Gillian Russell

Philosophy Professor

Phil 301 : Symbolic Logic (Fall 2011)

Class Times: Tuesdays and Thursdays, 11.30am-1pm
Location: McDonnell Hall, 162
Course Website:

Instructor: Professor Gillian Russell
Office hours: Thursdays 2.30-3.30pm or by appointment
Office Location: 209 Wilson Hall
Email: grussell – at – wustl – dot – edu

Teaching Assistant: Justin Taylor
Office Hours: Mondays and Wednesdays 11am-noon.
Location of office hours: Justin Taylor’s office in the Danforth University Center
Email: wjtaylor – at – go – dot – 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 already taken that course, or for students who 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’ll 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 three different styles of proof: tableaux, axiomatic, and natural deduction. 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 30th August

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

Thursday 1st September

Semantics for truth-functional languages.

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

Tuesday 6th September

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

Thursday 8th 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 9th September.

Tuesday 13th September

Expressive adequacey. Pages 45-48.

Thursday 15th September

Mathematical Induction.
Reading: Pages 48-56 of Bostock.
Exercises (2): 2.5.1, 2.5.3, 2.6.1 Due Friday 16th September.

Tuesday 20th September

Expressive adequacey II.

Reading: Pages 56-62 of Bostock.

Thursday 22nd September

Duality and truth-value analysis.
Reading: Pages 62-69 of Bostock.

Exercises (3): 2.7.1, 2.8.1 , 2.8.2, 2.8.3. Due Monday 26th September.

Tuesday 27th September

The language of first order logic.
Reading: Pages 70-81 of Bostock.

Thursday 29th September

Model theory for first order logic.
Reading: Pages 81-96 of Bostock.
Exercises (4): 2.9.1, 2.9.2, 2.10.1, 2.11.1 Due Friday 30th September.

Tuesday 4th October

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

Thursday 6th October

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

Exercises (5): 3.3.1, 3.3.4, 3.5.1 Due Friday 7th October.

Tuesday 11th October

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

Thursday 13th October

Midterm Preparation – your homework this week is to prepare for the exam.

Tuesday 18th October


Thursday 20th October

No Class. No Homework due. Professor Russell’s office hours will be on Wednesday at 2.30pm this week.

Tuesday 25th October

Proofs and Counterexamples. Pages 131-138 of Bostock.

Thursday 27th October

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

Tuesday 1st November

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

Thursday 3rd November

No Class. Professor Russell’s office hours will be on Wednesday at 2.30pm this week.

Exercises (6): 3.6.3, 3.7.1, 3.7.2 Due Friday 4th November.

Tuesday 8th November

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

Thursday 10th November

Axtiomatic proofs I – proofs and the deduction theorem.
Reading: Pages 190 – 208 of Bostock. No homework this week.

Tuesday 15th November

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

Thursday 17th November

NO CLASS. Professor Russell’s office hours will be on Wednesday at 2.30pm this week.

Tuesday 22nd November

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

Thurday 24th November


Tuesday 29th November

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

Thursday 1st December

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

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 2nd December.

Tuesday 6th December

Scheduled catch up class (in case any of these topics take more time than planned.)

Thursday 8th December

Review class for final examination (Monday 19th December 1-3pm in usual room.)

Homework Exercises (8): 5.3.1, 5.3.2, 5.4.1 Due Friday 9th 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 appropriate drawer of the "turn-in" filing cabinent in the philosophy department office (2nd floor of Wilson Hall, opposite Professor Russell’s office.)

  • 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.


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 October 18th and 25% from the final exam, which will be held during the official exam period, on Monday 19th 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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