3.7b Propositional Syntax 7: Advanced Conditional Proof

Final of two videos (3.7a, 3.7b) on Advanced Conditional Proof (CP). We discuss the important strategy of nesting multiple assumptions within one another. We discuss some creative applications.

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)