
Re: Ordinals describable by a finite string of symbols
Posted:
Jul 10, 2013 11:31 AM


On Wed, 10 Jul 2013 16:52:46 +0300, Aatu Koskensilta <aatu.koskensilta@uta.fi> wrote:
>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.
Nice string of symbols there...

