Gillian Russell

Philosophy Professor

Phil 455 (Ling 455) Symbolic Logic – Fall 2019

Class times: Mondays and Wednesdays 10.10-11.25am, Caldwell 213

Course Website:

Course Instructor:

  • Professor Gillian Russell

  • Office hours: Monday, 11.25am-12.25pm, Friday 1.30-2.30pm

  • Office Location: Caldwell Hall, 203

  • Email: gillian UNDERSCORE russell AT unc DOT edu

This is a course in first-order classical logic and its metatheory. It presupposes at least one previous course in formal logic, such as Phil 155 Introduction to Mathematical Logic or Phil 456 Advanced Symbolic Logic. It might be possible for students with unusually mature mathematical skills to take this course without a previous course in logic (and even such students are likely to find chapters 9 and 10 of the textbook especially challenging) but most students will experience much less trauma if they do things in the expected order.

We will work our way through the “intermediate logic” track of the 5th edition of Boolos, Burgess, and Jeffrey’s classic textbook Logic and Computability. You may buy this at the bookstore, or order it online from the usual vendors. It is the only book you will need for the course.

Topics and Readings

The assigned readings for the course are listed in the syllabus below. “L&C” stands for Logic and Computability (our textbook.) If a section of the textbook is marked with a “star” (*) for “optional”, it is not part of the required reading, unless it explicitly says otherwise below.

Wednesday 21st August

First class – no assigned reading

Monday 26th August – enumerability

Reading: chapter 1 of L&C.

Wednesday 28th August – diagonalisation

Reading – chapter 2 of L&C

Monday 2nd September

NO CLASS – Labour Day

Wednesday 4th September

No additional reading

Monday 9th September – Primitive Recursive Functions (I)

Reading: Section 6.1 of L&C.

Wednesday 11th September – Primitive Recursive Functions (II)

Monday 16th September – Recursive Functions (I)

Reading: Section 6.2 of L&C.

Wednesday 18th September – Recursive Functions (II)

Monday 23rd September – Recursive relations (I)

Reading: section 7.1

Wednesday 25th September – Recursive relations (II)

Monday 30th September – Semi-recursive relations (I)

Reading: section 7.2

Wednesday 2nd October – Semi-recursive relations (II)

Monday 7th October – First-order logic – syntax

Reading: section 9.1

Wednesday 9th October

Reading: section 9.2

Monday 14th October

In-class Midterm Examination

Wednesday 16th October

NO CLASS – I’ll be at a philosophy of logic workshop in Bergen

Monday 21st October – First-order logic – model theory

Reading: Section 10.1

Wednesday 23rd October

Reading: Section 10.2

Monday 28th October

NO CLASS (I’ll be in Mexico City at the LLL logic workshop)

Wednesday 30th October – The Size and Number of Models

Reading: section 12.1

Monday 4th November – The Löwenheim-Skolem and Compactness Theorems

Reading: sections 12.2 and 12.3

Wednesday 6th November – The Existence of Models

Reading: sections 13.1, 13.2, 13.3, 13.4

Monday 11th November – Proofs

Reading: section 14.1 13.5

Wednesday 13th – Proofs and Completeness (I)

Reading: Section 14.2

Monday 18th November – Proofs and Completeness (II)

Reading: Section 14.2 and 14.3

Wednesday 20th November – Arithmetization

Reading: Sections 15.1 – 15.3

Monday 25th November – Representability of Recursive Functions

Reading: Sections 16.1 and 16.2

Wednesday 27th November

NO CLASS – Thanksgiving Break

Monday 2nd December – Representability of Recursive Functions

Reading: sections 16.3 and 16.4

Wednesday 4th December – Indefinability, Undecidability, Incompleteness

Reading: chapter 17.


  • 50% of your grade will come from the problem sets. (I’ll drop your worst two grades and average the rest.)

  • 25% of your grade will come from the in-class midterm examination.

  • 25% of your grade will come from the take-home 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: Ex 1.1, 1.3 Tuesday 3rd September
Problem set 2: 2.2, 2.4 Tuesday 10th September
Problem set 3: 6.1, 6.2 Tuesday 17th September
Problem set 4: 6.4, 6.5 Tuesday 24th September
Problem set 5: 7.1, 7.12 7.3 Tuesday 1st October
Problem set 6: 9.2, 9.4 Tuesday 8th Thursday 10th October
Midterm Examination Monday 14th October
Problem set 7 10.1, 10.6 Tuesday 29th October
Problem set 8: 12.3, 12.8 Tuesday 5th 12th November
Problem set 9: 13.8, 13.9 Tuesday 12th 19th November
Problem set 10: 14.5, 14.7 Tuesday 19th26th November
Problem set 11: 15.4, 16.2, Tuesday 26th November 3rd December
Problem set 12: 16.3, 16.9 Tuesday 3rd December
Final Examination Given out: 6th Dec, 8am. Turn in: 13th Dec, 8am.

The final exam will be a week-long take-home exam, due at the start of our official exam time. We will use the exam-time for a wrap up session.

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.

Total required written work for this course will come to significantly more than 10 pages.

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.