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 give students an understanding of introductory 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).

The grades for these assignments sum to determine 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 natural deduction. This is the style used in most introductory courses to symbolic logic.

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




Here is a proof of ¬P∨¬Q ⊢ ¬(P∧Q) in the Gentzen style:



For a good discussion of the Fitch and Gentzen styles, see Natural Deduction Systems in Logic in 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. The standard is lower if you contact me before the due date. Incompletes are given only to accommodate serious illnesses and family emergencies, which must be adequately documented.

I work with Barrett students on Honors Enrichment Contracts. Email me in the first week of the semester.

Textbook for the Course

The required textbook for this course 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.

This textbook comes in a "paperless" and "physical" package. You can download the paperless package to your computer. The physical package is made of paper. YOU MUST BUY THE TEXTBOOK NEW (in the paperless or physical package) 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 (which is 68 of the 100 points in the course) is invaluable for learning logic and for doing well in this course. DO NOT BUY THE TEXTBOOK USED.

For helpful information, visit the home page for the book and the support page.

How to do Well in this Course

Most of the final grade consists in the homework assignments (68 points) and the debriefing sessions (12 points).

The debriefing sessions are the easiest. You just need to write something coherent about your experience.

The homework is harder, but Grade Grinder is your friend. In the "Introduction" to Language, Proof, and Logic, the authors explain how to use this service. In their explanation, they say the following:

"[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 their advice. Try not to send your homework 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 are not difficult, but they all 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 your mastery of logic will be.

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 (10 points) and final examination (10 points) consist in multiple choice questions about concepts. I will tell you the concepts on which you will be tested well in advance of these examinations.

Finally, and perhaps most importantly, ask questions when you think or worry you do not understand.

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