Formal Logic

Description

Formal Logic is an undergraduate text suitable for introductory, intermediate, and advanced courses in symbolic logic. The book’s nine chapters offer thorough coverage of truth-functional and quantificational logic, as well as the basics of more advanced topics such as set theory and modal logic. Complex ideas are explained in plain language that doesn’t presuppose any background in logic or mathematics, and derivation strategies are illustrated with numerous examples. Translations, tables, trees, natural deduction, and simple meta-proofs are taught through over 400 exercises. A companion website offers supplemental practice software and tutorial videos. Contents Acknowledgements I Informal Notions Informal Introduction Logic: What, Why, How? Arguments, Forms, and Truth Values Deductive Criteria Quirky Cases of Deductive Validity Inductive Criteria Other Deductive Properties Exercises Chapter Glossary II Truth-Functional Logic The Language S Introducing S Compound Sentences and Truth-Functional Logic Negation—It is not the case that… Conjunction—Both…and - - - Disjunction—Either…or - - - Material Conditional—If…,then - - - Material Biconditional—…if and only if - - - Conditionals and Non-Truth-Functionality Some Technical Bits Object Language and Metalanguage Use and Mention Metavariables Syntax and Semantics The Syntax of S Defining the Language Syntactic Concepts and Conventions Exercises Symbolizations Negation, Conjunction, Disjunction Exercises Conditionals and Biconditionals Exercises Complex Symbolizations Exercises Alternate Symbols and Other Choices Chapter Glossary Formal Semantics for S Truth Value Assignments and Truth Tables Semantic Properties of Individual Wffs Exercises Semantic Properties of Sets of Wffs Exercises Semantic Properties, Their Interrelations, and Simple Metalogic Exercises Truth Trees Tests with Truth Trees Exercises Chapter Glossary SD: Natural Deduction in S The Basic Idea Reiteration—R Wedge Rules—I,E Arrow Rules—I,E Hook Rules—I,E Vee Rules—I,E Double Arrow Rules—I,E Exercises Derivations: Strategies and Notes Proof Theory in SD Exercises SDE, an Extension to SD The Inference Rules of SDE Exercises The Replacement Rules of SDE Exercises Chapter Glossary III Quantificational Logic The Language P Introducing P Quantificational Logic Predicates and Singular Terms Predicate Letters and Individual Constants in P Pronouns and Quantifiers Variables and Quantifiers in P The Syntax of P Defining the Language Syntactic Concepts and Conventions Exercises Simple Symbolizations Non-categorical Claims Exercises Categorical Claims Exercises Complex Symbolizations Basics of Overlapping Quantifiers Exercises Identity, Numerical Quantification, and Definite Descriptions Exercises Chapter Glossary Formal Semantics for P Semantics and Interpretations Basics of Interpretations Interlude: A Little Bit of Set Theory Formal Interpretation of P Constructing Interpretations Semantic Properties of Individual Wffs Exercises Semantic Properties of Sets of Wffs Exercises Quantifier Scope and Distribution Exercises Properties of Relations Exercises Chapter Glossary PD: Natural Deduction in P Derivation Rules for the Quantifiers Universal Elimination—E Existential Introduction—I Universal Introduction—I Existential Elimination—E Exercises Derivations: Strategies and Notes Proof Theory in PD Exercises PDE, an Extension to PD Quantifier Negation—QN Exercises Chapter Glossary IV Advanced Topics Basic Set Theory, Paradox, and Infinity Basics of Sets Russell's Paradox The Axiom Schema of Separation Subset, Intersection, Union, Difference Exercises Pairs, Ordered Pairs, Power Sets, Relations, and Functions Infinite Sets and Cantor's Proof Exercises Chapter Glossary Modal Logic Necessity, Possibility, and Impossibility Modalities Logical, Metaphysical, Physical Possible Worlds The Language S The Syntax of S Exercises Basic Possible Worlds Semantics for S Semantic Properties of Wffs and Sets of Wffs Exercises Possible Worlds and Trees Exercises Natural Deduction in S System K System D System T System B System S4 System S5 Relations Between Modal Systems Exercises Chapter Glossary V Appendices Answers to Exercises Answers to 1.6 Answers to 2.3.3 Answers to 2.4.2 Answers to 2.4.4 Answers to 2.4.6 Answers to 3.2.1 Answers to 3.3.1 Answers to 3.4.1 Answers to 3.5.2 Answers to 4.1.7 Answers to 4.3.1 Answers to 4.4.2 Answers to 4.4.4 Answers to 5.2.3 Answers to 5.3.2 Answers to 5.3.4 Answers to 5.4.2 Answers to 5.4.4 Answers to 6.2.1 Answers to 6.3.1 Answers to 6.4.1 Answers to 6.5.1 Answers to 7.1.5 Answers to 7.3.1 Answers to 7.4.2 Answers to 8.4.1 Answers to 8.6.1 Answers to 9.2.2 Answers to 9.3.2 Answers to 9.3.4 Answers to 9.4.8 Glossary Truth Tables, Tree Rules, and Derivation Rules Characteristic Truth Tables Truth Tree Rules for S Modal Tree Rules for S The Derivation System SD The Derivation System SDE The Derivation System PD The Derivation System PDE Modal Derivation Systems