# Introduction to Symbolic Logic

PHI 333. Syllabus. Welcome to the Course!

**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.

This textbook comes in a "paperless" and "physical" package. The paperless
package downloads 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 is invaluable for
learning logic and thus for doing well in this course. DO NOT BUY THE TEXTBOOK USED.

For information about the book and the software, visit the home and support pages.

## 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