lussell : Courses: Phil 301 http://wwvv.artsci .wustl .edu/~grusseil/Phil301-S 10.html

Phil 301 : Symbolic Logic (Spring 2010)

Class Times: Tuesdays and Thursdays, 1130am-lpmLocation: Psychology Building 251

Office hours: Tuesdays 5-6pm or by appointmentOffice Location: 209 Wilson Hall

Email: srussell - at - wustl - dot - edu

This course continues on where Phil 100: An introduction to Logic and Criticial Analysis leavesoff. It is recommended for students who have already taken that introductory course, and forstudents 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-orderclassical logics, and in particular we'll investigate the model theory for first-order logic in muchgreater depth than in Phil 100. After spring break, we'll go on to study four different styles ofproof: tableaux, axiomatic , natural deduction and, time permitting, sequent calculus.

BooksThe 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 handcopies are fine.

Readings , Topics and Homework AssignmentsHomework exercises listed by a Thursday class (below) will be due the following Tuesday at3.30pm (the office closes at 4pm and we try to discourage students from knocking on the door at4.01pm when the staff are leaving to go home.) They may be turned in by placing them in theappropriate file in the "turn in" cabinet in the philosophy department office on the ground floor ofWilson Hall.

Solutions to most problem sets will be given out in class. Any homework set received after thesolutions 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.

•illian Russell : Courses : Phil 301 http://www.artsci.wustl.edu/~grussell/Phil301-S10.html

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, 24.1(a), (c), (e), (g), (i), 2.4.2.

Tuesday 26th January

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

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

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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 FebruaryNo class.

Tuesday 23rd February

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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 MarchMidterm preparation class

Thursday 4th MarchTV /TTT--.rT->-r-^T-*1V X T^^t/" A 11 TT X 7 ATT/^XT ' 'TXT /"IT A OONivIiiji tJxJYi bAAMlfNAt 1UJN ijJN lla^oi

Tuesday 9th March

SPRING BREAK

Thursday 11th March

SPRING BREAK

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.

Tuesday 30th March

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

Gillian Russell : Courses : Phil 301 http://www.artsci. vvustl ,edu/~grussell/Phil301-S 10.html

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Semantic tableaux II - Soundness and Completeness.Readings: pages 164 - 189 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 6th April

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

Thursday 8th April

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

Homework Exercises (8): 53.1,532,5.4.1

Tuesday 13th April

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

Thursday 15th April

Natural deduction I - rules for the truth-functors.Reading: Pages 239 - 254 of Bostock.Exercises (9): 5.6.1, 5.7.1, 6.1.1,6.2.1

Tuesday 20th AprilNatural deduction II - rules for the quantifiers. Alternative proof styles.Reading: Pages 254-272.

Thursday 22nd April

Sequent Calculus I - an introductionReading: Pages 273-282

Exercises (10): 7.1.1

Tuesday 27thth April

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

Thursday 29th April

Preparation for final examination.

Gillian Russell: Courses : Phil 301 http://vvvvvv.artsci.vvustl.edu/~grussell/PhiI301-S10.html

Final Exampination: TBA (it will be during the official examperiod)

Assessment50% of the grade for this course will come from the 10 sets of homework exercises completedduring the semester. 25% will come from the in-class midterm exam on March 4th (the Thursdaybefore spring break), and 25% from the final exam, which will be held during the official examperiod.

Academic IntegrityIt is very important that you understand the rules for collaboration on this course. You may workwith 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 theexercises 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 youmake notes on another student's written solutions. You may not lend or copy digital or paperhomework 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 tothese rules, or whether it counts as misconduct, but it is your duty to ensure that ALL yourcollaborations are clearly permissible. One good way to do this is not to write anything down onpaper whilst investigating problems with other students: use a chalk board or white board to workout ideas, (or, if you use paper, dispose of the written solutions before you separate to write upyour individual homeworks alone.)

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

Pass/Fail OptionFor 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%.