Logic I (Phil 279)

Course Information

The course will introduce you to the semantics and proof-theory of first-order logic (FOL). We will learn how to “speak” the language of FOL, study the method of truth tables, become proficient in giving forma proofs, and learn how to construct and argue about first-order interpretations. These methods will enable you to answer, in particular cases, the questions that logic is primarily concerned with: When does something follow from something else? What are logical truths? Which arguments are logically valid? But the main payoff will be to get you to become comfortable with formal methods, and to use them to clarify and make precise logical relationships that are hard to understand or express otherwise. We will also look at some results and notions which are important for the applications of formal logic, such as the expressive power of truth-functional and first-order logic, as well as some important theorems relating semantics and proof theory (soundness, completeness). We will touch on applications of logic to philosophy, mathematics, and computer science.

Prerequisites

There are no prerequisites.

Course Objectives

By the end of the course, you should be able to …

  1. work with the formal languages of truth-functional and first-order logic, with the ability to translate natural language sentences into a formal language.
  2. use truth tables to evaluate sentences and arguments in truth-functional logic.
  3. understand the basic semantic concepts such as validity, entailment and logical equivalence, when they apply and how they can be used.
  4. construct correct derivations in a natural deduction system for truth-functional and first-order logic, with and without identity.
  5. use a proof system to determine whether or not a sentence is a logical truth, whether an argument is valid, and whether two formal sentences are equivalent.
  6. construct interpretations that make first-order sentences true or false and to show using them that arguments are invalid.
  7. appreciate some basic metatheoretic results, such as truth-functional completeness, and soundness and completeness of a natural deduction system for truth-functional logic.

Required Readings

The textbook

P.D. Magnus, et. al., forall x: Calgary. An Introduction to Formal Logic (Fall 2019 edition)

is required for this course. It will be made available electronically via D2L.

Assessment Components

Tests

There will be three in-class tests, on October 18, November 6, and December 6, each worth 15% of the final mark. Tests are closed book—no reference materials will be allowed during the tests. There will be no registrar-scheduled final exam.

Pre-class quizzes

There will be open-book quizzes covering the background readings for each week to be taken on D2L. There will be 10 quizzes in total. Quizzes will be available on D2L for seven days. There will be no quizzes due in the weeks of September 9 and December 2. Quizzes account for 5% of your final grade.

Problem sets

There will be 5 problem sets, each worth 10% of the final mark for a total of 50%. Problem sets are due by 12:00 noon on the following dates: September 27, October 11, October 25, November 8, and November 29. Problem sets may be submitted to the “Phil 279 L01” dropbox in the hallway outside SS 1253 or turned in at the beginning of class. Problem sets will not be accepted electronically.

Grade scheme

Each test, quiz, and problem set will be assigned a raw point score, which is then normalized to a score out of 100 points. The final score is then computed according to the percentages given above. The following table will be used to convert the final score to letter grades (the ranges include the lower score and exclude the upper, e.g., 64 earns a B, not a B–):

95–100A+80–85B+67–70C+55–60D+
90–95A75–80B64–67C50–55D
85–90A–70–75B–60–64C– < 50F

Course policies

Late policy

You may turn in one problem set by 12:00 noon on the Monday following the due date, no questions asked. Otherwise, problem sets will not normally be accepted after the deadlines unless special permission has been given by the instructor ahead of time. Failure to submit a problem set on time will normally result in a mark of zero. Students who cannot submit an assignment or a test due to medical reasons or other reasonable grounds should contact the instructor as soon as possible.

Checking your grades and reappraisals of work

University policies for reappraisal of term work and final grades apply (see the Calendar section “Reappraisal of Grades and Non-Disciplinary Academic Appeals”). In particular, term work will only be reappraised within 10 calendar days of the date you are advised of your marks. Please keep track of your assignments (make sure to pick them up in lecture or in office hours) and your marks (check them on D2L) and compare them with the graded work returned to you.

Peer Assisted Study Sessions

This course is supported by the PASS (Peer Assisted Study Sessions) program. PASS provides students with free, organized study groups facilitated by a student who has been successful in the course before. Attending PASS can help you build your understanding of course content as well as learn valuable study skills which will help you to succeed in the course. You will meet your PASS leader and receive more information in the first weeks of classes.