fom
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Re: Ordinals describable by a finite string of symbols
Posted:
Jul 10, 2013 11:16 PM


On 7/10/2013 8:52 AM, Aatu Koskensilta 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. >
Could you provide some references concerning the augmentation by truth predicates?
Just something to give me an idea of where to look.
Thanks

