PHIL240: Introduction to Logic
Summer I 2022
Summer I 2022
Monday - Friday, 12:00pm-1:35pm, YMCA 113/114
Office: YMCA 423
Office Hours: by appointment
Language, Proof, and Logic by John Barwise and John Etchemendy
The textbook and software will be available in all computers in class, as well as most open-access computers on campus (e.g. in the library). You can buy an electronic copy of the textbook, which includes all software and a unique code for submitting assignments, online for $55 here. Make sure you keep the unique code with you (ideally somewhere in your phone) at all times during class. Once you associate an e-mail address with this key, you can only change the e-mail address once, so be sure to use the email address that you plan to use for all your school work, preferably your TAMU email address.
You will be graded on completion of in-class and homework assignments, and three (non-cumulative) exams. The grade breakdown will be:
Assignments: 25%
Midterm 1: 25%
Midterm 2: 25%
Final Exam: 25%
Assignments will be submitted either through the GradeGrinder software or, if needed to be done by hand (indicated by a pencil icon next to the specific exercise problem), a scan or picture of the solution will be submitted in Canvas. All assignments will be due by the beginning of next class.
This course introduces students to the tools and reasoning involved in deductive logic and inductive logic. It will give students practice in abstract reasoning and illuminate connections between concepts. The skills learned in this course will be applicable to any subject that uses reasoning in some way.
We will start with the basic concepts in first-order propositional logic, then move to using truth tables for determining validity and invalidity. Following this we will discuss methods of formal proofs and see how these methods are applied. We will then discuss quantification and predicate logic, and end with a section on probability.
Class time will be used for two purposes:
Lecture covering the main ideas and topics for that day, and
Practice in using and applying the ideas to exercises and problems.
Logic typically cannot be learned unless practiced, so much of class time will be devoted to working through problems together and talking through the concepts they demonstrate. You are strongly encouraged to work with a partner to complete the in-class assignments together.
Homework will be assigned based on what we accomplish during class time.
An Aggie does not lie, cheat, or steal, or tolerate those who do. http://aggiehonor.tamu.edu
Basic Logical Concepts
Tues, May 31
Reading: 1.1 - 1.4: Individual Constants, Predicate Symbols, Atomic Sentences, and General First-Order Languages
Assignment 1: 1.1-1.4, 1.10
June 1
Reading: 2.1 - 2.3: Valid and Sound Arguments, Methods of Proof, and Formal Proofs
Assignment 2: 2.2, 2.7, 2.8, 2.10-2.14
June 2
Reading: 2.4 - 2.5: Constructing Proofs in Fitch and Demonstrating Nonconsequence
Assignment 3: 2.15 (YTI), 2.17, 2.18, 2.19, 2.21 (YTI), 2.26
A video of the first "You Try It" exercise in 2.4.
A video of the second "You Try It" exercise in 2.4.
A video of the "You Try It" exercise in 2.5.
Boolean Logic
June 3
Reading: 3.1 - 3.3: Negation Symbol, Conjunction Symbol, and Disjunction Symbol
Assignment 4: 3.3, 3.7, 3.10, 3.13-3.15
Monday, June 6
Reading: 3.5 - 3.7: Ambiguity and Parentheses, Equivalent Ways of Saying Things, and Translation
Assignment 5: 3.12, 3.18, 3.20-3.22
June 7
Reading: 4.1 – 4.2: Tautologies and Logical Truth, and Logical and Tautological Equivalence
Assignment 6: 4.1 (YTI), 4.5, 4.7, 4.12-4.14, 4.17
A video of the "You Try It" exercise on Boole and truth tables in 4.1.
June 8
Reading: 4.3: Logical and Tautological Consequence
Assignment 7: 4.20, 4.22
A video of the "You Try It" exercise in 4.4.
June 9 Midterm I
Proofs
June 10
Reading: 5.1 – 5.3: Valid Inference Steps, Proof by Cases, and Indirect Proof: Proof by Contradiction
Assignment 8: 5.1, 5.5, 5.10, 5.16, 5.17
June 13
Reading: 6.1 – 6.3: Conjunction Rules, Disjunction Rules, and Negation Rules
Assignment 9: 6.1 (YTI), 6.4, 6.6, 6.7 (YTI), 6.9, 6.11, 6.13
A video of the Conjunction Elimination You Try It in section 6.1.
A video of the Conjunction Introduction You Try It in section 6.1.
A video of the Conjunction Elimination shortcut You Try It in section 6.1.
A video of the Fitch rule defaults You Try It in section 6.1.
June 14
Reading: 6.4; 7.1: The Proper Use of Subproofs, Material Conditional Symbol →, and Necessary and Sufficient Conditions
Assignment 10: 6.18, 6.19, 6.20, 6.21 (YTI), 7.1, 7.2, 7.5
June 15
Reading: 7.2: Biconditional Symbol ↔
Assignment 11: 7.11, 7.12, 7.13, 7.14
June 16
Reading: 8.1 – 8.2: Informal Methods of Proof, and Formal Rules of Proof for → and ↔
Assignment 12: 8.17 (YTI) -- 8.23
A video of the first conditional rules and subproof You Try It in section 8.2.
A video of the second conditional rules and subproof You Try It in section 8.2.
A video of the biconditional You Try It in section 8.2.
June 17: NO CLASS (Reading Day)
Mon, June 20
Reading: 8.4: Valid Arguments: Some Review Exercises; Proof Review
Assignment 13: 8.27, 8.48
June 21: Midterm 2
Quantification and Predicate Logic
June 22
Reading: 9.1 – 9.3: Variables and Atomic Wffs, The quantifier symbols ∀, ∃, and Wffs and Sentences
Assignment 14: 9.1, 9.2, 9.5
June 23
Reading: 9.5 – 9.6: The Four Aristotelian Forms, and Translating Complex Noun Phrases
Assignment 15: 9.8 (YTI), 9.9, 9.12, 9.15 (YTI), 9.18
A video of the You Try It exercise in 9.5 on Aristotelian form.
A video of the You Try It exercise in 9.6 on vacuously true sentences.
June 24
Reading: 10.1 – 10.2: Tautologies and Quantification, and First-order Validity and Consequence
Assignment 16: 10.1, 10.4, 10.15, 10.16
A video of the first You Try It exercise in 10.2 on consequence for quantification.
A video of the second You Try It exercise in 10.2 on tautological consequence.
Mon, June 27
Reading: 10.3: First-order Equivalence and DeMorgan's Laws
Assignment 17: 10.20, 10.22, 10.24, 10.25, 10.27, 10.29
June 28
Reading: 11.1 – 11.3: Multiple Uses of a Single Quantifier, Mixed Quantifiers, and The Step-by-Step Method of Translation
Assignment 18: 11.1 (YTI), 11.2, 11.4, 11.5, 11.6, 11.8 (YTI), 11.11, 11.16
A video of the You Try It exercise in 11.1 on variables and multiple uses of a single quantifier.
Methods of Proof for Quantifiers and Formal Proofs and Quantifiers
June 29
Reading: 12.1 - 12.2: Valid Quantifier Steps and The Method of Existential Instantiation
Assignment 19: 12.5, 12.6, 12.10
Reading: 13.1: Universal Quantifier Rules
Assignment 20: 13.1 (YTI), 13.2, 13.5, 13.7
A video of the first You Try It exercise in 13.1 on the universal quantifier rules for proofs.
A video of the second You Try It exercise in 13.1 on the universal quantifier rules for proofs.
June 30
Reading: 13.2: Existential Quantifier Rules
Assignment 21: 13.8, 13.10 (YTI), 13.11, 13.13, 13.16
A video of the You Try It exercise in 13.2 on the existential quantifier rules for proofs.
July 1 Probability
Reading: Probability and Inductive Logic by Kenny Easwaran
Disjunction: Power of Logic Web Tutor 10.4B
Conjunction/Conditional: Power of Logic Web Tutor 10.4C
Tues, July 5
Review for the Exam
Wed, July 6 Final Exam: 12:00pm - 1:30pm
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