PHIL 220–009: Introduction to Formal Logic

Winter 2020–21, Term 1

The latest version of this syllabus is always available at

Course Meetings:                 MWF, 1–1:50 pm, Online

Instructor:                        Dr. Jonathan Jenkins Ichikawa —*

Office Hours:                        Mondays and Fridays, 12–1 pm.

*Please consult email policy before writing.


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 ideas 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.

COVID and Course Format

For public health reasons, this course will not include any in-person components. (There is no requirement that you be in Vancouver.) Lectures will be delivered online, via Collaborate Ultra in Canvas. Recordings of lectures will be made available to students.

Students will have a choice at the start of term whether they wish to sign up for synchronous lecture participation, or review lectures on their own (asynchronous) schedule. For students for whom it is feasible, I recommend the synchronous version. This version has several advantages:

If our course meeting time is not convenient for you, however, or if you prefer asynchronous delivery for another reason, you can opt out of that component of the course. You will be responsible for watching the lectures on your own schedule and doing enough practice to learn the course material.

Note that this is not a distance learning course; it is a course where traditional lectures have been moved online due to a public health emergency. It is an imperfect solution, but we will do our best. (I did teach this course’s material online in the latter part of 2019W2, so I have experience with the relevant technology, and am confident I can make it work.)

I will ask students to sign up for one version or the other near the start of term. If you are considering whether to sign up, this is a course that works best if you can regularly attend lectures online, MWF 1:00 Vancouver time. But it is possible to be successful at this course in an asynchronous format, and I am happy to accommodate that.

Students will need to sit exams at the specified times; plan around those syllabus dates. I will however make a suitable option available for students in distant time zones.


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 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.)

Backup Communication Policy:

In case of a sudden communication outage via Canvas, e.g. during a lecture or exam, I will provide updates to students via my twitter feed, @jichikawa. If there is a technical problem that keeps me from communicating with students as intended there, check my twitter page.

Teaching Assistants:

I employ TAs for grading only; students won’t interact with them directly. For all points of contact, including questions about grading, students should talk to me.

Office Hours:

My regular office hours are times for students to ask any questions about the course material. There is no need to make an appointment. (I may occasionally need to adjust my office hours from week to week; I’ll announce this on Canvas if I do.) I am also available to arrange meetings at other times by appointment.


This is a large course that generates a lot of email. Please observe the following guidelines when writing to me about course business:

In general, I cannot respond to substantive logic questions via email; email is primarily for course administration. (Unfortunately it is just too time-consuming to offer involved explanations to individual students by typing emails.) If you want me to teach you something, please ask in class, in office hours, or on the Canvas forums.

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. It is also linked on Canvas.

You can read more about the book here.


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.

Estimated costs for required course materials:

$12 USD or $0, depending on whether you choose to include the participation component.


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. (I do not drop the lowest score.) If you join the course late the earlier homework assignments you miss can be waived.

It is fine to work with classmates as you prepare your homework. You can compare notes, compare answers, etc. But you must submit your own work; do not simply copy material someone else has prepared.

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.

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 receive credit for participation, unless you opt out. Consequently, you should consider regular attendance for this course to be mandatory. You can find instructions for signing up for Learning Catalytics on Canvas. Students will need to purchase a license to use Learning Catalytics; 6 months’ access costs $12 USD. Please ensure that you add your UBC student ID to your Learning Catalytics account.

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.

There is one participation point available each class session. Students receive it for answering at least 50% of the Learning Catalytics questions asked that day. (Credit is for answering at all — whether or not the answer is correct.) The last question each day, an open-ended request for feedback, is not included in the total and does not come with credit.

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


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. For the most part, the exams will contain questions very similar to the homework questions, making the homework exercises the most useful practice. Up to 10% of the possible credit on the exam might be devoted to a more challenging/creative questions at the end of the exam, that measures deeper comprehension.

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.

Re-Marking Policy:

Grading errors happen from time to time. Please check the grading to see that you have gotten the credit you deserve. If there is a mistake, come to office hours or send me an email with a photo/screenshot of the issue, and make sure to include your student number in the email. All re-marking requests must be made within two weeks after the assignment is returned to you. (If you don’t check within two weeks, I will take this as an indication that you don’t care enough about your credit on the assignment to make it worth the effort to fix it.)


Specific deadlines and topic dates are still provisional and subject to change.




HW due



Sept 9

Introduction, course policies



Sept 11

Arguments, argument forms, validity

Ch. 1


Sept 14

Sentential Logic: Sentences, Connectives

Ch. 2


Sept 16

Sentential Logic: Translation, Grammaticality



Sept 18

Truth Tables

HW 1

Ch. 3


Sept 21

Truth Tables



Sept 23

Entailment and Models

Ch. 4


Sept 25

SL Trees

HW 2



Sept 28

SL Trees

Ch. 5


Sept 30

SL Trees, Introduction to Soundness and Completeness

Oct 2

Exam 1

HW 3


Oct 5

Soundness and Completeness for SL Trees

Ch. 6


Oct 7

Soundness and Completeness for SL Trees

Oct 9

Catch-up/flex day

HW 4


Oct 12

Holiday — no class


Oct 14

SL Natural Deduction

HW 5

  Ch. 7


Oct 16

SL Natural Deduction


Oct 19

SL Natural Deduction


Oct 21

Review Session

HW 6


Oct 23

Exam 2



Oct 26

QL: Names and Predicates

 Ch. 8


Oct 28

QL: Quantifiers


Oct 30

QL: Translation Practice



Nov 2

Models for QL

HW 7

 Ch. 9


Nov 4

Models for QL


Nov 6

QL Trees

Ch. 10


Nov 9

QL Trees

HW 8

Nov 11

Holiday — No Class



Nov 13

QL Trees

Ch. 11


Nov 16

Soundness and Completeness for QL Trees


Nov 18

Soundness and Completeness for QL Trees

HW 9


Nov 20

Exam 3



Nov 23


Ch. 12


Nov 25




Nov 27




Nov 30

QL Natural Deduction

HW 10

Ch. 13


Dec 2

QL Natural Deduction


Dec 7

no class but the last HW is due

HW 11


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 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.

Distributing recorded lectures or student questions or discussion without consent of all parties is both a copyright violation and a serious privacy violation.

The exception to the above is my textbook, which is produced under a Creative Commons license; it may be freely redistributed, so long as it retains that license and is duly credited.

Departmental Resources to Support Student Learning:

The Philosophy Department may have additional resources available outside of this course; for information, see the department website.

Mandatory Syllabus Statement about UBC’s Values and Policies:

UBC provides resources to support student learning and to maintain healthy lifestyles but recognizes that sometimes crises arise and so there are additional resources to access including those for survivors of sexual violence. UBC values respect for the person and ideas of all members of the academic community. Harassment and discrimination are not tolerated nor is suppression of academic freedom. UBC provides appropriate accommodation for students with disabilities and for religious and cultural observances. UBC values academic honesty and students are expected to acknowledge the ideas generated by others and to uphold the highest academic standards in all of their actions. Details of the policies and how to access support are available here.