List of Figures | p. xi |

Preface | p. xii |

Acknowledgements | p. xvi |

How to Think Logically | p. 1 |

Validity and Soundness | p. 2 |

Deduction and Induction | p. 7 |

The Hardness of the Logical 'Must' | p. 9 |

Formal Logic and Formal Validity | p. 10 |

Identifying Logical Form | p. 14 |

Invalidity | p. 17 |

The Value of Formal Logic | p. 19 |

A Brief Note on the History of Formal Logic | p. 23 |

How to Prove that You Can Argue Logically #1 | p. 31 |

A Formal Language for Formal Logic | p. 32 |

The Formal Language PL | p. 34 |

Arguments and Sequents | p. 42 |

Proof and the Rules of Natural Deduction | p. 47 |

Defining: 'Proof-in-PL' | p. 52 |

Conditionals 1: MP | p. 53 |

Conditionals 2: CP | p. 56 |

Augmentation: Conditional Proof for Exam Purposes | p. 63 |

Theorems | p. 65 |

The Biconditional | p. 66 |

Entailment and Material Implication | p. 69 |

How to Prove that You Can Argue Logically #2 | p. 73 |

Conditionals Again | p. 74 |

Conditionals, Negation and Double Negation | p. 77 |

Introducing Disjunction | p. 82 |

vElimination | p. 86 |

More on vElimination | p. 90 |

Arguing Logically for Exam Purposes: How to Construct Formal Proofs | p. 94 |

Reductio Ad Absurdum | p. 101 |

The Golden Rule Completed | p. 106 |

A Final Note on Rules of Inference for PL | p. 110 |

Defining 'Formula of PL': Syntax, Structure and Recursive Definition | p. 114 |

Examination 1 in Formal Logic | p. 118 |

Formal Logic and Formal Semantics #1 | p. 121 |

Syntax and Semantics | p. 122 |

The Principle of Bivalence | p. 123 |

Truth-Functionality | p. 125 |

Truth-Functions, Truth-Tables and the Logical Connectives | p. 126 |

Constructing Truth-Tables | p. 133 |

Tautologous, Inconsistent and Contingent Formulas in PL | p. 141 |

Semantic Consequence | p. 144 |

Guide to Further Reading | p. 148 |

Truth-Tables Again: Four Alternative Ways to Test for Validity | p. 151 |

Semantic Equivalence | p. 160 |

Truth-Trees | p. 163 |

More on Truth-Trees | p. 167 |

The Adequacy of the Logical Connectives | p. 177 |

Examination 2 in Formal Logic | p. 185 |

An Introduction to First Order Predicate Logic | p. 189 |

Logical Form Revisited: The Formal Language QL | p. 190 |

More on the Formulas of QL | p. 197 |

The Universal Quantifier and the Existential Quantifier | p. 202 |

Introducing the Notion of a QL Interpretation | p. 205 |

Valid and Invalid Sequents of QL | p. 210 |

Negation and the Interdefinability of the Quantifiers | p. 214 |

How to Think Logically about Relationships: Part One | p. 217 |

How to Think Logically about Relationships: Part Two | p. 222 |

How to Think Logically about Relationships: Part Three | p. 224 |

How to Think Logically about Relationships: Part Four | p. 228 |

Formal Properties of Relations | p. 235 |

Introducing Identity | p. 240 |

Identity and Numerically Definite Quantification | p. 245 |

Russell #1: Names and Descriptions | p. 249 |

Russell #2: On Existence | p. 256 |

Examination 3 in Formal Logic | p. 261 |

How to Argue Logically in QL | p. 265 |

Introduction: Formal Logic and Science Fiction | p. 266 |

Reasoning with the Universal Quantifier 1: The Rule UE | p. 268 |

Reasoning with the Universal Quantifier 2: The Rule UI | p. 273 |

Introducing the Existential Quantifier: The Rule EI | p. 281 |

A Brief Note on Free Logic | p. 287 |

Eliminating the Existential Quantifier: The Rule EE | p. 292 |

Reasoning with Relations | p. 303 |

Proof-Theory for Identity: The Rules =I and =E | p. 310 |

Strategies for Proof-Construction in QL #1 | p. 315 |

Strategies for Proof-Construction in QL #2 | p. 320 |

Examination 4 in Formal Logic | p. 330 |

Formal Logic and Formal Semantics #2 | p. 333 |

Truth-Trees Revisited | p. 334 |

More on QL Truth-Trees | p. 347 |

Relations Revisited: The Undecidability of First Order Logic | p. 357 |

A Final Note on the Truth-Tree Method: Relations and Identity | p. 368 |

Glossary | p. 375 |

Bibliography | p. 399 |

Index | p. 403 |

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