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Preface to the Eleventh Edition | |
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Preface to the Tenth Edition | |
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Introduction | |
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The Elements of an Argument | |
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Deduction and Induction | |
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Deductive Argument Forms | |
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Truth and Validity | |
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Soundness | |
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Consistency | |
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Contexts of Discovery and Justification | |
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The Plan of This Book | |
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Key Terms | |
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Sentential Logic | |
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Symbolizing in Sentential Logic | |
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Atomic and Compound Sentences | |
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Truth-Functions | |
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Conjunctions | |
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Non-Truth-Functional Connectives | |
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Variables and Constants | |
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Negations | |
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Parentheses and Brackets | |
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Use and Mention | |
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Disjunctions | |
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"Not Both" and "Neither . . . Nor" | |
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Material Conditionals | |
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Material Biconditionals | |
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"Only If" and "Unless" | |
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Symbolizing Complex Sentences | |
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Alternative Sentential Logic Symbols | |
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Key Terms | |
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Truth Tables | |
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Computing Truth-Values | |
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Logical Form | |
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Tautologies, Contradictions, and Contingent Sentences | |
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Logical Equivalences | |
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Truth Table Test of Validity | |
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Truth Table Test of Consistency | |
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Validity and Consistency | |
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The Short Truth Table Test for Invalidity | |
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The Short Truth Table Test for Consistency | |
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A Method of Justification for the Truth Tables | |
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Key Terms | |
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Proofs | |
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Argument Forms | |
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The Method of Proof: Modus Ponens and Modus Tollens | |
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Disjunctive Syllogism and Hypothetical Syllogism | |
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Simplification and Conjunction | |
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Addition and Constructive Dilemma | |
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Principles of Strategy | |
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Double Negation and DeMorgan's Theorem | |
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Commutation, Association, and Distribution | |
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Contraposition, Implication, and Exportation | |
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Tautology and Equivalence | |
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More Principles of Strategy | |
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Common Errors in Problem Solving | |
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Key Terms | |
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Conditional and Indirect Proofs | |
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Conditional Proofs | |
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Indirect Proofs | |
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Strategy Hints for Using CP and IP | |
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Zero-Premise Deductions | |
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Proving Premises Inconsistent | |
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Adding Valid Argument Forms | |
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An Alternative to Conditional Proof? | |
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The Completeness and Soundness of Sentential Logic | |
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Introduction and Elimination Rules | |
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Key Terms | |
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Sentential Logic Truth Trees | |
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The Sentential Logic Truth Tree Method | |
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The Truth Tree Rules | |
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Details of Tree Construction | |
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Normal Forms and Trees | |
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Constructing Tree Rules for Any Function | |
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Key Terms | |
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Predicate Logic | |
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Predicate Logic Symbolization | |
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Individuals and Properties | |
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Quantifiers and Free Variables | |
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Universal Quantifiers | |
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Existential Quantifiers | |
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Basic Predicate Logic Symbolizations | |
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The Square of Opposition | |
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Common Pitfalls in Symbolizing with Quantifiers | |
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Expansions | |
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Symbolizing "Only," "None but," and "Unless" | |
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Key Terms | |
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Predicate Logic Semantics | |
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Interpretations in Predicate Logic | |
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Proving Invalidity | |
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Using Expansions to Prove Invalidity | |
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Consistency in Predicate Logic | |
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Validity and Inconsistency in Predicate Logic | |
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Key Terms | |
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Predicate Logic Proofs | |
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Proving Validity | |
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The Four Quantifier Rules | |
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The Five Main Restrictions | |
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Precise Formulation of the Four Quantifier Rules | |
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Mastering the Four Quantifier Rules | |
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Quantifier Negation | |
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Key Term | |
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Relational Predicate Logic | |
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Relational Predicates | |
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Symbolizations Containing Overlapping Quantifiers | |
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Expansions and Overlapping Quantifiers | |
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Places and Times | |
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Symbolizing "Someone," "Somewhere," "Sometime," and So On | |
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Invalidity and Consistency in Relational Predicate Logic | |
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Relational Predicate Logic Proofs | |
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Strategy for Relational Predicate Logic Proofs | |
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Theorems and Inconsistency in Predicate Logic | |
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Predicate Logic Metatheory | |
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A Simpler Set of Quantifier Rules | |
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Rationale Behind the Precise Formulation of the Four Quantifier Rules | |
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Cases Involving the Five Major Restrictions | |
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One-to-One Correspondence Matters | |
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Accidentally Bound Variables and Miscellaneous Cases | |
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Predicate Logic Proofs with Flagged Constants | |
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Predicate Logic Truth Trees | |
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Introductory Remarks | |
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General Features of the Method | |
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Specific Examples of the Method | |
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Some Advantages of the Trees | |
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Example of an Invalid Argument with at Least One Open Path | |
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Metatheoretic Results | |
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Strategy and Accounting | |
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Key Terms | |
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Identity and Philosophical Problems of Symbolic Logic | |
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Identity | |
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Definite Descriptions | |
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Properties of Relations | |
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Higher-Order Logics | |
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Limitations of Predicate Logic | |
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Philosophical Problems | |
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Logical Paradoxes | |
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Key Terms | |
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Syllogistic Logic | |
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Categorical Propositions | |
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Existential Import | |
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The Square of Opposition | |
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Conversion, Obversion, Contraposition | |
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Syllogistic Logic - Not Assuming Existential Import | |
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Venn Diagrams | |
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Syllogisms | |
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Determining Syllogism Validity | |
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Venn Diagram Proofs of Validity or Invalidity | |
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Five Rules for Determining Validity or Invalidity | |
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Syllogistics Extended | |
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Enthymemes | |
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Sorites | |
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Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared | |
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Key Terms | |
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Answers to Even-Numbered Exercise Items | |
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Bibliography | |
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Special Symbols | |
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Index | |