Theories of Mind and Mathematics

The course website is the syllabus you are currently reading, available online at http://math.northwestern.edu/~theojf/Seminar2015/.

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Intellectual and academic dishonesty will not be tolerated in this or any Northwestern class. Suspected violations of academic integrity will be reported to the Dean's Office. For detailed discussion of academic integrity, see http://www.weinberg.northwestern.edu/handbook/integrity/.

It is the responsibility of students to review this syllabus as soon as it is distributed and to consult the professor promptly regarding any possible conflicts. Upon the timely request of students, assignment deadlines that fall on religious holidays will be rescheduled. Students will not be penalized for class absences because of religious holidays, but must notify the professor of conflicts well in advance of any anticipated absence, and provide accurate information about the obligations entailed in the observance of that particular holiday. Northwestern's policy on the observance of religious holidays is available at http://www.northwestern.edu/provost/policies/faculty-leave-and-holidays/statement-on-academic-accommodations-for-religious-holidays.html.

Table of Contents

• Guiding questions
• Methods and course requirements
• Required readings
• Active reading
• Calendar

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Guiding questions

What is it that mathematicians accomplish? Does mathematics accurately describe the world? Is mathematics consistent? Is science consistent? How can mere humans comprehend and communicate mathematics? How can mere humans comprehend human thought?

One feature of human consciousness is our ability to make choices and to create art; are these abilities consistent with a materialist scientific understanding of the universe? Another feature of human consciousness is our ability to think about ourselves; is a computer conscious if it can report on its own status? Mathematics can be used to study the structure of mathematics, and humans can think about the structure of thought; how are these forms of self-reference related, and does this relation shed light on the aforementioned questions?

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Methods and course requirements

We will spend the majority of class time discussing the assigned readings. Students should arrive having thought about the readings and prepared to share those thoughts; see the discussion of active reading below. We will also devote some class time to peer review and other activities in small groups. Because in-class discussion is a core component of the class, daily attendence and daily participation are required. Except in rare instances, two or more absences will negatively impact your final grade.

This class will also demand a fair amount of work outside of class time, including reading and writing assignments. You should expect to devote six hours per week outside of class. If you find that you are working significantly more than this, let me know.

The requirements for the class fall into the following four categories:

1. Reading and discussion.
2. Four short (two to three pages) essays.
3. One long (eight to ten pages) final paper.
4. One short (five to seven minutes) presentation at the end of class symposium.

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Required readings

Students are expected to purchase the following three texts:

• Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books; 20 Anv edition (1999), ISBN: 0465026567. (Henceforth abbreviated GEB.)
• MLA Handbook for Writers of Research Papers, 7th Edition (January 1, 2009), ISBN: 1603290249. (Henceforth abbreviated MLA Handbook.)
• A course packet available from Quartet (825 Clark St., 847-328-0720) containing the following articles:
  • Kathleen Akins, What is it like to be boring and myopic?, Dennet and His Critics: Demystifying Mind, pp. 124–160, Blackwell, 1993. PDF
  • Greg Egan, Luminous, Luminous, pp. 52–88, Millenial, 1998. PDF
  • Evelyn Fox Keller, Feminism and Science, Signs, Vol. 7, No. 3, Feminist Theory (Spring, 1982), pp. 589–602. PDF
  • Thomas Nagel, What is it like to be a bat?, The Philosophical Review, Vol. 83, No. 4 (October, 1974), pp. 435–450. PDF
  • Roger Penrose, Mathematical intelligence, What is Intelligence, pp. 107–136, Press Syndicate of the University of Cambridge, 1994. PDF
  • Roger Penrose, The Road to Reality: A complete guide to the laws of the universe, Chapter 1: The roots of science, pp. 7–24, Knopf, 2006. PDF
  • William P. Thurston, On proof and progress in mathematics, Bulletin of the American Mathematical Society, vol. 30, no. 2 (April 1994), pp. 161–177. PDF
  • Alan M. Turing, Computing Machinery and Intelligence, Mind, New Series, Vol. 59, No. 236 (Oct., 1950), pp. 433–460. PDF
  • Eugene Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Communications in Pure and Applied Mathematics, Vol. 13, No. 1 (February 1960), pp. 1–14. PDF
  Note: The PDFs linked above are provided in compliance with academic fair use guidelines, and are the intellectual property of their authors (and generally the legal property of their publishers). The copies posted here should not be downloaded or distributed for any reason except nonprofit academic scholarship; any other use may constitute a violation of federal copyright law.

GEB is a long book, and touches on many topics. A non-exhaustive list includes: number theory; logic; computer science; artificial intelligence; cognitive psychology; modern art; Baroque music; Zen Buddhism; quantum physics; molecular biology. In places it is profound, in places it is pedantic, and in places it is quite dated. The course packet essays cover a similar range of topics, and provide important alternative perspectives. The MLA Handbook is an invaluable resource that you should consult when questions come up during your writing for this class, although you will sometimes make informed decisions to disregard its advice, and that you should continue to use throughout your Northwestern career.

