Lecture on Validity in Deductive Arguments

Introduction

• Presenter: Paul Henney, philosophy graduate student at Duke University
• Topic: Validity in deductive arguments, distinct from everyday use of 'valid' meaning 'good point' or 'true statement'.

Understanding Validity

• Argument Structure:
  • Set of statements
  • Premises: statements supporting another
  • Conclusion: statements being supported
• Validity: Specifically pertains to deductive arguments

Definition of Validity

• Valid Argument: If the premises are true, the conclusion must also be true.
  • Validity is not about the truth of premises or conclusion.
  • It's about the guarantee that true premises lead to a true conclusion (premises entail the conclusion).
• Properties:
  • Statements can be true or false
  • Arguments can be valid or invalid

Examples of Valid Arguments

1. Example 1:

   • P1. All humans are mortal
   • P2. Iris Murdoch is a human
   • C. Therefore, Iris Murdoch is mortal
   • Valid because if premises are true, conclusion is true.

2. Example 2 (False Premises):

   • P1. All humans are immortal
   • P2. Iris Murdoch is a human
   • C. Therefore, Iris Murdoch is immortal
   • Valid due to structure, despite false premises.

3. Example 3 (Unknown Truth):

   • P1. All aliens speak English
   • P2. Splock is an alien
   • C. Therefore, Splock speaks English
   • Valid if premises are true, regardless of our knowledge about them.

4. Example 4 (Undefined Terms):

   • P1. All slith are splat
   • P2. Sniff is a slith
   • C. Therefore, Sniff is a splat
   • Valid due to logical structure.

Invalid Argument Example

• Example:
  • P1. All dogs have fur
  • P2. Claire has a lot of fur
  • C. Therefore, Claire is a dog
  • Invalid because the conclusion does not necessarily follow from the premises.

Importance of Validity

• Purpose: Validity checks whether an argument follows valid inference rules (laws of deductive logic).
• Ensures good inferences are made in an argument.

Final Example to Consider

• Exercise:
  • P1. All fruit is a chair
  • P2. Square is a chair
  • C. Therefore, square is a fruit
  • Determine validity or invalidity.