2: Modus Ponens

Formal Logic

Key Terms

Deductive Logic
Sentential Logic
Affirming the Antecedent
Modus Ponens

  • Based on deductive logic
  • General statement leads to a logically certain conclusion
  • Also called Sentential Logic because it is concerned with the relationship between sentences

Modus Ponens

  • Also called Affirming the Antecedent (what came before)

Modus Ponens

Premise(s): If P, then Q
Premise(s): P
Conclusion: Therefore, Q

  • If you replace P and Q with any sentence, this results in a valid argument
    • Recall valid only means the conclusion follows from the premise
    • A valid argument may not be true, and thus would not be sound


  • If cake is made with sugar, then the cake is sweet
  • Cake is made with sugar
  • Therefore, the cake is sweet


  • If the sky is blue, then it is not raining.
  • The sky is blue
  • Therefore it is not raining.

  • If it is bright outside, then I will wear sunglasses.
  • It is bright outside.
  • Therefore, I am wearing sunglasses.


  • Valid structure does not always lead to a sound argument
  • The cake may not be sweet if vinegar was also added.
  • The sky may be mostly blue, but it still rain.
  • I may have lost my sunglasses.
  • Modus Ponens speaks only to the format of the statement, not if it is true.