Philosophy 60: Symbolic Logic

Return to Home Page

Administrative:

• Philosophy 60 Section 2 Syllabus
• Grading and Expectations
• Getting Logical Symbols in MS Word
• Convert Grade to Percentage

EXTRA CREDIT:

• Indirect Proof

Final Exam Schedule:

• Section 3:

Review For Midterm Exam:

• List of Midterm Topics
• Translating Into Sentential: Easy Answers
• Translating Sentential Logic: Moderate Answers
• Translating Conditionals And Biconditionals: Practice
• Practice: From Logic to English: Answers
• Practice Symbolizing & Deduction: Gustason p. 94: Answers
• Sentential Deduction: Practice Problems: Answers
• Summary of Predicate/Quantified Deduction
• Practice Indirect Proof
• Deducing Sentential Theorems: Answers

Review For Final Exam:

• List of Review Topics
• Practice I: Symbolizing in Predicate Logic with Only Constants
• Practice II: Symbolizing In Predicate Logic (One quantifier-- Multiple Choice)
• Practice III:Symbolizing Predicate Logic (One class & AEIO): Answers
• Practice IV: Symbolize Predicate Logic Review Steps, Every type : Answers
• Practice V: Logic to English, Multiply Quantified (multiple choice)
• Practice VI: Symbolizing Predicate Logic Multiple Quant: Answers
• Practice VII: Putting it All Together: Jobs
• Symbolizing Sentences, Gustason, p. 177: Answers
• Review Deduce Deductions with Multiply Quantified Predicates
• Review Deducing Theorems
• Chapter 6 and 7 Review Questions

• Modal Logic: Chart and Examples
• Modal Logic: Review: Answers
• Many Valued Logic: Review Questions: Answers

Homework Assignments:

Section 2

• Homework #1, Chapter 1
• Homework #2, Chapter 2
• Homework #3, Chapter 3
• Homework #4, Chapter 5
• Homework #5, Chapter 6
• Homework #6, Chapter 7

OVERHEADS

Chapter 1:

• Arguments Vs. Explanations
• Analyzing Passages: Arguments & Parts
• Classifying Arguments:Deductive/Inductive
• Validity, Implication, Soundness

• Sentential Logic: Skills and Uses
• Introduction to Sentential Logic
• Finding the Main Connective: English
• Sentence and Argument Forms
• Introduction to Symbolizing in Sentential Logic
• Summary of Symbolizing in Sentential Logic
• Examples: Translating Sentential Logic
• Exercise: Symbolize English Sentences
• Truth Functional Sentence Connectives
• Properties of 'and' and 'or'
• Translating Conditionals and Biconditionals
• Sentence Connectives Chart
• Unless
• Symbolizing Sentences and Sentence Forms
• Finding the Main Connective & Sentence Type Maia: Practice 1
• Finding the Main Connective: Practice 2
• Translating from Logic to English: Maia Practice 1: Answers 1

Chapter 2: Statement Logic: Semantic Methods

• Logical Properties of Sentences and Sentence Forms
• Truth Tables for Sentence Connectives
• Introduction to Truth Tables
• Creating Truth Tables: Number of Rows
• Practice: Logical Properties of Sentences
• Implication and Equivalence Between Sentences: English
• Use TT Show Implication/Equivalence Between Sentences Directions
• Implication and Equivalence: Examples

• The Corresponding Conditional
• Valid Argument Forms: Modus Ponens, Etc.
• Using Truth Tables to Show Validity: Easy to Hard
• Valid Argument Forms: Using Truth Tables
• The Corresponding Conditional of a Truth Table Valid Argument
• Representing Tautologies: Double Turnstile
• Prove Constructive Dilemma

• Short Truth Table Method Outline
• The Short Truth Table Method: Simplest Case -- Longer Version
• The Short Truth Table Method: Two Rows Needed to Show Valid
• The Short Truth Table Method: More Rows Needed To Show Invalid
• Short TT: More Than One Way to Make Conclusion False
• Practice: The Short Truth Table Method
• Truth Table Method: Long and Short Compared

Chapter 3: Statement Logic: Deductive Methods

• Validity, Deductive Rules and Deductions
• Introduction to Deduction
• Rules of Inference Vs. Rules of Replacement
• Rules of Inference & Replacement: Conjunctions
• Rules of Inference & Replacement: Disjunction
• Rules of Inference & Replacement: Implication & Equivalence
• De Morgan's Law
• Class Exercise: Deduct DM, Dis, Add, MP, MT, Exp
• General Deduction Strategies
• Practice Sentential Deduction: One Liners: Answers
• Practice Deduction: Simp, Add, Conj, DS, MP: Answers
• Practice Deduction: Moderate

