Deduction

Daniel Bonevac is Professor of Philosophy at the University of Texas at Austin. He is the author of Reduction in the Abstract Sciences (1982), which received the Johnsonian Prize from The Journal of Philosophy, as well as The Art and Science of Logic (1990), Simple Logic (1999), and Worldly Wisdom (2001). He also edited Today's Moral Issues (fourth edition, 2002), Understanding Non-Western Philosophy (with Stephen Phillips, 1993), and Beyond the Western Tradition: Readings in Moral and Political Philosophy (with William Boon and Stephen Phillips, 1992).

• Preface to the Second Edition viiiAcknowledgments x1 Basic Concepts of Logic 11.1 Arguments 11.2 Validity 161.3 Implication and Equivalence 231.4 Logical Properties of Sentences 271.5 Satisfiability 312 Sentences 362.1 The Language of Sentential Logic 362.2 Truth Functions 402.3 A Sentential Language 462.4 Symbolization 492.5 Validity 562.6 Truth Tables 602.7 Truth Tables for Formulas 632.8 Truth Tables for Argument Forms 682.9 Implication, Equivalence, and Satisfiability 713 Truth Trees 763.1 Thinking Backwards 763.2 Constructing Truth Trees 803.3 Negation, Conjunction, and Disjunction 843.4 The Conditional and Biconditional 933.5 Other Applications 1014 Natural Deduction 1074.1 Natural Deduction Systems 1074.2 Rules for Negation and Conjunction 1104.3 Rules for the Conditional and Biconditional 1184.4 Rules for Disjunction 1224.5 Derivable Rules 1255 Quantifiers 1375.1 Constants and Quantifiers 1385.2 Categorical Sentence Forms 1445.3 Polyadic Predicates 1485.4 The Language Q 1535.5 Symbolization 1566 Quantified Truth Trees 1736.1 Rules for Quantifiers 1746.2 Strategies 1786.3 Interpretations 1896.4 Constructing Interpretations from Trees 1997 Quantified Natural Deduction 2067.1 Deduction Rules for Quantifiers 2067.2 Universal Proof 2147.3 Derived Rules for Quantifiers 2208 Identity and Function Symbols 2258.1 Identity 2258.2 Truth Tree Rules for Identity 2318.3 Deduction Rules for Identity 2358.4 Function Symbols 2389 Necessity 2499.1 If 2499.2 Modal Connectives 2519.3 Symbolization 2569.4 Modal Truth Trees 2619.5 Other Tree Rules 2659.6 World Travelling 2689.7 Modal Deduction 2789.8 Other Modal Systems 28910 Between Truth and Falsehood 29510.1 Vagueness and Presupposition 29510.2 Many-Valued Truth Tables 30010.3 Many-Valued Trees 31410.4 Many-Valued Deduction 32510.5 Fuzzy Logic 33210.6 Intuitionistic Logic 34411 Obligation 36111.1 Deontic Connectives 36211.2 Deontic Truth Trees 37011.3 Deontic Deduction 38111.4 Moral and Practical Reasoning 38712 Counterfactuals 39512.1 The Meaning of Counterfactuals 39912.2 Truth Tree Rules for Counterfactuals 40212.3 Deduction Rules for Counterfactuals 40912.4 Stalnaker’s Semantics: System CS 41812.5 Lewis’s Semantics: System CL 42313 Common-Sense Reasoning 43413.1 When Good Arguments Go Bad 43513.2 Truth Trees 43913.3 Defeasible Deduction 45413.4 Defeasible Deontic Logic 46614 Quantifiers and Modality 47514.1 Quantified S5 47514.2 Free Logic 487Bibliography 504Index 507

“Deduction is the best logic textbook on the market. It is modern, clean, elegant, sharp and direct. It is a perfect accompaniment to the most recent developments in philosophy and logic; in every sense the logic textbook for the twenty-first century.” Rick Benitez, University of Sydney