  Recently Feferman (Rev. Symb. Logic 6: 6-15, 2013) has outlined a program for
the development of a foundation for naive category theory. While Ernst (ibid.
8: 306-327, 2015) has shown that the resulting axiomatic system is still
inconsistent, the purpose of this note is to show that nevertheless some
foundation has to be developed before naive category theory can replace
axiomatic set theory as a foundational theory for mathematics. It is argued
that in naive category theory currently a 'cookbook recipe' is used for
constructing categories, and it is explicitly shown with a formalized argument
that this 'foundationless' naive category theory therefore contains a paradox
similar to the Russell paradox of naive set theory.
