Bibliography

Below is a list of works relevant to the seminar. We will not read and discuss all of them! To avoid flagrant copyright violations, some of the works are in a password protected directory.

Galois theory - primary sources

• Abel, Niels Henrik, "Mémoire sur les équations algébriques, où l'on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré," 1824. In his Ouvres, 1:28-33. Pesic translation: pdf.
• Abel, Niels Henrik, "Démonstration de l'impossibilité de la résolution algébrique des équations générales qui passent le quatrième degré," 1826. In his Ouvres, 1:66-86. German version published in Crelle's Journal, volume 1, 1826.
• Abel, Niels Henrik, summary of the preceding article, published in Bulletin des sciences math., astr., phys., et chim. 6:347, 1826. In his Ouvres, 1:87-94. Manders translation: pdf.
• Galois, Évariste, "Mémoire sur les conditions de resolubilité des equations par radicaus,"1831-1832. Translation by Harold Edwards. pdf.
• Dedekind, Richard, Suplement XI to the fourth edition Dirichlet's Vorlesungen über Zahlentheorie, Vieweg, Braunschweig, 1894. Reprinted in Dedekind's Werke, volume 3, 1-222. Excerpt: pdf.
• Weber, Heinrich, Lehrbuch der Algebra, Vieweg, Braunschweig, 1895.
• Artin, Emil, Galois Theory, University of Notre Dame Press, Notre Dame, 1942. Reprinted by Dover Publications, New York, 1998. Chapter II, A-H: pdf. Chapter III, A-E: pdf.

Galois theory - secondary sources

• Edwards, Harold M., Galois Theory, Springer-Verlag, New York, 1984. Excerpts: pdf, pdf, pdf.
• Kiernan, B. M., "The development of Galois theory from Lagrange to Artin," Archive for History of Exact Science 8, 1971, 40-154. pdf (first file), pdf (second file).
• Pesic, Peter, Abel's Proof: an essay on the sources and meaning of mathematical unsolvability, MIT Press, Cambridge, MA, 2003.
• Manders, Kenneth, "Algebra in Roth, Faulhaber, and Descartes," pdf.
• Keranen, Jukka, Cognitive Control in Mathematics (PhD thesis): pdf.

Mathematical background

• Birkhoff, Garret, and Saunders Mac Lane, A Survey of Modern Algebra, third edition, Macmillan, New York, 1965.
• Hill, Victor E., IV, Groups and Characters, Chapman and Hall / CRC, Boca Raton, 2000. Chapters 1-4: pdf.
• Milne, J.S., Fields and Galois theory: html
• Stahl, Saul, Introductory Modern Algebra: A Historical Approach, John Wiley & Sons, New York, 1996.

Kant - primary sources

• Kant, Emmanuel, Critique of Pure Reason. (Either Kemp Smith or Guyer / Wood translation.) B introduction: pdf. Transcendental doctrine of method, discipline of pure reason in dogmatic use: pdf.
• Kant, Emmanuel, Prolegomena to Future Metaphysics.

Kant - secondary sources

• Friedman, Michael, Kant and the Exact Sciences, Harvard University Press, Cambridge, Massachusetts, 1992. Chapters 1 and 2. pdf.
• Parsons, Charles, "Kant's philosophy of arithmetic," in Morganbesser, Suppes, and White, eds., Philosophy, Science, and Methods. Essays in Honour of Ernest Nagel. London and New York: Macmillan and St. Martin's Press, 568-94, 1971. Reprinted in Walker, Ralph C. S., editor, Kant on Pure Reason, Oxford University Press, Oxford, 13-40, 1982. pdf.
• Shabel, Lisa, "Kant’s Philosophy of Mathematics" forthcoming in The Cambridge Companion to Kant, 2nd edition, Paul Guyer, ed., Cambridge University Press. pdf.
• Shabel, Lisa, "Kant on the 'Symbolic Construction' of Mathematical Concepts, " Studies in History and Philosophy of Science 29:4, December 1998 . pdf.