• Conditional Proof Demo and Steps
• Introduction to Conditional Proof
• More On Conditional Proof
• Practice Problem Set: Conditional Proof: Answers
• Indirect Proof Method
• Conditional Proof Vs. Indirect Proof
• Practice Indirect Proof: Last Steps
• Practice Indirect Proof
• Proof Strategies: Expanded Set
• Introduction to Proving Theorems
• Introduction to Proving Conditional Theorems
• Practice: Proving Theorems: Answers

• Proving Rule of Replacement: Distribution

Chapter 4: Consistency Between Semantic & Deductive Methods

• Soundness & Completeness: The Steps
• Proving Metatheorem I
• Proving Metatheorem II
• Proving Strong Completeness: Metatheorem IV by Modus Ponens
• Proving Metatheorem IV by Disjunctive Syllogism

Chapter 5: Predicate Logic: Symbolizing

• Why Predicate Logic?
• The Need for Internal Structure: Example
• Sentential Vs. Predicate Logic: Chart
• Claims: Compound, Atomic and Internal Structure
• Types of Noun Phrases
• Types of Predicates
• Generalizing: The Need For Quantifers
• Role Of Variables
• Open Sentences and Substitution Instances
• Predicate Logic: Terminology
• Recursive Definition of a Formula in Predicate Logic
• Practice: Symbolize Sentences With Constants Only
• Representing Sentences with Relational Predicates
• Relational Verbs: Order of Variables
• Practice: Symbolize in Predicate Logic, One Quantifier (include relational)

• Sentences of Categorical Logic: A, E, I and O
• Introduction to Multiple Quantification
• April 6th Worksheet
• Worksheet Answers
• Exercise: Find Main Connective, Sentence Type
• Universe of Discourse
• Practice Multiple Quantification
• Exercise: Practice for Quiz Translate Predicate Logic
• Predicate Logic and Identity
• Definite Descriptions

Chapter 6: Predicate Logic: Semantic Methods

• Predicate Logic: Semantic Concerns
• Semantic Definitions
• Semantic Methods for Predicate Logic
• Semantic Methods: Chart
• Why Truth Tables Won't Work
• Method 1: Showing Invalidity by English Interpretation
• Practice 1: Show Argument Invalid English Interpretation
• Practice 2: Show Arg Invalid using English Interpretation
• Practice 3: Show Argument Invalid by English Interpretation
• Exercise: Use English Interpretation 4 Premises
• Universe of Discourse Size and Showing Invalidity
• Method 2: Showing Invalidity Using Instantiation
• Instantiate With More Than One Individual
• Practice 1: Showing Invalidity by Instantiation
• Practice 2: Showing Invalidity Via Instantiation
• Instantiate Multiply Quantified Sentences
• Instantiate Multiply Quantified Arguments

Chapter 7: Predicate Logic: Deductive Methods

• Deduction Policies: Acceptable Shortcuts
• Why We Need Quantified Deduction
• Introduction To Quantified Deduction
• Introduction to Universal Instantiation
• Introduction to Existential Instantiation
• Rules of Instantiation
• Rules of Generalization
• Existential Proof Demo
• Summary of Proof Strategies
• Introduction to Universal Generalization
• Universal Proof: Applying the Rule of UG
• Universal Proof Practice 1
• Universal Conditional Proof Practice: Simple
• Universal Conditional Proof Practice: Simple 2
• Nested Universal Proof Demo (with Indirect Proof)
• Existential Proofs: Practice 1
• Conditional Quantified Proof Demo (Nested)
• Practice 1: Conditional Proof
• Practice 2: Conditional Proof
• Rule of Quantifier Negation
• Quantifier Negation Demo
• Proof Strategies

• Deducing Theorems Demo: Answers
• Rules of Quantified Identity
• Summary of Quantified Deduction

• Relational Logic: Multiply Quantified Demo 1:
• Practice 1: Multiply Quantified Predicates
• Practice 2: Multiply Quantified Predicates
• Relational Logic: Multiply Quantified Two Existential Premises

Beyond Classical Logic: Bonevac Deduction

Necessity

• Problems With Material Implication
• Modal Logic Definitions
• Five Theses of Modal Logic

Many-Valued Logic

• Comparison: Classical and Many Valued Logic
• Many Valued Truth Connectives

Fuzzy Logic

• Sentence Connectives Definitions