
Re: Ordinals describable by a finite string of symbols
Posted:
Jul 10, 2013 9:52 AM


dullrich@sprynet.com 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 welldefined totality of "all possible meanings" a string or a set of strings could have, just as there is no welldefined totality of "all possible works of art" or "all possible attitudes to life" or "all meaningful English sentences", and consequently no welldefined 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 (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus

