Number and Title: **PHI 333**, *Introduction to Symbolic Logic*, Credits 3

Pre-requisites: ENG 102 (or 105 or 108) with C or better; Minimum 25 hours

Required course for the Philosophy Major.

Satisfies a course requirement in Area I for the
Symbolic, Cognitive and Linguistic Systems Certificate

# Course Description

This course is an introductory study of the use of symbolic techniques in first-order logic to represent statements and deductive arguments.

First-order logic is introduced slowly as the
course progresses, beginning with names and predicates, continuing with truth-functional
connectives (*and*, *or*, *if_then_*, and *not*), and finishing with the existential and universal
quantifiers (*some* and *every*). The language of first-order logic is used to symbolize English sentences, to
construct proofs to demonstrate the validity of arguments involving these sentences, and
to construct models to represent truth-conditions for these sentences. The
truth-conditions are used to represent the propositional content of the sentences, and the models
are used to provide counterexamples to demonstrate the invalidity of arguments involving
these sentences.

At the completion of this course, students will have an understanding of some of the logical structure of sentences, the nature of arguments and theories, logical consequence, validity, and the method of refutation by counterexample. This understanding is valuable generally and especially in disciplines where rigorous thinking is necessary, such as in the sciences, medicine, business, and the legal profession.

# Grading

Your final grade for the class is a function of your grades on six homework assignments, a midterm and final examination, and six debriefings. The homework counts for 68% of your total grade. Logic is not really all that difficult, but it takes a certain amount of practice to master it. Practice is the key! It is important to keep this point firmly in mind. Most of your time in the course should be spent working on and thinking about the homework assignments. The midterm examination counts for 10% of your final grade. The final examination counts for 10% of your final grade. The remaining 12% of your final grade is in "debriefing," where you share your experiences in learning logic with the class.

The six homework assignments (totaling to 68 points), midterm examination (10 points), final examination (10 points), and six debriefing sessions (totaling to 12 points) sum to 100 points. The point total determines the final letter grade: A+ (100-97), A (96-94), A- (93-90), B+ (89-87), B (86-84), B- (83-80), C+ (79-77), C (76-70), D (69-60), E (59-0).

There is no possibility for extra credit, but I am more than happy to help students with independent projects. Late work will not be accepted without good reason. Incompletes are given only to accommodate serious illnesses and family emergencies, which must be adequately documented.

# Textbook Information

The required textbook for the class is
*Language, Proof, and Logic*,
2nd Edition by Dave Barker-Plummer, Jon Barwise, and John Etchmendy.
This book comes packaged with software. The included CD-ROM has several applications
(*Tarski’s World*, *Fitch*, and *Boole*) that are required for the successful completion of
the course. These applications are very instructive. They will make it much easier for
you to understand the material. Also, if you buy the book new, you have access to the
*Grade Grinder*, which is an Internet grading service required in this course.

Access to *Grade Grinder* is a necessary for completing your homework.
Do not buy the book used! You cannot pass the course without *Grade Grinder*.

For helpful information, visit the homepage for the book, the FAQ page, the hints and solutions to selected exercises, and the notes for a version of a logic course based on the book.

# Homework

In the "Introduction" to your book, in the section entitled "Essential instructions about homework exercises," the authors explain how to use the Grade Grinder software package (which is an internet grading service). In the course of this explanation, they offer the following advice:

"[Y]ou can always do a trail submission to see if you got the answers right, asking that the results be sent just to you. When you are satisfied with your solutions, submit the files again, asking that the results be sent to the instructor too" (10).

If you want a high grade in the course, you should take this advice. Try not to send your homework to the instructor until your answers are right! You increase your chances if you do not leave your homework to the last minute. With only a few exceptions, the homework assignments are not difficult. They all, however, take time to understand and to complete.

Keep in mind also that the book contains many more exercises than those assigned for homework. If you want a deep understanding of logic, you should do as many of them as possible.

# Schedule

Unit 1. Atomic Sentences

• Homework 10 points, Debriefing 2 points

Unit 2. Boolean Connectives

• Homework 10 points, Debriefing 2 points

Unit 3. Formal Proofs involving Boolean Connectives

• Homework 15 points, Midterm examination 10 points, Debriefing 2 points

Unit 4. Quantifiers

• Homework 10 points, Debriefing 2 points

Unit 5. Methods of Proof for Quantifiers

• Homework 8 points, Debriefing 2 points

Unit 6. Formal Proofs involving Quantifiers

• Homework 15 points, Final examination 10 points, Debriefing 2 points

# Contact Information:

Thomas A. Blackson

Philosophy Faculty

School of Historical, Philosophical, and Religious
Studies

Lattie F.
Coor Hall, room 3356

PO Box 874302

Arizona State University

Tempe, AZ. 85287-4302

blackson@asu.edu,
tomblackson.com,
www.public.asu/~blackson