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A comprehensive introduction to formal logic, LOGIC AND PHILOSOPHY: A MODERN INTRODUCTION is a rigorous yet accessible text, appropriate for students encountering the subject for the first time. Reading the text is much like having a talented and patient instructor walking a student through difficult concepts in a lecture or during office hours. Abundant carefully crafted exercise sets accompanied by a clear, engaging exposition give students a firm grasp of basic concepts, which build to an exploration of sentential logic, first-order predicate logic, the theory of descriptions, and identity. As the title suggests, this is a book devoted not merely to logic; students will also examine the philosophical debates that led to the development of the field.
- Revised and updated exercises and explanations ensure that students receive an accurate and accessible introduction to logical concepts.
- New feature on the "Logical Revolution" of the 20th century, and the debates among prominent philosophers and mathematicians that led to the creation of modern formal logic.
- This edition is accompanied by several useful supplements, available through CourseMate. These resources include quizzing, supplemental chapters, and Logic Coach. For information on packaging CourseMate with the text, contact your Cengage Learning representative.
- This edition offers three new appendices, one dealing with an alternative to conditional proof; one with predicate logic instantiations, including an extensive discussion of alternatives; and one with problematic translations.
- In addition to revisions made to ensure accuracy of print and thought, this new edition of LOGIC AND PHILOSOPHY: A MODERN INTRODUCTION, 12E contains additional discussions of philosophical interest, such as: special historical discussions of key philosophers and logicians who have made substantive contributions to the development of modern symbolic logic; additions of material concerning definite descriptions and properties of relations (Chapter 13); a revised approach to the semantics of instantiation (Chapter 9); an in-depth discussion of assumptions using apparently free variables (Chapter 9); and a new discussion of demonstrating consistency of predicate logic statements, using interpretations and expansions (Chapter 10).
- Answers to the even-numbered exercises are found in the back of the book, providing immediate feedback to students as they work through the exercises in the text.
- Walk-Through sections: For crucial exercises, these "how-to" sections show, step by step, the process of solving a moderately difficult sample problem.
- Coverage of basic concepts: Beginning with the first chapter, attention is paid to such topics as logical form and the relationship between consistency and validity. The fundamental concept of a semantic interpretation is used to provide a unified explanation of such basic concepts as validity, consistency, logical equivalence, and logical implication in both sentential and predicate logic.
- Help for the mathematically anxious or averse: The text stresses the relationships between mathematical and philosophical concepts, in ways that are designed to engage student interest and to provide reader-friendly explanations of why the mathematical symbols work as they do.
- Sections covering informal fallacies and modal logic, are available in an alternative versions of the text.
- Glossaries following each chapter assist students in reviewing key concepts.
Preface to the Tenth Edition.
The Elements of an Argument. Deduction and Induction. Deductive Argument Forms. Truth and Validity. Soundness. Consistency. Contexts of Discovery and Justification. The Plan of This Book. Key Terms.
PART I: SENTENTIAL LOGIC.
2. Symbolizing in Sentential Logic.
Atomic and Compound Sentences. Truth-Functions. Conjunctions. Non–Truth-Functional Connectives. Variables and Constants. Negations. Parentheses and Brackets. Use and Mention.
Disjunctions. "Not Both" and "Neither . . . Nor". Material Conditionals. Material Biconditionals. "Only If" and "Unless". Symbolizing Complex Sentences. Alternative Sentential Logic Symbols. Key Terms.
3. Truth Tables.
Computing Truth-Values. Logical Form. Tautologies, Contradictions, and Contingent Sentences. Logical Equivalences. Truth Table Test of Validity. Truth Table Test of Consistency. Validity and Consistency. The Short Truth Table Test for Invalidity. The Short Truth Table Test for Consistency. A Method of Justification for the Truth Tables. Key Terms.
Argument Forms. The Method of Proof: Modus Ponens and Modus Tollens. ,Disjunctive Syllogism and Hypothetical Syllogism. Simplification and Conjunction. Addition and Constructive Dilemma. Principles of Strategy. Double Negation and DeMorgan''s Theorem. Commutation, Association, and Distribution. Contraposition, Implication, and Exportation. Tautology and Equivalence. More Principles of Strategy. Common Errors in Problem Solving.
