In a certain small town, there is a barber named Bill. Since Bill is the only barber in the town, he decides that he will shave all the town's residents who do not shave themselves, but (obviously) not the ones who do.

If Bill follows this rule, will he shave himself or not?

This question essentially assumes that every object must be able to be classified exclusively as one thing or the other, when this is quite often not the case. To be a little more specific, why must we assume that the only possible categories for people in the town are people that the barber shaves or people that shave themselves? I have heard the problem stated "Assume everyone in town is either shaved exculsively by the barber or by themselves" Is this assumption even a logical one to make? It seems not, as for the paradox that follows it.

I have also heard the question asked as defining a word that indicates an adjective that describes itself (such as tiny, polysyllabic, etc) and defining another word for the opposite (such as long, monosyllablic, etc). [I wish I could remember what these words were for clarity's sake] A paradox then arises when one tries to classify the adjective itself that is used to describe adjectives that do not describe themselves. (!!) On the outside, these seem non-related but again the essential question is: must every adjective fit exactly one of these catagories?

Blah, now I'm just rambling....
--Graatz

Posted by Jeff on 2003-12-23 21:15:16