Husserl - primary sources

• Husserl, Edmund, Philosophie der Arithmetik. Pyschologische und logische Untersuchungen. Erster Band. Halle-Saale: C.E. M. Pfeffer (Robert Stricker), 1891. Translated by Dan Willard as Philosophy of Arithmetic: Psychological and Logical Investigations, Kluwer, Dordrecht, 2003. Excerpt: pdf.
• Husserl, Edmund, Logische Untersuchungen. Halle a.d.S.: Max Niemeyer, 1900/1901. Excerpts from the Prolegomena and the introduction to volume 2: pdf, pdf. Excerpts from the first and sixth investigations: pdf.
• Husserl, Edmund, Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. In Jahrbuch für Philosophie und phänomenologische Forschung, 1 Halle a.d.S., 1913. [Ideas Pertaining to Pure Phenomenology and Phenomenological Philosophy.]

Husserl - secondary sources

• Beyer, Christian, "Edmund Husserl", in Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. html.
• Kennedy, Juliette, and Mark van Atten, "On the philosophical development of Kurt Gödel." Bulletin of Symbolic Logic, 9:425-476, 2003. pdf.
• McIntyre, Ronald, "Husserl and Frege," Journal of Philosophy 84:528-535, 1988. pdf. (See also McInyre's list of publications.)
• McIntyre, Ronald, "Husserl and the Representational Theory of Mind," Topoi 5:101-113, 1986. pdf
• McIntyre, Ronald, and David Woodruff Smith, "Husserl's identification of meaning and noema," in Hubert L. Dreyfus, ed., Husserl, Intentionality, and Cognitive Science, MIT Press, Cambridge, MA, 1982. pdf.
• Tieszen, Richard, "Mathematics," in Barry Smith and David Woodruff Smith, The Cambridge Companion to Husserl, Cambridge, Cambridge University Press, 438-462, 1995. pdf.

Wittgenstein - primary sources

• Wittgenstein, Ludwig, Philosophical Grammar, edited by Rush Rhees, translated by Anthony Kenny, Blackwell, 1974.
• Wittgenstein, Ludwig, Lectures on the Foundations of Mathematics, Cambridge, 1939, edited by Cora Diamon, Ithaca, N.Y., Cornell University Press, 1976.
• Wittgenstein, Ludwig, Remarks on the Foundations of Mathematics, revised edition, edited by G. H. von Wright, R. Rhees, G. E. M. Anscombe, translated by G. E. M. Anscombe. MIT Press, Cambridge, MA, 1983. Part VI: pdf. Part VII: pdf.
• Wittgenstein, Ludwig, Philosophische Untersuchungen. Translated as Philosophical Investigations by G. E. Anscombe, Prentice Hall, 3rd edition, 1999.

Wittgenstein - secondary sources

• Kripke, Saul, Wittgenstein on Rules and Private Language, Harvard University Press, reprint edition, 2004.
• Goldfarb, Warren, "Kripke on Wittgenstein on rules," The Journal of Philosophy, 82:471-488, 1985. JSTOR.
• McDowell, John, "Wittgenstein on following a rule," Synthese, 58:325-363, 1984. pdf, pdf.
• Tait, W. W., "Wittgenstein and the 'skeptical paradoxes,'" The Journal of Philosophy, 83: 475-488, 1986. JSTOR.
• See also the "Wittgenstein on Rules and Private Language Ultimate HomePage," html

Philosophical background

• Avigad, Jeremy, "Philosophy of Mathematics in the 20th Century" (draft). pdf.
• Shapiro, Stuart, Thinking about Mathematics: the Philosophy of Mathematics. Oxford University Press, Oxford, 2000.

Other items

• Abhyankar, Shreeram, "Galois theory on the line in nonzero characteristic," Bulletin of the American Mathematical Society, 27:68-133, 1992. pdf.
• Abhyankar, Shreeram, "Historical ramblings in algebraic geometry and related algebra," The American Mathematical Monthly, 83:409-448, 1976, JSTOR.
• Avigad, Jeremy, "Mathematical method and proof," to appear in Synthese. pdf.
• Avigad, Jeremy, "Methodology and metaphysics in the development of Dedekind's theory of ideals," to appear in José Ferreirós and Jeremy Gray, editors, The Architecture of Modern Mathematics, Oxford University Press. pdf.
• Gowers, W. T., "The two cultures of mathematics," in Mathematics: frontiers and perspectives, 65-78, American Mathematical Society, Providence, RI, 2000. pdf.