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# Logic and Philosophy A Modern Introduction

**by**Hausman, Alan; Kahane, Howard; Tidman, Paul

11th

### 9780495601586

0495601586

Paperback

3/12/2009

Wadsworth Publishing

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## Summary

LOGIC AND PHILOSOPHY: A MODERN INTRODUCTION, 11E is a comprehensive introduction to logic that is both rigorous and user-friendly. Numerous carefully crafted exercise sets accompanied by crisp, clear exposition take you from sentential logic through first-order predicate logic, the theory of descriptions, and identity. As the title suggests, this is a book devoted not merely to logic; you also will encounter an abundance of philosophy.

## Table of Contents

Preface to the Eleventh Edition | p. ix |

Preface to the Tenth Edition | p. xi |

Introduction | p. 1 |

The Elements of an Argument | p. 1 |

Deduction and Induction | p. 5 |

Deductive Argument Forms | p. 7 |

Truth and Validity | p. 8 |

Soundness | p. 11 |

Consistency | p. 12 |

Contexts of Discovery and Justification | p. 14 |

The Plan of This Book | p. 14 |

Key Terms | p. 16 |

Sentential Logic | p. 17 |

Symbolizing in Sentential Logic | p. 19 |

Atomic and Compound Sentences | p. 20 |

Truth-Functions | p. 21 |

Conjunctions | p. 21 |

Non-Truth-Functional Connectives | p. 25 |

Variables and Constants | p. 25 |

Negations | p. 27 |

Parentheses and Brackets | p. 28 |

Use and Mention | p. 29 |

Disjunctions | p. 30 |

"Not Both" and "Neither . . . Nor" | p. 33 |

Material Conditionals | p. 35 |

Material Biconditionals | p. 38 |

"Only If" and "Unless" | p. 40 |

Symbolizing Complex Sentences | p. 41 |

Alternative Sentential Logic Symbols | p. 48 |

Key Terms | p. 50 |

Truth Tables | p. 53 |

Computing Truth-Values | p. 53 |

Logical Form | p. 58 |

Tautologies, Contradictions, and Contingent Sentences | p. 63 |

Logical Equivalences | p. 69 |

Truth Table Test of Validity | p. 70 |

Truth Table Test of Consistency | p. 73 |

Validity and Consistency | p. 74 |

The Short Truth Table Test for Invalidity | p. 76 |

The Short Truth Table Test for Consistency | p. 80 |

A Method of Justification for the Truth Tables | p. 81 |

Key Terms | p. 85 |

Proofs | p. 86 |

Argument Forms | p. 86 |

The Method of Proof: Modus Ponens and Modus Tollens | p. 88 |

Disjunctive Syllogism and Hypothetical Syllogism | p. 91 |

Simplification and Conjunction | p. 93 |

Addition and Constructive Dilemma | p. 94 |

Principles of Strategy | p. 97 |

Double Negation and DeMorgan's Theorem | p. 103 |

Commutation, Association, and Distribution | p. 106 |

Contraposition, Implication, and Exportation | p. 107 |

Tautology and Equivalence | p. 107 |

More Principles of Strategy | p. 111 |

Common Errors in Problem Solving | p. 115 |

Key Terms | p. 122 |

Conditional and Indirect Proofs | p. 123 |

Conditional Proofs | p. 123 |

Indirect Proofs | p. 132 |

Strategy Hints for Using CP and IP | p. 137 |

Zero-Premise Deductions | p. 138 |

Proving Premises Inconsistent | p. 139 |

Adding Valid Argument Forms | p. 141 |

An Alternative to Conditional Proof? | p. 142 |

The Completeness and Soundness of Sentential Logic | p. 144 |

Introduction and Elimination Rules | p. 146 |

Key Terms | p. 149 |

Sentential Logic Truth Trees | p. 151 |

The Sentential Logic Truth Tree Method | p. 151 |

The Truth Tree Rules | p. 152 |

Details of Tree Construction | p. 154 |

Normal Forms and Trees | p. 160 |

