Barber paradox vs. Zermello

I would like to share my view on following homework.

russelzermelloI’d like to visualize storyline from my perspective operating on barber paradox, and why it is somewhat nonsense question.

Paradox states: The barber is the “one who shaves all those, and those only, who do not shave themselves.” The question is, does the barber shave himself?[Reference Wikipedia]

barber1But wait a minute, what is “all those, and those only, who do not shave themselves”?

It sounds like a group, or set. Many objects, which by some condition can be seen as a single entity.


Now if to think, that barber is inside redbox, and it is possible to “draw” him from the superset “ALL” by predicate “those who doesnt have themselves”, that indeed leads to quite amusing but useless paradox.

ZFC theory avoids fallacy here, and points that there is not enough reason to consider barber as possible candidate for “all those” set.

Giving it a little bit formal approach, one should be careful defining set and deriving subsets. It is quite easy to imagine self set of all real things, ie universe. However when one considers notion of , it is very obvious that this concept is far from reality. After all, “all” implies “all real” things.