Department of Philosophy (PHI)

Characteristics of a valid argument

• It cannot have true premises and a false conclusion
• If its premises are true, its conclusion must be true
• If its conclusion is false, it must have at least one false premise
• All of the information in the conclusion is also in the premises
• The probability of its conclusion, given its premises, is 1

Characteristics of an invalid argument

• It can have true premises and a false conclusion.
• Even if its premises are true, it may have a false conclusion.
• Even if its conclusion is false, it may have true premises.
• There is information in the conclusion that is not in the premises.
• Probability of its conclusion, given its premises, is less than 1.

Deductive Validity and Truth (1)

• A deductively valid argument can go from…
  
  • …true premises to a true conclusion
  • …false premises to a true conclusion
  • …false premises to a false conclusion
• A deductively valid argument cannot go from
  
  • ...true premises to a false conclusion

Deductive Validity and Truth (2)

• An argument consisting of true statements can be invalid.
• An argument consisting of false statements can be valid.
• In a valid argument…
  
  • ...true premises guarantee a true conclusion
  • ...a false conclusion guarantees at least one false premise
  • ...a false premise does not guarantee a false conclusion
  • ...a true conclusion does not guarantee true premises