Gillian Russell

Philosophy Professor

Phil 301 : Symbolic Logic (Fall, 2012)

Class Times: Tuesdays and Thursdays, 1-2.30pm
Location: Psychology, 249
Course Website:
Final Exam: Tuesday 18th December 1-3pm.

Instructor: Professor Gillian Russell
Office hours: Thursdays 2.45-3.45pm or by appointment
Office Location: 209 Wilson Hall
Email: grussell – at – wustl – dot – edu

Teaching Assistant: Nati Friedenberg
Office Hours: Wednesdsays 2.45-3.45pm
Location of office hours: 104 Wilson (the seminar room)
Email: nati – dot – friedenberg – at – wustl – dot – edu

This course continues on where Phil 100: An introduction to Logic and Criticial Analysis leaves off. It is recommended for students who have taken that course, or for students who already have a strong background in mathematics. It is intended to help bridge the gap between Phil 100 and Phil 403: Mathematical Logic. To that end will we gradually introduce more metatheoretical results and more challenging proof methods, with a particular focus on proof by induction.

In the first half of the course we will be studying some features of truth-functional and first-order classical logics, and in particular we will investigate the model theory for first-order logic in much greater depth than in Phil 100. After the midterm, we’ll go on to study four different styles of proof: tableaux, axiomatic, natural deduction and sequent calculi. We will study completeness results for these systems.


The textbook for this course is David Bostock’s Intermediate Logic, published by Oxford (Clarendon). It is the only text you need to buy and there has only been one edition. Second hand copies are fine.

Readings, Topics and Homework Assignments

Tuesday 28th August – First day of class

Truth-functions and truth-functors.
Reading: Pages 3-24 of Bostock.

Thursday 30th August

Semantics for truth-functional languages.

Reading: Pages 24-30 of Bostock. No homework this week.

Tuesday 4th September

Principles of entailment (thinning, cut, etc.)
Reading: Pages 30-37 of Bostock.

Thursday 6th September

Normal forms (DNF, PNF, etc.)
Pages 37-45 of Bostock.
Exercises (1): 2.1.1, 2.2.1, 2.3.1, 2.4.1(a), (c), (e), (g), (i), 2.4.2. Due Friday 7th September

Tuesday 11th September

Expressive adequacey. Pages 45-48.

Thursday 13th September

Mathematical Induction.
Reading: Pages 48-56 of Bostock.
Exercises (2): 2.5.1, 2.5.3, 2.6.1 Due Friday 14th September.

Tuesday 18th September

Expressive adequacey II.

Reading: Pages 56-62 of Bostock.

Thursday 20th September

Reading: Pages 62-65 of Bostock.

Exercises (3): 2.7.1, 2.8.1, 2.8.2, Due Friday 21st September.

Tuesday 25th September

Truth-value analysis
Reading: pages 65-69 of Bostock.

Thursday 27th September

The language of first order logic.
Reading: Pages 70-81 of Bostock.
Exercises (4): 2.9.1, 2.9.2, 2.10.1, 2.11.1 Due Friday 28th September.

Tuesday 2nd October

Model theory for first order logic.
Reading: Pages 81-96 of Bostock.

Thursday 4th October

More principles of entailment.
Reading: Pages 96-108 of Bostock.

Exercises (5): 3.3.1, 3.3.4, 3.5.1 Due Friday 5th October.

Tuesday 9th October

Prenex normal form.
Reading: Pages 109-115 of Bostock.

Thursday 11th October

Decision procedures for monadic predicate formulas. Pages 115-126 of Bostock.

Your homework this week is to prepare for the midterm exam.

Tuesday 16th October

Review class for the Midterm

Thursday 18th October


Tuesday 23th October

Proofs and Counterexamples. Pages 131-138 of Bostock.

Thursday 25th October

Semantic tableaux I – proofs with truth-functors.
Reading: Pages 141-147 of Bostock. No homework this week.

Tuesday 30th October

Semantic Tableaux II – proofs with quantifiers
Reading: Pages 149-165 of Bostock

Thursday 1st November

Semantic tableaux III – Soundness and Completeness.
Readings: pages 164 – 189 of Bostock.

Exercises (6): 3.6.3, 3.7.1, 3.7.2 Due Friday 2nd November.

Tuesday 6th November

Axtiomatic proofs I – proofs and the deduction theorem.
Reading: Pages 190 – 208 of Bostock.

Thursday 8th November

Axiomatic proofs II – Laws of negation. Truth-functional completeness.
Reading: Pages 208 – 220 of Bostock.

Tuesday 13th November

Axiomatic proofs III – Axioms for the quantifiers. Alternative axiomatisations.
Reading: Pages 220 – 238 of Bostock.

Thursday 15th November

Natural deduction I – rules for the truth-functors.
Reading: Pages 239 – 254 of Bostock.

Homework exercises (7): 4.1.2, 4.2.1, 4.4.1 (a), (e) and (k) and 4.4.2(a), (b) and (c) Due Friday 16th November.

Tuesday 20th November

Natural deduction II – rules for the quantifiers. Alternative proof styles.
Reading: Pages 254-272.

Thurday 22nd November


Tuesday 27th November

Sequent Calculi I
Reading: pages 272-283

Thursday 29th November

Sequent Calculi II
Reading: pages 283-319

Tuesday 4th December

Make-up class in case any of these topics take up more time than anticipated.

Thursday 6th December

Review class for final examination (Tuesday 18th December 1-3pm.)

Homework Exercises (8): 5.3.1, 5.3.2, 5.4.1 Due Friday 7th December.


  • 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 cabinent 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 date 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.

  • 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 (you should not put your student number on your work.) Do not turn in “rough” work, or work with lots of crossings-out.

  • Solutions to the problem sets will be given out in class.

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

    If you have questions or doubts about grading, by far the simplest way to resolve things will be to talk to Nati directly. If you would like to appeal your grade on a homework, please put a COPY of
    your graded work in Professor Russell’s mailbox with a written explanation of the problem and she will take a look.


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 October 18th and 25% from the final exam, which will be held during the official exam period, on Tuesday 18th December, 1pm-3pm, 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 exams.

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.

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