Gillian Russell

Philosophy Professor

Phil 155 Introduction to Mathemantical Logic (Fall 2016)

Class Times: M/W/F
Lecture M/W 10.10-11am, Manning 209
Recitation Fridays
Course Website:
Website for the Grade Grinder:

Course Instructor:

  • Professor Gillian Russell
  • Office hours: Monday 11am-noon, Tuesday noon-1pm.
  • Office Location: Caldwell Hall, 203
  • Email: gillian UNDERSCORE russell AT unc DOT edu

Teaching Assistants (TAs):

  • Phil Bold, Email: philbold AT live DOT unc DOT edu
  • Office Hours: Tuesdays 4-5pm, Thursdays at 10-11am
  • Office Location: Caldwell 206C
  • Joanna Lawson,
    • Email: jrlawson AT live DOT unc DOT edu
    • Office Hours: Monday 2-3pm, Tuesday 1-2pm
    • Office Location: Caldwell 210C
  • Francesco Nappo
    • Email: fn7 AT live DOT unc DOT edu
    • Office Hours: Monday 2-3pm and Wednesday 11-12am
    • Office Location: Caldwell 107C

    Final Exam: Friday December 16th at 8am in our usual room. If you decide to take this course you need to make sure that you will be on campus for the exam.

    Course Description:

    This course is an introduction to formal logic for students who have no previous experience with the subject. Logic is the study of arguments and their properties, where an argument is a set of statements, one of which is supposed to follow from, or be supported by, the others, as in:

    All men are mortal. All women are immortal Some men are mortal.
    Socrates is a man. Professor Russell is a woman. Socrates is a man.
    Therefore, Socrates is mortal. Therefore, Professor Russell is immortal. Therefore, Socrates is mortal.

    In logic we are interested in characterising what makes an argument a good argument, and our methods for doing this will look rather mathematical. We will study the semantics and proof theory for truth-functional logic and first order predicate logic with quantifiers, concluding with soundness and completeness proofs. (By the end of the course you will know what that last sentence means.)


    • The book we will use is Language, Proof and Logic, 2nd Edition, by Barwise and Etchemendy. You can either buy the physical book (e.g. in the bookstore, or via Amazon) or download a virtual copy of the book from the book’s website: The virtual version of the book is slightly cheaper.
    • Either way, you must by a new copy of this book, and take good care of your registration ID. Don’t lose it and don’t share it with others; keep it secret.
    • The book comes with 4 software packages, which you can use to practice problems and get feedback. Many homework questions also require the software.
    • You will need your own unique registration ID in order to submit your homework. (If you were to rent a copy of the book, or buy someone else’s old copy, your registration ID might already have been taken by someone else and you would get into trouble with the anti-plagiarism part of the Grade Grinder software!)
    • A new copy of this book is the only purchase you will need to make for this course.

    Deadlines, Reading Assignments, Homework, Exams etc.

    • Readings marked (LPL) are in the course textbook (Language, Proof, and Logic)
    • Sections marked “optional” on the book’s content’s page are not required reading unless I explicitly say that they are to be read (below or in class.)

    Week 1

    • Wednesday 24th August: Introduction (LPL) and the Software Manual (on the LPL cd and downloadable from the website)

    Use this week to familiarize yourself with the computer software, sorting out technical problems so that you know what you are doing when it is time to submit the first graded homework assignment. There will be a practice assignment and you should complete this and submit it to your TA as a way of familiarising yourself with the process.

    Week 2

    • Monday 29th August: Chapter 1 : Atomic Sentences
    • Wednesday 31st August: Chapter 2 : The Logic of Atomic Sentences

    Week 3

    • Monday 5th September: NO CLASS – Labor Day
    • Wednesday 7th September: Chapter 3 : The Boolean Connectives – including section 3.8

    Week 4

    • Monday 12th September: Chapter 4 : The Logic of Boolean Connectives – including sections 4.5 and 4.6
    • Wednesday 14th September: Chapter 5 : Methods of Proof for Boolean Logic

    Week 5

    • Monday 19th September: Chapter 6 : Formal Proofs and Boolean Logic – including section 6.6
    • Wednesday 21st September: Chapter 7 – Conditionals

    Week 6

    • Monday 26th September: Chapter 8 (including 8.3): The Logic of Conditionals, Soundness
    • Wednesday 28th September: Conditionals Review session (no new reading)

    Week 7

    • Monday 3rd October: The Logic of Conditionals In Class Midterm Examination
    • Wednesday 5th October: NO CLASS

