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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