Gillian Russell

Philosophy Professor

Phil 155: Introduction to Mathematical Logic : Fall 2018

Class Times: Mondays, Wednesdays and Fridays
Lecture: Mondays and Wednesdays 9.05–9.55am, Gardner 0008
Recitation: Fridays, at your assigned time and location.
Course Website:
Website for the Language, Proof, and Logic textbook:

The textbook is available from the campus bookstore, and from the usual online bookstores as well. You can also purchase an e-version of the book from the LPL website.

You will need to buy a new copy of the book because it comes with a unique registration ID which you will need for submitting your homework.

Website for the Grade Grinder:

Course Instructor:

  • Professor Gillian Russell
  • Office hours: Mondays 10am-11am, Fridays 1-2pm.
  • Office Location: Caldwell Hall, 203
  • Email: gillian UNDERSCORE russell AT unc DOT edu

Teaching Assistants (TAs):

  • Aliosha Barranco Lopez
  • Office Hours: Mondays 10-11:00am and Tuesdays 3:35-4:35pm.
  • Office Location: Caldwell 12B
  • Email: aliosha AT live DOT unc DOT edu
  • Joseph Porter
  • Office Hours: Tuesdays 3-4pm and Fridays 10-11am
  • Office Location: Caldwell 107C
  • Email: jjporter AT live DOT unc DOT edu

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. In more detail: we will study the semantics and proof theory for both truth-functional logic, and for 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 campus bookstore, or via an online bookseller) or download a virtual copy of the book from the book’s website:
  • Either way, you must by a new copy of the 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.

Course Timetable and Readings

  • 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 August 22nd: 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 27th August: Chapter 1 : Atomic Sentences

  • Wednesday 29th August: Chapter 2 : The Logic of Atomic Sentences

Week 3

  • Monday 3rd September: NO CLASS – Labor Day

  • Wednesday 5th September: Chapter 3 : The Boolean Connectives – including section 3.8

Week 4

  • Monday 10th September: Chapter 4 : The Logic of Boolean Connectives – including sections 4.5 and 4.6

  • Wednesday 12th September: Chapter 5 : Methods of Proof for Boolean Logic Hurricane Disruption!

Week 5

  • Monday 17th September: Chapter 6 : Formal Proofs and Boolean Logic – including section 6.6 Hurricane Disruption! The syllabus from this point on has been reorganised in the wake of Hurricane Florence.

  • Wednesday 19th September: Normal forms (NNF and DNF) from Chapter 4.

Week 6

  • Monday 24th September: More on Normal forms. Reading: Chapters 5 and 6: Methods of Proof for Boolean Logic

  • Wednesday 26th September: NO CLASS Review class taught by Joseph Porter!

Week 7

  • Monday 1st October: Formal proofs (Ch.6 – no new reading)

  • Wednesday 3rd October: Formal proofs

Week 8

  • Monday 8th October: More on formal proofs

  • Wednesday 10th October: Review Session ahead of Midterm Exam

Week 9

  • Monday 15th October: In Class Midterm Examination

  • Wednesday 17th October: Chapter 7: Conditionals

Week 10

  • Monday 22th October: Chapter 8 (including 8.3): The Logic of Conditionals

  • Wednesday 24th October: More on the Logic of Conditionals (no new reading)

Week 11

  • Monday 29th October: Chapter 9: Introduction to Quantifiers.

  • Wednesday 31st October: Chapter 10: The Logic of Quantifiers

Week 12

  • Monday 5th November: Chapter 11: Multiple quantifiers

  • Wednesday 7th November: Chapter 12: Methods of Proof for Quantifiers

Week 13

  • Monday 12th November: Chapter 13: Formal Proofs and Quantifiers.

  • Wednesday November 14th: NO CLASS.

Week 14

  • Monday 19th November: More formal proofs with quantifiers. (no additional reading)

  • Wednesday 21st November: NO CLASS (Thanksgiving)

Week 15

  • Monday 26th November: Chapter 14: More about Quantification.

  • Wednesday 28th November: Chapter 15: First-Order Set Theory

Week 16

  • Monday 3rd December: What else is there in logic? (no reading)

  • Wednesday 5th December: Review Session for the Final Exam.


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. (If you send them to her by mistake, she will probably send you an email reminding you that this is not a way of submitting your homework. But she prefers it when she doesn’t have to do this.)

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

The work required to complete the problem sets will exceed the work required to complete 10 pages of writing.

Homework Assignments and Exams

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

Tuesday 4th September

Assignment One

Wednesday 19th September

Assignment Two

Monday October 8th

Assignment Three

Monday 29th October (note that this is after the midterm)


In class, Monday 15th October

Assignment Four

Monday 12th 19th November

Assignment Five

Wednesday 19th 26th 28th November

Assignment Six

Monday 3rd December


Saturday December 8th 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.)

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.

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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