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Logic : The Laws of Truth - Nicholas J.J. Smith


The Laws of Truth

Hardcover Published: 1st April 2012
ISBN: 9780691151632
Number Of Pages: 544

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Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website.

Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject.

  • Provides an essential introduction to classical logic

  • Emphasizes the how and why of logic

  • Covers both formal and philosophical issues

  • Presents all the major forms of proof--from trees to sequent calculus

  • Features numerous exercises, with solutions available at http://www-personal.usyd.edu.au/~njjsmith/lawsoftruth

  • The ideal textbook for undergraduates and graduate students

Industry Reviews

"[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

Prefacep. xi
Acknowledgmentsp. xv
Propositional Logicp. 1
Propositions and Argumentsp. 3
What Is Logic?p. 3
Propositionsp. 5
Argumentsp. 11
Logical Consequencep. 14
Soundnessp. 21
Connectivesp. 23
The Language of Propositional Logicp. 32
Motivationp. 32
Basic Propositions of PLp. 32
Connectives of PLp. 36
Wff Variablesp. 39
Syntax of PLp. 40
Semantics of Propositional Logicp. 49
Truth Tables for the Connectivesp. 49
Truth Values of Complex Propositionsp. 51
Truth Tables for Complex Propositionsp. 54
Truth Tables for Multiple Propositionsp. 58
Connectives and Truth Functionsp. 59
Uses of Truth Tablesp. 63
Argumentsp. 63
Single Propositionsp. 67
Two Propositionsp. 69
Sets of Propositionsp. 74
More on Validityp. 75
Logical Formp. 79
Abstracting from Content: From Propositions to Formsp. 81
Instances: From Forms to Propositionsp. 82
Argument Formsp. 84
Validity and Formp. 87
Invalidity and Formp. 91
Notable Argument Formsp. 94
Other Logical Propertiesp. 95
Connectives: Translation and Adequacyp. 97
Assertibility and Implicaturep. 97
Conjunctionp. 103
Conditional and Biconditionalp. 110
Disjunctionp. 117
Negationp. 122
Functional Completenessp. 124
Trees for Propositional Logicp. 134
Tree Rulesp. 136
Applying the Rulesp. 140
Uses of Treesp. 146
Abbreviationsp. 156
Predicate Logicp. 161
The Language of Monadic Predicate Logicp. 163
The Limitations of Propositional Logicp. 164
MPL, Part I: Names and Predicatesp. 167
MPL, Part II: Variables and Quantifiersp. 172
Syntax of MPLp. 182
Semantics of Monadic Predicate Logicp. 189
Models; Truth and Falsity of Uncomplicated Propositionsp. 191
Connectivesp. 196
Quantified Propositions: The General Casep. 197
Semantics of MPL: Summaryp. 204
Analyses and Methodsp. 206
Trees for Monadic Predicate Logicp. 211
Tree Rulesp. 212
Using Treesp. 223
Infinite Treesp. 228
Models, Propositions, and Ways the World Could Bep. 242
Translationp. 243
Valuationp. 247
Axiomatizationp. 251
Propositionsp. 253
Logical Consequence and NTPp. 257
Postulatesp. 261
General Predicate Logicp. 264
The Language of General Predicate Logicp. 264
Semantics of GPLp. 276
Trees for General Predicate Logicp. 282
Postulatesp. 286
Moving Quantifiersp. 293
Identityp. 298
The Identity Relationp. 299
The Identity Predicatep. 303
Semantics of Identityp. 306
Trees for General Predicate Logic with Identityp. 311
Numerical Quantifiersp. 321
Definite Descriptionsp. 326
Function Symbolsp. 343
Foundations and Variationsp. 355
Metatheoryp. 357
Soundness and Completenessp. 358
Decidability and UndecidabUityp. 368
Other Logical Propertiesp. 374
Expressive Powerp. 382
Other Methods of Proofp. 385
Axiomatic Systemsp. 386
Natural Deductionp. 407
Sequent Calculusp. 421
Set Theoryp. 438
Setsp. 438
Ordered Pairs and Ordered n-tuplesp. 449
Relationsp. 453
Functionsp. 454
Sequencesp. 458
Multisetsp. 460
Syntaxp. 462
Notesp. 467
Referencesp. 509
Indexp. 515
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780691151632
ISBN-10: 0691151636
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 544
Published: 1st April 2012
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 24.2 x 16.5  x 5.0
Weight (kg): 0.892

Earn 139 Qantas Points
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