User blog comment:Wythagoras/All my stuff/@comment-10429372-20130718073726/@comment-1605058-20130718122804

Finitistic argument time! There is only finitely many symbols in use, thus finitely many 1000 character long strings. Each of them either defines a number or not (possibly due to self reference). So only finitely many numbers can be defined. If you still think there is ill-definition there, I think we can exclude them by disallowing any mention of "being definable" in sentences.