# An Introduction to Formal Logic

Cambridge University Press, Nov 6, 2003 - Mathematics - 357 pages
This is a highly accessible guide to the fundamental aims and basic elements of formal logic. Peter Smith introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises, and also provides provides illuminating philosophical commentary. It will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

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Some explanations are drawn out, but this drawn out approach gives Smith the opportunity to repeat himself - thus making the material easier to retain. It may take me longer than other works to cover a subject, but I feel like my ability to recall the material is far better than other Formal Logic book's i've attempted to read. Also, unlike most Formal Logic texts, solutions to the many exercises are provided online.

### Contents

 What is logic? 1 Validity and soundness 9 Patterns of inference 18 The counterexample technique 29 Proofs 36 Validity and arguments 44 Logic formal and informal 51 Three prepositional connectives 53
 After prepositional logic 192 Quantifiers 194 QL introduced 202 QL explored 210 More QL translations 219 Introducing QL trees 228 The syntax of QL 242 Qvaluations 250

 The syntax of PL 63 The semantics of PL 72 As and Bs Ps and Qs 82 Truth functions 88 Tautologies 101 Tautological entailment 107 Propositional logic 123 PLC and the material conditional 125 More on the material conditional 137 Introducing PL trees 145 Rules for PL trees 157 PLC trees 171 PL trees vindicated 179 Trees and proofs 185
 Qvalidity 262 More on QL trees 272 QL trees vindicated 286 Developing predicate logic 294 Extensionality 296 Identity 303 The language QL 309 Descriptions and existence 316 Trees for identity 325 Functions 339 Further reading 348 Index 352 Copyright

### References to this book

 Logic: Key Concepts in PhilosophyLaurence GoldsteinNo preview available - 2005