>firstname.lastname@example.org writes: > >> 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.