User blog comment:Wythagoras/All my stuff/@comment-10429372-20130715145943/@comment-5529393-20130715170806

Well, we don't have a problem with contradiction, since I am restricting "definition" to definitions that don't refer to the notion of definable. So "smallest undefinable ordinal" is not a proper definition;  we can call it a type 1 definition. However, the question remains whether the notion of "definable" is to vague to define explicit objects. Of course, the same question plagues the ¥ function;  basically if ¥ exists, then the smallest undefinable ordinal exists and vice versa.