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Young, Robyn V. “Bertrand Russell.” In Young, 1998, pp. 428-31.
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9. 希尔伯特VS布劳威尔
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Barrow, John D. “The Comedy of Hilbert and Brouwer” In Barrow, 1992, pp. 216-26.
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Brouwer, Luitzen Egbertus Jan. “Intuitionist Set Theory.” Paper presented to the Royal Academy of Sciences, December 18, 1920. In Mancosu, 1998, pp. 23-39.
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Hatcher, Donald L. “Epistemology and Education: A Case for Fallibilism.” Online, undated: www.bakeru.edu/crit/literature/dlh_ct_epistemology.htm.
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1701058690
Hays, John. “The Battle of the Frog and the Mouse (from the Fables of Aleph).” Mathematical Intelligencer 6, no. 2 (1984): 77-80.
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Hilbert, David. “From ‘Mathematical Problems: Lecture Delivered before the International Congress of Mathematicians at Paris in 1900. (Paris Problems and the Formalist Program).’” In Calinger, 1995, pp. 698-718.
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Mancosu, Paolo. From Brouwer to Hilbert. New York: Oxford University Press, 1998.
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Nyikos, Peter. “Hilbert’s First and Second Problems and the Foundations of Mathematics.” Topology Atlas Invited Contributions 9, no. 3 (2004): 1-6. Online: PDF form is http://arxiv.org/PS_cache/math/pdf/0412/0412555.pdf.
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Peckhaus, Volker. “The Pragmatism of Hilbert’s Program.” Synthese 137 (2003): 141-56. Online, pp. 1-17: www-fakkw.upb.de/institute/philosophie/Personal/Peckhaus/Texte_zum_Download/pragmatism-h.pdf.
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Reid, C. Hilbert. New York: Springer-Verlag, 1970.
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Simpson, Stephen G. “Partial Realizations of Hilbert’s Program,” February 4, 1986, pp. 1-22. Online: ftp://ftp.math.psu.edu/simpson/papers/hilbert.pdf. Published in the Journal of Symbolic Logic 53 (1988): 349-63.
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1701058704
Snapper, Ernst. “The Three Crises in Mathematics: Logicism, Intuitionism, and Formalism.” Chapter 106 in Swetz, 1994, pp. 697-707.
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Stein, Howard. “Logos, Logic, and Logistiké: Some Philosophical Remarks on Nineteenth-Century Transformation of Mathematics ” In Aspray and Kitcher, 1988, pp. 238-59.
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van Dalen, Dirk. Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer. New York: Oxford University Press. Vol. 1, The Dawning Revolution, 1999. Vol. 2, Hope and Disillusion, 2005.
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——. “The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen.” Mathematical Intelligencer 12, no. 4 (1990): 17-31.
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van Stigt, Walter P. Brouwer’s Intuitionism. New York: Elsevier Science, 1990.
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——. “Brouwer’s Intuitionist Program.” In Mancosu, 1998, pp. 1-22.
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von Mises, Richard. “Logistic” and “The Foundations of Mathematics.” Sections in “Mathematical Postulates and Human Understanding” (1951). In Newman, vol. 3, 1956, pp. 1733-54.
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Weyl, Hermann. “David Hilbert and His Mathematical Work” (1944). In Reid, 1970, pp. 245-83. (Especially Axiomatics, pp. 264-74).
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Young, Robyn V. “David Hilbert.” In Young, 1998, pp. 244-47.
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1701058722
——. “Luitzen Egbertus Jan Brouwer.” In Young, 1998, p. 81.
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1701058724
10. 绝对主义者/柏拉图主义者VS易误论着/建构主义者
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1701058726
Barnard, Tony, and Peter Saunders. “Superior Sums That Don’t Add Up to Much. How Mathematics Is Taught Is in Dispute, and Our Children’s Knowledge of It Is Worse Than Ever.” The Guardian (December 28, 1994), Features, p. 18.
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Barrow, John D. “Platonic Heavens above and Within.” Chapter 6 in Barrow, 1992, pp. 249-97.
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