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Friday, February 24, 2006

It's only logical

With my math students in Brooklyn, I would often use the following logical proof to drive them crazy and motivate them to pay attention.

Start with a simple "or" statement, where the first clause is clearly true, and the second clause is clearly false:

Either the sky is blue, or Mr. Wheeler can shoot lasers with his eyes.

Now take any false statement--a student's casual lie, perhaps, or a presidential quote that was patently dishonest, or the spurious proof that 1=2--and use its logical opposite, which is true, as in "1 is not equal to 2". Substitute this for the true part of the earlier "or" statement:

Either 1 is not equal to 2, or Mr. Wheeler can shoot lasers with his eyes.

Using disjunction (if memory serves), you next show that if the first clause was false, then the second clause would have to be true:

If 1 is equal to 2, then Mr. Wheeler can shoot lasers with his eyes.

Now you bring in the earlier false statement:

But according to my earlier proof, 1 is equal to 2!

And conclude the supposedly false clause must be true:

Therefore, Mr. Wheeler can shoot lasers with his eyes.

Other favorite conclusions have been:

  • (Since Iraq has WMDs,) Bush listens to Kanye West
  • (Since Sean "did" his homework but "just forgot it",) Sean is a visitor from another dimension
  • (Since Cherie "never" said Kamrin was gay,) Cherie eats slugs for dinner

etc.

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