Gillian Russell

Philosophy Professor

Phil 455 Symbolic Logic

Class times: Mondays and Wednesdays, 10.10-11.25am

Class location: Caldwell Hall, Room 213

  • Professor: Gillian Russell
  • Email:
  • Office hours: Mondays 11.25am-12.25pm and Fridays 1.30-2.30pm
  • Office Location: 2nd Floor of Caldwell Hall (upstairs, then turn right twice.)

Course description:

This is a course in the model theory, proof theory and metatheory of first-order classical logic, aimed at students who have taken at least one course in formal logic in the past. In the first part of the class we will study sentential logic and practice some skills that we want to apply later, especially proof by induction and the production of informal proofs. Then in the second part we will work our way through the First-Order Logic sections of the Open Logic Project (OLP) textbook. Among the topics we will cover are sequent calculus proofs, completeness, compactness, and the Löwenheim-Skolem theorem.

Readings and Topics

N.B. Until Wednesday 11th October there is no pre-assigned reading. Starting 2nd October there will be a section from the “First-Order Logic” chapter of the Open Logic Project to be read before class.

Wednesday 22nd August – First day of class

Introduction to the course.
Soundness and Validity
Syntax for the sentential language

Monday 28th August


Wednesday 30th August

Logical Properties

Monday 4th September

No class – Labour Day

Wednesday 6th September

Informal Proofs

Monday 11th September

Normal forms

Wednesday 13th September

Expressive adequacy

Monday 18th September

Proof by induction

Wednesday 20th September

No class.

Monday 25th September

Expressive adequacy revisited

Wednesday 27th September

Post Completeness Syntax revisited

Monday 2nd October

First-order syntax (I)
Reading: pages 52-56 of The Open Logic Project (OLP)

Wednesday 4th October

Review Session for the Midterm

Monday 9th October

In Class Midterm Examination

Wednesday 11th October

First-order syntax (II)
Pages 56-63 of (OLP)

Monday 16th October

First-order structures
Pages 64-74.

Wednesday 18th October

First-order Logical Properties
pages 74-78.

Monday 23th October

Theories and Models
Pages 79-84

Wednesday 25th October

More First-order Theories
Pages 85-89

Monday 30th October

Sequent Calculus (I)
Pages 90-103

Wednesday 1st November

No class.

Monday 6th November

Sequent Calculus (II)
Pages 103-110

Wednesday 8th November

Pages 110-117.

Monday 13th November

Completeness (I)
Pages 142-149

Wednesday 15th November

Completeness (II)
Pages 149-151

Monday 20th November

Adding Identity
Pages 151-154

Wednesday 22nd November

No class – Thanksgiving

Monday 27th November

Compactness and the Löwenheim-Skolem Theorem
Pages 154-159

Wednesday 29th November

Monday 4th December

“Catch Up” class (in case any of the above topics take more time than planned)

Friday 15th December at 8am

Final exam.


  • 50% of your grade will come from the problem sets. (I’ll drop your worst grade and average the rest.)
  • 25% of your grade will come from the in-class midterm examination.
  • 25% of your grade will come from the final examination.

I will give out (either in class or by email) solutions to the problem sets approximately one week after the assignments
are due. Any work turned in after the solutions have been given out will receive a zero.

Since the two exams are an important part of your grade, you should make sure that
you will be on campus to take them before you decide to take this course.

Our textbook has a helpful manual containing some recommendations and hints for students attempting the problems. I recommend that you take a look.

Assessment Due Date
Problem set 1 Friday 1st September
Problem set 2 Friday 15th September
Problem set 3 Friday 6th October
Midterm Examination Wednesday 9th October
Problem set 4 Friday 27th October
Problem set 5 Friday 17th November
Problem set 6 Friday 1st December
Final Examination Friday 15th December, 8am

Problem sets should be turned in by placing them in my mailbox on the 1st floor of Caldwell
Hall by 3pm on the day they are due.

Permissible collaboration

It is important that you understand the rules for working with other students on this course. You may work with other students in order to work out solutions to the problems in the take-home problem sets; in fact, I encourage you to do this. However, you must write up your homework answers on your own. You may not write your homework from notes which another student has made, nor may you make notes on another student’s written solutions. You may not lend or copy digital or paper homework solutions at any stage of completion.

One way of working within these rules is to work through ideas for solving the problems with others using an erasable white or blackboard (or paper which you dispose of) and then wipe it clean before you each write up your homework alone.

Sometimes it may be unclear whether a certain action would be permissible according to the rules above, but it is your responsibility to ensure that your actions are always clearly permissible.

Honor Code

All students must be familiar with and abide by the Honor Code, which covers issues such as plagiarism, falsification, unauthorized assistance or collaboration, cheating, and other grievous acts of academic dishonesty. Violations of the Honor Code will not be taken lightly.

The Center for Student Success and Academic Counselling

Located in the Student Academic Services Building, the CSSAC offers support to all students through units such as the Learning Center and the Writing Center.

Reasonable Accommodations Policy

Any student in this course who has a disability that may prevent them from fully demonstrating their abilities should contact Disability Services as soon as possible to discuss accommodations.