Readings

[Rucker] = Rucker, Rudy. Infinity and the Mind: The Science and Philosophy of the Infinite. Princeton University Press, 2004. ISBN: 9780691121277.

Course readings.
WEEK #	TOPICS	READINGS
1	Introduction	No readings
2	Time Travel / Free Will	Required Reading Lewis, David. "The Paradoxes of Time Travel." (PDF) American Philosophical Quarterly 13, no. 2 (1976): 145–52. Optional Readings Baber, H. E. "The Paradoxes of Time Travel: David Lewis." sandiego.edu. Arntzenius, Frank, and Tim Maudlin. "Time Travel and Modern Physics." Stanford Encyclopedia of Philosophy, 2009. Yudkowsky, Eliezer. "Causal Universes." LessWrong.com.
3	Newcomb's Paradox	Required Reading Lewis, David. "Prisoners' Dilemma is a Newcomb Problem." Philosophy & Public Affairs 8, no. 3 (1979): 235–40. Optional Readings ———. "Causal Decision Theory." Chapter 27 in Philosophical Papers: Volume II. Oxford University Press, 1987. ISBN: 9780195036466. [Previw with Google Books] Weirich, Paul. "Causal Decision Theory." Stanford Encyclopedia of Philosophy, 2012. Yudkowsky, Eliezer. "Newcomb's Problem and Regret of Rationality." LessWrong.com. Newcomb's paradox, Wikipedia.org. Prisoner's dilemma, Wikipedia.org.
4	Coordination Game: Nash Equlibria, Schelling Points and the Prisoner's Dilemma (This session was conducted by TA Owain R. Evans.)	No readings
5	Foundations of Probability	Required Reading Lewis, David. Sections 1 through 4 of "Humean Supervenience Debugged." (PDF) Mind 103, no. 412 (1994): 473–90. Optional Readings Read sections 5 through 10 of the above article.
6	Zeno's Paradoxes	Required Reading Parsons, Josh. "The Eleatic Hangover Cure." Analysis 64, no. 4 (2004): 364–66.
7	Infinity	Required Reading [Rucker] Chapter 2: "All The Numbers." Optional Readings Drake, F. R., and D. Singh. "Cardinals." Chapter 4 in Intermediate Set Theory. Wiley, 1996. ISBN: 9780471964964.
8	The Higher Infinite	Required Reading [Rucker] Excursion 1: "The Transfinite Cardinals." Optional Readings Drake, F. R., and D. Singh. "Cardinals." Chapter 4 in Intermediate Set Theory. Wiley, 1996. ISBN: 9780471964964.
9	The Axiom of Choice	Optional Reading Arntzenius, Frank, Adam Elga, et al. "Bayesianism, Infinite Decisions, and Binding." Mind 113, no. 450 (2004): 251–83.
10 and 11	Computability	Optional Readings Boolos, George S., John P. Burgess, and Richard C. Jeffrey. "Turing Computability." Chapter 3 in Computability and Logic. 5th ed. Cambridge University Press, 2007. ISBN: 9780521701464. ———. "Uncomputability." Chapter 4 in Computability and Logic. 5th ed. Cambridge University Press, 2007. ISBN: 9780521701464.
12 and 13	Computability (cont.) / Gödel's Theorem	Optional Readings [Rucker] Excursion 2: "Gödel's Incompleteness Theorems." For those who want to have a look at the proofs, the following book is recommended Boolos, George S., John P. Burgess, and Richard C. Jeffrey. Computability and Logic. 5th ed. Cambridge University Press, 2007. ISBN: 9780521701464. Also Recommended Is Mendelson, Elliott. "Formal Number Theory." Chapter 3 in Introduction to Mathematical Logic. 4th ed. Chapman and Hall/CRC, 1997. ISBN: 9780412808302.
14	Concluding remarks	No readings

Beach-Side Reading

If you want to go further down the rabbit-hole, here are some mathy philosophy readings:

Aaronson, Scott. Quantum Computing Since Democritus. Cambridge University Press, 2013. ISBN: 9780521199568. [Preview with Google Books]

Doxiadis, Apostolos, and Christos H. Papadimitriou. Logicomix: An Epic Search for Truth. Art by Alecos Papadatos and Annie DiDonna. Bloomsbury USA, 2009. ISBN: 9781596914520. [Preview with Google Books]

Drescher, Gary L. Good and Real: Demystifying Paradoxes from Physics to Ethics. A Bradford Books, 2006. ISBN: 9780262042338. [Preview with Google Books]

Yudkowsky, Eliezer. Highly Advanced Epistemology 101 for Beginners, LessWrong.com.

The Beginning of Infinity, Wikipedia.org.