# Short Videos on Logical Theory

#### Videos by Paul Herrick (Shoreline Community College) and Mark Storey (Bellevue College)

###### Our thanks to the Bill and Melinda Gates foundation, and to the Washington State Board for Technical and Community Colleges, for the grant they awarded us that helped us create these videos. Thanks also to Shoreline Community College videographer Dwight Edwards for filming and editing our demonstrations. These videos correspond to chapters in *Introduction to Logic* by Paul Herrick (Oxford University Press, 2012).

#### Table of Contents

## Fundamental Concepts of Logic

#### Welcome and Intro

Welcome to Logic Class and Introduction to the Series

#### What is Logic?

An overview of the discipline and what you’ll be studying.

#### What is an Argument?

An overview of the basic build blocks of logic

#### Arguments vs NonArguments

What makes an argument

#### What is a Deductive Argument?

The strongest argument you can make on the strongest argument you can make

#### What is an Inductive Argument?

Probably the most common type of argument.

#### What is a Valid Argument?

An overview of how arguments should (and shouldn’t) be structured.

#### What is a Deductively Sound Argument?

Valid + True = Sound

#### What is a Strong Argument?

There’s a high degree of probability that you’ll enjoy this video.

#### Inductively Sound or Cogent Arguments

Strong + True = Cogent

#### The Fundamental Concepts of Logic

Consistency, Inconsistency, Implication, Equivalence, Necessity, Contingency

#### Overview of the Fundamental Concepts of Logic

Argument, Deduction, Induction, Validity, Strength, Consistency, Inconsistency, Implication, Equivalence, Necessity, and so forth.

## Categorical Logic

#### Translating Categorical Sentences into Standard Form–1

#### Translating Categorical Sentences into Standard Form–2

.#### Constructing the Converse, Obverse, and Contrapositive of a Cat Sentence

#### Form of a Categorical Syllogism–1

#### Logical Form of a Categorical Syllogism–2

#### Constructing Venn Diagrams–1

#### Constructing Venn Diagrams–2

#### Aristotelian vs Boolean Standpoints

#### Constructing Venn Diagrams–3

#### More Venn Diagrams

#### Constructing Venn Diagrams–4

#### Constructing Venn Diagrams Yet Again

#### Venn Diagraming Unicorns

## Truth-Functional Logic

#### What is a “Truth-functional” Compound Sentence?

#### Argument Forms and Substitution Instances

#### Symbolizing Truth-functional Sentences -1

#### Alternative Truth-functional Symbols Used in Various Logic Texts

#### Symbolizing Truth functional Sentences–2

#### Symbolizing Truth-functional Sentences–3

#### Symbolizing Truth-functional Sentences –4

#### Symbolizing Truth-functional Sentences –5

#### Symbolizing Truth-functional Sentences –6

#### Truth table for “and”

#### Truth table for “or” (With “Thing”)

#### Truth table for “if then”

#### Calculating Truth-values Using the Replacement Method

#### Identifying the Main Connective

#### Truth table Analysis 1: Testing a Single Sentence for Logical Status

#### Truth table Analysis 2: Testing a Single Sentence for Logical Status

#### Truth table Analysis 3: Constructing 8-row Tables

#### Truth table Analysis 4: Testing an Argument for Validity

#### Truth table Analysis 5:Testing a Pair of Sentences for Equivalence

#### Argument Forms and Substitution Instances

#### Introducing the Inference Rules Modus Ponens (MP) and Modus Tollens (MT)

#### Proofs Using the First Four Inference Rules–MP, MT, DS, HS

#### Introducing the Second Four Inference Rules—Simp, Conj, Add, CD

#### The Constructive Dilemma Rule (CD)

#### Proofs Using the Second Four Inference Rules-1

#### Proofs Using the Second Four Inference Rules-2

#### Proofs Using the Second Four Inference Rules-3

#### Proofs Using the Second Four Inference Rules-4

#### Proofs Using the Second Four Inference Rules-5

#### Common Errors Made in Truth-functional Proofs-1

#### Common Errors Made in Truth-functional Proofs-2

#### Replacement Rules 1—Comm, Assoc

#### Replacement Rules 2—Double Negation

#### Replacement Rules 3–DeMorgan

#### Replacement Rules–Distribution

#### Replacement Rules–Implication

#### Replacement rules–Tautology

#### Extra Replacement Rule Proofs–1

#### Extra Replacement Rule Proofs–2

#### Indirect Proof Explanation–1

#### Indirect Proof Explanation–2

#### Indirect Proof Demo

#### Indirect Proof Explanation–3

#### Indirect Proof in Math

#### Introducing Conditional Proof

#### Conditional Proof Once More

#### Intro to Nested Proofs

#### Nested Conditional Proof

#### More Nested Proofs

#### Premise–free Proofs–1

#### Premise-free Proofs-2

## Predicate Logic

#### Predicate Logic Intro to Translations –1

#### Predicate Logic Translations Introduction– 2

#### Translating Existentials

#### Translating Exceptives–1

#### Translating Exceptives–2

#### Translating Dyadic Predicates and Overlapping Quantifiers

#### Calculating Truth-values Using the Replacement Method

#### Identifying the Main Connective

#### Calculating Truth-values Using the Replacement Method

#### Main Connectives in Predicate Logic

#### Two Meanings of Identity

#### Predicate Proofs–1–UI and EG

#### Predicate Proofs–2

#### Predicate Proofs–3

#### Predicate Proofs–4

#### Predicate Logic Interpretations

#### Predicate Proofs with Overlapping Quantifiers

#### Premise-free Predicate Proofs

#### Predicate Proofs with Identity–1

#### Predicate Proofs with Identity–2

#### Common errors in Predicate Logic Proofs

## Informal and Inductive Logic

#### Definitions–1

#### Definitions–2

#### Definitions–3

#### Informal Fallacies–1

#### Informal Fallacies–2

#### Analogical Arguments

#### Enumerative Induction

#### More on Analogical induction and Enumerative Induction

#### Logic of Science

#### Hypothetical Reasoning

#### “Inference to the Best Explanation”

#### Inference to the Best Explanation Again

#### Very Elementary Probability Theory

## Modal Logic

#### Very Elementary Modal Logic