9780495601586

Logic and Philosophy A Modern Introduction

by ; ;
  • ISBN13:

    9780495601586

  • ISBN10:

    0495601586

  • Edition: 11th
  • Format: Paperback
  • Copyright: 3/12/2009
  • Publisher: 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 Editionp. ix
Preface to the Tenth Editionp. xi
Introductionp. 1
The Elements of an Argumentp. 1
Deduction and Inductionp. 5
Deductive Argument Formsp. 7
Truth and Validityp. 8
Soundnessp. 11
Consistencyp. 12
Contexts of Discovery and Justificationp. 14
The Plan of This Bookp. 14
Key Termsp. 16
Sentential Logicp. 17
Symbolizing in Sentential Logicp. 19
Atomic and Compound Sentencesp. 20
Truth-Functionsp. 21
Conjunctionsp. 21
Non-Truth-Functional Connectivesp. 25
Variables and Constantsp. 25
Negationsp. 27
Parentheses and Bracketsp. 28
Use and Mentionp. 29
Disjunctionsp. 30
"Not Both" and "Neither . . . Nor"p. 33
Material Conditionalsp. 35
Material Biconditionalsp. 38
"Only If" and "Unless"p. 40
Symbolizing Complex Sentencesp. 41
Alternative Sentential Logic Symbolsp. 48
Key Termsp. 50
Truth Tablesp. 53
Computing Truth-Valuesp. 53
Logical Formp. 58
Tautologies, Contradictions, and Contingent Sentencesp. 63
Logical Equivalencesp. 69
Truth Table Test of Validityp. 70
Truth Table Test of Consistencyp. 73
Validity and Consistencyp. 74
The Short Truth Table Test for Invalidityp. 76
The Short Truth Table Test for Consistencyp. 80
A Method of Justification for the Truth Tablesp. 81
Key Termsp. 85
Proofsp. 86
Argument Formsp. 86
The Method of Proof: Modus Ponens and Modus Tollensp. 88
Disjunctive Syllogism and Hypothetical Syllogismp. 91
Simplification and Conjunctionp. 93
Addition and Constructive Dilemmap. 94
Principles of Strategyp. 97
Double Negation and DeMorgan's Theoremp. 103
Commutation, Association, and Distributionp. 106
Contraposition, Implication, and Exportationp. 107
Tautology and Equivalencep. 107
More Principles of Strategyp. 111
Common Errors in Problem Solvingp. 115
Key Termsp. 122
Conditional and Indirect Proofsp. 123
Conditional Proofsp. 123
Indirect Proofsp. 132
Strategy Hints for Using CP and IPp. 137
Zero-Premise Deductionsp. 138
Proving Premises Inconsistentp. 139
Adding Valid Argument Formsp. 141
An Alternative to Conditional Proof?p. 142
The Completeness and Soundness of Sentential Logicp. 144
Introduction and Elimination Rulesp. 146
Key Termsp. 149
Sentential Logic Truth Treesp. 151
The Sentential Logic Truth Tree Methodp. 151
The Truth Tree Rulesp. 152
Details of Tree Constructionp. 154
Normal Forms and Treesp. 160
Constructing Tree Rules for Any Functionp. 161
Key Termsp. 163
Predicate Logicp. 165
Predicate Logic Symbolizationp. 167
Individuals and Propertiesp. 167
Quantifiers and Free Variablesp. 171
Universal Quantifiersp. 172
Existential Quantifiersp. 177
Basic Predicate Logic Symbolizationsp. 178
The Square of Oppositionp. 180
Common Pitfalls in Symbolizing with Quantifiersp. 180
Expansionsp. 183
Symbolizing "Only," "None but," and "Unless"p. 186
Key Termsp. 190
Predicate Logic Semanticsp. 191
Interpretations in Predicate Logicp. 191
Proving Invalidityp. 193
Using Expansions to Prove Invalidityp. 196
Consistency in Predicate Logicp. 197
Validity and Inconsistency in Predicate Logicp. 198
Key Termsp. 199
Predicate Logic Proofsp. 200
Proving Validityp. 200
The Four Quantifier Rulesp. 202
The Five Main Restrictionsp. 209
Precise Formulation of the Four Quantifier Rulesp. 213
Mastering the Four Quantifier Rulesp. 216
Quantifier Negationp. 220
Key Termp. 225
Relational Predicate Logicp. 226
Relational Predicatesp. 226
Symbolizations Containing Overlapping Quantifiersp. 229
Expansions and Overlapping Quantifiersp. 229
Places and Timesp. 234
Symbolizing "Someone," "Somewhere," "Sometime," and So Onp. 235
Invalidity and Consistency in Relational Predicate Logicp. 240
Relational Predicate Logic Proofsp. 241
Strategy for Relational Predicate Logic Proofsp. 248
Theorems and Inconsistency in Predicate Logicp. 250
Predicate Logic Metatheoryp. 253
A Simpler Set of Quantifier Rulesp. 254
Rationale Behind the Precise Formulation of the Four Quantifier Rulesp. 257
Cases Involving the Five Major Restrictionsp. 257
One-to-One Correspondence Mattersp. 260
Accidentally Bound Variables and Miscellaneous Casesp. 264
Predicate Logic Proofs with Flagged Constantsp. 269
Predicate Logic Truth Treesp. 272
Introductory Remarksp. 272
General Features of the Methodp. 273
Specific Examples of the Methodp. 273
Some Advantages of the Treesp. 278
Example of an Invalid Argument with at Least One Open Pathp. 279
Metatheoretic Resultsp. 280
Strategy and Accountingp. 283
Key Termsp. 285
Identity and Philosophical Problems of Symbolic Logicp. 286
Identityp. 286
Definite Descriptionsp. 292
Properties of Relationsp. 294
Higher-Order Logicsp. 297
Limitations of Predicate Logicp. 299
Philosophical Problemsp. 303
Logical Paradoxesp. 310
Key Termsp. 317
Syllogistic Logicp. 319
Categorical Propositionsp. 322
Existential Importp. 322
The Square of Oppositionp. 323
Conversion, Obversion, Contrapositionp. 326
Syllogistic Logic - Not Assuming Existential Importp. 329
Venn Diagramsp. 332
Syllogismsp. 334
Determining Syllogism Validityp. 336
Venn Diagram Proofs of Validity or Invalidityp. 337
Five Rules for Determining Validity or Invalidityp. 342
Syllogistics Extendedp. 345
Enthymemesp. 348
Soritesp. 349
Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Comparedp. 351
Key Termsp. 355
Answers to Even-Numbered Exercise Itemsp. 358
Bibliographyp. 419
Special Symbolsp. 421
Indexp. 423
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