Course Description

This course is an introduction to formal logic. Formal logic is the formal study of the structures of language, reasoning, inference, and proof. This course will focus on deductive logic, including formal analysis of statements and arguments, logical connectives, sentential and quantified logics, identity, formal semantics and models, and logical proofs.

Core Learning Outcomes (CLOs)

Quantitative Literacy
Knowledge of the Physical, Natural, and Cultural Worlds
Inquiry and Analysis
Critical Thinking

Student Learning Objectives (SLOs)

Upon successful completion of this course, students will:

Understand basic concepts in logic, such as truth functionality, validity, soundness, counter-examples, tautology, self-contradiction, logical equivalence, logical contradictoriness, and logical consistency. (CLOs 1, 2)
Determine the logical structure of English arguments by identifying premises and conclusions. (CLOs 2, 3, 4)
Translate English statements to and from (a) Sentential Logic (SL) and Quantified Logic (QL). (CLOs 1, 3)
Semantically evaluate statements and the validity of arguments (a) in SL using truth tables and (b) in QL using models. (CLOs 1, 2, 4)
Make derivations of valid symbolic logical arguments using natural deduction (a) in SL and (b) in QL. (CLOs 1, 4)

Textbook

P.D. Magnus, forall x: An Introduction to Formal Logic (Order Print on Demand) (Download for Free)

Carnap

You need to sign up for the class in Carnap via the link provided on D2L. Practice Exercises and some exam questions will be provided via Carnap.

Note: You need to access Carnap through D2L in a modern web browser on a computer, not on your phone. Some students have reported technical difficulties using Safari on Mac; if you encounter such problems, try using a different browser (Firefox, Chrome, etc.).

Schedule of Readings and Assignments

This course is self-paced and mastery-based rather than organized according to a weekly schedule. You are required to work through the material in order, by Unit. Once you watch the lectures and complete at least one practice exercise in each unit, the exam in that unit will unlock. Exams are mastery-based; satisfactory score on each exam is required before moving on to the next unit. (“Satisfactory” criteria will be specified for each exam. For most exams, it is 80% correct or better.)

If you do not achieve mastery on your first try on the exam, you will have to wait 48 hours and complete additional practice exercises to unlock re-takes.

Unit 0: Course Introduction: Read the Syllabus
Watch Lecture 0: Welcome and Introduction
Log in to Carnap
Practice Exam
Unit 1: Basic Concepts in Logic: (SLOs 1, 2)
Read Chapter 1
Lecture 1: Basic Concepts
Practice Exercises 1.A-D
Exam 1: Basic Concepts
Unit 2: Sentential Logic: Syntax and Symbolization: (SLO 3a)
Read Chapter 2, §§1-2
Lecture 2: Sentence Letters & Connectives
Practice Exercises 2.A-C
Read Chapter 2, §3
Lecture 3: SL Symbolization
Practice Exercises 2.D-F
Read Chapter 2, §4
Lecture 4: Well-Formed Formulae of SL
Practice Exercises 2.G-H
Exam 2: Sentential Logic – Symbolization
Unit 3: Truth Tables: Semantics of Sentential Logic: (SLO 4a)
Read Chapter 3
Lecture 5: Truth Tables
Practice Exercises 3.A-D
Lecture 6: Truth Tables 2
Practice Exercises 3.D-F
Exam 3: Sentential Logic – Truth Tables
Unit 4: Proofs in Sentential Logic: (SLO 5a)
Lecture 7: The Concept of Proof, SL Basic Rules, Direct Proof
Read Chapter 6, §1
Lecture 8: SL Basic Rules, Indirect Proof
Practice Exercises 6.A
Read Chapter 6, §§2-3
Lecture 9: Derived Rules, Replacement
Practice Exercises 6.B-C
Read Chapter 6, §§6-7
Lecture 10: Proof strategy
Practice Exercises 6.D-G
Exam 4: Sentential Logic – Proofs
Unit 5: Quantified Logic: Syntax and Symbolization: (SLO 3b)
Available starting March 18
Read Chapter 4, §§1-4
Lecture 11: Building Blocks of Quantified Logic
Practice Exercises 4.A-B
Lecture 12: Translation to QL
Practice Exercises 4.C-D
Read Chapter 4, §5
Lecture 13: Well-Formed Formulae of QL
Practice Exercises 4.E-G
Read Chapter 4, §6
Lecture 14: Identity in QL
Practice Exercises 4.H-K
Exam 5: Quantified Logic – Symbolization
Unit 6: Formal Semantics: (SLO 4b)
Available starting April 1
Read Chapter 5, §§1-2
Lecture 15: Formal Semantics in SL and QL
Practice Exercises 5.A-C
Read Chapter 5, §§3-5
Lecture 16: Formal Semantics using Models
Practice Exercises 5.D-J
Exam 6: Formal Semantics & Models
Unit 7: Proofs in Quantified Logic: (SLO 6b)
Available starting April 15
Read Chapter 6, §4
Lecture 17: Proofs in Quantified Logic
Practice Exercises 6.H-I
Lecture 18: Translations and Proofs
Practice Exercises 6.J-M
Read Chapter 6, §§8-9
Lecture 19: Proofs & Semantics
Practice Exercises 6.N-V
Exam 7: Quantified Logic – Proofs

Grading Policy

Grades will be determined as follows:

A:: Satisfactory Grade on all 7 Exams
A-:: Satisfactory Grade on Exams 1-6
B+:: Satisfactory Grade on Exams 1-5
Completion of at least one attempt on Exam 6
B:: Satisfactory Grade on Exams 1-5
B-:: Satisfactory Grade on Exams 1-4
Completion of at least one attempt on Exam 5
C+:: Satisfactory Grade on Exams 1-4
C:: Satisfactory Grade on Exams 1-3
Completion of at least one attempt on Exam 4
C-:: Satisfactory Grade on Exams 1-3
D:: Satisfactory Grade on Exams 1-2
F:: Failure to satisfy the criteria for grades A-D.

Course and Instructor Policies

Contacting the Instructor

I strongly encourage you to contact me if you have any questions that are not answered by the materials on D2L or if you find any errors in the online course materials. However, I expect that you will look carefully at the syllabus and at the materials on D2L before reaching out with a question. During my weekly office hours, I will be available to answer questions promptly by email, phone, and Teams as well as in person. I encourage you to come in or call on Teams to work problems together during those times. I will try to respond within one business day to any contact outside of those hours, but you should feel welcome to send a reminder after that, in case your message has slipped through the cracks.

Cheating and Plagiarism

Cheating consists of turning in someone else’s work as your own or collaborating on work that is meant to be individual. What counts as cheating depends on the type of assignment in question:

You are permitted to discuss and work together on Practice Exercise problems with the instructor, other students, or a tutor, though it is to your advantage to make sure you understand how to do that work.
You are not under any circumstances to discuss the content of exams with other students or to work together on any exams. You are not permitted to have someone take the exam on your behalf, to use solutions provided to you by someone else, or to use any form of AI/LLM or computer assistant not provided to you in the exam itself.

The sanction for any form of cheating in this course will be a failing grade for the course and a referral for academic misconduct.