Sweet Reason: A Field Guide to Modern Logic
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More About This Title Sweet Reason: A Field Guide to Modern Logic
English
Sweet Reason is a unique introductory logic text 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.
English
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
TRIVIAL 231
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
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
TRIVIAL 231
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