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Active reading

Scholarly reading is more than words passing in front of eyes. It requires pauses to think, to organize, and to look things up. Always have paper and pen with you as you read. Moreover, please get into the habit of looking up everything mentioned in a reading: find every in-text citation in the bibliography, and encode the author and title; find every work of visual art on Google Images, and listen to a bit of every work of music on either Youtube or Naxos Music Library.

For each reading, keep track of those passages that:

1. Are the core of the reading.
2. You don't understand.
3. You do understand, but disagree with.
4. Are intriguing and easily overlooked.

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Calendar

I will continuously update this calendar with links to handouts and other in-class material. All readings should be completed by the start of class on the day listed. All essays are due by email by 9am on the day listed. The abbreviation "GEB" always refers to

• Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books; 20 Anv edition (1999).

Tuesday, September 22 Introduction.
Handouts: Syllabus. The MU Puzzle. Thinking about the MU Puzzle.
Recommended reading:

• Apostolos Doxiadis and Christos H. Papadimitriou, Logicomix: An Epic Search for Truth, Bloomsburry (2009), ISBN: 978-1-59691-452-0.

Thursday, September 24 Read by the start of class:

• GEB pp. P-1–74 (Preface – Chapter III: Figure and Ground).

• Scott Kim, Inversions, BYTE Books (1981), ISBN: 0-07-034546-5.

Tuesday, September 29 First short essay due by email by 9am.
Read by the start of class:

• William P. Thurston, On proof and progress in mathematics, Bulletin of the American Mathematical Society, vol. 30, no. 2 (April 1994), pp. 161–177.

Thursday, October 1 Read by the start of class:

• GEB pp. 75–176 (Contracrostipunctus – Chapter VI: The Location of Meaning).

• Luigi Serafini, Codex Seraphinianus, Rizzoli (1981), ISBN: 978-0847842131

Tuesday, October 6 Read by the start of class:

• Roger Penrose, The Road to Reality: A complete guide to the laws of the universe, Chapter 1: The roots of science, pp. 7‐24, Knopf, 2006.

Recommended reading:

• Roger Penrose, The Road to Reality: A complete guide to the laws of the universe, Knopf (2006), ISBN: 978-0679776314.

• GEB pp. 177–272 (Chromatic Fantasy, And Feud – end of Part I).

Tuesday, October 13 Read by the start of class:

• Eugene Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Communications in Pure and Applied Mathematics, Vol. 13, No. 1 (February 1960), pp. 1–14.

Thursday, October 15 Read by the start of class:

• GEB pp. 275–336 (Prelude... – ... Ant Fugue).

Tuesday, October 20 Read by the start of class:

• Evelyn Fox Keller, Feminism and Science, Signs, Vol. 7, No. 3, Feminist Theory (Spring, 1982), pp. 589-602.

Thursday, October 22 Third short essay due by email by 9am.
Read by the start of class:

• Thomas Nagel, What is it like to be a bat?, The Philosophical Review, Vol. 83, No. 4 (October, 1974), pp. 435–450.

• GEB pp. 337–390 (Chapter XI: Brains and Thoughts – Chapter XII: Minds and Thoughts).

Thursday, October 29 Read by the start of class:

• Kathleen Akins, What is it like to be boring and myopic?, Dennet and His Critics: Demystifying Mind, pp. 124–160, Blackwell, 1993.

Tuesday, November 3 Fourth short essay due by email by 9am.
Read by the start of class:

• GEB pp. 391–479 (Aria with Diverse Variations – Chapter XV: Jumping out of the System).

Thursday, November 5 Read by the start of class:

• Greg Egan, Luminous, Luminous, pp. 52–88, Millenial, 1998.

Tuesday, November 10 Read by the start of class:

• GEB pp. 480–548 (Edifying Thoughts of a Tobacco Smoker – Chapter XVI: Self-Ref and Self-Rep).

Thursday, November 12 Read by the start of class:

• Roger Penrose, Mathematical intelligence, What is Intelligence, pp. 107–136, Press Syndicate of the University of Cambridge, 1994.

Tuesday, November 17 Read by the start of class:

• GEB pp. 549–585 (The Magnificrab, Indeed – Chapter XVII: Church, Turing, Tarski, and Others).

• GEB pp. 586–632 (SHRDLU, Toy of Man's Designing – Chapter XVIII: Artificial Intelligence: Retrospects).

Thursday, November 19 Read by the start of class:

• Alan M. Turing, Computing Machinery and Intelligence, Mind, New Series, Vol. 59, No. 236 (Oct., 1950), pp. 433–460.

Tuesday, November 24 Flip through, but don't feel obligated to read carefully:

• GEB pp. 633–680 (Contrafactus – Chapter XIX: Artificial Intelligence: Prospects).

• GEB pp. 681–742 (Sloth Canon – Six-Part Ricercar).

Thursday, November 26 Thanksgiving break.

Tuesday, December 1 and Thursday, December 3 In-class symposium.

Monday, December 7 Final paper due via email by 12noon.

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