| |
| |
| |
Sentential Logic | |
| |
| |
| |
Introduction to Logic Why Study Logic? | |
| |
| |
What Logic Is All About Induction and Deduction | |
| |
| |
Form and Validity Truth and Validity | |
| |
| |
The Nature of Symbolic Logic | |
| |
| |
The Scope of Symbolic Logic | |
| |
| |
Definitions Study | |
| |
| |
Questions | |
| |
| |
Exercises | |
| |
| |
| |
The Structure of Sentential Logic Simple and Compound Sentences Sentential Operators | |
| |
| |
The Structure and Symbolism of Sentential Logic | |
| |
| |
Definitions Study | |
| |
| |
Questions | |
| |
| |
Exercises | |
| |
| |
| |
Computing Truth Values Truth Tables for the Operators | |
| |
| |
Computing Truth Values Truth-functional Operators | |
| |
| |
Non-truth-functional Operators | |
| |
| |
Definitions Study | |
| |
| |
Questions | |
| |
| |
Exercises | |
| |
| |
| |
Symbolizing English Sentences Simple Sentences Truth-functional and Non-truth-functional | |
| |
| |
Compounds Symbolizing Truth-functional | |
| |
| |
English Operators Symbolizing Multiply Complex Sentences | |
| |
| |
Exercises | |
| |
| |
| |
Truth Tables for Testing Validity Constructing Base Columns for Truth Tables | |
| |
| |
The Truth Table | |
| |
| |
Test for Validity | |
| |
| |
Shortcut Validity | |
| |
| |
Tests Mechanical Decision Procedures | |
| |
| |
Definitions Study | |
| |
| |
Questions | |
| |
| |
Exercises | |
| |
| |
| |
Further Applications of the Truth Table Method Tautologies, Contradictions, and Contingencies | |
| |
| |
Logical Implication and Logical | |
| |
| |
Equivalence Rules of Inference, Logical Implication, and Logical Equivalence | |
| |
| |
Consistency Four Kinds of Truth Table | |
| |
| |
Problems and the Relations Between Them | |
| |
| |
Definitions Study | |
| |
| |
Questions | |
| |
| |
Exercises | |
| |
| |
| |
The Proof Method: Eight Basic | |
| |
| |
Inference Rules Form and Substitution | |
| |
| |
Instance The Proof Process Eight Basic | |
| |
| |
Inference Rules Derivations and Proofs | |
| |
| |
Constructing Simple Proofs | |
| |
| |
Constructing More Complex Proofs | |
| |
| |
Summary of Rules of Inference | |
| |
| |
Definitions | |
| |
| |
Exercises | |
| |
| |
| |
Replacement Rules | |
| |
| |
The Structure of Replacement Rules | |
| |
| |
The Ten Replacement Rules Constructing Simple Proofs | |
| |
| |
with Replacement Rules Strategies for More Complex Proofs | |
| |
| |
Summary of Replacement Rules | |
| |
| |
Exercises | |
| |
| |
| |
Conditional Proof and Indirect Proof | |
| |
| |
Conditional Proof | |
| |
| |
Indirect Proof | |
| |
| |
Discharging Assumptions; Restrictions on C.P. and I.P. Using C.P. and I.P. Proofs of Theorems Invalidity Truth and Proof | |
| |
| |
Summary of Rules of Conditional Proof and Indirect Proof | |
| |
| |
Definitions | |
| |
| |
Exercises | |
| |
| |
| |
Monadic Predicate Logic | |
| |
| |
| |
Singular Sentences | |
| |
| |
Singular Sentences and Propositional | |
| |
| |
Functions Symbolizing Singular Sentences | |
| |
| |
Definitions | |
| |
| |
Exercises | |
| |
| |
| |
Quantifiers Universal and Existential Quantifiers | |
| |
| |
Free and Bound Variables; Scope of a Quantifier Negated Quantifiers | |
| |
| |
Definitions | |
| |
| |
Exercises | |
| |
| |
| |
Categorical Propositions | |
| |
| |
The Four Categorical Propositions | |
| |
| |
Individuals, Sets, and Properties | |
| |
| |
Venn Diagrams Symbolizing Categorical Propositions | |
| |
| |
Negated Categorical Propositions | |
| |
| |
Deriving C.Q.N. Rules from Q.N. Rules Symbolizing English Categorical Sentences | |
| |
| |
Summary of Categorical Propositions | |
| |
| |
Definitions | |
| |
| |
Exercises | |
| |
| |
| |
Complex Subjects and Predicates Complex | |
| |
| |
Subjects and Predicates Equivalent Symbolizations | |
| |
| |
Exercises | |
| |
| |
| |
Quantifier Form and Truth-Functional | |
| |
| |
Compounds of Quantifier Statements Quantifier | |
| |
| |
Form Truth-functional Compounds and Quantifier | |
| |
| |
Form Symbolizing Truth-functional Compounds | |
| |
| |
Definitions | |
| |
| |
Exercises | |
| |
| |
| |
Proofs in Predicate Logic Preliminary Statement of the Four Quantifier Rules Instances of Quantified Formulas | |
| |
| |
The Rules of Universal Instantiation (U.I.) and Existential Generalization (E.G.) | |
| |
| |
The Rules of Existential Instantiation (E.I.) adn Universal Generalization (U.G.) | |
| |
| |
Flagging Restrictions Constructing Proofs for "Pure" | |
| |
| |
Quantifier Arguments Constructing Proofs for Arguments Containing Truth-functional Compounds | |
| |
| |
Constructing Proofs of Quantifier Theorems Statement of the Quantifier Rules, with All Necessary Restrictions | |
| |
| |
Exercises | |
| |
| |
| |
Invalidity in Quantifier Logic | |
| |
| |
The Natural Interpretation Method Truth Conditions for Quantifier Statements | |
| |
| |
The Model Universe Method Definitions Exercises | |
| |
| |
| |
Relational Predicate Logic | |
| |
| |
| |
Symbolization in Relational Predicate Logic | |