Preface xi
What Is Logic? 1
Chapter One 3
1.1 Introducing Formal Logic 4
1.2 Constants and Relations 7
1.3 Quantifiers and Variables 9
1.4 Introducing Informal Logic 11
1.5 Conclusions 13
1.6 Dialects of Logic 15
Chapter Two 18
2.1 Formal Inference 19
2.2 Informal Inference 21
2.3 Diagramming Arguments 25
2.4 Saying No 32
2.5 Metalogic 35
Chapter Three 37
3.1 Basic Sentential 37
3.2 Truth Tables 43
3.3 English to Sentential 50
3.4 Negating Statements 56
3.5 Rebutting Premises 59
3.6 Computer Logic 65
Chapter Four 69
4.1 Validity 69
4.2 The Logic of English 73
4.3 Negating Conditionals 76
4.4 Rebutting Inferences 80
4.5 The Logic of Sets 87
Chapter Five 94
5.1 Well-formed Formulas 94
5.2 The Shortcut Method 101
5.3 Local and Global 108
5.4 More on Trees 111
5.5 Rebutting Everything 115
5.6 Polish Logic 122
Chapter Six 129
6.1 Predicate 130
6.2 English to Predicate 139
6.3 Reading Between the Lines 145
6.4 Multi-valued Logic 153
Chapter Seven 162
7.1 Universes 162
7.2 Syllogisms 167
7.3 Validity 172
7.4 Diagramming Your Argument 176
7.5 Inductive Logic 187
Chapter Eight 192
8.1 Predicate Wffs 192
8.2 Outlining Your Argument 196
8.3 The Logic of Chance 205
Chapter Nine 213
9.1 Simple Deduction 213
9.2 Simple Strategy 221
9.3 Writing Your Argument 227
9.4 Basic Modal Logic 234
Chapter Ten 240
10.1 Sentential Deduction 240
10.2 Sentential Strategy 250
10.3 Arguing with Yourself 263
10.4 Sophisticated Modal Logic 279
Chapter Eleven 287
11.1 Predicate Deduction 287
11.2 Predicate Strategy 296
11.3 Why We Argue 306
11.4 Presidential Debating 310
11.5 The Logic of Paradox 315
Chapter Twelve 327
12.1 Deduction with Identity 327
12.2 Deduction, FMTYEWTK 332
12.3 Parliamentary Debating 336
12.4 Cathy, A Decade On 338
12.5 Incomplete Logic 343
What is Logic? 349
Answers to Odd-Numbered Exercises 350
Index 384
James M. Henle is Professor of Mathematics at Smith College.His books include Calculus: the Language of Change (withDavid Cohen), Infinitesimal Calculus (with EugeneKleinberg), and An Outline of Set Theory. Jay L. Garfield is Doris Silbert Professor in theHumanities and Professor of Philosophy at Smith College, Professorin the Graduate Faculty of Philosophy at the University ofMassachusetts, Professor of Philosophy at Melbourne University, andAdjunct Professor of Philosophy at the Central University ofTibetan Studies. Thomas Tymoczko was, until his death, Professor ofPhilosophy at Smith College. He was editor of New Directions inthe Philosophy of Mathematics.
Sweet Reason pulls off the impossible: it provides a fun-to-read but also competent introduction to logic. Students in any discipline will find the text to be an intriguing first course in logical theory. J.C. Beall, University of Connecticut and University of Otago Introductory logic books are a dime a dozen. But this one's different. No, really. With a unique combination of philosophical nous, paradox, humor, and - often provocative - exercises, it teaches the elements of both formal logic and critical reasoning. And it shows logic as a living, breathing, evolving, stimulating, subject. If you don't want to get interested in logic, don't use this book. Graham Priest, City University of New York Graduate Center This extraordinary book, refined over the years in a very successful course at Smith College, is unique in scope among introductory logic texts, beginning with critical thinking, moving through a first-rate treatment of standard propositional and predicate logic, and introducing students along the way to a variety of more advanced topics, including modal logic, many-valued logics, set theory, cardinal and ordinal arithmetic, the logic of probability, and the logic of paradox. John Horty, University of Maryland
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