Gillian Russell

Philosophy Professor

Phil 301 : Symbolic Logic (Spring 2010)

Class Times: Tuesdays and Thursdays, 11.30am-1pm
Location: Psychology Building 251
Course Website:

Instructor: Professor Gillian Russell
Office hours: Mondays 1-2pm or by appointment
Office Location: 209 Wilson Hall
Email: grussell – 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 already taken that introductory course, and for students who already have a strong background in mathematics.

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 spring break, we’ll go on to study four different styles of proof: tableaux, axiomatic, natural deduction and, time permitting, sequent calculus.


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

Homework exercises listed by a Thursday class (below) will be due the following Tuesday at 3.30pm (the office closes at 4pm and we try to discourage students from knocking on the door at 4.01pm when the staff are leaving to go home.) They may be turned in by placing them in the appropriate file in the "turn in" cabinet in the philosophy department office on the ground floor of Wilson Hall.

Solutions to most 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.

Tuesday 19th January – Introduction

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

Thursday 21st January

Semantics for truth-functional languages.

Reading: Pages 24-30 of Bostock.
Exercises (1): 2.1.1, 2.2.1, 2.3.1, 2.4.1(a), (c), (e), (g), (i), 2.4.2.

Tuesday 26th January

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

Thursday 28th January

Normal forms (DNF, PNF, etc.)
Pages 37-45 of Bostock.
Exercises (2): 2.5.1, 2.5.3, 2.6.1

Tuesday 2nd February

Expressive adequacey. Pages 45-48.

Thursday 4th January

Mathematical Induction.
Reading: Pages 48-56 of Bostock.
Exercises (3): 2.7.1, 2.8.1 , 2.8.2, 2.8.3.

Tuesday 9th February

Expressive adequacey II.

Reading: Pages 56-62 of Bostock.

Thursday 11th February

Duality and truth-value analysis.
Reading: Pages 62-69 of Bostock.
Exercises (4): 2.9.1, 2.9.2, 2.10.1, 2.11.1

Tuesday 16th February

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

Thursday 18th February

No class.

Tuesday 23rd February

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

Thursday 25th February

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

Exercises (5): 3.3.1, 3.3.4, 3.5.1

Tuesday 2nd March

Midterm preparation class

Thursday 4th March


Tuesday 9th March


Thursday 11th March


Tuesday 16th March

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

Thursday 18th March

Decision procedures for monadic predicates. Pages 115-126 of Bostock.
Exercises(6): 3.6.3, 3.7.1, 3.7.2

Tuesday 23th March

More decision procedures. Pages 126-131 of Bostock.
Proofs and Counterexamples. Pages 131-138 of Bostock.

Thursday 25th March

No class.

Exercises(6): 3.6.3, 3.7.1, 3.7.2

Tuesday 30th March

Semantic tableaux I – proofs.
Reading: Pages 141-165 of Bostock.

Tuesday 6th April

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

Thursday 8th April

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

Tuesday 13th April

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

Thursday 15th April

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

Homework Exercises (8): 5.3.1, 5.3.2, 5.4.1

Tuesday 20th April

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

Thursday 22nd April

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

Exercises (9): 5.6.1, 5.7.1, 6.1.1, 6.2.1

Tuesday 27th April

Sequent Calculus I – an introduction
Reading: Pages 273-282

Thursday 29th April

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

Preparation for final examination.

Final Examination:

Monday May 10, 2010 1:00 PM – 3:00 PM


50% of the grade for this course will come from the 10 sets of homework exercises completed during the semester. 25% will come from the in-class midterm exam on March 4th (the Thursday before spring break), and 25% from the final exam, which will be held during the official exam period on Monday 10th May from 1pm-3pm.

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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