By Kmowles I.W. (ed.), Saito Y. (ed.)

ISBN-10: 0387184791

ISBN-13: 9780387184791

ISBN-10: 3540184791

ISBN-13: 9783540184799

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Notice that the new orientation in the philosophy of mathematics is highly interdisciplinary. Some authors emphasize knowledge of mathematics itself and logic [. . ]; some others stress the role of cognitive science [. . ] or sociological approaches [. . ]; and the list goes on, with mathematics education, anthropology, biology, etcetera. (Ferreirós, 2015, pp. 1–2) The quotes by Mancosu, Van Bendegem, and Ferreirós emphasis that the philosophy of mathematical practice is not dealing with entirely new philosophical questions, but is a particular approach to philosophy of mathematics.

The Study of Cultures and Practices of Mathematics 29 derivations hides many important and interesting features of what it is to do mathematics: [From the early 20th century onwards,] the foundations of mathematics became a central research interest. This resulted in a widely accepted notion of formal derivation as the explication of mathematical proof. [. . ] In mathematical practice, proofs are written down in a more condensed, semi-formal style. [. . ] The traditional view would consider these proofs enthymematic, leaving out technical detail for purely pragmatic reasons.

2004). A mathematician’s apology. Cambridge: Cambridge Univ. Press [Original edition 1940]. Hegel, G. W. F. (1821). Elements of the philosophy of right. (Original German title: Grundlinien der Philosophie des Rechts). Hersh, R. (2006). 18 unconventional essays on the nature of mathematics. New York: Springer. Hofstede, G. (1984). National cultures and corporate cultures. In L. A. Samovar & R. E. ), Communication between cultures. Belmont, CA: Wadsworth. Hofstede, G. (1986). Cultural differences in teaching and learning.