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Sweet Reason: A Field Guide to Modern Logic

ISBN: 978-0-470-41418-7
666 pages
November 1999, ©2000
Sweet Reason: A Field Guide to Modern Logic (0470414189) cover image


Sweet Reason is a unique introductory text for modern logic courses that covers both the basic rudiments of formal and informal logic as well as the real world where the discipline of logic adds substance and meaning to human discourse.  As the text alternately discusses, instructs, questions, teases and challenges, readers will find themselves absorbing the fundamentals of the discipline, becoming fluent in the language of logic, understanding how logic works in the real world, and enjoying logic's ability to entertain, surprise, discover, and enlighten.
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Table of Contents

Preface for the General Reader  xv
Preface for Logic Teachers: How to Use This Book in Logic Courses  xix
Introduction  1
Formal Logic
1  A Taste of Logic
Introducing the Language of Logic  8
Paradox  17
Negation  17
Quiz  24
2  Everything All at Once and a Warning
Truth and Falsity  26
Logical Form: The Key to Logic  31
Argument Form: The Key to Reasoning  35
Paradox and W.S. Gilbert  39
The Orb and Post  41
Paradoxes and Psychology  42
The Title of the Section on Self-Reference  44
How to Argue  53
Rebuttal  59
Law Boards: Reading Comprehension  64
The Digestor's Digest, page 1  72
Exam Warning I  73
Talking Heads  74
3  Statement Logic, Formal Languages, and Informal Arguments
Formal Languages: Sentential  76
Formal Languages: Variations on Sentential  84
Logical Theory for Statement Logic  90
Some Basic Tautologies and Implications  93
Buffalo Buffalo Buffalo  99
Artificial and Natural Languages  100
Rewrite Rules and Finite Automata  104
Loofah Loofah Loofah  109
Conclusions  115
Supporting Statements  115
Relevance  119
Premises  124
Cathy has breakfast  128
The Digestor's Digest, page 2  130
Exam Warning II  131
A Nonlogical Puzzle  132
Self-Referential Puzzles  132
4 Valid Arguments, Convincing Arguments, and Punk Logic
Valid Argument Forms  136
Formalizing for Validity  138
A Shortcut for Checking Arguments  142
Formalizing English  144
Miniac  153
Flipism  156
Sets  157
Logic Circuits  162
Bertrand the First  165
Criticizing Arguments  165
Writing Arguments  169
A Good Paragraph  173
Cathy Goes to War  176
The Digestor's Digest, page 3  177
Exam Warning III  178
The Family Reunion 179
Punk Logic  181
5  Predicates, Programs, and Antique Logic
Predicate Languages  184
Variations on the Theme of Predicate Languages  189
From Statement Logic to Predicate Logic  193
Interpreting Predicate Logic  196
Logical Theory for Predicate Logic  201
Logical Laws: Basic Valid WFFS and Implications  204
Symbolization in Predicate Logic  218
Poles and Norwegians  218
Games  220
BASIC  223
Binary  228
Algorithm  236
The Busy Beaver  238
Syllogisms  238
Fallacies  241
Rabbinic Logic  247
Cathy Meets God  251
The Digestor's Digest, page 4  253
Exam Warning IV 254
The Game of Logic  255
The Sorites or Lewis Carroll 258
6 Deduction, Infinity, and a Haircut
Main Connectives  264
Deduction  266
Hypothetical Reasoning: Deduction from Assumptions  273
Proving Validity  279
Proving Invalidity  187
Formalizing for Validity in Predicate Logic  292
In Hell with Raymond Smellyan  294
No (Certain) Escape  298
Infinite Tasks  302
Infinity: Potential and Actual  306
Proof by Contradiction  308
Anita Hill and Arlen Specter  312
Bush, Clinton, and Perot  316
The Adventure of the Dancing Man  321
Commercial Logic I  323
The Digestor's Digest, page 5  324
Exam Warning V  325
The Barbershop Problem  326
English 254  329
7 Symbolic Sophistication, Induction, and Business Logic
Quantifiers and Arithmetic  334
Functions  337
"The": Russell's Theory of Definite Descriptions  343
Measuring Uncertainty  351
Bayes' Law and Sherlock Holmes  354
Inductive Logic  358
Logic Programming  362
The W-4  371
Canadian Customs  376
The Logic Tea  377
Commercial Logic II  383
The Digestor's Digest, page 6  384
Exam Warning VI  385
Lewis Carroll's "what the tortoise said to Achilles"  387
The Far Side  391
8 Completeness, Disbelief, Debates, and Dinner
Geometry  394
The Completeness Theorem  399
Axiomatization and Boolean Algebra  404
Believing and Knowing  411
The Law of the Excluded Middle  415
From Puzzle to Paradox  420
More Bush, Clinton, and Perot  429
Presidential Debates  435
Parliamentary Debates  439
Commercial Logic III  442
The Digestor's Digest, page 7  442
Exam Warning VII  443
Peano's Dots  444
Charles Dana Gibson  445
The Family Reunion II: The Women  446
9 Paradox, Impossibility, and the Law
Where do Numbers Come From?  450
The Paradox of the Heap  458
Russell's Paradox and Frege's Mistake  468
Life  474
Hypergame  480
The Busy Beaver is not Computable  481
Impossibility  483
Quayle, Gore, and Stockdale  486
Law Boards: Logical Reasoning  491
Law Boards: Analytical Reasoning  499
Law Boards: Rules and Disputes  506
The Digestor's Digest, page 8  513
Exam Warning VIII  514
Quiz on Polish Notation  515
Tom and Jim's Excellent Adventure  516
The Last Word  517
Notes, References, Hints, and Some Answers
1 A Taste of Logic  519
2 Everything All at Once and a Warning  526
3 Statement Logic, Formal Languages, and Informal Arguments  531
4 Valid Arguments, Convincing Arguments, and Punk Logic  546
5 Predicates, Programs, and Antique Logic  562
6 Deduction, Infinity, and a Haircut  580
7 Symbolic Sophistication, Induction, and Business Logic  601
8 Completeness, Disbelieve, Debates, and Dinner  613
9 Paradox, Impossibility, and the Law  624
Index  639
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The Wiley Advantage

  • Puzzles, paradoxes, mathematical proofs, cartoons, campaign debate excerpts, and more are used to show how philosophers, mathematicians and other use logic
  • Two basic courses are presented: general introduction to logic--formal and informal--for first-year students and introduction to symbolic logic
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