3: Modus Tollens

Modus Tollens

Key Terms

Modus Ponens
Modus Tollens

  • Also called Denying the Consequences
  • Notice how the form is similar to Modus Ponens

Modus Tonens

Premise(s): If P, then Q
Premise(s): Not P
Conclusion: Therefore, not Q

  • If you replace P and Q with any sentence, this results in a valid argument
    • Recall, a valid argument may not be true, and thus not sound


  • If cake is made with sugar, then the cake is sweet
  • Cake is not made with sugar
  • Therefore, the cake is not sweet


  • If the watch dog detects an intruder, the dog will bark.
  • The dog did not bark.
  • So the dog did not detect an intruder

  • If I own an elephant, then I own an animal.
  • I do not own an elephant.
  • So I do not own an animal.


  • Valid structure does not always lead to a sound argument
  • The cake may be sweet if vinegar if a sugar substitute is added
  • The watch dog didn't bark because he wasn't a good watch dog.
  • I may own other animals
  • Modus Tollens speaks only to the format of the statement, not if it is true.