User blog comment:Ikosarakt1/Uncountable function cannot exists/@comment-1605058-20130802172024/@comment-1605058-20130804161107

This is a question touching very point of definability. Definability is not mathematical concept, as if theory can define its own definability, it would imply some serious consequences, worse than inconsistency. In the sense of mathematical consistent theories this ordinal marks limit of what can we define - but we can't define it due to undefinability of definability. We can, of course, define it in English or something else, but inconsistency of such systems is inavoidable. (First time ever I used so many long words in one statement)