Sweet Reason

James M. Henle is Professor of Mathematics at Smith College. His books include Calculus: the Language of Change (with David Cohen), Infinitesimal Calculus (with Eugene Kleinberg), and An Outline of Set Theory. Jay L. Garfield is Doris Silbert Professor in the Humanities and Professor of Philosophy at Smith College, Professor in the Graduate Faculty of Philosophy at the University of Massachusetts, Professor of Philosophy at Melbourne University, and Adjunct Professor of Philosophy at the Central University of Tibetan Studies.Thomas Tymoczko was, until his death, Professor of Philosophy at Smith College. He was editor of New Directions in the Philosophy of Mathematics.

• Preface xi What Is Logic? 1Chapter One 31.1 Introducing Formal Logic 41.2 Constants and Relations 71.3 Quantifiers and Variables 91.4 Introducing Informal Logic 111.5 Conclusions 131.6 Dialects of Logic 15Chapter Two 182.1 Formal Inference 192.2 Informal Inference 212.3 Diagramming Arguments 252.4 Saying No 322.5 Metalogic 35Chapter Three 373.1 Basic Sentential 373.2 Truth Tables 433.3 English to Sentential 503.4 Negating Statements 563.5 Rebutting Premises 593.6 Computer Logic 65Chapter Four 694.1 Validity 694.2 The Logic of English 734.3 Negating Conditionals 764.4 Rebutting Inferences 804.5 The Logic of Sets 87Chapter Five 945.1 Well-formed Formulas 945.2 The Shortcut Method 1015.3 Local and Global 1085.4 More on Trees 1115.5 Rebutting Everything 1155.6 Polish Logic 122Chapter Six 1296.1 Predicate 1306.2 English to Predicate 1396.3 Reading Between the Lines 1456.4 Multi-valued Logic 153Chapter Seven 1627.1 Universes 1627.2 Syllogisms 1677.3 Validity 1727.4 Diagramming Your Argument 1767.5 Inductive Logic 187Chapter Eight 1928.1 Predicate Wffs 1928.2 Outlining Your Argument 1968.3 The Logic of Chance 205Chapter Nine 2139.1 Simple Deduction 2139.2 Simple Strategy 2219.3 Writing Your Argument 2279.4 Basic Modal Logic 234Chapter Ten 24010.1 Sentential Deduction 24010.2 Sentential Strategy 25010.3 Arguing with Yourself 26310.4 Sophisticated Modal Logic 279Chapter Eleven 28711.1 Predicate Deduction 28711.2 Predicate Strategy 29611.3 Why We Argue 30611.4 Presidential Debating 31011.5 The Logic of Paradox 315Chapter Twelve 32712.1 Deduction with Identity 32712.2 Deduction, FMTYEWTK 33212.3 Parliamentary Debating 33612.4 Cathy, A Decade On 33812.5 Incomplete Logic 343What is Logic? 349Answers to Odd-Numbered Exercises 350Index 384