Logic and Philosophy A Modern Introduction

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

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ISBN: 9780495601586 | 0495601586
Cover: Paperback
Copyright: 3/12/2009

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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.

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
Table of Contents provided by Ingram. All Rights Reserved.

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Logic and Philosophy A Modern Introduction

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