Wednesday, September 27, 2006

A close shave

Logic is a powerful tool; it can be used to discern and to discover truth. Sometimes though, this tool falls into the hands of those who would abuse it. I would not abuse it as my logic is nothing to write home about. Or may be due to a lack of logic I might be abusing it unknowingly!

I read this paradox of the Barber recently which incidentally is attributed to the British philosopher Bertrand Russell.

The barber paradox asks us to consider the following situation:

In a village, the barber shaves everyone who does not shave himself, but no one else.
The question that prompts the paradox is this:

Who shaves the barber?

No matter how we try to answer this question, we get into trouble.

If we say that the barber shaves himself, then we get into trouble. The barber shaves only those who do not shave themselves, so if he shaves himself then he doesn’t shave himself, which is self-contradictory.

If we say that the barber does not shave himself, then problems also arise. The barber shaves everyone who does not shave himself, so if he doesn’t shave himself then he shaves himself, which is again absurd.

Both cases, then, are impossible; the question ‘Who shaves the barber?’ is unanswerable.

Perplexed and confused?

3 comments:

Abhipraya said...

My right brain shut down after reading this!

Sav said...

Duh! San, why is it that you are not even thinking of the possibility that the barber was a woman? Has it to do with the way men's brains work?

Pavithra Sankaran said...

Ask me! Ask me! He grew a beard!