Gillian Russell

Philosophy Professor

Phil 456 : Advanced Symbolic Logic

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

Instructor: Professor Gillian Russell
Office hours: Thursdays 3.15-4.15pm, 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. (Graduate students might be interested to know that Phil 755 : Advanced Studies in Philosophy of Logic will be taught in the spring of 2017. The present course would be good preparation for it, though it is not a prerequisite.)

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. Some additional readings will be posted on the course’s electronic reserve page (accessible online through UNC’s library.)

Readings, Topics and Homework Assignments

Tuesday 12th January – Classical Consequence

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

Thursday 14th January – Classical Sequent Proofs

Reading: section 2.5 of Sider.
Sequent proofs

Tuesday 19th January – Classical Axiomatic Proofs

Section 2.6 in Sider
Axiomatic Proofs

Thursday 21st January – Łukasiewicz’s three-valued logic

Sections 3.3 and 3.4.1

Homework Exercises (1): Ex 2.2, 2.3, and 2.4 (from Sider) Due Monday 25th January.

Tuesday 26th January – Strong and Weak Kleene tables

Reading: sections 3.42, 3.43.

Thursday 28th January – The Logic of Paradox

Section 3.44, plus selection from Graham Priest (on ares.)

Tuesday 2nd February – Supervaluations

Section 3.4.5

Thursday 4th February – Intuitionistic Logic

Section 3.5

Homework Exercises (2): Ex 3.4, 3.5, 3.6 and 3.10. Due Monday 8th February.

Tuesday 9th February – First Order Classical Logic

Sections 4.1-4.3

Thursday 11th February – Axiomatic Proofs

Section 4.4

Homework Exercises (3): 3.12, 3.13, 3.14. Due Monday 15th February

Tuesday 16th February – Identity

Section 5.1

Thursday 18st February – Function symbols

Section 5.2

Tuesday 23rd February – Definite Descriptions

Section 5.3

Thursday 25th February – Further quantifiers

Section 5.4
Homework Exercises (4): 4.2, 4.3, 4.4. Due Monday 29th February (unusual date for a HW to be due, I know.)

Tuesday 1st March – Complex predicates

Section 5.5

Thursday 3rd March – Free Logic

No Class

Homework Exercises (5): 5.1, 5.2, 5.3, 5.4, 5.5. Due Monday 7th March.

Syllabus after this point updated 3/2/2016

Tuesday 8th March – Further quantifiers

Section 5.4

Thursday 10th March – Complex predicates

Section 5.5

Homework Exercises (6): 5.9, 5.10, 5.12, 5.13. Due Monday 21st March (because of spring break. If you want to get them done early, I’ll happily accept them before the break too.)

Tuesday 15th March


Thursday 17st March


Tuesday 22nd March – Free Logic

Section 5.6

Thursday 24th March

MIDTERM EXAM (1 hour, in class)

Tuesday 29th March- Introduction to Tense Logic

No required reading

Thursday 31st March – Modal Logic, History and Model Theory

Sections 6.1 – 6.3.2

Tuesday 5th April – Modal Counterexamples

Section 6.3.3

Thursday 7th April

No Class
Homework Exercises (7): 6.2, 6.3a, c, e, g, and i (i.e. you don’t need to do 6.3b, d, f, or h – we are just doing every second problem in 6.3.) Due Monday 11th April.

Tuesday 12th April – Proof Theory for K

Sections 6.4 and 6.4.1

Thursday 14th April – Proof Theory for Stronger Logics


Tuesday 19th April – Deontic Logic, epistemic logic, tense logic

Sections 7.1-7.3.4

Thursday 21st April – Intuitionistic Logic

Section 7.4
Homework exercises (8): 6.4, 6.5. Due Monday 25th April

Tuesday 26th 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 Thursday 24th March (the week after spring break) and 25% from the final exam on Friday 29th April at noon. If you decide to take this course, you will need to make sure that you are on campus for the exams.

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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