PHIL 220-005: Introduction to Formal Logic

Winter 2018–19, Term 2

This is a ‘live’ online syllabus. It is subject to change. Please consult the online version regularly, rather than printing the current version for later use. Students are responsible for familiarity with the current version of the syllabus, which is available at

Course Meetings:                 MWF, 10–10:50, BUCH A103

Instructor:                        Dr. Jonathan Jenkins Ichikawa —

Office Hours:                        Wednesdays, 12:30–2:30 and by appointment

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This course is an introduction to formal logic. Logic is the study of argument forms; “formal” in this context means that we will be studying arguments using rigid rules and procedures. A formal logic course is very different from other courses in Philosophy, or in Arts in general; it is in many ways more like mathematics. Students will produce proofs, not essays, for this course. We will learn the syntax and semantics of propositional and predicate logic, and develop proof systems for each. We will draw connections to significant historical and contemporary arguments in philosophy, but the main goal of the course is the mastery of formal logic itself, as well as an introduction to metalogic, where we will examine significant proofs about our formal system.


This course has three central aims: (1) to help students think more clearly about arguments and argumentative structure, in a way applicable to informal arguments in philosophy and elsewhere; (2) to provide some familiarity and comfort with formal proof systems, including practice setting out formal proofs with each step justified by a syntactically-defined rule; and (3) to provide the conceptual groundwork for metatheoretical proofs, introducing the ideas of rigorous informal proofs about formal systems, preparing students for possible future courses focusing on metalogic and computability.


I’m Jonathan Jenkins Ichikawa. I’ve been teaching at UBC since 2011; most of my research is in epistemology. Please feel free to call me “Jonathan,” “Dr. Ichikawa,” or “Professor Ichikawa”, whichever makes you most comfortable. FYI, “Jenkins” is my middle name. (Note that “Mr.” and “Ms.” are inappropriate titles for anyone with a PhD, which includes me and most of your professors.)

Teaching Assistants:

This course has TA graders who will do most of the grading for the course; they are not asked to interact directly with students. So you can bring questions about grading to me.

Course Texts:


Our main text for this term will be my own UBC edition of forall x, an open-access logic textbook originally developed by P.D. Magnus. You can download the pdf for free here. If I find significant errors or make updates, I’ll put corrections up on Canvas. You can read more about the book here. You may wish to print out the textbook, or to just work with the pdf version; the choice is yours.


If you’d like something else to read, here are two introductory logic texts I like, which will fit reasonably well with our main text:

These are not required; I will not refer to them directly in class.

Student Interactivity and Participation:

This course will use Learning Catalytics, an interactive system that allows me to gauge student comprehension during the lectures. You will (or may) receive credit for participation; see the Homework and Participation notes below. Consequently, you should consider regular attendance for this course to be mandatory. You can find instructions for signing up for Learning Catalytics on Canvas.

There is a $12 fee to use Learning Catalytics. (This gives you six months of access to an unlimited number of courses, so if you have another class using this system, you only have to pay once.) I take seriously the financial impact of instructors’ decisions on students, and wouldn’t ask you to pay for this if there weren’t clear advantages over free alternatives like Top Hat. Because the textbook is free for this course, this is the only extra cost I’m asking students to incur. You can buy access here.

Using Learning Catalytics in class requires a device with a web browser—typically a smartphone, tablet, or laptop. If you don’t have regular access to such a device, or if you don’t want to pay to subscribe, you can opt out of the Learning Catalytics participation component without penalty. But participation via Learning Catalytics is strongly encouraged. Please ensure that you add your UBC student ID to your Learning Catalytics account.

I offer extra credit for participation for students who identify errors in the textbook. See the instructions on Canvas.


I will assign weekly exercises for you to practice at home. These are useful both for developing the skills introduced in lecture, and for indicating what sorts of questions to expect on exams.

Homework will be worth 20% of the total grade. Homework must be completed every week in which it is assigned, or it will be given a grade of 0. No late homework will be accepted, because answers will be posted with the deadline. All homework is required, with the exception of HW11, which is optional because it is due after classes end. (I do not drop the lowest score.)

As in the case of participation, students who prefer to be assessed via more heavily-weighted exams may opt out of assessed homework. In this case, homework will not be submitted or graded (but it is still recommended practice). This decision needs to be made at the beginning of the term.

I have found, over many years teaching this course, that opting out of homework is not a good decision for most students; the grade incentive to keep up with the material helps most students to perform better on exams.


Exams and homework will be handled via Crowdmark, an online grading program. This is free for students to use, but you will need to sign up with an email address that will be used to send you your graded homework and exams. Instructions will be given early in the semester.

