DEL SÍMBOLO Y DE SU OBJETO:  REFLEXIONES EN TORNO A LA TEORÍA DE LA CONCEPTUALIZACIÓN DE CASSIRER

Luis Radford

Artículos

Vol. 7 No. 2 (2004): Julio

ON SINGS AND THEIR OBJECTS: REFLECTIONS ON CASSIRER’S THEORY OF CONCEPTS

Luis Radford^▸^▾

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Published: July 31, 2004

Abstract

Through the concept of the schema, as elaborated in The Critique of Pure Reason, and then refined in The Critique of Judgement, Kant tried to find an answer to the problem surrounding the epistemological relationship between symbol and object. In his answer, Kant combined elements from both the empiricism and rationalism of his time in such a way that its theory of knowledge cannot overcome an irreducible duality between intellectual activity and sensory activity. In trying to abolish this duality Cassirer—just like Piaget, although taking a different path—developed a genetic theory around a reformulation of the Kantian concept of the schema. The goal of the present article is to analyze Cassirer’s genetic theory of conceptualization and to present, in the end, a brief comparison with Piaget’s genetic epistemology. The Kantian source common to both thinkers allows us to evaluate the reach of Kantian constructivism more clearly and to better understand its limits and possibilities.

References

Adorno, T. W. (2001). Kant’s Critique of Pure Reason. Stanford, USA: Stanford University Press.
Buck-Morss, S. (1975). Socio-Economic Bias in Piaget's theory and its implications for cross-culture studies. Human Development 18, 35-49.
Hintikka, J. (1980) La philosophie des mathématiques chez Kant. París: Presses Universitaires de France.
Cassirer, E. (1943). Hermann Cohen. Social Research, 10, 219-232.
Cassirer, E. (1953). Language and Myth. New York: Dover.
Cassirer, E. (1957). The Philosophy of Symbolic Forms. Vol. 3. London: Oxford University Press.
Cassirer, E. (1977). Substance et fonction. Éléments pour une théorie du concept. Paris: les éditions de minuit (Publicado inicialmente en 1910).
Cassirer, E. (2000). The logic of the cultural sciences. New Haven: Yale University Press.
De las Casas, B. (1951). Historia de las Indias. México: Fondo de Cultura Económica.
Friedman, M. (2000). A parting of the ways. Carnap, Cassirer, and Heidegger. Chicago: Open Court.
Gawronsky, D. (1949). Ernst Cassirer: his life and his work. En A. Schilpp, (editor), The philosophy of Ernst Cassirer (pp. 3-37). New York: Tudor
Kant, M. (1781/1787/1987). Crítica de la razón pura. México: editorial Porrúa.
Leibniz, G. W. (1705/1949). New Essays concerning Human Understanding. Translated from the 1705 text by A. G. Langley. La Salle, Ill: The open Court.
Leont’ev, A. N. (1978). Activity, Consciousness, and Personality. New Jersey: Prentice-Hall.
Lukács, G. (1960). Histoire et conscience de classe. Paris: Les editions de minuit.
Radford, L. (2002). The Object of Representations: Between Wisdom and Certainty. En F. Hitt (ed.), Representations and Mathematics Visualization (219-240). Mexico: Departamento de matemática educativa Cinvestav-IPN.
Radford, L. (2003). On Culture and Mind. A post-Vygotskian Semiotic Perspective, with an Example from Greek Mathematical Thought. En M: Anderson, A. Sáenz-Ludlow, S. Zellweger y V. V. Cifarelli (eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing (pp. 49-79). Ottawa: Legas Publishing.
Radford, L. (en prensa). The semiotics of the schema: Kant, Piaget, and the Calculator. En Michael Hoffmann, Johannes Lenhard, Falk Seeger (eds.), Activity and Sign – Grounding Mathematics Education. Festschrift for Michael Otte. Dordrecht: Kluwer.
Russell, B. (1920). Introduction to mathematical philosophy. Reimpreso por Dover, New York, 1993.
Stephens, I. K. (1949). Cassirer’s doctrine of the a priori. En A. Schilpp, (editor), The philosophy of Ernst Cassirer (pp. 151- 181). New York: Tudor.

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Keywords

abstraction
Cassirer
epistemology
kantian schema
symbolic forms
Piaget
semiotics
sense
mathematical signs

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How to Cite

Radford, L. (2004). ON SINGS AND THEIR OBJECTS: REFLECTIONS ON CASSIRER’S THEORY OF CONCEPTS. Revista Latinoamericana de Investigación en Matemática Educativa, 7(2), 157-170. https://relime.org/index.php/relime/article/view/538

Most read articles by the same author(s)

[1] Adorno, T. W. (2001). Kant’s Critique of Pure Reason. Stanford, USA: Stanford University Press.

[2] Buck-Morss, S. (1975). Socio-Economic Bias in Piaget's theory and its implications for cross-culture studies. Human Development 18, 35-49.

[3] Hintikka, J. (1980) La philosophie des mathématiques chez Kant. París: Presses Universitaires de France.

[4] Cassirer, E. (1943). Hermann Cohen. Social Research, 10, 219-232.

[5] Cassirer, E. (1953). Language and Myth. New York: Dover.

[6] Cassirer, E. (1957). The Philosophy of Symbolic Forms. Vol. 3. London: Oxford University Press.

[7] Cassirer, E. (1977). Substance et fonction. Éléments pour une théorie du concept. Paris: les éditions de minuit (Publicado inicialmente en 1910).

[8] Cassirer, E. (2000). The logic of the cultural sciences. New Haven: Yale University Press.

[9] De las Casas, B. (1951). Historia de las Indias. México: Fondo de Cultura Económica.

[10] Friedman, M. (2000). A parting of the ways. Carnap, Cassirer, and Heidegger. Chicago: Open Court.

[11] Gawronsky, D. (1949). Ernst Cassirer: his life and his work. En A. Schilpp, (editor), The philosophy of Ernst Cassirer (pp. 3-37). New York: Tudor

[12] Kant, M. (1781/1787/1987). Crítica de la razón pura. México: editorial Porrúa.

[13] Leibniz, G. W. (1705/1949). New Essays concerning Human Understanding. Translated from the 1705 text by A. G. Langley. La Salle, Ill: The open Court.

[14] Leont’ev, A. N. (1978). Activity, Consciousness, and Personality. New Jersey: Prentice-Hall.

[15] Lukács, G. (1960). Histoire et conscience de classe. Paris: Les editions de minuit.

[16] Radford, L. (2002). The Object of Representations: Between Wisdom and Certainty. En F. Hitt (ed.), Representations and Mathematics Visualization (219-240). Mexico: Departamento de matemática educativa Cinvestav-IPN.

[17] Radford, L. (2003). On Culture and Mind. A post-Vygotskian Semiotic Perspective, with an Example from Greek Mathematical Thought. En M: Anderson, A. Sáenz-Ludlow, S. Zellweger y V. V. Cifarelli (eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing (pp. 49-79). Ottawa: Legas Publishing.

[18] Radford, L. (en prensa). The semiotics of the schema: Kant, Piaget, and the Calculator. En Michael Hoffmann, Johannes Lenhard, Falk Seeger (eds.), Activity and Sign – Grounding Mathematics Education. Festschrift for Michael Otte. Dordrecht: Kluwer.

[19] Russell, B. (1920). Introduction to mathematical philosophy. Reimpreso por Dover, New York, 1993.

[20] Stephens, I. K. (1949). Cassirer’s doctrine of the a priori. En A. Schilpp, (editor), The philosophy of Ernst Cassirer (pp. 151- 181). New York: Tudor.

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