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.
Author(s): Peter Smith
Series: Cambridge Introductions to Philosophy
Edition: 2
Publisher: Cambridge University Press
Year: 2020
Language: English
Pages: 428
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
