**SYMBOLIC LOGIC**

PHIL 301, Sec. 01: MWF 12pm-12:50pm in Wren 301

The College of William and Mary

Fall 2001

Instructor: James Woodbridge

email address: jawoo2@wm.edu

Course Webpage: http://faculty.wm.edu/jawoo2/wm/wmlogic.htm

Office Hours: W 2:30pm-4:30pm and by
appointment

Office: 126 Blair Hall

Office Phone: 221-2713

Dept. Phone: 221-2735

**I. COURSE DESCRIPTION**

This course aims to introduce students to the basic concepts and achievements of modern logic. Symbolic logic is the application of formal, mathematical methods in the study of reasoning. The type of reasoning under consideration is specifically *deductive* (as opposed to *inductive*) reasoning. Deductive reasoning gives rise to a rich, abstract theoretical structure that is both of intrinsic interest and practical importance. Identifying general inferential moves that are guaranteed to have true outputs provided they have true inputs improves one's ability to reason effectively about real-world matters, and helps one discover when a line of reasoning is not effective. Beyond its central role as a tool in philosophical inquiry, deductive logic is also important in the foundations of mathematics and computer science, and in linguistics and psychology. The material covered in this course will include such topics as the nature and general features of deductive arguments, logical form, argument validity and soundness, symbolization, truth-functional logical connectives, and using truth-tables to check argument validity. The bulk of the course will be devoted to the development of two artificial formal languages (that of sentential logic or the propositional calculus and that of quantificational logic or the predicate calculus) that capture certain formal aspects of our talk and thought. We will study the techniques for constructing formal deductive proofs in these languages and for evaluating such proofs as valid or invalid.

**II. REQUIRED CLASS MATERIALS**

**Books:**

Forbes, Graeme. *Modern Logic: A Text
in Elementary Symbolic Logic*. Oxford:
Oxford University Press, 1994.

The book for the course is available at **The
William and Mary Bookstore** located in the basement of Barnes and Noble in
Merchant's Square.

(It is also on reserve at the Library.)

**III. CLASS REQUIREMENTS AND GRADING SCHEME**

__Requirements__.............................................__Percent
of Final Grade__

Homework/Participation.............................................10%

Long Assignments.......................................................25%

Midterm Exam............................................................30%

Final Exam..................................................................35%

*About the Requirements:*

__Homework/Participation__—The main component of this requirement is completion of the weekly short homework assignments (typically handed out Monday and due Friday). The homework serves to provide practice with the techniques presented in class, so *it is
crucial that you keep up with the assignments*. These shorter assignments will be graded on a credit/no-credit basis with solutions posted for self correction. Assignments are due at the beginning of class. No late assignments will be accepted. This requirement is also designed to take into account class participation (e.g., suggesting moves for proofs done in class) and improvement throughout the course of the term.

__Long Assignments__—During the term there will be four longer homework
assignments (one approximately every three weeks, typically handed out Wednesday and due Monday). There will be no short assignment during any week there is a long assignment. The long assignments will receive numerical grades. Again, assignments are due at the beginning of class, and no late assignments will be accepted.

__The Midterm Exam__—There will be a timed, in-class midterm exam in mid
October. The exam questions will
include problems like those on the homework assignments, as well as questions
concerning definitions and concepts we have covered.

__The Final Exam__—There will be a timed, in-class final exam given
during our scheduled exam time, **December 10th at 8:30am**. Because of the nature of the material the
final will essentially be cumulative, but it will emphasize the material covered since
the midterm. Again, the exam questions
will include problems similar to those from the homework as well as some
pertaining to definitions and concepts.

** **

IV. CLASS FORMAT

The class will consist mostly of lectures, demonstrations of problem-solving techniques, and sample exercises. However, I want to encourage student participation throughout the class--both in the form of questions and suggestions about how to approach problems we are considering. In the first part of each meeting I will lecture on the material you have read about for the day and work some sample problems. In the second part of the class I will answer questions about problems from homework assignments that students would like to go over.

**V. TOPICS**

All of the readings (and most likely all of the assignments) will be from
the textbook, *Modern Logic*, by Forbes. The readings (and assignments) will be listed on the course webpage by chapter and section number, subject, and page (and exercise) numbers (in parentheses).

The general topics covered in the course (and their order of presentation) are as follows:

- Basics: Arguments, Logical Form, Validity (Chapter 1)
- Symbolizing Arguments in Sentential Logic (Chapter 2)
- Syntax and Semantics for Sentential Logic (Chapters 2 and 3)
- Testing Argument Validity: Truth-Tables and Interpretations (Chapter 3)
- Natural Deduction (Proofs) in Sentential Logic (Chapter 4)
- Predication and Quantification: Syntax and Semantics (Chapters 5 and 6)
- Proofs in Predicate (Quantificational) Logic (Chapter 6)
- First-Order Logic with Identity (Chapters 7 and 8)