Midterm Exams:

There will be three in-class exams. See the schedule below.


Final Exam:

There will be a final exam during the April examination period. This is a cumulative exam, covering all the material in the course.



Midterm 1:                     10%

Midterm 2:                     15%

Midterm 3:                     20%

*Homework:                   20%

*Participation:                10%

Final Exam:                    25%


*The homework and participation components allow an opt-out. If you prefer not to have either or both elements assessed, you may request that option in week 2. If you opt out of one or both elements, the credit for those elements will be distributed proportionally over the other components of the course.


This is a large courses and I get a lot of email. I typically only handle teaching-related email during work hours, and it’s not unusual for it to take a few days to get back to students. So please plan ahead if you’re going to email about urgent matters.

Due to the large enrolment I am not able to answer substantive questions about grading decisions over email. I am of course happy to discuss grading in person via office hours or by appointment.

If you do send me an email related to your account in the course, please include your student number with all correspondence.





HW due



Jan. 2

Introduction, course policies



Jan. 4

Propositions, arguments, validity

Ch. 1


Jan. 7

Sentential Logic

Ch. 2


Jan. 9

Sentential Logic

HW 1



Jan. 11

Truth Tables

Ch. 3


Jan. 14

Truth Tables



Jan. 16

Entailment and Models

HW 2

Ch. 4


Jan. 18

SL Trees


Jan. 21

Exam 1


Jan. 23

SL Trees

HW 3

Ch. 5


Jan. 25

SL Trees, Introduction to Soundness and Completeness



Jan. 28

Soundness and Completeness for SL Trees

Ch. 6


Jan. 30

Soundness and Completeness for SL Trees

HW 4


Feb. 1

Trees Review and Catch-Up



Feb. 4

SL Natural Deduction



Feb. 6

SL Natural Deduction

HW 5

Ch. 7


Feb. 8

SL Natural Deduction


Feb. 11



Feb. 13

Exam 2

HW 6



Feb. 15

no class


midterm break


Feb. 25

Predicates and names

Ch. 8


Feb. 27





Mar. 1

Predicate Logic — Translation Practice



Mar. 4

Models for QL

Ch. 9


Mar. 6

Models for QL

HW 7



Mar. 8

QL Trees

Ch. 10


Mar. 11

QL Trees



Mar. 13

QL Trees

HW 8



Mar. 15

Soundness and Completeness for QL Trees

Ch. 11


Mar. 18




Mar. 20


HW 9

 Ch. 12

Mar. 22

Exam 3


Mar. 25




Mar. 27





Mar. 29

QL Natural Deduction

Ch. 13


Apr. 1

QL Natural Deduction



Apr. 3

QL Natural Deduction

HW 10


Apr. 10

no class but the last HW is due this day

HW 11

April TBD

Final Exam

Note on Academic Misconduct:

It is your responsibility to understand rules regarding plagiarism. The most basic principle is, the work you present must be your own. (Proper citation procedure is also an important element in most philosophy courses, but the issue will arise less often in this course, where students won’t be writing essays.) Here is a link about Academic misconduct.

Plagiarism will not be tolerated in this course. It is possible to plagiarize accidentally. Minor infractions will result in a 0% for the assignment; major infractions will be escalated via university procedures, and are grounds for failing the entire course.

Note on Technology:

Students using Learning Catalytics will need to keep a laptop, smartphone, or tablet handy. I don’t make any kind of rule restricting the use of computers in class, but I do ask students to keep two things in mind. First, there is a growing body of research that suggests that using computers during class time leads to wasting time and worse educational outcomes. Evidence also suggests that taking notes by hand leads to better learning than typing them digitally. It is up to each student to decide for themself how they will best learn, but for most students, using the computer is probably not a good idea.

Second, using a laptop to play games or check facebook is distracting to other students around you. It’s up to you whether you want to pay attention in class, but please be considerate to others who do want to pay attention. If there are students sitting behind you, don’t goof off conspicuously.

Note on Intellectual Property:

The course materials I provide—this syllabus, handouts, homework, sample questions, slides, the textbook, etc.—are my own intellectual property. It is a violation of Canadian and international copyright law to distribute such material without the owner’s consent. For example, you may not upload my course materials to commercial websites that want to turn around and sell them to other students. Any notes you take are your own intellectual property, and you can do what you like with them, but most of the material that I am providing to you is only for students in this course.

Note however that the textbook is produced under a Creative Commons license; it may be freely redistributed, so long as it retains that license and is duly credited.