Introduction to Symbolic Logic

⊕ PHI 333: Introduction to Symbolic Logic
Required for the Philosophy Major
Satisfies an Area I requirement for the Symbolic, Cognitive and Linguistic Systems Certificate


This course is an introduction to symbolic logic. It is designed to provide an understanding of symbolic techniques to represent and evaluate sentences, arguments, and theories.

Assignments and Grades

The grade for the course is a function of six homework assignments (68 points), a midterm examination (10 points), a final examination (10 points), and six debriefing sessions (12 points).

Grades for the assignments sum to the grade for the course: 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).

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

⊕ Natural deduction proofs are a large part of what students learn in introductions to symbolic logic. There are different ways to present these proofs. The Fitch style is a modern version of the presentation Stanislaw Jaśkowski introduced in 1934. The Gentzen style is the main alternative. It is the presentation Gerhard Gentzen introduced in the same year.

Language, Proof and Logic uses the Fitch style. This is the style of natural deduction most introductory courses use.

Here is a proof of ¬P∨¬Q ⊢ ¬(P∧Q) in the Fitch style written in the software used in the course:




Here is a corresponding proof in the Gentzen style:




For discussion of the two styles, see Natural Deduction Systems in Logic (The Stanford Encyclopedia of Philosophy). There is no possibility for extra credit, but I am happy to help students with independent projects. Late work will not be accepted without good reason. (If you are going to submit work late, I accept more reasons as good reasons if you contact me before the due date.) I give incompletes only to accommodate serious illnesses and family emergencies.

I enjoy working with Barrett students on Honors Enrichment Contracts.

Textbook for the Course

The required textbook is Language, Proof and Logic, 2nd Edition (CSLI Publications, 2011) by the Stanford University authors Dave Barker-Plummer, Jon Barwise, and John Etchemendy.

For learning logic, there is no better combination of written explanation, software, and videos.

YOU MUST BUY THE TEXTBOOK NEW to have access to the online grading service, Grade Grinder. This service is REQUIRED FOR THE COURSE. You cannot pass the course without it. Even if you could, you get more from the course with it than without it. The instant feedback it provides on homework is invaluable for learning logic and thus for doing well in this course. DO NOT BUY THE TEXTBOOK USED.

This textbook comes in a "paperless" and "physical" package. The paperless package works in your browser. The physical package includes a printed textbook and CD. I RECOMMEND THE PAPERLESS PACKAGE. The physical package is not getting updates.

How to do Well in this Course

The homework and the debriefing sessions are 80% of the final grade.

The debriefing sessions require only that you write something coherent about your experience.

The homework is harder, but Grade Grinder is your friend. As part of their explanation of how to use this service, the authors of Language, Proof and Logic offer the following advice:

"[Y]ou can always do a trial 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 this course, take this advice. Try not to send your homework assignments to me until Grade Grinder tells you your answers are correct.

This means that YOU CANNOT LEAVE THE WORK TO THE LAST MINUTE. The assignments take time to understand and complete. Learning logic is mastering a skill. No one is born with this skill. Everyone has to practice it to acquire it. The book contains more exercises than those assigned for homework. The more you do, the better.

To complete the homework assignments, you must use the software for the course: Boole, Fitch, Tarski's World, and Submit (the service that submits your work to Grade Grinder.) To learn how to use this software, I strongly recommend that you read the documentation and watch the tutorial videos on the support page and that you read the description of the plagiarism detection mechanism in the link to Grade Grinder on the home page.

The midterm and final examinations are multiple choice questions about concepts. I tell you the concepts on which you will be tested, and you have two attempts for each exam.

I host periodic zoom sessions and am happy to meet individually by zoom.

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
Email: blackson@asu.edu
Academic Webpage: tomblackson.com