Index: |
Objectives | Texts | Topics | Assignments | Grades | Exams | WWW Sites |

**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:**- APPARATUS: THEORY OF FORMAL SYSTEMS
- Readings: Hofstadter, Chapters I-IV.
- References: Hodel, Chapter 1; Smullyan, Parts I & II.
- Exercise #1.

- MODELS & MEANINGS: FROM SYNTAX TO SEMANTICS
- Readings: Hofstadter, Chapters V-IX.
- References: Hodel, Chapters 2-5; Smullyan, Part III.
- Exercise #2.

- MACHINES & MENTALITY: FOREVER UNDECIDED
- Readings: Hofstadter, Chapters X-XV.
- References: Hodel, Chapters 6 & 7; Smullyan, Parts V-IX.
- Exercise #3.

- ARTIFICIAL INTELLIGENCE: SIMULATING STIMULI, STIMULATING SIMILE
- Readings: Hofstadter, Chapters XVI-XIX.
- Readings: Hofstadter, Chapters XVI-XIX.
- Exercise #4.

- MU: NOT KNOTS
- Readings: Hofstadter, Chapter XX.
- Creative Project
- Final Examination.

- APPARATUS: THEORY OF FORMAL SYSTEMS

**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**