Table of Contents

Preface

Chapter 1: Introduction
Logic
Valid arguments
Sound arguments
The plan of this book

Chapter 2: Syllogistic Logic
Easier translations
The star test
English arguments
Harder translations
Deriving conclusions
Venn diagrams
Idiomatic arguments
The Aristotelian view

Chapter 3: Basic Propositional Logic
Easier translations
Simple truth tables
Truth evaluations
Unknown evaluations
Complex truth tables
The truth-table test
The truth-assignment test
Harder translations
Idiomatic arguments
S-rules
I-rules
Combining S- and I-rules
Extended inferences
Logic gates and computers

Chapter 4: Propositional Proofs
Two sample proofs
Easier proofs
Easier refutations
Multiple assumptions
Harder proofs
Harder refutations
Other proof methods

Chapter 5: Basic Quantificational Logic
Easier translations
Easier proofs
Easier refutations
Harder translations
Harder proofs

Chapter 6: Relations and Identity
Identity translations
Identity proofs
Relational translations
Relational proofs
Definite descriptions

Chapter 7: Basic Modal Logic
Translations
Proofs
Refutations

Chapter 8: Further Modal Systems
Galactic travel
Quantified translations
Quantified proofs
A sophisticated system

Chapter 9: Deontic and Imperative Logic
Imperative translations
Imperative proofs
Deontic translations
Deontic proofs

Chapter 10: Belief Logic
Belief translations
Belief proofs
Believing and willing
Willing proofs
Rationality translations
Rationality proofs
A sophisticated system

Chapter 11: A Formalized Ethical Theory
Practical rationality
Consistency
The golden rule
Starting the GR proof
GR logical machinery
The symbolic GR proof

Chapter 12: Metalogic
Metalogical questions
Symbols
Soundness
Completeness
Corollaries
An axiomatic system
Gödel's theorem

Chapter 13: Inductive Reasoning
The statistical syllogism
Probability calculations
Philosophical questions
Reasoning from a sample
Analogical reasoning
Analogy and other minds
Mill's methods
Scientific laws
Problems with induction

Chapter 14: Meaning and Definitions
Logic and meaning
Uses of language
Lexical definitions
Stipulative definitions
Explaining meaning
Making distinctions
Analytic and synthetic
A priori and a posteriori

Chapter 15: Fallacies and Argumentation
Good arguments
Informal fallacies
Inconsistency
Constructing arguments
Analyzing arguments

Appendix: LogiCola Software

Answers to Selected Problems

Glossary

Index of Names