Part I: SENTENTIAL LOGIC.
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.
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. Key Terms.
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. An Alternative to Conditional Proof? 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". Key Terms.
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 (QN). Key Terms.
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 Formulaton 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.
Answers to Even-Numbered Exercise Items.