Tuesday, June 10, 2008

A paradox in logic

Mr Lee, the teacher, announces to the class that there will be a surprise test next week. It can occur on any day from Monday to Friday afternoon. Alex, the smartest student in the class, stood up and pointed out the following to Mr Lee.

"Mr Lee"

"Yes, Alex?"

"Well there can't be a spring test on any day next week."

"Why not Alex?"

Alex begins to explain his argument:

"Let's assume you are telling the truth and the test is indeed a surprise. If there is no test by Friday morning, then it is no surprise that the test will be on Friday afternoon. Hence the test cannot occur on Friday, so it must occur between Monday and Thursday. However, if the test does not occur on Friday, then we would have known by Thursday morning that the test must be on Thursday afternoon, which again is no surprise. After ruling out Thursday and Friday, we can apply a similar argument to the rest of the days. Hence there cannot be a surprise test from Monday to Friday"

"Very well Alex, we shall see how it goes next week."

In the following week, a test was given out on Wednesday when the students did not expect it. It was indeed a surprise test.

Analyse Alex's argument using Paul's Wheel of Reasoning:

  1. What is the problem in the question?
  2. What information is given by Mr Lee?
  3. What are the assumptions made by Alex?
  4. What are the implications and consequences of his assumptions?
  5. Whose perspectives should be considered?
  6. What are the main concepts in this paradox?


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