Gillian Russell

Philosophy Professor at UNC Chapel Hill

Phil 405 : Philosophical Logic (Spring 2013)

Class Times: Tuesdays and Thursdays, 11 am-12.30 pm
Location: Wilson 104
Course Website:

Instructor: Professor Gillian Russell
Office hours: Tuesdays 4-5pm or by appointment
Office Location: Wilson 209

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. (There will be a course in philosophy of logic taught next semester. 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. 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 15th January – Classical Consequence

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

Thursday 17th January – Classical Sequent Proofs

Reading: section 2.5 of Sider.
Sequent proofs

Tuesday 22nd January – Classical Axiomatic Proofs

Section 2.6 in Sider
Axiomatic Proofs

Thursday 24th 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 by 3.30pm on Friday 25th January

Tuesday 29th January – Strong and Weak Kleene tables

Reading: sections 3.42, 3.43, plus selection from Stephen C. Kleene (on ares.)

Thursday 31st January – The Logic of Paradox

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

Tuesday 5th February – Supervaluations

Section 3.4.5

Thursday 7th February – Intuitionistic Logic

Section 3.5 plus selection from Brouwer (on ares.)
Homework Exercises (2): Ex 3.4, 3.5, 3.6 and 3.10. Due Friday 8th February.

Tuesday 12th February – First Order Classical Logic

Sections 4.1-4.3

Thursday 14th February – Axiomatic Proofs

Section 4.4

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

Tuesday 19th February – Identity

Section 5.1

Thursday 21st February – Function symbols

Section 5.2
Homework Exercises (4): 4.2, 4.3, 4.4. Due Friday 22nd February.

Tuesday 26th February – Definite Descriptions

Section 5.3

Thursday 28th February – Further quantifiers

Homework Exercises (5): 5.1, 5.2, 5.3, 5.4, 5.5. Due Friday 1st March.

Section 5.4

Tuesday 5th March – Complex predicates

Section 5.5

Thursday 7th March – Free Logic

Section 5.6

Homework Exercises (6): 5.9, 5.10, 5.12, 5.13. Due Friday 8th March.

Tuesday 12th March


Thursday 14th March


Tuesday 19th March – Introduction to Tense Logic

No assigned reading.

Thursday 21st March – History and Model Theory

Sections 6.1 – 6.3.2

Tuesday 26th March – review session for the exam

No additional reading.

Thursday 28th March

MIDTERM EXAM (1 hour, in class)

Tuesday 2nd April


Thursday 4th April


Tuesday 9th April – Modal Counterexamples

Section 6.3.3

Thursday 11th April – Proof Theory for K

Sections 6.4 and 6.4.1

Homework Exercises (7): 6.2, 6.3. Due Friday 12th April.

Tuesday 16th April – Proof Theory for Stronger Logics

Pages 183-192
Deontic logic, epistemic logic, tense logic

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

Sections 7.1-7.3.4
Homework exercises (8): 6.4, 6.5. Due Friday 19th April.

Tuesday 23rd April – Intuitionistic Logic

Section 7.4

Thursday 25th April – Review Class

Review class for final examination (Monday May 6th 1-3pm.)

  • Homework exercises are listed on the syllabus, with their due dates (always a Friday.) They are to be completed on paper and turned in to the dropbox on the side of the "turn-in" filing cabinet in the philosophy department office (2nd floor of Wilson Hall.) The office is closed over the lunch hour and no work may be dropped off at this time.

  • Homework is due by 3.30pm on the Friday after the date it is listed. Please be considerate of the office staff; the office closes at 4pm and we try to discourage students from knocking on the door at 4.01pm, when the office staff are trying to go home.

  • 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 in class, 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 homework exercises completed during the semester. 25% will come from the in-class midterm exam on Thursday March 28th and 25% from the final exam, which will be held during the official exam period, on Monday May 6, 2013 1:00 PM – 3:00 PM, in our usual room. If you decide to take this course, you will need to make sure that you are still on campus for the exam.

For students taking the course pass/fail, the minimum letter grade required for a pass will be a D, which can be obtained with an overall percentage grade of 50%.

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.)

Students suspected of plagiarism or any other form of academic dishonesty or misconduct will be reported to the academic integrity officer for Arts and Sciences (currently Dean Killen), so that the incident may be handled in a consistent, fair manner, and so that substantiated charges of misconduct may be noted in students’ records.