Gillian Russell

Philosophy Professor

Phil 456: Advanced Philosophical Logic – Spring 2019

Class Times: Tuesdays and Thursdays, 11 am-12.15 pm
Location: Caldwell Hall, 213
Course Website:
Final Exam: Monday April 29th at noon

Instructor: Professor Gillian Russell
Office hours: Tuesdays 3.30-4.30pm, Fridays 1.30-2.30pm
Office Location: Caldwell Hall, 203
Email: gillian UNDERSCORE russell AT unc DOT edu

What this course is: this is a course in philosophical logic. Since it is a logic course, it will be assessed largely though problem sets and exams. And since it is a course on philosophical logic, it will focus on areas of logic which are likely to be of interest to philosophers. We will begin with a brief review of classical logic and then move on to study some alternatives, such as three-valued logics, and extensions, such as various modal logics.

What this course is not: This is not a course in the philosophy of logic, which would be a philosophy course, assessed mainly by papers, focusing on topics like the metaphysics and epistemology of logic, truth, necessity, possible worlds and logical consequence.

The course is aimed at students who have already completed an introductory course in logic, such as Phil 155: Introduction to Mathematical Logic, and/or Phil 455: Symbolic Logic. At any rate, it will be assumed that you already have a good grasp of first-order classical logic. If you are a student with a strong background in mathematics it might possible to succeed without taking either of these two previous courses, but such students are advised to spend some extra time with pages 1-62 and 90-106 of Sider, as this class will pass over the standard topics in classical logic quite quickly.


The course textbook is Ted Sider’s Logic for Philosophy.

Readings, Topics and Homework Assignments

Thursday 10th January – Classical Consequence

Reading: Sections 1.1-1.7 and 2.1-2.4 of Sider
Logical consequence in PL.

Tuesday 15th January – Classical Sequent Proofs

Reading: section 2.5 of Sider.
Sequent proofs

Thursday 17th January – Classical Axiomatic Proofs

Section 2.6 in Sider
Homework Exercises (1): Ex 2.2, 2.3, and 2.4 (from Sider) Due Monday 21st Tuesday 22nd January (Monday is a holiday!)

Tuesday 22nd January – Łukasiewicz’s three-valued logic

Sections 3.3 and 3.4.1

Thursday 24th January – Strong and Weak Kleene tables

Reading: sections 3.42, 3.43.

Tuesday 29th January – The Logic of Paradox

Section 3.4

Thursday 31st January – Supervaluations

Section 3.4.5

Tuesday 5th February – Intuitionistic Logic

Section 3.5

Homework Exercises (2): Ex 3.4, 3.5, 3.6 and 3.10. Due Monday 11th February.

Thursday 7th February – First Order Classical Logic (1)

Sections 4.1-4.3

Tuesday 12th February – First Order Classical Logic (2)

Homework Exercises (3): 3.12, 3.13, 3.14. Due Monday 18th February

Thursday 14th February – Axiomatic Proofs

Section 4.4

Tuesday 19th February – Identity and Function symbols

Section 5.1 and 5.2

Homework Exercises (4): 4.2, 4.3, 4.4. Due Monday 25th February.

Thursday 21st February

No class. (APA)

Tuesday 26th February – Definite Descriptions

Section 5.3

Homework Exercises (5): 5.1, 5.2, 5.3, 5.4, 5.5. Due Monday 4th March (Note – the day before the midterm exam.)

Thursday 28th February – Further quantifiers

Section 5.4

Tuesday 5th March


Thursday 7th March

No class (SYR)

Tuesday 12th March

SPRING BREAK – no class

Homework Exercises (6): 5.9, 5.10, 5.12, 5.13. Due Monday 25th March.

Thursday 14th March

SPRING BREAK – No class.

Tuesday 19th March – Complex predicates

Section 5.5

Thursday 21st March – Free Logic

Section 5.6

Tuesday 26th March

Scheduled “catch up” class in case any of the above takes longer than expected.

Thursday 28th March – Introduction to Tense Logic

No required reading

Tuesday 2nd April – Modal Logic, History and Model Theory

Sections 6.1 – 6.3.2

Thursday 4th April – Modal Counterexamples

Section 6.3.3

Tuesday 9th April

No Class
Homework Exercises (7): 6.2, 6.3b, c, e, and f. (i.e. you don’t need to do 6.3a, d, g, etc. – we are just doing four problems from 6.3. Note – the solutions to 6.3a and d are in the back of the textbook and would make a good model for your own answers.) Due Monday 15th April.

Thursday 11th April – Proof Theory for K

Sections 6.4 and 6.4.1

Tuesday 16th April – Proof Theory for Stronger Logics


Thursday 18th April – Deontic Logic, epistemic logic, tense logic

Sections 7.1-7.3.4

Tuesday 23rd April – Intuitionistic Logic

Section 7.4
Homework exercises (8): 6.4, 6.5. Due Monday 22nd April

Thursday 25th April

Make-up class in case any of the above topics take extra time.

  • Homework exercises are listed on the syllabus, with their due dates (always a Monday.) They are to be completed on paper and turned in to my mailbox in the common room on the 1st floor of Caldwell Hall by 4pm.

  • You may handwrite your homework (in fact, this is often faster and less prone to unfortunate typing errors) but you should always turn in neat, legible work, clearly marked with your name on each piece of paper. Do not turn in “rough” work, or work with lots of crossings-out.

  • Solutions to the problem sets will be given out (usually by email) approximately 1 week after the due date.

  • Any homework set received after the solutions have been given out will receive a grade of zero.


50% of the grade for this course will come from the 8 homework exercises completed during the semester. I will drop your worst homework grade and average the rest. 25% will come from the in-class midterm exam on Tuesday 5th March (the week before spring break) and 25% from the final exam on Monday 29th April. If you decide to take this course, you will need to make sure that you are on campus and able to attend both exams.

The work required to complete the problem sets will exceed the work required to complete 10 pages of writing.

Academic Integrity

It is very important that you understand the rules for collaboration on this course. You may work with other students in order to work out solutions to the exercises in your take-home problem sets; in fact, this is encouraged. However, each student must write up his or her solutions to the exercises alone. You may not do it with another student looking over your shoulder to correct you. 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.

Collaboration is, of course, completely forbidden during the midterm and final examinations.

Sometimes it is unclear whether a hypothetical case of collaboration is permissible according to these rules, or whether it counts as misconduct, but it is your duty to ensure that ALL your collaborations are clearly permissible. One good way to do this is not to write anything down on paper whilst investigating problems with other students: use a chalk board or white board to work out ideas, (or, if you use paper, dispose of the written solutions before you separate to write up your individual homeworks alone.)

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 Counseling

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.

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