Formal Logic
PHIL 1600 / MATH 1580 / COSC 1580
M W 2:30 - 3:50
Pearson House Room 3
Instructor information
Dr. Bruce Umbaugh
office: Pearson House basement
phone: 961-2660 x7826 (office) or 968-7170 (PHIL office)
office hours: Mon 2-2:30
and by appointment
e-mail: bumbaugh@webster.edu
Course description
This course will serve as a general introduction to the discipline of symbolic logic. The core of this course is predicate logic, including quantification, identity, and proof theory. The (more) fun part of the course is extensions of that logic, model theory, possible applications, and the philosophical issues raised.
Topics will include the modern propositional or sentential calculus, predicate calculus, basic model theory, semantics for our formal languages, theory of computation, infinity, definite descriptions, and completeness. Students who complete the course successfully should understand well such concepts as validity, proof, definite description, consistency, and counterexample; should be able to translate between English and our formal languages, and to construct proofs in a formal system; and they should understand some of the mathematical and philosophical implications of standard systems of and approaches to formal logic.
Textbook
Tom Tymoczko and Jim Henle, Sweet Reason: A Field Guide to Modern Logic, Springer-Verlag, 2000.
Course Outline
January 15 - 22 Introduction
January 24 - February 14 Sentential logic (propositional calculus)
February 19 - April 9 Predicate logic (including quantification, identity)
April 11 - May 2 Infinity, functions, definite description, arithmetic, and other really cool stuff
The work of the course.
A typical week involves some assigned readings and homework problems, class discussion, work on exercises in class, and a quiz.
There is no substitute in this course for study and practice.
You will be tested on your ability to solve problems and explain concepts. The problems to be solved and concepts to be explained bear a striking resemblance to problems in exercises in the textbook and concepts explained and illustrated in the textbook. You should study so as to learn the concepts and develop your facility for solving problems. Doing the homework is the chief means for doing this.
Attend class.
Besides doing homework yourself, it is valuable to get feedback on your efforts. Come to class. Problems will be worked and explained, and much information will be presented in class. You are responsible for knowing all of it and for having any additional materials distributed. Although I will be available to help students outside of class, I am absolutely guaranteed to be available to you in class. For all these reasons, there is strong evidence that regular, engaged, active attendance improves students' grades in classes such as this one. Finally, note that I reserve the right to reward students who have attended class faithfully and displayed significant effort.
Be smart about how you do your homework.
The point is to learn. So, it is important that you do varied problems and that you work problems you have trouble solving rather than ones you find easy. Above all, it is important that you work some problems yourself on a regular basis; do not try to get by having watched me work problems in class or listening to a classmate solve them herself. On quizzes and on the final exam it is up to you: prepare yourself.
Course Schedule:
January
15: Birthday of The Rev. Dr. Martin Luther King, Jr. No class.
16: Introduction. A Taste of Logic.
22: Everything all at once and a warning. Exam warning I.
24: Statement logic, formal languages. Sentential. Variations on sentential. Truth tables. Quiz.
29: Truth tables. Logical theory for statement logic. Some basic tautologies and implications.
February
5: Valid arguments, convincing arguments, and punk logic. Valid argument forms. Formalizing for validity.
12: Formalizing for validity. Formalizing English.
14: Happy Valentine's/Cyril and Methodius Day! with and about logic, curiosities & puzzles. Exam warning III. Quiz.
19: Predicates, programs, and antique logic. Predicate languages. Variations on predicate languages. Quiz.
21: Predicate languages. Variations on predicate languages. From statement logic to predicate logic.
26: From statement logic to predicate logic. Interpreting predicate logic. Quiz.
March
5: Logical laws. Symbolization in predicate logic. Quiz.
7: Symbolization in predicate logic. with and about logic, curiosities & puzzles
12: Spring recess. No class meeting.
19: Review. with and about logic, curiosities & puzzles. Exam warning IV.
21: Deduction, Infinity, and a Haircut. Main connectives. Deduction. Quiz.
26: Deduction. Hypothetical reasoning.
30: Deduction. Proving validity. Quiz.
April
2: Proving validity. Proving invalidity.
11: Formalizing for validity in predicate logic. in Hell with Raymond Smullyan and related ideas. Quiz.
16: Formalizing for validity in predicate logic. Infinity.
18: Formalizing for validity in predicate logic. Exam warning V. Symbolic sophistication. Quantifiers and arithmetic. Quiz.
23: Functions. Quiz.
25: Definite descriptions. Exam warning VI.
May
7: 3:20-5:20 p.m. Final examination.
Grading
Fourteen regular quizzes 50%
Final examination (May 7, 2001) 50%
(Students with an "A" average for the quizzes are excused from taking the final exam.)
Over the course of the semester, fourteen quizzes will be administered. No points will be awarded for quizzes not taken, unless absence from the quiz has been expressly excused. Ordinarily, make-up quizzes will be given only when (1) I approve your absence in advance of the administration of the quiz in question, and (2) you present a legitimate, written excuse on your return.
The final examination is scheduled for May 7, 2001, at 3:20 p.m. It will ask you to solve problems much like those presented on your quizzes. (Problems on quizzes will be much like those contained in your homework. (So, you see, the course is designed to give you ample practice solving problems as needed to earn a good grade.))
For most students, course grades will be based on the average of the student's quiz grades and the final exam performance, with the two weighted equally. The exceptions are these:
(1) any student earning an "A" average on his or her quizzes will receive a grade of "A" for the course and is excused from the final examination;
(2) any student earning a grade of "A" on the final examination will receive a grade of "A" for the course regardless how well or how poorly he or she performed on quizzes.
I will hold regular office hours as listed at the top of this syllabus, and I am around Pearson House often during the week. I can also be reached via e-mail (bumbaugh@webster.edu). Although I will make myself available to help students outside of class, students who do not attend class meetings should not expect to be rewarded with intensive assistance. Finally, note that I reserve the right to reward students who have attended class faithfully and displayed significant effort.
Policy on Academic Dishonesty:
You are adults, attending a university. I expect you to behave responsibly. Students in this class are expected to do their own work and not to rely on the work of others. Students are encouraged to work with one another to understand the material, but any student cheating on a quiz or the exam, aiding another student to cheat, or committing any other act of academic dishonesty will be referred for appropriate disciplinary action. Please consult with me if you have questions in this regard, either about your own work or that of another person.