24.118 Paradox and Infinity

Spring 2014

Instructor: Agustín Rayo (arayo@mit.edu)

Lectures: MW 1-2pm, room 4-231

[Short URL of this site: <goo.gl/Gk0vi7>]

General Information


Class Schedule

0. Introduction

1. Time Travel / Free Will

2. Newcomb’s Problem

3. What is Probability?

4. The Axiom of Choice

5. Infinite Cardinalities

6. Omega-Sequences

7. Orderings and the Higher Infinite

8. Turing Machines

9. Computability / Gödel’s Theorem

10. Russell’s Paradox (Damien Rochford)

11. Gödel’s Theorem

12. TBA

13. Concluding Remarks


General Information

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. The class aims to be an introduction to the highlights of the more technical side of philosophy.




Date and Time


Room Number

Office Hours


Room Number

Nilanjan Das

Friday, 10am


Thurs., 2-3


Nilanjan Das

Friday, 11am


Thurs., 2-3


Rose Lenehan

Friday, 10am


Thurs., 12:30-1:30


Agustin Rayo



by appt.


Kevin Richardson

Friday, 12pm


by appt



There is one required textbook:

Other readings will be available on Stellar.


The class will be graded as follows:

Problem sets

Problem sets will be linked to from the Class Schedule.

If there are N assignments in class, we will only take into account your (N-1) best scores. Problem sets are due most Fridays by 10am, and must be uploaded onto Stellar. With the exception of extraordinary circumstances— typically involving a medical problem—late assignments will not be accepted.

Late assignments will not be accepted. (I just thought you might have missed that from the previous paragraph.)

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

End-of-Term Assignment

The end-of-term assignment will due on Wednesday May 14 by 1:05 pm, and will be posted by Wednesday May 7.

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.

Regrading of Assignments

If you feel like you got the wrong grade on your assignment and you’re not able to sort things out with your TA, you’re welcome to send it to me for regrading. Please keep in mind, however, that this can cause your grade to go down rather than up. I am not as tenderhearted as some of my TAs.

Academic Integrity

Any suspicion of plagiarism or academic dishonesty will be aggressively pursued. This is no joke: please consult MIT's Handbook on Academic Integrity.

Laptop Policy

It is okay to use laptops and other electronic devices in class, as long as they are being used for class-related purposes.

Class Schedule

0. Introduction

Lecture: Wed Feb 05

NO CLASS: Fri Feb 07

[No need to read anything in advance. Just show up!]

1. Time Travel / Free Will

Lecture: Mon Feb 10

Lecture:  Wed Feb 12

Section: Fri Feb 14

Reading: Lewis, ‘The Paradoxes of Time Travel

[Lecture Notes] [Problem Set 1 due on Fri Feb 14, by 10am.]

2. Newcomb’s Problem

Lecture: Tue Feb 18 [Guest Lecturer: Alan Guth]

Lecture: Wed Feb 19

Section: Fri Feb 21

[Lecture Notes] [Problem Set 2, due on Fri Feb 21, by 10am.]

3. What is Probability?

Lecture: Mon Feb 24

Lecture: Wed Feb 26

Section: Fri Feb 28

[Lecture Notes] [Problem Set 3, due on Fri Feb 28, by 10am.]

4. Non-Measurable Sets

Lecture: Mon Mar 3

Lecture: Wed Mar 5

Section: Fri Mar 7

[Lecture Notes] [Problem Set 4, due on Fri Mar 7, by 10am.]

5. The Concept of Infinity

Lecture: Mon Mar 10

Lecture: Wed Mar 12

Section: Fri Mar 14

Reading: chapter 2 of Rucker’s Infinity and the Mind

Optional Reading: chapter 4 of Drake and Singh's Intermediate Set Theory.

[Lecture Notes] [Problem Set 5, due on Fri Mar 14, by 10am.]

6. Omega-Sequences

Lecture: Mon Mar 17

Lecture: Wed Mar 19 [Guest lecturer: Steve Yablo]

Section: Fri Mar 21

[Lecture Notes] [Problem Set 6, due on Fri Mar 21, by 10am.]

7. Ordinals and the Higher Infinite

Lecture: Mon Mar 31

Lecture: Wed Apr 2

Section: Fri Apr 4

Recommended Reading: Rucker: Excursion 1.

Optional Reading: chapter 4 of Drake and Singh's Intermediate Set Theory.

[Lecture Notes] [Problem Set 7, due on Fri Apr 4, by 10am.]

8. Turing Machines

Lecture: Mon Apr 7

Lecture: Wed Apr 9

Section: Fri Apr 11

[Lecture Notes] [No problem set due this week.]

9. Computability / Gödel’s Theorem

Lecture: Mon Apr 14 [Guest Lecturer: Scott Aaronson]

Lecture: Wed Apr 16

Section: Fri Apr 18

[Lecture Notes] [Problem Set 8, due on Fri Apr 18, by 10am]

10. Russell’s Paradox (Damien Rochford)

NO CLASS: Mon Apr 21

TBA (Agustin away): Wed Apr 23

Section: Fri Apr 25

[Lecture Notes] [Bonus Problem Set, due Fri Apr 25, by 10am]

11. Gödel’s Theorem

Lecture: Mon Apr 28

Lecture: Wed Apr 30

Section: Fri May 2

[Lecture Notes] [Problem Set 9, due Fri May 2, by 10am]

12. Surprise Exam Paradox (Nilanjan Das and Ian Wells)

Lecture: Mon May 5

Lecture: Wed May 7

Section: Fri May 9

[Lecture Notes] [Problem Set 10, due Fri May 9, by 10am]

13. Concluding Remarks

Lecture: Mon May 12

Class Cancelled: Wed May 14

[End-of-Term Assignment]

Released: Wed May 7, 8:00am. Due: Wed May 14, by 1:05pm.