24.118  Paradox & Infinity

Spring 2013
Instructor: Agustin Rayo

TA: Owain Evans
Lecture: MW 1:00pm-2:00pm, room 14E-310

Section: F 1:00pm-2:00pm, , room 14E-310


General Information

Readings

Grading

Problem sets

End-of-Term Assignment

Academic Integrity

Class Schedule

1. Introduction

2. Time Travel / Free Will

3. Foundations of Probability

4. TBA

5. Newcomb’s Paradox

6. Zeno’s Paradox

7. Infinity

8. The Higher Infinite

9. The Axiom of Choice

10. Computability

11. Computability / Godel’s Theorem

12. Godel’s Theorem

13. TBA

14. 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.


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:

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


3. Newcomb’s Paradox

Lecture: Tue Feb 19

Lecture: Wed Feb 20

Section: Fri Feb 22


 

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


 

6. Zeno’s Paradox

Lecture: Mon Mar 11

Lecture: Wed Mar 13

Section: Fri Mar 15


 

7. Infinity

Lecture: Mon Mar 18

Lecture: Wed Mar 20

Section: Fri Mar 22


 

8. The Higher Infinite

Lecture: Mon Apr 1

Lecture: Wed Apr 3

Section: Fri Apr 5


 

9. The Axiom of Choice

Lecture: Mon Apr 8

Lecture: Wed Apr 10

Section: Fri Apr 12


 

10. Computability

Lecture: Wed Apr 17

Section: Fri Apr 19


 

11. Computability

Lecture: Mon Apr 22

Lecture: Wed Apr 24

Section: Fri Apr 26


 

12. Computability / Godel’s Theorem

Lecture: Mon Apr 29

Lecture: Wed May 1

Section: Fri May 3


 

13. Godel’s Theorem

Lecture: Mon May 6

Lecture: Wed May 8

Section: Fri May 10

 


 

14. Concluding Remarks

Lecture: Mon May 13

End-of-Term Assignment Due: Wed May 15

No readings. Just show up!