3 More Paradoxes, Part III

Headache Photo by futureatlas.com

Here are even more amazing paradoxes to baffle your students: Buridan’s Bridge, the Bootstrap Paradox, and the Barber Paradox.

Buridan’s Bridge

Buridan’s Bridge stars Plato and Socrates and was created sometime in the 1300s.

  • Socrates wants to cross the bridge. Plato is standing on it.
  • Plato says: Make a statement. If it’s true, you may cross, but if your statement is false, I’ll throw you into the river.
  • Socrates says: You’ll throw me into the river.

The paradox is:

  • If Plato throws him in the water, he broke his own rule since now the statement is true. And he promised to let him pass.
  • If Plato lets him pass, he has broken his own rule also since the statement is false. And he promised to throw him in.

Bootstrap Paradox

There are several bootstrap paradoxes, and they all have to do with Time Travel, which of course opens up incredible paradoxes.

In this one, a man receives a visitor. It’s himself from the future… with the plans for a time machine! It takes years, but the man uses the plans to build the time machine then travels back and gives himself the plans.

The paradox is: was the time machine ever actually designed, or were these plans just passed down infinitely?

Barber Paradox

In the Barber Paradox, there is one barber in a town. He follows this one rule: he shaves all men in town, but only if they don’t shave themselves.

So, does the barber shave himself?

  • If he shaves himself, then he violates the rule since he only shaves those who don’t shave themselves. But he does shave himself.
  • If he doesn’t shave himself, then he violates the rule since he claims to shave all men in town as long as they don’t shave themselves. And he doesn’t shave himself.