Constructing Tree Rules for Any Function | p. 161 |

Key Terms | p. 163 |

Predicate Logic | p. 165 |

Predicate Logic Symbolization | p. 167 |

Individuals and Properties | p. 167 |

Quantifiers and Free Variables | p. 171 |

Universal Quantifiers | p. 172 |

Existential Quantifiers | p. 177 |

Basic Predicate Logic Symbolizations | p. 178 |

The Square of Opposition | p. 180 |

Common Pitfalls in Symbolizing with Quantifiers | p. 180 |

Expansions | p. 183 |

Symbolizing "Only," "None but," and "Unless" | p. 186 |

Key Terms | p. 190 |

Predicate Logic Semantics | p. 191 |

Interpretations in Predicate Logic | p. 191 |

Proving Invalidity | p. 193 |

Using Expansions to Prove Invalidity | p. 196 |

Consistency in Predicate Logic | p. 197 |

Validity and Inconsistency in Predicate Logic | p. 198 |

Key Terms | p. 199 |

Predicate Logic Proofs | p. 200 |

Proving Validity | p. 200 |

The Four Quantifier Rules | p. 202 |

The Five Main Restrictions | p. 209 |

Precise Formulation of the Four Quantifier Rules | p. 213 |

Mastering the Four Quantifier Rules | p. 216 |

Quantifier Negation | p. 220 |

Key Term | p. 225 |

Relational Predicate Logic | p. 226 |

Relational Predicates | p. 226 |

Symbolizations Containing Overlapping Quantifiers | p. 229 |

Expansions and Overlapping Quantifiers | p. 229 |

Places and Times | p. 234 |

Symbolizing "Someone," "Somewhere," "Sometime," and So On | p. 235 |

Invalidity and Consistency in Relational Predicate Logic | p. 240 |

Relational Predicate Logic Proofs | p. 241 |

Strategy for Relational Predicate Logic Proofs | p. 248 |

Theorems and Inconsistency in Predicate Logic | p. 250 |

Predicate Logic Metatheory | p. 253 |

A Simpler Set of Quantifier Rules | p. 254 |

Rationale Behind the Precise Formulation of the Four Quantifier Rules | p. 257 |

Cases Involving the Five Major Restrictions | p. 257 |

One-to-One Correspondence Matters | p. 260 |

Accidentally Bound Variables and Miscellaneous Cases | p. 264 |

Predicate Logic Proofs with Flagged Constants | p. 269 |

Predicate Logic Truth Trees | p. 272 |

Introductory Remarks | p. 272 |

General Features of the Method | p. 273 |

Specific Examples of the Method | p. 273 |

Some Advantages of the Trees | p. 278 |

Example of an Invalid Argument with at Least One Open Path | p. 279 |

Metatheoretic Results | p. 280 |

Strategy and Accounting | p. 283 |

Key Terms | p. 285 |

Identity and Philosophical Problems of Symbolic Logic | p. 286 |

Identity | p. 286 |

Definite Descriptions | p. 292 |

Properties of Relations | p. 294 |

Higher-Order Logics | p. 297 |

Limitations of Predicate Logic | p. 299 |

Philosophical Problems | p. 303 |

Logical Paradoxes | p. 310 |

Key Terms | p. 317 |

Syllogistic Logic | p. 319 |

Categorical Propositions | p. 322 |

Existential Import | p. 322 |

The Square of Opposition | p. 323 |

Conversion, Obversion, Contraposition | p. 326 |

Syllogistic Logic - Not Assuming Existential Import | p. 329 |

Venn Diagrams | p. 332 |

Syllogisms | p. 334 |

Determining Syllogism Validity | p. 336 |

Venn Diagram Proofs of Validity or Invalidity | p. 337 |

Five Rules for Determining Validity or Invalidity | p. 342 |

Syllogistics Extended | p. 345 |

Enthymemes | p. 348 |

Sorites | p. 349 |

Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared | p. 351 |

Key Terms | p. 355 |

Answers to Even-Numbered Exercise Items | p. 358 |

Bibliography | p. 419 |

Special Symbols | p. 421 |

Index | p. 423 |

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