Course Objectives:

The course is designed as an introduction to the theory of formal systems for students without any specialist training in mathematics. Primary emphasis will be placed on the role of formal analysis in the representation and evaluation of natural language arguments. Initially, students will learn to manipulate the nuts and bolts of a formal system of first-order logic; subsequently, some extensions of, and alternatives to, classical first-order theory (modal logic, free and fuzzy logics, binary and substitutional quantification), especially apropos the design of artificially intelligent systems, will be presented. Selected topics in the philosophy of logic will also be introduced.

Texts:

The following text is required:
-- Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Random House, 1989.

The following texts are recommended:
-- Hodel, Richard E.. An Introduction to Mathematical Logic. Boston: PWS Publishing Co., 1995.
-- Smullyan, Raymond M. Forever Undecided: A Puzzle Guide to Gödel. New York: Knopf (Borzoi Books), 1987.

Course Division:

1. APPARATUS: THEORY OF FORMAL SYSTEMS
   • Readings: Hofstadter, Chapters I-IV.
   • References: Hodel, Chapter 1; Smullyan, Parts I & II.
   • Exercise #1.
2. MODELS & MEANINGS: FROM SYNTAX TO SEMANTICS
   • Readings: Hofstadter, Chapters V-IX.
   • References: Hodel, Chapters 2-5; Smullyan, Part III.
   • Exercise #2.
3. MACHINES & MENTALITY: FOREVER UNDECIDED
   • Readings: Hofstadter, Chapters X-XV.
   • References: Hodel, Chapters 6 & 7; Smullyan, Parts V-IX.
   • Exercise #3.
4. ARTIFICIAL INTELLIGENCE: SIMULATING STIMULI, STIMULATING SIMILE
   • Readings: Hofstadter, Chapters XVI-XIX.
   • Readings: Hofstadter, Chapters XVI-XIX.
   • Exercise #4.
5. MU: NOT KNOTS
   • Readings: Hofstadter, Chapter XX.
   • Creative Project
   • Final Examination.

Assignments:

For the most part, reading assignments will be made on a weekly basis. Inasmuch as the lecture and discussion periods will ordinarily focus finely on the technical apparatus presented in the required text, it is essential that you keep well abreast of the readings. Exercises will generally be assigned at least one calendar week before coming due; however, exercises will be accepted for credit ONLY on or before the assigned days. The final examination period is scheduled for Wednesday, 13 December at 12:00 p.m. The exercises and exam are intended strictly to advance and measure your technical skills; in order to mature and assess your philosophical understanding, you will also be asked to submit a creative project in the form of a 'metaphorical fugue' (ā la Hofstadter) reflecting formal isomorphism between/among at least two and at most six themes. The project will come due Friday, 1 December.

Grades:

All exercises and exams will be graded using a numerical scale. Final grades sent to the registrar are based on cumulative average performance, according to the schedule provided below.

Schedule of Exercises & Exams:

 
NAME		TOPIC				TOTAL	GRADE	CUM.
						POINTS	PERCENT	PERCENT
***************	***************************	******	*******	*******

Exercise #1	Apparatus			20	10	 10

Exercise #2	Models & Meanings		20	10	 20

Exercise #3	Machines & Mentality		20	10	 30

Exercise #4	Artificial Intelligence		20	10	 40

Final Exam	Theory of Formal Systems	60	30	 70

Project		Metaphorical Fugue		60	30	100

Course Links on the World Wide Web

Mysticism and Logic

Douglas Hofstadter's Homepage

The Kurt Gödel Society

MIT AI Lab's Research

MTSU Philosophy Department Homepage

The Retrograde Analysis Corner

Some Abstracts of Logical Papers

The rec.puzzles FAQ