3.6c Propositional Syntax 6: Conditional Proof

Final of three videos (3.6a, 3.6b, 3.6c) on Conditional Proof (CP). This important rule of inference is a useful problem solving technique. We use it on syntactic deductions, syntactic proofs, and we see some creative applications of it.

Bivalent Logic Explained Table of Contents:

Chapter 1: Propositional Symbolization
1.1 Propositions, Arguments, Validity, and Soundness
1.2 The Law of Bivalence
1.3 Propositional Symbolization 1: Constants, Variables, Negation, Conjunction, Disjunction
1.4 Propositional Symbolization 2: Advanced Conjunctions and Disjunctions
1.5 Propositional Symbolization 3: Material Conditionals
1.6 Propositional Symbolization 4: Material Biconditionals
1.7 Propositional Symbolization 5: Formation Rules for Forms and the Main Connective
1.8 Propositional Symbolization 6: Substitution Instances

Chapter 2: Propositional Semantics
2.1 Propositional Semantics 1: Truth Tables
2.2 Propositional Semantics 2: Semantic Properties of Propositions
2.3 Propositional Semantics 3: Logical Equivalence
2.4 Propositional Semantics 4: Semantic Properties of the 16 Logical Connectives
2.5 Propositional Semantics 5: Semantic Consistency
2.6 Propositional Semantics 6: Semantic Validity
2.7 Propositional Semantics 7: Common Semantically Valid Forms
2.8 Propositional Semantics 8: Advanced Semantic Validity

Chapter 3: Propositional Syntax
3.1 Propositional Syntax 1: Rules of Inference for &, v
3.2 Propositional Syntax 2: Rules of Inference for →
3.3 Propositional Syntax 3: Rules of Replacement for ~, &, v
3.4 Propositional Syntax 4: Rules of Replacement for →, ≡
3.5 Propositional Syntax 5: Axioms and Theorems
3.6 Propositional Syntax 6: Conditional Proof
3.7 Propositional Syntax 7: Advanced Conditional Proof
3.8 Propositional Syntax 8: Indirect Proof
3.9 Propositional Syntax 9: Advanced Indirect Proof

Chapter 4: Quantificational Symbolization
4.1 Quantificational Symbolization 1: Elementary Subject Predicate Discourse
4.2 Quantificational Symbolization 2: Quantificational Forms and Substitution Instances
4.3 Quantificational Symbolization 3: The Mechanics of the Universal Quantifier
4.4 Quantificational Symbolization 4: The Meaning of the Universal Quantifier
4.5 Quantificational Symbolization 5: The Mechanics of the Existential Quantifier
4.6 Quantificational Symbolization 6: The Meaning of the Existential Quantifier
4.7 Quantificational Symbolization 7: Formal Relationships Between the Quantifiers
4.8 Quantificational Symbolization 8: The Mechanics of Relations
4.9 Quantificational Symbolization 9: The Meaning of Relations
4.10 Quantificational Symbolization 10: Relations on the Unrestricted Domain
4.11 Quantificational Symbolization 11: Formal Properties of Relations
4.12 Quantificational Symbolization 12: The Mechanics of Identity Sentences
4.13 Quantificational Symbolization 13: The Meaning of Identity Sentences

Chapter 5: Quantificational Semantics
5.1 Quantificational Semantics 1: Interpretations
5.2 Quantificational Semantics 2: Tableaux Techniques
5.3 Quantificational Semantics 3: Relation Tableaux
5.4 Quantificational Semantics 4: Identity Tableaux
5.5 Quantificational Semantics 5: Central Semantic Concepts
5.6 Quantificational Semantics 6: Expansions
5.7 Quantificational Semantics 7: Expansions with Relations
5.8 Quantificational Semantics 8: Expansions with Identity
5.9 Quantificational Semantics 9: The Limits of Quantificational Semantics

Chapter 6: Quantificational Syntax
6.1 Quantificational Syntax 1: Old Rules New Sentences
6.2 Quantificational Syntax 2: Universal Instantiation
6.3 Quantificational Syntax 3: Universal Generalization
6.4 Quantificational Syntax 4: Existential Generalization
6.5 Quantificational Syntax 5: Existential Instantiation
6.6 Quantificational Syntax 6: Quantifier Negation
6.7 Quantificational Syntax 7: Conditional and Indirect Proof with Quantifiers
6.8 Quantificational Syntax 8: Theorems 1 and Central Syntactic Concepts
6.9 Quantificational Syntax 9: Quantifier Rules with Relations
6.10 Quantificational Syntax 10: Theorems 2 (Relations)
6.11 Quantificational Syntax 11: Identity Substitution
6.12 Quantificational Syntax 12: Theorems 3 (Identity)