Der Autor vermittelt logisches Grundwissen, fundamentale Beweisprinzipien und Methoden der Mathematik. Dabei geht er u. a. folgenden Fragen nach: Was unterscheidet endliche von unendlichen Mengen? Wie lassen sich die ganzen, rationalen und reellen Zahlen aus den natürlichen Zahlen konstruieren? Welche grundlegenden topologischen Eigenschaften besitzt die Menge der reellen Zahlen? Lassen sich die natürlichen oder reellen Zahlen vollständig axiomatisch beschreiben? Pflichtlektüre für alle Studierenden der Mathematik, Physik und Informatik Preface 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

lgrsnf/M_Mathematics/MA_Algebra/MAml_Mathematical logic/Smith N.J.J. Logic.. the laws of truth (PUP, 2012)(ISBN 0691151636)(O)(545s)_MAml_.pdf

nexusstc/Logic : the laws of truth/3bc8cbc7d1bbf3b0a3b71e2a47114a7d.pdf

zlib/Society, Politics & Philosophy/General & Miscellaneous Philosophy/Nicholas J J Smith/Logic : the laws of truth_2065297.pdf

Smith, Nicholas J.J.

Princeton University, Department of Art & Archaeology

United States, United States of America

Princeton, N.J, New Jersey, 2012

Princeton, cop. 2012

Kolxo3 -- 61-62

lg910926

{"isbns":["0691151636","9780691151632"],"last_page":545,"publisher":"Princeton University Press"}

Includes bibliographical references and index.

Cover......Page 1
Contents......Page 8
Preface......Page 12
Acknowledgments......Page 16
PART I: Propositional Logic......Page 18
1.1 What Is Logic?......Page 20
1.2 Propositions......Page 22
1.3 Arguments......Page 28
1.4 Logical Consequence......Page 31
1.5 Soundness......Page 38
1.6 Connectives......Page 40
2.2 Basic Propositions of PL......Page 49
2.3 Connectives of PL......Page 53
2.4 Wff Variables......Page 56
2.5 Syntax of PL......Page 57
3.1 Truth Tables for the Connectives......Page 66
3.2 Truth Values of Complex Propositions......Page 68
3.3 Truth Tables for Complex Propositions......Page 71
3.4 Truth Tables for Multiple Propositions......Page 75
3.5 Connectives and Truth Functions......Page 76
4.1 Arguments......Page 80
4.2 Single Propositions......Page 84
4.3 Two Propositions......Page 86
4.4 Sets of Propositions......Page 91
4.5 More on Validity......Page 92
5 Logical Form......Page 96
5.1 Abstracting from Content: From Propositions to Forms......Page 98
5.2 Instances: From Forms to Propositions......Page 99
5.3 Argument Forms......Page 101
5.4 Validity and Form......Page 104
5.5 Invalidity and Form......Page 108
5.6 Notable Argument Forms......Page 111
5.7 Other Logical Properties......Page 112
6.1 Assertibility and Implicature......Page 114
6.2 Conjunction......Page 120
6.3 Conditional and Biconditional......Page 127
6.4 Disjunction......Page 134
6.5 Negation......Page 139
6.6 Functional Completeness......Page 141
7 Trees for Propositional Logic......Page 151
7.1 Tree Rules......Page 153
7.2 Applying the Rules......Page 157
7.3 Uses of Trees......Page 163
7.4 Abbreviations......Page 173
PART II: Predicate Logic......Page 178
8 The Language of Monadic Predicate Logic......Page 180
8.1 The Limitations of Propositional Logic......Page 181
8.2 MPL, Part I: Names and Predicates......Page 184
8.3 MPL, Part II: Variables and Quantifiers......Page 189
8.4 Syntax of MPL......Page 199
9 Semantics of Monadic Predicate Logic......Page 206
9.1 Models; Truth and Falsity of Uncomplicated Propositions......Page 208
9.2 Connectives......Page 213
9.3 Quantified Propositions: The General Case......Page 214
9.4 Semantics of MPL: Summary......Page 221
9.5 Analyses and Methods......Page 223
10 Trees for Monadic Predicate Logic......Page 228
10.1 Tree Rules......Page 229
10.2 Using Trees......Page 240
10.3 Infinite Trees......Page 245
11 Models, Propositions, and Ways the World Could Be......Page 259
11.1 Translation......Page 260
11.2 Valuation......Page 264
11.3 Axiomatization......Page 268
11.4 Propositions......Page 270
11.5 Logical Consequence and NTP......Page 274
11.6 Postulates......Page 278
12.1 The Language of General Predicate Logic......Page 281
12.2 Semantics of GPL......Page 293
12.3 Trees for General Predicate Logic......Page 299
12.4 Postulates......Page 303
12.5 Moving Quantifiers......Page 310
13 Identity......Page 315
13.1 The Identity Relation......Page 316
13.2 The Identity Predicate......Page 320
13.3 Semantics of Identity......Page 323
13.4 Trees for General Predicate Logic with Identity......Page 328
13.5 Numerical Quantifiers......Page 338
13.6 Definite Descriptions......Page 343
13.7 Function Symbols......Page 360
PART III: Foundations and Variations......Page 372
14 Metatheory......Page 374
14.1 Soundness and Completeness......Page 375
14.2 Decidability and Undecidability......Page 385
14.3 Other Logical Properties......Page 391
14.4 Expressive Power......Page 399
15 Other Methods of Proof......Page 402
15.1 Axiomatic Systems......Page 403
15.2 Natural Deduction......Page 424
15.3 Sequent Calculus......Page 438
16.1 Sets......Page 455
16.2 Ordered Pairs and Ordered n-tuples......Page 466
16.3 Relations......Page 470
16.4 Functions......Page 471
16.5 Sequences......Page 475
16.6 Multisets......Page 477
16.7 Syntax......Page 479
Notes......Page 484
References......Page 526
B......Page 532
C......Page 533
D......Page 534
F......Page 535
I......Page 536
M......Page 537
N......Page 538
P......Page 539
Q......Page 540
S......Page 541
T......Page 543
V......Page 544
Z......Page 545

<p>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.</p>
<p><i>Logic</i> is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject.</p>
<ul>
<li>Provides an essential introduction to classical logic</li>
<li>Emphasizes the how and why of logic</li>
<li>Covers both formal and philosophical issues</li>
<li>Presents all the major forms of proof—from trees to sequent calculus</li>
<li>Features numerous exercises, with solutions available at personal.usyd.edu.au/~njjsmith/lawsoftruth</li>
<li>The ideal textbook for undergraduates and graduate students</li>
</ul>

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. This title provides an essential introduction to classical logic. It emphasizes the how and why of logic. It covers both formal and philosophical issues. It presents all the major forms of proof - from trees to sequent calculus. It features numerous exercises. This is the ideal textbook for undergraduates and graduate students

2013-04-15