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 | |
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