An Introduction to Formal Logic

Peter Smith

Cambridge University Press, Nov 6, 2003 - Mathematics - 357 pages

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He 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. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

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
• 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
• 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
• 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

About the author

Peter Smith's publications include The Philosophy of Mind (1986) and Explaining Chaos (1998).

Bibliographic information

• Title: An Introduction to Formal Logic
• Author: Peter Smith
• Edition: illustrated, reprint
• Publisher: Cambridge University Press, 2003
• ISBN: 0521008042, 9780521008044
• Length: 357 pages
• Subjects: Mathematics / Logic; Philosophy / General; Philosophy / Logic