The barber of Seville is that inhabitant of Seville who shaves every man in
Seville that does not shave himself
Back
This is a paradox, because who will shave the barber of Seville himself ?
if the barber does not shave himself, he - according to definition - must
shave himself, because he shaves all who do not shave themselves
if the barber does shave himself, he - according to definition - can not
shave himself, because the barber only shaves those who do not shave themselves
This is actually and example of an invalid recursive definition: In the
definition the barber appears twice: one as the defined entity "barber of
Seville" and again as a member of all men living in Seville. Such a
recursive definition is invalid, and in fact leads to a contradiction in
this case.
Interactive Real Analysis, ver. 1.9.5 (c) 1994-2007, Bert G. Wachsmuth Page last modified: Mar 26, 2007
Back