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Topic: Ordinals describable by a finite string of symbols
Replies: 24   Last Post: Jul 27, 2013 12:38 PM

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 fom Posts: 1,968 Registered: 12/4/12
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 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.
>

Could you provide some references concerning
the augmentation by truth predicates?

Just something to give me an idea of where
to look.

Thanks

Date Subject Author
7/10/13 Aatu Koskensilta
7/10/13 David C. Ullrich
7/10/13 Sandy
7/10/13 fom
7/12/13 apoorv
7/15/13 fom
7/16/13 Shmuel (Seymour J.) Metz
7/19/13 apoorv
7/19/13 fom
7/20/13 apoorv
7/20/13 Peter Percival
7/20/13 apoorv
7/21/13 apoorv
7/21/13 apoorv
7/21/13 fom
7/22/13 apoorv
7/22/13 fom
7/23/13 apoorv
7/23/13 apoorv
7/24/13 apoorv
7/27/13 apoorv
7/27/13 fom
7/10/13 Aatu Koskensilta