    Week 8

    • Monday 10th October: Review Session Chapter 9 : Introduction to Quantifiers
    • Wednesday 12th October: In Class Midterm Chapter 10 : The Logic of Quantifiers

    Week 9

    • Monday 17th October: Chapter 9: Introduction to Quantifiers.
    • Wednesday 19th October: Chapter 10: The Logic of Quantifiers

    Week 10

    • Monday 24th October: Chapter 11: Multiple quantifiers
    • Wednesday 26th October: Chapter 12: Methods of Proof for Quantifiers

    Week 11

    • Monday 31st October: Chapter 13: Formal Proofs and Quantifiers.
    • Wednesday 2nd November: More formal proofs with quantifiers. (no additional reading)

    Week 12

    • Monday 7th November: Chapter 14: More about Quantification.
    • Wednesday 9th November: Even more about quantifiers (no additional reading)

    Week 13

    • Monday 14th November: Chapter 15: First Order Set Theory
    • Wednesday November 16th: NO CLASS.

    Week 14

    • Monday 21st November: Chapter 16: Mathematical Induction
    • Wednesday 23rd November: NO CLASS (Thanksgiving)

    Week 15

    • Monday 28th November: Chapter 17: Advanced Topics in Propositional Logic Chapter
    • Wednesday 30th November: Chapter 18: Advanced Topics in FOL (18.1-18.3 only)

    Week 16

    • Monday 5th December: Chapter 19: Soundness and Completeness
    • Wednesday 7th December: More Completeness and Review


    The subject is largely mathematical in nature and assessment in this course will be by way of 6 problem sets to be done at home (60%), and the midterm (20%) and final (20%) examinations. Problem sets are to be turned in to your TA, not to Professor Russell.

    Problems sets for this course are downloadable as .pdf files from the table below.

    Policy on Late Work

    Late work will incur a penalty at a rate of 20 percent of the total possible grade every 24 hours.

    Honor Code

    All students must be familiar with and abide by the Honor Code, which covers issues such as plagiarism, falsification, unauthorized assistance or collaboration, cheating, and other grievous acts of academic dishonesty. Violations of the Honor Code will not be taken lightly.

    It is very important that you understand the rules for collaboration on this course. You may work with other students in order to solve the problems in your take-home problem sets, in fact, this is encouraged. However each student must write up his or her own solutions alone. You may not do it with another student looking over your shoulder to correct you. You may not do this 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 take any written notes whilst working 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.

    N.B. Please note that the Grade Grinder incorporates a sophisticated mechanism for detecting copied files (the “timestamp” method) and I recommend that you read about it on the LPL website and in the LPL book. In past incarnations of this course, students have been caught borrowing and copying files and when the matter was brought to the attention of the academic integrity committee at their university, hearings were held and they were found guilty. They all failed the course and one student was obliged to leave the university. I hope not to have to go through that process here with any of you, (or indeed, ever again) but in the interests of protecting the integrity of the course and its grades, I am committed to reporting any and all cases of academic misconduct.

    Homework Assignments

    There will be one practice and six regular homework assignments during the semester. The assignments may be downloaded from this table. Handwritten parts to be “turned in” go in your TA’s mailbox in the philosophy department mailroom in Caldwell Hall by 3.30pm on the day they are due. Files to be submitted via the Grade Grinder should be sent to your TA (not to Professor Russell) before midnight, so please make sure that you have entered the right email address in the Submit application. (You can find your TA’s email at the top of this syllabus.)



    Practice assignment

    Friday 2nd September

    Assignment One

    Friday 16th September

    Assignment Two

    Friday 30th September Friday 23rd September

    Assignment Three

    Friday 7th October Friday 30th September


    Wednesday 12th October, 2016, in class.

    Assignment Four

    Friday 28th October

    Assignment Five

    Friday 11th November

    Assignment Six

    Friday 25th November Friday December 2nd


    Friday December 16th at 8am in our usual room.

    (If you want to take this course, you will need to make sure you are still on campus then.)

    The Center for Student Success and Academic Counselling

    Located in the Student Academic Services Building, the CSSAC offers support to all students through units such as the Learning Center and the Writing Center.

    Reasonable Accommodations Policy

    Any student in this course who has a disability that may prevent them from fully demonstrating their abilities should contact Disability Services as soon as possible to discuss accommodations.

    Related Links

    The website for the book is here:

    Richard Zach’s guide to the LPL celebrities: Who are Fitch, Boole and Tarski?

    Greg Restall’s Great Moments in Logic

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