5. Conditional and Indirect Proofs.
Conditional Proofs. Indirect Proofs. Strategy Hints for Using CP and IP. Zero-Premise Deductions. Proving Premises Inconsistent. Adding Valid Argument Forms. The Completeness and Soundness of Sentential Logic. Introduction and Elimination Rules. Key Terms.
6. Sentential Logic Truth Trees.
The Sentential Logic Truth Tree Method. The Truth Tree Rules. Details of Tree Construction. Normal Forms and Trees. Constructing Tree Rules for Any Function. Key Terms.
PART II: PREDICATE LOGIC.
7. Predicate Logic Symbolization.
Individuals and Properties. Quantifiers and Free Variables. Universal Quantifiers. Existential Quantifiers. Basic Predicate Logic Symbolizations. The Square of Opposition. Common Pitfalls in Symbolizing with Quantifiers. Expansions. Symbolizing "Only," "None but," and "Unless".
8. Predicate Logic Semantics.
Interpretations in Predicate Logic. Proving Invalidity. Using Expansions to Prove Invalidity. Consistency in Predicate Logic. Validity and Inconsistency in Predicate Logic. Key Terms.
9. Predicate Logic Proofs.
Proving Validity. The Four Quantifier Rules. The Five Main Restrictions. Precise Formulation of the Four Quantifier Rules. Mastering the Four Quantifier Rules. Quantifier Negation. Key Term.
10. Relational Predicate Logic.
Relational Predicates. Symbolizations Containing Overlapping Quantifiers. Expansions and Overlapping Quantifiers. Places and Times. Symbolizing "Someone," "Somewhere," "Sometime," and So On. Invalidity and Consistency in Relational Predicate Logic. Relational Predicate Logic Proofs. Strategy for Relational Predicate Logic Proofs. Theorems and Inconsistency in Predicate Logic. Predicate Logic Metatheory. A Simpler Set of Quantifier Rules.
11. Rationale Behind the Precise Formulation of the Four Quantifier Rules.
Cases Involving the Five Major Restrictions. One-to-One Correspondence Matters. Accidentally Bound Variables and Miscellaneous Cases. Predicate Logic Proofs with Flagged Constants.
12. Predicate Logic Truth Trees.
Introductory Remarks. General Features of the Method. Specific Examples of the Method. Some Advantages of the Trees. Example of an Invalid Argument with at Least One Open Path. Metatheoretic Results. Strategy and Accounting. Key Terms.
13. Identity and Philosophical Problems of Symbolic Logic.
Identity. Definite Descriptions. Properties of Relations. Higher-Order Logics. Limitations of Predicate Logic. Philosophical Problems. Logical Paradoxes. Key Terms.
14. Syllogistic Logic.
Categorical Propositions. Existential Import. The Square of Opposition. Conversion, Obversion, Contraposition. Syllogistic Logic--Not Assuming Existential Import. Venn Diagrams. Syllogisms.
Determining Syllogism Validity. Venn Diagram Proofs of Validity or Invalidity. Five Rules for Determining Validity or Invalidity. Syllogistics Extended. Enthymemes. Sorites. Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared. Key Terms.
Appendix A: An Alternative to Conditional Proof.
Appendix B: Instantiations and Semantics.
Answers to Even-Numbered Exercise Items.
"The book develops formal logic rigorously, but with an approach that students will find clear and accessible, especially with respect to the explanations of key concepts and the featured "walk-throughs" of proof techniques, etc."
"I would describe the book as a 'real logic book that is about as accessible as it gets."
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
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Cengage Learning's CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. Maximize your course success with the integrated eBook and chapter-specific learning tools that include flashcards, quizzes, videos, and more in your CourseMate. Key Features: Interactive eBook, Engagement Tracker, Learning Objectives, Tutorial Quizzes, Glossary and Flashcards, and Web Links and References.