Upon re-reading my reply, it might be worthwhile to simply quote Hamkins' conclusion in full. > And therefore neither are you able to do this in general. The c

Upon re-reading my reply, it might be worthwhile to simply quote Hamkins' conclusion in full. > And therefore neither are you able to do this in general. The claims made in both in your question and the Wikipedia page [the Wikipedia page has now since been updated] on the existence of non-definable numbers and objects, are simply unwarranted. For all you know, our set-theoretic universe is pointwise definable, and every object is uniquely specified by a property.