Lecture Notes: Truth and Validity in Arguments

Introduction

• Speaker: Julianne Chung, Yale University
• Topic: Truth and validity in arguments
• Focus: Understanding the qualities of truth and validity in determining acceptance of conclusions

Characteristics of Arguments

• Arguments can possess various qualities: clarity, interest, persuasion
• Key focus:
  • Truth of premises: Agreement with facts
  • Validity of argument: Logical connection between premises and conclusion

Definitions

• Truth and Falsity: Properties of statements, not arguments
• Validity: An argument is valid if the truth of its premises guarantees the truth of its conclusion
• Invalidity: When the conclusion doesn't logically follow from premises
• Soundness: When an argument is both true and valid

Examples

1. True Premises, Valid Argument

• Premises:
  • All Australian Shepherds are dogs
  • Split is an Australian Shepherd
• Conclusion: Split is a dog

2. True Premises, Invalid Argument

• Premises:
  • All dogs are animals
  • All cats are animals
• Conclusion: All cats are dogs (invalid conclusion)

3. True Premises, True Conclusion, Invalid Argument

• Premises:
  • All dogs are animals
  • All Australian Shepherds are animals
• Conclusion: All Australian Shepherds are dogs (invalid conclusion)

4. False Premises, Valid Argument

• Premises:
  • You can't teach an old dog new tricks
  • Split is an old dog
• Conclusion: You can't teach Split new tricks (valid reasoning)

5. False Premises, Invalid Argument

• Premises:
  • I like Split
  • Training dogs is easy
• Conclusion: I'll win awards for teaching Split to roll over (invalid reasoning)

Combinations of Truth and Validity

1. True Premises, Valid Reasoning: Sound arguments
2. True Premises, Invalid Reasoning
3. False Premises, Valid Reasoning
4. False Premises, Invalid Reasoning

Evaluating Arguments

• Accept conclusions only if premises are true and reasoning is valid (sound)
• Importance of Validity:
  • Helps determine truth of premises
  • Inference of false conclusions indicates false premises

Practical Example

• Scenario: John calls in sick with flu
• Premises:
  • John is in bed with flu
  • If flu, then not bowling
• Conclusion: John is not bowling (valid)
• Observation: If boss sees John bowling, premise 1 is false

Conclusion

• Validity helps in determining truth or falsity of claims
• Recommended further resources: Videos by Paul (validity) and Aaron (soundness)