Mathematics and Culture

fakultatywne

The course assumes a basic willingness to do a bit of mathematics with pleasure. You should understand the concept of proof and be prepared to apply it in case of relatively simple examples. For instance, if you can prove the Pythagorean theorem, or at least understand 1-2 proofs of it you’re probably all set. Serious mathematicians are welcome to take the course, but they should be prepared to talk to students who are not so prepared.

This course will explore mathematics as a humanities subject. We will introduce and discuss basic problems in the philosophy of mathematics, but the focus will be on understanding and discussing the cultural impact of mathematics in the light of these problems. Topics will include questions about whether human intelligence is unitary or plural (whether, as Pascal said, there is an esprit géométrique as well as an esprit de finesse), and the related problem of “two cultures”; the reality of mathematical objects and the significance of this problem for epistemology; the concept of Renaissance perspective and its significance for art; the modern discovery of the infinite; Cartesian and anti-Cartesian theories of mind and the world; mathematics and the irrational; Wittgenstein and the logical turn; algorithms and the mind. Viewing and discussing artworks (and films) will be an important part of the course.

1. Are there “two cultures”?

Readings: C.P. Snow: Two Cultures

G.H. Hardy: A Mathematician’s Apology

Aldous Huxley: Little Archimedes

2. Topics in the Philosophy of Mathematics

Readings: Plato: The Republic (selections): Timaeus (selections); Meno

3. Perspective and Painting

Readings: Leon Battista Alberti: On Painting; Nicholas of Cusa: On Learned Ignorance (selections)

4. Cartesian and anti-Cartesian Subjects: Descartes and his Opponents

Readings: Renè Descartes: Discourse on Method; Denis Diderot: Letter on the Blind; Montaigne: Essais (selections)

5. Galileo and Religion

Readings: Galileo Galilei: Letter to the Duchess Christina; Immanuel Kant: The Critique of Pure Reason (selections)

6. The Irrational Infinite: Pascal, Chance, and the Baroque

Readings: Pascal: Pensées (selections); Russell and Copleston: Debate on the Existence of God; Erwin Panofsky: What is Baroque?

Film: My Night at Maud’s (1969, dir. Éric Rohmer)

7. Wittgenstein and Logic

Readings: Ludwig Wittgenstein: Tractatus Logico-Philosophicus (short selections); Philosophical Investigations (short selections)

8. Algorithms and the Mind

Douglas Hofstadter: Gödel, Escher, Bach: An Eternal Golden Braid (selections)

Alberti, L. B. (1966). On Painting (Translated with Introduction and Notes by John. R. Spencer). Yale University Press.

Cardano, G. (2002). The book of my life = (De vita propria liber). New York Review Books. https://www.goodreads.com/en/book/show/25012.The_Book_of_My_Life

Carman, C. H. (2014). Leon Battista Alberti and Nicholas Cusanus: Towards an Epistemology of Vision for Italian Renaissance Art and Culture. Ashgate Publishing Limited.

Cusa, N. of. (1997). Selected Spiritual Writings. Paulist Press.

Davis, P. J., & Hersh, R. (1998). The mathematical experience. Houghton Mifflin. https://books.google.de/books/about/The_Mathematical_Experience.html?id=lMdz84dWNnAC&redir_esc=y

Descartes, R. (2017). Discourse on the Method of Rightly Conducting one’s Reason and Seeking Truth in the Sciences. https://www.earlymoderntexts.com/assets/pdfs/descartes1637.pdf

Friedberg, A. (2006). The Virtual Window: from Alberti to Microsoft. The MIT Press.

Galilei, G. (n.d.). Letter to the Grand Duchess Christina of Tuscany (1615) (abridged). Retrieved November 23, 2022, from https://web.stanford.edu/~jsabol/certainty/readings/Galileo-LetterDuchessChristina.pdf

Hardy, G. H. (n.d.). A Mathematician’s Apology. Retrieved November 23, 2022, from http://www.math.ualberta.ca/mss/

Harries, K. (2001). Infinity and Perspective. The MIT Press.

Heintz, B. (1999). Die Innenwelt der Mathematik: Zur Kultur und Praxis einer beweisenden Disziplin. Springer; Auflage: 2000. http://www.amazon.de/Innenwelt-Mathematik-Naturwissenschaften-Wissenschaften-Zivilisierung/dp/321182961X

Hofstadter, D. R. (1999). Gödel, Escher, Bach : an eternal golden braid. Basic Books. https://www.goodreads.com/book/show/24113.G_del_Escher_Bach

Huxley, A. (2000). Young Archimedes, and other stories. Transaction Publishers. https://archive.org/details/youngarchimedeso0000huxl

Kant, I., Guyer, P., & Wood, A. W. (n.d.). Critique of pure reason. Retrieved November 23, 2022, from https://www.amazon.de/Critique-Pure-Reason-Paul-Guyer/dp/0521657296

Montaigne, M. de, & Screech, M. A. (Michael A. (1993). The complete Essays. Penguin Books. https://www.goodreads.com/book/show/30735.The_Complete_Essays

Pacioli, L. F. (1498). De Diva Proportione (Translated). https://www.scribd.com/document/244035060/tennenbaum-pacioli-divine-proportion-pdf

Pascal, B. (1966). Pensées. Translated by A.J. Krailsheimer (Penguin Bo).

Peterson, M. A. (1997). The Geometry of Piero della Francesca. The Mathematical Intelligencer, 19(3), 33–40. https://doi.org/10.1007/BF03025346

Plato. (1977). Timaeus and Critias. Translated by Desmond Lee. Penguin Books.

Plato. (2000). The Republic. Translated by Tom Griffith (G. R. F. Ferrari (ed.); Cambridge).

Plato., & Guthrie, W. K. C. (William K. C. (1956). Protagoras and Meno. Penguin Books.

Shanker, S. (2003). Philosophy of science, logic, and mathematics in the twentieth century. Routledge.

Snow, C. P. (Charles P. (1993). The two cultures. Cambridge University Press. https://www.goodreads.com/book/show/375369.The_Two_Cultures

Text of the Russell-Copleston Debate. (n.d.). https://doi.org/10.1007/978-3-030-85368-6

Tunstall, K. E., & Diderot, D. (2011). Blindness and enlightenment : an essay. Continuum. https://books.google.de/books/about/Blindness_and_Enlightenment_An_Essay.html?id=BA6iF87eMeIC&redir_esc=y

Wittgenstein, L., & Anscombe, G. E. M. (Gertrude E. M. (2001). Philosophical investigations : the German text, with a revised English translation. Blackwell. https://www.goodreads.com/book/show/12073.Philosophical_Investigations

Wittgenstein, L., & Ogden, C. K. (Charles K. (1990). Tractatus logico-philosophicus. Routledge

Familiarity with basic philosophical problems of mathematics as well as their cultural implications; analytical essay writing skills, text comprehension, critical thinking;

In-class participation; essay