Considerations about the notion of mathematical intuition
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Abstract
The history of mathematics shows how mathematical intuition has been present in the invention and development of mathematical concepts, theories and procedures. Likewise, it has permeated the philosophical debate, the foundations of mathematics and educational discourses; giving validity to the study of this subject. In this article, the arguments are presented under which it is possible to support that intuition is a process, that takes ideas that are presented, initially in a “messy” way, and that thanks to the context and previous knowledge of the individual focus on a "fixed" idea that will be incorporated into mathematics by logic and formalization.
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Ardeshir, M. (2008). Brouwer’s notion of intuition and theory of knowledge by presence. En M. van Atten, P. Boldini, M. Bourdeau, & G. Heinzmann (Eds.), One Hundred Years of Intuitionism (1907-2007). The Cerisy Conference Basel, Birkhäuser, 2008, pp. 115–130. https://doi.org/10.1007/978-3-7643-8653-5_8
Aspray, W. & Kitcher, P. History and Philosophy of Modern Mathematics, Minneapolis, University of Minnesota Press, 1988.
Bergson, H. La Energía Espiritual, Madrid, Espasa Calpe, 1982.
Bunge, M. Intuición y razón, Buenos Aires, Editorial Sudamericana, 1996.
Chudnoff, E. "Intuition in Mathematics", en L. M. Osbeck & B. S. Held (Eds.), Rational Intuition: Philosophical Roots, Scientific Investigations, Cambridge, Cambridge University Press, 2014, pp. 174–191. https://doi.org/10.1017/CBO9781139136419.010
Fedyk, M. "Intuitions, Naturalism, and Benacerraf’s Problem", en S. Bangu (Ed.), Naturalizing Logico-Mathematical Knowledge, New York, Routledge, 2018, pp. 89–105. https://doi.org/10.4324/9781315277134-5
Fischbein, E. Intuition in Science and Mathematics. An Educational Approach, Dordrecht, Reidel, 2002.
Gödel, K. Obras Completas, Madrid, Alianza editorial, 2006.
Kant, I. Crítica de la Razón Pura, Madrid, Alfaguara, 1978.
Kitcher, P. The Nature of Mathematical Knowledge, New York, Oxford University Press, Inc., 1984.
Maddy, P. "Perception and Mathematical Intuition", The Philosophical Review, (1980), 163–196. https://doi.org/10.2307/2184647
Poincaré, H. "La intuición y la lógica en las Matemáticas". En El valor de la ciencia, 1905, pp. 1–9. Recuperado de http://casanchi.com/ref/logicaintuicion01.pdf 1905.
Popper, K. & Eccles, J. El yo y su cerebro, Barcelona, Editorial Labor, 1977.
Sierpinska, A. & Lerman, S. "Epistemologies of mathematics and of mathematics education", en A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education, Dordrecht, HL: Kluwer, 1996, pp. 827–876.
Stisman, A. F. "El realismo conjuntista de Penelope Maddy", Epistemología e historia de la ciencia, (2006), 533–539.
Tieszen, R. Mathematical intuition: phenomenology and mathematical knowledge, Dordrecht, Kluwer Academic Publishers, 1989. https://doi.org/10.1007/978-94-009-2293-8