> It is very probable that every line has many different meaning, but no > line has uncounatbly many meanings.
Every line has an indefinite and indeterminate number of possible meanings. It makes no sense to speak of the cardinality of the totality of all possible meanings of a string of symbols.
> Therefore the list contains only countably many finite definitions.
The list contains just random, meaningless strings. Whenever we instill, with mathematical precision, these strings with some definite meaning, so that they become definitions of reals, we find there are definitions not included in the list. There is an absolute notion of computability in logic. There is no absolute notion of definability.
-- Aatu Koskensilta (firstname.lastname@example.org)
"Wovon man nicht sprechan kann, darüber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus