Introduction to Propositional Logic
This is a free course I have made available through my YouTube channel. The textbook I use is Nicholas J. J. Smith's Logic: The Laws of Truth.
Read 1.1 What is logic? (pp. 3-4)
What is logic? How is it different from good reasoning?
Read 1.2 Propositions (p. 5-6)
What is a proposition? What is truth?
Do 1.2.1 Exercises (p. 6)
Can you tell which one is a proposition?
Optional: Read 1.2.2 Sentences, Contexts, and Propositions (pp. 6-8)
Optional: What is the difference between a type and a token?
Optional: Read 1.2.2 Sentences, Contexts, and Propositions (pp. 8-10)
Optional: Is a proposition a sentence type? A sentence token?
Optional: Read 1.2.2 Sentences, Contexts, and Propositions (pp. 10-11)
Optional: What elements make up our communication?
Read 1.3 Arguments (pp. 11-13)
What is a logical argument? Why is it useful?
Do 1.3.1 Exercises (pp. 13-14)
Can you identify the argument?
Read 1.4 Logical Consequence (pp.14-21)
What is a logical consequence? What is validity?
Read 1.4 Logical Consequence (pp. 19-21)
Do 1.4.1 Exercises (p. 21)
Can you tell a valid argument from an invalid one?
Read 1.5 Soundness (pp. 21-23)
What is a sound argument? How is it different from a valid argument? Or a true argument?
Do 1.5.1 Exercises (p. 23)
Can you tell the difference between a valid argument and a true one?
Read 1.6 (pp. 23-24)
What is a connective? What is 'truth-functional'?
Read 1.6.1 Negation (pp. 24-26)
Do 1.6.1.1 Exercises (p. 26)
Can you tell what has been negated?
Read 1.6.2 Conjunctions (pp. 26-27)
Do 1.6.2.1 Exercises (p. 27)
Can you discern the two claims of a conjunction?
Read 1.6.3 Disjunction (pp. 27-28)
Read 1.6.4 Conditional (pp. 28-29)
Do 1.6.4.1 Exercises (p. 29)
Can you identify the antecedent and consequent?
Read 1.6.5 Biconditional (pp. 30-31)
Do 1.6.6 Exercises (p. 31)
Read 2.1 Motivation (p. 32)
Why make logic full of weird symbols and formulas?
Read 2.2 Basic Propositions of PL - 2.2.1 Glossaries (pp. 32-35)
How do I symbolize basic propositions? Sentence letters
Read 2.3.1 Negation - 2.3.2 Conjunction
Do 2.3.3 Exercises (pp.36-37)
How do I symbolize negation and conjunction?
Read 2.3.4 Disjunction
Do 2.3.5 Exercises (pp. 36-37)
How do I symbolize a disjunction?
Read 2.3.6 Conditional, 2.3.7 Biconditional
Do 2.3.5 Exercises
Read 2.3.9 Review (pp. 37-39)
How do I symbolize conditionals and biconditionals?
Read 2.4 Wff Variables, 2.5 Syntax of PL (pp. 39-42)
Do 2.5.1 Exercises Question 1 (p. 42)
What is a well-formed formula (WFF)?
Do 2.5.1 Exercises Question 2 (p. 42)
What is a recursive definition?
Read 2.5.2 Logical and Nonlogical Vocabulary
Logical v. non-logical v. auxiliary symbols?
Read 2.5.3 Constructing Wffs; do 2.5.3.1 Exercises (pp. 42-44)
How do I construct WFFs? How can I tell which is the main connective?
Read 2.5.4 Abbreviations, Do 2.5.4.1 Exercises (pp. 44-47)
Read 2.5.5 Polish Notation; Do 2.5.5.1 Exercises (pp. 47-48)
Read 2.5.6 Finite Alphabets (p.48)
Read the first two paragraphs of Chapter 3 (p. 49)
What is the Principle of Bivalence?
Read 3.1 Truth Tables for the Connectives
Read 3.2 Truth Values of Complex Propositions
Do 3.2.1 Exercises
What's the truth value of complex propositions?
Read 3.3 Truth Tables for Complex Propositions
Do 3.3.1 Exercises
Truth Tables for Complex Propositions
Read 3.4 Truth Tables for Multiple Propositions
Do 3.4.1 Exercises
Truth Tables for Multiple Propositions
Read 3.5 Connectives and Truth Functions
Do 3.5.1 Exercises
What is a truth-functional connective?
Read 4.1 Arguments & sub-sections
Read 4.1 Arguments, 4.1.1 Counterexamples, 4.1.3 Soundness
Do 4.1.2 Exercises
Truth Tables and Valid Arguments
Read 4.2 Single Propositions
Do 4.2.1 Exercises
What is a tautology? A contradiction?
Read 4.3 TwoPropositions
Do 4.3.1 Exercises
Contraries, Contradictories, Equivalences, and Joint Satisfiability
Read 4.3.2 More Abbreviations
Why ∧ and ∨ Strings Are Okay, but Not → or ↔︎
4.4 Sets of Propositions
Do 4.4.1 Exercises
Satisfiable Sets of Propositions
Read 4.5 More on Validity
Read 5, 5.1 Abstracting from Content
Do 5.1.1 Exercises
What is the form of an argument (and why should I care)?
Read 5.2 Instances: From Forms to Propositions
Do 5.2.1 Exercises
What is an instance of a form?
Read 5.3 Argument Forms
Do 5.3.1 Exercises
What is the form of an argument?
Read 5.4 Validity and Form, 5.5 Invalidity and Form
Do 5.4.1 and 5.5.1 Exercises
How validity isn't the same for argument forms
Read 5.6 Notable Argument Forms
Modus Ponens, Affirming the Consequent, Modus Tollens, Denying the Antecedent
Read 5.7 Other Logical Properties
Read 6.1 Assertibility and Implicature
What is Conversational Implicature?
Read 6.2 6.2 Conjunction
Ands that Aren't Conjunctions?
Read 6.3.1 Indicative and Counterfactual Conditionals
Counterfactual vs. Material Conditionals
Read 6.3.2 Indicative and Material Conditionals
Is the indicative conditional the same as the material conditional?
Read 6.3.3 Conditional and Biconditional without "If"
Read 6.3.4 "If" without Conditional
Read 6.4 Disjunction
Read 6.5 Negation
Do 6.5.1 Exercises
Read 6.6 Functional Completeness
Defining connectives with other connectives
Read 6.6.2 The Range of Possible Connectives
Read 6.6.2 The Range of Possible Connectives
Functionally Complete Sets of Connectives
Do 6.6.3 Exercises
How can we tell if a set of connectives is functionally complete?
Read 7 Trees for Propositional Logic, 7.1 Tree Rules, 7.2 Applying the Rules
Read 7.3.1 Validity
Do 7.3.1.1 Exercises
Read 7.3.2 Satisfiability
Do 7.3.2.1 Exercises
Satisfiability with Truth Trees
Read 7.3.3 Contraries and Contradictories
Do 7.3.3.1 Exercises
Contraries and Contradictories with Truth Trees
Read 7.3.4 Tautologies
Do 7.3.4.1 Exercises
Read 7.3.5 Equivalences
Do 7.3.5.1 Exercises
Read 7.3.6 Summary
Read 7.4 Abbreviations
Material Fallacies
Material (informal) fallacies of reasoning are not errors in the structure of an argument, but in what is assumed.Â