> Sigh. Taking 'describable' to mean 'describable (definable?) by any > String of symbols' makes no sense! Symbols don't mean anything - it's > impossible to use a string of symbols to describe anything.
As you say, we must assign some meaning to a string of symbols for it to describe anything. There is no well-defined totality of "all possible meanings" a string or a set of strings could have, just as there is no well-defined totality of "all possible works of art" or "all possible attitudes to life" or "all meaningful English sentences", and consequently no well-defined totality of all definable or describable ordinals. For a language with a mathematically defined semantics -- such as given by a truth definition for the language of set theory, analysis, arithmetic, ... -- there is such a totality, but, provided we accept the definition as legitimate, we can always move to a more expressive language, e.g. by introducing a truth predicate.
-- Aatu Koskensilta (email@example.com)
"Wovon man nicht sprechen kann, darüber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus