Full Table Of Contents

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An Introduction To Reasoning

Cathal Woods

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Preface & Introductory Chapter (P&I)

PREFACE

1 Welcome

2 The Critical Reasoner

3 Overview

4 Request For Help

5 Thanks

6 Dedication

SOME EVERYDAY REASONING

1 Introduction

2 Reasoning Based On Properties

3 Part-Whole Relationships

4 Reasoning With Relations

5 The Tricky Verb 'To Be'

6 Reasoning With Categorical Generalizations

7 Mixing General & Specific Propositions

8 Reasoning With Conditionals

9 Elimination

10 Induction

11 Fallacious Reasoning & Degree Of Difficulty

12 Concluding Remarks & Summary*

Propositional & Categorical Reasoning (P&C)

CHAPTER 1 ENGLISH & LOGICALLY STRUCTURED ENGLISH

1.1 Validity*

1.2 Simple Propositions, Complex Propositions

1.3 Simple Propositions, Complex Propositions, Ambiguous Propositions

1.4 Some Extras On Negations, Disjunctions, & Conjunctions*

1.5 Some Extras On Conditionals*

CHAPTER 2 THE BIG 8 METHOD

2.1 Standard Form

2.2 The Big 8 Method

2.3 Matching The Antecedent

2.4 Matching The Consequent

2.5 Contradicting The Consequent

2.6 Contradicting The Antecedent*

2.7 Chain Inference

2.8 Constructive Dilemma, Destructive Dilemma

2.9 Elimination Inference

2.10 Summary*

2.11 A Summary Of Inference Patterns—The Big 8

CHAPTER 3 THE METHOD OF DERIVATION

3.1 Advantages Of The Method Of Derivation

3.2 Logically Structured Symbolic Propositions*

3.3 The Method Of Derivation & The Rules Of Inference*

3.4 The "Backwards" Strategy Of Derivation*

3.5 Three Additional Rules Of Inference*

3.6 Rules Of Equivalence**

3.7 Conditional Derivations & Indirect Derivations*

3.8 A Summary Of Rules—Method of Derivation

CHAPTER 4 THE TRUTH TABLE METHOD & THE TRUTH TREE METHOD

4.1 Advantages & Disadvantages Of The Truth Table & Truth Tree Methods

4.2 Truth Values & Truth Tables For The Logical Operators*

4.3 Setting Up Truth Tables

4.4 The Truth Table Method*

4.5 Logical Equivalence & Inequivalence, & Logical Contradiction*

4.6 Targeted Truth Tables*

4.7 The Truth Tree Method*

4.8 A Summary Of Truth Conditions—Truth Tables & Truth Trees

CHAPTER 5 THE VENN DIAGRAM METHOD

5.1 Categorical Generalizations

5.2 Some Extras On Categorical Generalizations

5.3 Venn Diagrams & Categorical Generalizations

5.4 Existential Commitment

5.5 Immediate Inferences, Categorical Syllogisms & The Venn Diagram Method*

A SUMMARY OF TERMINOLOGY & FORMS—PROPOSITIONAL & CATEGORICAL REASONING

Inductive & Scientific Reasoning (I&S)

CHAPTER 1 VALID, STRONG & WEAK INFERENCE

1.1 Valid, Strong & Weak Inference*

CHAPTER 2 GETTING CLEAR ABOUT "CAUSE"

2.1 Causation In Everyday Language

2.2 Causally Sufficient & Causally Necessary*

2.3 Inference To An Effect

2.4 Inference To A Cause*

2.5 A Summary Of Terminology & Forms—Sufficiency, Necessity, Causal Inferences

CHAPTER 3 ASSOCIATION & CAUSAL EXPLANATION

3.1 Association*

3.2 Cross-Tabulations & The Present-Present Fallacy*

3.3 Association & Causation

3.4 Contributing Factors As INUS Conditions*

3.5 Explanation

3.6 A Summary Of Terminology & Forms—Association, Causation, Explanation

CHAPTER 4 INDUCTION

4.1 Introduction

4.2 Inductive Generalization (IG)*

4.3 Instantiation Syllogism (IS)

4.4 Induction To A Particular (IP)

4.5 Distinguishing Between IG, IS & IP*

4.6 A Summary Of Forms—IG, IS, IP

APPENDIX TO CHAPTER 4 PROBLEMS IN INDUCTION

4A.1 The Problem Of Induction

4A.2 The New Riddle Of Induction

4A.3 The Lottery Paradox

CHAPTER 5 SCIENTIFIC REASONING

5.1 Introduction

5.2 Generation Of Hypotheses & Analogy*

5.3 Experimental Methods*

5.4 Inference To The Best Explanation (IBE)**

5.5 A Summary Of Terminology & Forms—AAn, IBE, "Best"

APPENDIX TO CHAPTER 5 MILL'S METHODS

1 Introduction

2 The Method Of Agreement

3 The Method Of Double Agreement

4 The Method Of Difference

5 The Method Of Concomitant Variation

6 The Methods & Strength*

7 Summary Of Forms—Mill's Methods

A SUMMARY OF TERMINOLOGY & FORMS—INDUCTIVE & SCIENTIFIC REASONING

Real World Reasoning (RW)

CHAPTER 1 CLASSIFYING & ANALYZING REASONING

1.1 Introduction

1.2 Reasoning, Arguing & Explaining

1.3 Identifying Reasoning Using Flag Words

1.4 The Relationship Between Arguing & Explaining*

1.5 Sentences & Propositions

1.6 Analysis—Things To Omit*

1.7 Summary—Recognizing & Classifying Reasoning

CHAPTER 2 DIFFICULTIES IN EVALUATING PREMISES

2.1 Two Criteria Of Evaluation*

2.2 Getting Clear On The Meaning*

2.3 Sources*

2.4 Appeal To Character Or Motives

2.5 Summary—Soundness, Sources, & Character

CHAPTER 3 DIFFICULTIES IN EVALUATING THE REASONING

3.1 Introduction

3.2 Avoid Giving Reasons

3.3 Promise Reasons

3.4 Repeat The Conclusion As A Reason*

3.5 Overstate The Strength Of The Reasoning*

3.6 Arguing With Emotional Reasons*

3.7 Summary—Reasoning Substitutes

CHAPTER 4 INCOMPLETE ARGUMENTS & EXPLANATIONS

4.1 Incomplete Arguments & Explanations

4.2 Warrants in Practical Arguments*

4.3 Warrants: Truth Vs. Strength

4.4 Sincerity & Charity*

4.5 Summary—Decision-Making

CHAPTER 5 DIAGRAMS & COMPLEX REASONING

5.1 Diagrams*

5.2 Reasoning With A Conjunction In The Target Proposition

5.3 Compound Reasoning

5.4 Objections*

5.5 Analyzing Long Passages

5.6 Analyzing Very Long Passages*

5.7 Evaluating The Various Reasoning Structures

5.8 Summary—Diagramming

A SUMMARY OF FORMS, TERMINOLOGY, ETC.—REAL-WORLD REASONING