In this class we will study a cluster of puzzles, paradoxes and intellectual wonders -- from the higher infinite to Godel's Theorem -- and discuss their philosophical implications.

Readings

There is one required textbook:

Rucker, R. Infinity and the Mind, Princeton University Press, 2004 or 2005.

(If you have the 1995 printing, that's okay too; all you'll be missing is a new preface by the author.)

Other readings will be available on Stellar.

Grading

The class will be graded as follows:

45% Problem Sets
50% End-of-Term Assignment
5% Class participation

Problem sets

Problem sets will be linked to from the Class Schedule, and will be posted on Stellar.

There are 9 problem-sets in all, but we will only take into account your 8 best scores. Problem-sets are due most Fridays, and must be uploaded on Stellar (Homework > Problem Set X > Add submission) by 1:05 pm. (With the exception of extraordinary circumstances -- typically involving a medical problem -- late assignments will not be accepted.)

It is okay to discuss problem-sets with other students taking the class, and to consult published materials. But each student must complete the assignment on his or her own.

End-of-Term Assignment

End-of-term assignment will due on Wednesday May 15 by 1:05 pm, and will be posted by Wednesday May 8.

Although individual consultation of published materials is okay, discussing the end-of-term assignment before the due-date with anyone - whether or not they are taking the class - is strictly prohibited. All work on the assignment must be the student's own.

Academic Integrity

Any suspicion of plagiarism or academic dishonesty will be aggressively pursued. Please consult MIT's Handbook on Academic Integrity.

Class Schedule

1. Introduction

Lecture: Wed Feb 06.

NO CLASS: Fri Feb 08.

No need to read anything. Just show up!

2. Time Travel / Free Will

Lecture: Mon Feb 11

Lecture: Wed Feb 13

Section: Fri Feb 15

Lecture Notes
Required Reading: David Lewis, The Paradoxes of Time Travel, American Philosophical Quarterly 1976 vol:13.
Problem set 1, due on Fri Feb 15, by 1:05pm.

3. Newcomb’s Paradox

Lecture: Tue Feb 19

Lecture: Wed Feb 20

Section: Fri Feb 22

Lecture Notes
Required Reading: Lewis, D. ' Prisoner's Dilemma is a Newcomb Problem'.
Optional reading (difficult): Lewis, D. 'Causal Decision Theory' in his Philosophical Papers volume II, Oxford University Press, 1986.
Problem set 2, due on Fri Feb 22, by 1:05pm. (Please submit using Stellar.)

4. Coordination games (Owain Evans)

Lecture: Mon Feb 25

Lecture: Wed Feb 27

Section: Fri Mar 1

Required Reading: TBA

Extra credit problem set (TBA)

5. Foundations of Probability

Lecture: Mon Mar 4

Lecture: Wed Mar 6

Section: Fri Mar 8

Lecture Notes
Required Reading: Sections 1-4 of Lewis, D. " Humean Supervenience Debugged". Optional: finish reading the article

Problem Set 3, due on Fri March 8, by 1:05pm. (Please submit using Stellar.)

6. Zeno’s Paradox

Lecture: Mon Mar 11

Lecture: Wed Mar 13

Section: Fri Mar 15

No Lecture notes this week
Required Reading: Josh Parsons' Eleatic Hangover Cure Analysis 64:4 (2004).
Problem Set 4, due on Fri March 15, by 1:05pm. (Please submit using Stellar.)

7. Infinity

Lecture: Mon Mar 18

Lecture: Wed Mar 20

Section: Fri Mar 22

Lecture Notes
Required Reading: Rucker, chapter 2.
Optional Reading: chapter 4 of Drake and Singh's excellent Intermediate Set Theory.
Problem Set 5, due on Fri March 22, by 1:05pm. (Please submit using Stellar.)

8. The Higher Infinite

Lecture: Mon Apr 1

Lecture: Wed Apr 3

Section: Fri Apr 5

No Lecture Notes
Required Reading: Rucker: Excursion 1.
Optional Reading: chapter 4 of Drake and Singh's excellent Intermediate Set Theory.
Problem Set 6, due on Fri April 5, by 1:05pm. (Please submit using Stellar.)

9. The Axiom of Choice

Lecture: Mon Apr 8

Lecture: Wed Apr 10

Section: Fri Apr 12

Lecture Notes.
Optional Reading: Frank Arntzenius, Adam Elga, John Hawthorne, 'Bayesianism, Infinite Decisions, and Binding'
Problem Set 7, due on Fri April 12, by 1:05pm. (Please submit using Stellar.)

10. Computability

Lecture: Wed Apr 17

Section: Fri Apr 19

No problem set this week
Optional: Boolos, Burgess and Jeffrey, Computability and Logic, chapters 3 and 4. (On reserve in main library.)

11. Computability

Lecture: Mon Apr 22

Lecture: Wed Apr 24

Section: Fri Apr 26

No lecture notes
Problem Set 8, due on Fri April 26, by 1:05pm. (Please submit using Stellar.)
Optional: Boolos, Burgess and Jeffrey, Computability and Logic, chapters 3 and 4. (On reserve in main library.)

12. Computability / Godel’s Theorem

Lecture: Mon Apr 29

Lecture: Wed May 1

Section: Fri May 3

For lecture notes, see problem set 9.
No problem set
Optional: Rucker, Excursion II.
For those who want to have a look at the proofs, I recommend Boolos, Burgess and Jeffrey, Computability and Logic, which is on reserve at the library. Alternatively, you can check out Chapter 3 of Mendelson, E. Introduction to Mathematical Logic, Fourth Edition, Chapman & Hall, 1997, which is also on reserve. (The proofs are difficult, but this is, after all, MIT.)

13. Godel’s Theorem

Lecture: Mon May 6

Lecture: Wed May 8

Section: Fri May 10

For lecture notes, see problem set 9.
Problem Set 9, due on Fri May 10, by 1:05pm. (Please submit using Stellar.)
Optional: Rucker, Excursion II.
For those who want to have a look at the proofs, I recommend Boolos, Burgess and Jeffrey, Computability and Logic, which is on reserve at the library. Alternatively, you can check out Chapter 3 of Mendelson, E. Introduction to Mathematical Logic, Fourth Edition, Chapman & Hall, 1997, which is also on reserve. (The proofs are difficult, but this is, after all, MIT.)

14. Concluding Remarks

Lecture: Mon May 13

End-of-Term Assignment Due: Wed May 15

No readings. Just show up!