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An "Argumentative" Teacher and Her "Argumentative" Pupil

Logic can create all kinds of problems. Consider this dilemma...


An ancient teacher of argumentation made a contract with one of her pupils. The pupil would not have to pay for the lessons if he did not win his first case. After the lessons were completed, the student did not take any cases. In order to receive payment, the teacher sued the pupil.

The pupil defended himself with the following argument:

  • Either I will win this case, or I will lose it.
  • If I win this case, I will not have to pay my teacher (because she will have lost her suit for payment).
  • If I lose this case, I will not have to pay my teacher (because of the terms of our agreement).
  • Thus, I do not have to pay my teacher.
The teacher, however, presented this argument:
  • Either I will win this case, or I will lose it.
  • If I win this case, the pupil must pay me (because I will have won my suit for payment).
  • If I lose this case, the pupil must pay me (because he will have won his first case).
  • Thus, the pupil must pay me.
How was the case decided?

 

Source: W. Salmon's Logic, 1963, p. 33


Hint: Go through each statement carefully...and then more carefully!

 


Solution Commentary: The key: The original contract contains a hidden self-contradiction....can you sort out the dilemma by finding it?