Gillian Russell

Philosophy Professor

Phil 301 : Symbolic Logic (Fall 2014)

Class Times: Tuesdays and Thursdays, 2.30-4pm
Location: Mallinckrodt 303
Course Website:

Instructor: Professor Gillian Russell
Office hours: Thursdays 12-1pm or by appointment
Office Location: 209 Wilson Hall
Email: grussell – at – wustl – dot – edu

Teaching Assistant: Seth Margolis
Office Hours: Mondays 1-2pm
Location of office hours: Fireplace Room (Wilson 212)
Email: sethmmargolis – at – gmail – dot – com

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 26th August

Basic Concepts: Arguments, soundness, validity, formality
Reading: Pages 1-8 of Bostock

Thursday 28th August

Truth-functions and truth-functors.
Reading: Pages 8-24 of Bostock.

No homework this first week.

Tuesday 2nd September

Semantics for truth-functional languages.

Reading: Pages 24-30 of Bostock.

Thursday 4th September

Principles of entailment (thinning, cut, etc.)
Reading: Pages 30-37 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 5th September.

Tuesday 9th September

Normal forms (DNF, PNF, etc.)
Pages 37-45 of Bostock.

Thursday 11th September

Expressive adequacy.
Reading: pages 45-48.
Exercises (2): 2.5.1, 2.5.3, 2.6.1 Due Friday 12th September.

Tuesday 16th September

Mathematical Induction.
Reading: Pages 48-56 of Bostock.

Thursday 18th September

Expressive adequacey II.

Reading: Pages 56-62 of Bostock.
Exercises (3): 2.7.1, 2.8.1 , 2.8.2 Due Friday 19th September 26th September.

Tuesday 23rd September

No class.

Thursday 25th September

No class.

Tuesday 30th September

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

Thursday 2nd October

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 3rd October.

Tuesday 7th October

Review session for midterm

Thursday 9th October

Midterm exam in class.

Tuesday 14th October

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

Thursday 16th October

More principles of entailment.
Reading: Pages 96-108 of Bostock.
Exercises (5): 3.3.1, 3.3.4, 3.5.1 Due Friday 17th October. (HW 5 postponed by 1 week)

Tuesday 21st October

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

Thursday 23rd October

Decision procedures for monadic predicate formulas. Pages 115-126 of Bostock.
Exercises (5): 3.3.1, 3.3.4, 3.5.1 Due Friday 24th October.

Tuesday 28th October

Proofs and Counterexamples. Pages 131-138 of Bostock.

Thursday 30th October

Semantic tableaux I – proofs with truth-functors.
Reading: Pages 141-147 of Bostock.

Exercises (6): 3.6.3, 3.7.1, 3.7.2 Due Friday 31st October. (HW 7 postponed by one week.)

Tuesday 4th November

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

Thursday 6th 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 7th November.

Tuesday 11th November

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

Thursday 13th November

Axiomatic proofs II – Laws of negation. Truth-functional completeness.
Reading: Pages 208 – 220 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 14th November.

Tuesday 18th November

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

Thursday 20th November

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

Homework Exercises (8): 5.3.1, 5.3.2, 5.4.1 Due Friday 5th December.

Tuesday 25th November

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

Thursday 27th November – Thanksgiving

No Class – Thanksgiving break
No homework this week.

Tuesday 2nd December

Reserved for a make-up class, in case any of these topics take up more time than anticipated.

Thursday 4th December

Review class for final examination (December 17th 3.30-5.30pm.)


  • 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 dropbox on the side of the “turn-in” filing cabinet 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 discourage students from knocking on the door at 4pm when the 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 (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 approximately one 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 (Thursday 9th October) and 25% from the final exam, which will be held during the official exam period, on 17th December from 3.30-5.30pm. Please note that our final exam is scheduled quite late this year. If you decide to take this course, you will need to make sure that you are on campus for all 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 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 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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