Numbers, Infinity, and Reality: An Interdisciplinary Undergraduate Philosophy of Mathematics Course – Appendix: Course Texts

Readings for each of the five units of the course are as follows, listed in the order assigned.

Historical Foundations

Pythagoras. n.d. Selected Fragments. In A Presocratics Reader: Selected Fragments and Testimonia, edited by Patricia Curd and translated by Richard McKirahan and Patricia Curd, 23–30. 2nd ed. Indianapolis: Hackett Publishing, 2011.

Plato. n.d. Meno 80A-98B. Translated by W. R. M. Lamb. In Plato: Meno and Phaedo, 79–97. Cambridge Texts in the History of Philosophy. Cambridge: Harvard University Press, 1990.

Lloyd, G.E.R. 2009. Mathematics. In Disciplines in the Making: Cross-Cultural Perspectives on Elites, Learning, and Innovation, 28–57. New York: Oxford University Press.

Metaphysics and Epistemology

Benacerraf, Paul. 1965. What Numbers Could Not Be. Philosophical Review 74:47–73.  Reprinted in Philosophy of Mathematics: Selected Readings, edited by Paul Benacerraf and Hilary Putnam, 272–294. 2nd ed. Cambridge: Cambridge University Press, 1983.

Kalderon, Mark. 1996. What Numbers Could Be (And, Hence, Necessarily Are). Philosophia Mathematica 3: 238–255.

McLarty, Colin. 1993. Numbers Can Be Just What They Have To. Nous, 27(4): 487–498.

Benacerraf, Paul. 1965. Mathematical Truth. Journal of Philosophy 70: 661–680. Reprinted in Philosophy of Mathematics: Selected Readings, edited by Paul Benacerraf and Hilary Putnam, 403–420. 2nd ed. Cambridge: Cambridge University Press, 1983.

Parsons, Charles. 1979. Mathematical Intuition. Proceedings of the Aristotelian Society 80: 145–168.

Cheyne, Colin. 1997. Getting in Touch with Numbers: Intuitionism and Mathematical Platonism. Philosophy and Phenomenological Research 57(1): 111–125.

Resnik, Michael. 1975. Mathematical Knowledge and Pattern Cognition. Canadian Journal of Philosophy 5(1): 25–39.

Katz, Jerrold. 2002. Mathematics and Metaphilosophy. Journal of Philosophy 99(7): 362–390.

Kitcher, Philip. 1975. Kant and the Foundations of Mathematics. Philosophical Review 84(1): 23–50.

Lakoff, George and Rafael Núñez. 2000. Where Mathematics Comes From (excerpts). New York: Basic Books.

Axiomatization

Euclid. n.d.  Definitions 1–23 and Postulates 1–5 from The Elements, Book I. Translated by Thomas Heath. Reprint; New York: Dover Publishing, 1956.

Greenberg, Marvin. 2008. Euclidean and Non-Euclidean Geometries: Development and History. 4th ed. New York: W.H. Freeman & Co.

Russell, Bertrand. 1919. Introduction to Mathematical Philosophy (selections). Reprinted in Philosophy of Mathematics: Selected Readings, edited by Paul Benacerraf and Hilary Putnam, 160–182. 2nd ed. Cambridge: Cambridge University Press, 1983.

Corry, Leo. 2008. The Development of the Idea of Proof. In The Princeton Companion to Mathematics, edited by Timothy Gowers, 129–142. Princeton: Princeton University Press.

Hilbert, David. 1926. Über das Unendliche (On the Infinite). Mathematische Annalen 95: 161–190. English translation by Erna Putnam and Gerald J. Massey. Reprinted in Philosophy of Mathematics: Selected Readings, edited by Paul Benacerraf and Hilary Putnam, 183–201. 2nd ed. Cambridge: Cambridge University Press, 1983.

Gödel, Kurt. 1947. What is Cantor’s Continuum Problem? The American Mathematical Monthly 54: 515–525. Revised and expanded version in  Philosophy of Mathematics: Selected Readings, edited by Paul Benacerraf and Hilary Putnam, 470–485. 2nd ed. Cambridge: Cambridge University Press, 1983.

Cross-disciplinary Relationships

Hardy, G. H. 1967. Mathematician’s Apology. Cambridge: Cambridge University Press.

Wigner, Eugene. 1960. The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications in Pure and Applied Mathematics 13(1):1–14.

Sociological Implications

Alexander, Amir. 2006. Tragic Mathematics: Romantic Narratives and the Refounding of Mathematics in the Early Nineteenth Century. Isis 97: 714–726. DOI: 10.1086/509952.

Colyvan, Mark. 2002. Mathematics and Aesthetic Considerations in Science. Mind 111(441): 69–74.