PHIL 320 – Spring 2024 – Professor Matthew J. Brown
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, sentential and quantified logics, formal semantics and models, and logical proofs.
Student Learning Objectives
Upon successful completion of this course, students will:
- Determine the logical structure of English arguments by identifying premises and conclusions.
- Understand basic concepts in logic, such as truth functionality, validity, soundness, counter-examples, tautology, self-contradiction, logical equivalence, logical contradictoriness, and logical consistency.
- Translate English statements into Sentential Logic (propositional notation) and vice versa.
- Translate English statements into Quantified Logic (predicate notation) and vice versa.
- Determine the validity of symbolic logical arguments in SL using (a) truth tables and (b) natural deduction.
- Determine the validity of symbolic logical arguments in QL using (a) models and (b) natural deduction.
Textbook
P.D. Magnus, forall x: An Introduction to Formal Logic (Order Print on Demand) (Download for Free)
Schedule of Readings and Assignments
This course is self-based and mastery-based rather than organized according to a 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
- Consider joining the class Discord server
- 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 3)
- Available starting January 29
- Read Chapter 2, section 1-2
- Lecture 2: Sentence Letters & Connectives
- Practice Exercises 2.A-C
- Read Chapter 2, section 3
- Lecture 3: SL Symbolization
- Practice Exercises 2.D-F
- Read Chapter 2, section 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 5a)
- Available starting Feb 12
- Read Chapter 3
- Lecture 5: Truth Tables
- Practice Exercises 3.A-C
- Lecture 6: Truth Tables 2
- Practice Exercises 3.D-F
- Exam 3: Sentential Logic – Truth Tables
Unit 4: Proofs in Sentential Logic
- (SLO 5b)
- Available starting Feb 26
- Lecture 7: The Concept of Proof, SL Basic Rules, Direct Proof
- Read Chapter 6, section 1
- Lecture 8: SL Basic Rules, Indirect Proof
- Practice Exercises 6.A
- Read Chapter 6, section 2-3
- Lecture 9: Derived Rules, Replacement
- Practice Exercises 6.B-C
- Read Chapter 6, section 6-7
- Lecture 10: Proof strategy
- Practice Exercises 6.D-F
- Exam 4: Sentential Logic – Proofs
Unit 5: Quantified Logic: Syntax and Symbolization
- (SLO 4)
- Available starting March 18
- Read Chapter 4, section 1-4
- Lecture 11: Quantified Logic – Basics and Symbolization
- Practice Exercises 4.A-D
- Read Chapter 4, section 5
- Lecture 12: Well-Formed Formulae of QL
- Practice Exercises 4.E-G
- Read Chapter 4, section 6
- Lecture 13: Identity in QL
- Practice Exercises 4.H-K
- Exam 5: Quantified Logic – Symbolization
Unit 6: Formal Semantics
- (SLO 6a)
- Available starting April 1
- Read Chapter 5, section 1-2
- Lecture 14: Formal Semantics in SL and QL
- Practice Exercises 5.A-C
- Read Chapter 5, section 3-5
- Lecture 15: 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, section 4
- Lecture 16 Proofs in Quantified Logic
- Practice Exercises 6.H-I
- Lecture 17: Translations and Proofs
- Practice Exercises 6.J-M
- Read Chapter 6, section 8-9
- Lecture 18: 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.
More Resources
Use the following resources as study aids and sources for additional practice problems. Keep in mind that not all textbooks will use the exact same conventions or notations we do, so you’ll have to do a little translating.
- TAUT – randomly-generated, self-correcting logic excercises
- Natural deduction proof editor and checker
- An Exposition of Symbolic Logic by Terrence Parsons
- Logic 2010 – An automated program that goes with the Parsons book. You can use the Demo version to get practice problems for Symbolization, Truth Tables, and Proofs
- There are different versions of forall x with slightly different explanations and extra practice problems:
- Lorain County Remix
- Calgary Remix
- Cambridge Edition
- SLU Edition
- Adelaide
- I have not checked all of these versions to see how different they are from one another
- The Carnap Book
- Symbolic Logic: A First Course by Gary Hardegree
- Paul Teller, A Modern Formal Logic Primer
- Ian Barland, et al. Intro to Logic
- Kevin Klement’s Interactive Lecture Notes and Practice Exercises
- Old Oxford Intro to Logic Page
- Support Page for The Logic Manual
- UCSD Logic Course Materials by Rick Grush
- Rick Grush Logic YouTube Channel
- Logic Primer by Colin Allen and Michael Hand
- Logic Daemon – check truth-tables, models, and Suppes-Lemmon derivations, and generate quizzes
- Gateway to Logic
- Logic and Proofs – Free online course by Carnegie Mellon University
- The Many Worlds of Logic
- WikiBooks Formal Logic
- Open Logic Project
- Some of the best commercial textbooks on logic are the ones by Gensler, Copi, and Hurley. They’re all somewhat expensive.
- The UTD Library has several intro to logic textbooks in its collection, including Copi and Genesereth.
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, Teams, and Discord as well as in person. 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.
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. You are permitted to discuss Practice Exercises with other students, but you must complete the work yourself. You are not under any circumstances to discuss the content of exams with other students or to work together on any exams.
The sanction for any form of cheating in this course will be a failing grade for the course and a referral for academic misconduct.