laterza, Roma-Bari.
  31. Marconi, D. (2000a). Il Tractatus. In Guida a Wittgenstein. Laterza, Roma-Bari, 15-58.
  32. Marconi, D. (2000b). Transizione. In Guida a Wittgenstein. Laterza, Roma-Bari, 59-102.
  33. Meinong, A. (1904). Über Gegenstandstheorie. In Meinong, A., Ameseder, R. & Mally, E., Untersuchungen zur Gegenstandstheorie und Psychologie. Barth, Leipzig, 1-50 (page numbers refer to Italian translation: Teoria dell’oggetto. Quodlibet, Macerata 2003).
  34. Messeri, M. (2000). Seguire la regola. In Marconi, D. (Ed.), Guida a Wittgenstein. Laterza, Roma-Bari, 151-192.
  35. Origgi, G. (2000). Introduzione a Quine. Laterza, Roma-Bari.
  36. Orilia, F. (2002). Ulisse, il quadrato rotondo e l’attuale re di Francia. ETS, Pisa.
  37. Penco, C. (2004). Introduzione alla filosofia del linguaggio. Laterza, Roma-Bari.
  38. Prior, A.N. (1955). Formal Logic. Oxford University Press, London.
  39. Putnam, H. (1992). Significato, riferimento e stereotipi. In Bottani A. & Penco, C. (Eds.), Significato e teorie del linguaggio. Franco Angeli, Milano.
  40. Quine, W.V.O. (1960). Word and Object. MIT Press, Cambridge MA. Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: towards a socio-cultural history of mathematics. For the Learning of mathematics, 17(1), 26- 33.
  41. Radford, L. (2003a). On the epistemological limits of language. Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123- 150.
  42. Radford, L. (2003b). On Culture and Mind. A post-Vygotskian Semiotic Perspective, with an Example from Greek Mathematical Thought, In Anderson, M. & Al. (Eds.), Educational Perspectives on Mathematics as Semiosis. Legas, Ottawa, 49-79.
  43. Rorty, R. (1979). Philosophy and the Mirror of Nature. Princeton University Press, Princeton NJ (page numbers refer to the German translation: Der Spiegel der Natur. Suhrkamp, Frankfurt a.M. 1981).
  44. Rorty, R. (1994). Sind Aussagen universelle Geltungsansprüche? Deutsche Zeitschrift für Philosophie, 42(6), 975-988.
  45. Ryve, A. (2004). Can collaborative concept mapping create mathematical productive discourses? Educational Studies in Mathematics, 26, 157-177.
  46. Russell, B. (1905). On Denoting. Mind, 14, 479-493.
  47. Russell, B. (1910). Knowledge by Acquaintance and Knowledge by Description. Proceedings of the Aristotelian Society, 11, 108-128.
  48. Schnädelbach, H. (1992). Thesen über Geltung und Wahrheit. Zur Rehabilitierung des animal rationale. Suhrkamp, Frankfurt a.M., 104-115.
  49. Sfard, A. & Kieran, C. (2001). Cognition as communication. Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, Activity, 8(1), 42-76.
  50. Sonesson, G. (1998). The Concept of Text in Cultural Semiotics. Trudy po znakyvym sistemam - Sign System Studies 26, Tartu University Press, Taru, 88-114.
  51. Strawson, P.F. (1950). On Referring. Mind, 59, 320-344 (Flew, A., Ed.: Essays in Conceptual Analysis. Macmillan, London 1960, 21-52).
  52. Vattimo, G. (Ed.) (1993). Enciclopedia Garzanti di Filosofia. Garzanti, Milano.
  53. Von Wright, G.E. (1951). An Essay in Modal Logic. North-Holland, Amsterdam.
  54. Wartofsky, M. (1979). Perception, representation and the forms of action: towards an historical epistemology. In Models. Representation and the scientific understanding. Reidel, Dordrecht,
  55. -209.
  56. Williams, M. (1996).Unnatural doubts. Princeton University Press, Princeton NJ.
  57. Wittgenstein, L. (1922). Tractatus logico-philosophicus. Routledge and Kegan Paul, London.

Downloads

Download data is not yet available.

Similar Articles

<< < 1 2 3 4 5 6 > >> 

You may also start an advanced similarity search for this article.