Readings

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

WEEK # TOPICS READINGS
1 Introduction No readings
2 Time Travel / Free Will

Required Reading

Lewis, David. This resource may not render correctly in a screen reader."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

Buy at Amazon ———. "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 This resource may not render correctly in a screen reader."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

Buy at Amazon 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

Buy at Amazon 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

Buy at Amazon 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.

Buy at Amazon ———. "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

Buy at Amazon Boolos, George S., John P. Burgess, and Richard C. Jeffrey. Computability and Logic. 5th ed. Cambridge University Press, 2007. ISBN: 9780521701464.

Also Recommended Is

Buy at Amazon 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:

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

Buy at Amazon Doxiadis, Apostolos, and Christos H. Papadimitriou. Logicomix: An Epic Search for Truth. Art by Alecos Papadatos and Annie DiDonna. Bloomsbury USA, 2009. ISBN: 9781596914520.

Buy at Amazon 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.