{"product_id":"logic-9780691151632","title":"Logic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eLogic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an introduction to classical logic, with an approach that emphasizes both the hows and whys of logic. It covers the formal tools and techniques of logic.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[I]f you are a teacher in the market for a new logic text, or a student looking for very helpful reading, this could indeed be the book for you.\"--Logic Matters blog \"This book provides an excellent comprehensive introduction to classical first-order logic with identity. It has the expected virtues of clarity, precision and accessibility... The book deserves to be used widely, both as a text for courses and for self-study.\"--Greg O'Hair, Australasian Journal of Philosophy \"You will find this book outstanding whenever you read it, but you'll be even smarter if you read it before other, even excellent, logic books in your library.\"--George Hacken, Computing Reviews \"[T]his volume displays a masterly combination of clarity, friendliness to the beginning student with technical accuracy, and carefully thought out choice of topics that is hard to find on the market. Smith succeeds in introducing his readers to the complexities of symbolic logic in a very gentle manner--there is not a formula or a definition in the book that is not thoroughly explained or illustrated with an abundance of examples.\"--F. Paoli, History and Philosophy of Logic \"An excellent textbook for an undergraduate course on this topic.\"-- Peter W. Evans, Philosophy in Review\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi  Acknowledgments xv      Part I Propositional Logic 1  Chapter 1: Propositions and Arguments 3  1.1 What Is Logic? 3  1.2 Propositions 5  1.3 Arguments 11  1.4 Logical Consequence 14  1.5 Soundness 21  1.6 Connectives 23  Chapter 2: The Language of Propositional Logic 32  2.1 Motivation 32  2.2 Basic Propositions of PL 32  2.3 Connectives of PL 36  2.4 Wff Variables 39  2.5 Syntax of PL 40  Chapter 3: Semantics of Propositional Logic 49  3.1 Truth Tables for the Connectives 49  3.2 Truth Values of Complex Propositions 51  3.3 Truth Tables for Complex Propositions 54  3.4 Truth Tables for Multiple Propositions 58  3.5 Connectives and Truth Functions 59  Chapter 4: Uses of Truth Tables 63  4.1 Arguments 63  4.2 Single Propositions 67  4.3 Two Propositions 69  4.4 Sets of Propositions 74  4.5 More on Validity 75  Chapter 5: Logical Form 79  5.1 Abstracting from Content: From Propositions to Forms 81  5.2 Instances: From Forms to Propositions 82  5.3 Argument Forms 84  5.4 Validity and Form 87  5.5 Invalidity and Form 91  5.6 Notable Argument Forms 94  5.7 Other Logical Properties 95  Chapter 6: Connectives: Translation and Adequacy 97  6.1 Assertibility and Implicature 97  6.2 Conjunction 103  6.3 Conditional and Biconditional 110  6.4 Disjunction 117  6.5 Negation 122  6.6 Functional Completeness 124  7 Trees for Propositional Logic 134  7.1 Tree Rules 136  7.2 Applying the Rules 140  7.3 Uses of Trees 146  7.4 Abbreviations 156      Part II Predicate Logic 161  Chapter 8: The Language of Monadic Predicate Logic 163  8.1 The Limitations of Propositional Logic 164  8.2 MPL, Part I: Names and Predicates 167  8.3 MPL, Part II: Variables and Quantifiers 172  8.4 Syntax of MPL 182  Chapter 9: Semantics of Monadic Predicate Logic 189  9.1 Models; Truth and Falsity of Uncomplicated Propositions 191  9.2 Connectives 196  9.3 Quantified Propositions: The General Case 197  9.4 Semantics of MPL: Summary 204  9.5 Analyses and Methods 206  Chapter 10: Trees for Monadic Predicate Logic 211  10.1 Tree Rules 212  10.2 Using Trees 223  10.3 Infinite Trees 228  Chapter 11: Models, Propositions, and Ways the World Could Be 242  11.1 Translation 243  11.2 Valuation 247  11.3 Axiomatization 251  11.4 Propositions 253  11.5 Logical Consequence and NTP 257  11.6 Postulates 261  Chapter 12: General Predicate Logic 264  12.1 The Language of General Predicate Logic 264  12.2 Semantics of GPL 276  12.3 Trees for General Predicate Logic 282  12.4 Postulates 286  12.5 Moving Quantifiers 293  Chapter 13: Identity 298  13.1 The Identity Relation 299  13.2 The Identity Predicate 303  13.3 Semantics of Identity 306  13.4 Trees for General Predicate Logic with Identity 311  13.5 Numerical Quantifiers 321  13.6 Definite Descriptions 326  13.7 Function Symbols 343      Part III Foundations and Variations 355  14 Metatheory 357  14.1 Soundness and Completeness 358  14.2 Decidability and Undecidability 368  14.3 Other Logical Properties 374  14.4 Expressive Power 382  15 Other Methods of Proof 385  15.1 Axiomatic Systems 386  15.2 Natural Deduction 407  15.3 Sequent Calculus 421  16 Set Theory 438  16.1 Sets 438  16.2 Ordered Pairs and Ordered n-tuples 449  16.3 Relations 453  16.4 Functions 454  16.5 Sequences 458  16.6 Multisets 460  16.7 Syntax 462      Notes 467  References 509  Index 515","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865525334359,"sku":"9780691151632","price":42.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691151632.jpg?v=1722274388","url":"https:\/\/bookcurl.com\/products\/logic-9780691151632","provider":"Book Curl","version":"1.0","type":"link"}