Science a GoGo's Home Page Forums General Discussion Not-Quite-Science Forum Christmas conundrum

This one is especially for you Bill S it involves infinity in abstraction but others might enjoy.

I am going to define a profession called "Barber"

Definition 1: A barber is someone who shaves people who do not shave themselves.

Definition 2: A barber is someone who shaves only people who do not shave themselves.

Happy with those definitions?

So is the barber a barber when he goes to get a shave?

Think about it .... and all the best of the seasons.

Of course not!

Definition 1: A barber is someone who shaves people who need shaving, but who do not shave themselves on those occasions when the barber shaves them.

Definition 2: A barber is someone who shaves not only people who do not shave themselves, but also people who shave themselves sometimes, but not always.



We now have to ask if the barber in question shaves himself, or if another barber shaves him.

Your wording suggests that he might go to someone else for a shave, in which case there is no problem, even with your definitions.

If he shaves himself, that simply establishes that my definitions are infinitely more apt.

Have a great Christmas. Don't stay too sober.

The problem is to resolve one paradox you have created more in what is a "profession" and a "barber".

Any male who shaves himself is by your changes above in the barber professions.

There is no solution to the paradox it is called Russell's paradox

http://en.wikipedia.org/wiki/Russell%27s_paradox

=>According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell's paradox.

Profession and Barber are naive sets and subject to the paradox.

The paradox is at the heart of your problem with infinity where you try and make numbers a naive set :-)

If a person is labelled by what they do to pay the bills, then yes, a barber is still a barber when someone else shaves them.

But if a person is only labelled by what they do to pay the bills, only when they are doing said activity; then no, the barber would be classified as a customer when getting shaved, not a barber.

A cook who cooks in a restaurant, is a cook. A cook who eats in a restaurant, is a consumer.

But I think this is lost on me. Seems like if you limit definitions (factors) to a set and unchangeable scenario, one can make a paradox out of anything. I do believe I simplified my answer through practical interpretation, and ignorance of a 'naive set'. The human mind saying F*&% you paradox! F&^$ you.