Gillian Russell

Philosophy Professor at UNC Chapel Hill

Phil 455 (Ling 455) Symbolic Logic – Fall 2019

This website is a DRAFT of my syllabus for Phil 455 – some changes are likely

Class times Wednesdays 10.10-11.25am, Caldwell 213

Course Website:

Course Instructor:

  • Professor Gillian Russell
  • Office hours: TBA
  • 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 right 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.

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.)

1,2,6,7,9,10, 12, 13, 14 15, 16, 17.

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 6th September – Primitive Recursive Functions (I)

Reading: Section 6.1 of L&C.

Wednesday 8th 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 – Further examples

Reading: section 7.3

Wednesday 9th October – First-order logic – syntax

Reading: section 9.1

Monday 14th October

Reading: section 9.2

Wednesday 16th October

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

Monday 21st October – First-order logic – semantics

Reading: Section 10.1

Wednesday 23rd October

Reading: Section 10.2

Monday 28th October – The Size and Number of Models

Reading: section 12.1

Wednesday 30th October – The Löwenheim-Skolem and Compactness Theorems

Reading: sections 12.2 and 12.3

Monday 4th November – The Existence of Models

Reading: sections 13.1, 13.2, 13.3

Wednesday 6th November

Reading: sections 13.3 and 13.5

Monday 11th November – Proofs

Section 14.1

Wednesday 13th – Proofs and Completeness

Reading: Section 14.2 and 14.3

Monday 18th November – Arithmetization

Reading: Sections 15.1 and 15.2

Wednesday 20th November

Section 15.3

Monday 25th November – Representability of Recursive Functions (1)

Reading: sections 16.1 and 16.2

Wednesday 27th November

NO CLASS – Thanksgiving Break

Monday 2nd December – Representability of Recursive Functions (2)

Reading: sections 16.3 and 16.4

Review for final exam

Wednesday 4th December

Reading: chapter 17.


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.