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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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 Aatu Koskensilta Posts: 2,639 Registered: 6/28/08
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 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.

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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