  A proof of G\"odel's incompleteness theorem is given. With this new proof a
transfinite extension of G\"odel's theorem is considered. It is shown that if
one assumes the set theory ZFC on the meta level as well as on the object
level, a contradiction arises. The cause is shown to be the implicit
identification of the meta level and the object level hidden behind the G\"odel
numbering. An implication of these considerations is stated.
