An Introduction to Formal Logic

Description

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 What is deductive logic? Validity and soundness Forms of inference Proofs The counterexample method Logical validity Propositions and forms Interlude: From informal to formal logic Three connectives PL syntax PL semantics `P's, `Q's, `'s, `'s – and form again Truth functions Expressive adequacy Tautologies Tautological entailment More about tautological entailment Explosion and absurdity The truth-functional conditional `If's and `'s Interlude: Why natural deduction? PL proofs: conjunction and negation PL proofs: disjunction PL proofs: conditionals PL proofs: theorems PL proofs: metatheory Interlude: Formalizing general propositions Names and predicates Quantifiers in ordinary language Quantifier-variable notation QL languages Simple translations More on translations Interlude: Arguing in QL Informal quantifier rules QL proofs More QL proofs Empty domains? Q-valuations Q-validity QL proofs: metatheory Interlude: Extending QL Identity QL= languages Definite descriptions QL= proofs Functions Appendix: Soundness and completeness The Greek alphabet Further reading