An Introduction to Formal Logic (2^nd Ed.) Cambridge Introductions to Philosophy Series

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 very accessible book, extensively revised and rewritten for the second edition, 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 develops natural deduction systems for evaluating arguments translated into these languages. His discussion is richly illustrated with worked examples and exercises, and 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.

Preface: .1 What is Deductive Logic?; 2. Validity and Soundness; 3. Forms of Inference; 4. Proofs; 5. The Counterexample Method; 6. Logical Validity; 7. Propositions and Forms; Interlude: From Informal to Formal Logic: 8. Three Connectives; 9. PL Syntax; 10. PL Semantics; 11. `P's, `Q's, `_'s, `_'s { and form again; 12. Truth Functions; 13. Expressive Adequacy; 14. Tautologies; 15. Tautological Entailment; 16. More about Tautological Entailment; 17. Explosion and Absurdity; 18. The Truth-Functional Conditional; 19. `If's and `!'s; Why Natural Deduction?: 20. PL Proofs: Conjunction and Negation; 21. PL Proofs: Disjunction; 22. PL Proofs: Conditionals; 23. PL Proofs:Theorems; 24. PL Proofs: Metatheory: Part IV. Interlude: Formalizing General Propositions; 25. Names and Predicates; 26. Quantifers in Ordinary Language; 27. Quantifer-variable Notation; 28. QL Languages; 29. Simple Translations; 30. More on Translations; Interlude: Arguing in QL: 31. Informal Quantifer Rules; 32. QL Proofs; 33. More QL Proofs; 34. Empty Domains?; 35. Q-valuations; 36. Q-validity; 37. QL Proofs: Metatheory; Interlude: Extending QL: 38. Identity; 39. QL= Languages; 40. Definite Descriptions; 41. QL= Proofs; 42. Functions. Appendix. Soundness and Completeness.

Peter Smith was formerly Senior Lecturer in Philosophy at the University of Cambridge. His books include Explaining Chaos (Cambridge, 1998) and An Introduction to Gödel's Theorems (Cambridge, 2007; 2013).