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Re: CG: Re: 'Meta' terminology

From: John F. Sowa <sowa@bestweb.net>
Date: Fri, 27 Apr 2001 13:59:19 -0400 (EDT)
Message-ID: <3AE9B374.19046B5E@bestweb.net>
To: cg@cs.uah.edu
Cc: Lee Jonas <ljonas@acm.org>, Chris Fox <cfox@lds.com>, phayes@ai.uwf.edu, www-rdf-interest@w3.org, seth@robustai.net, standard-upper-ontology@ieee.org
I just wanted to make some comments that might clarify a point
of disagreement between Chris Fox and Seth Russell:

CF>> 6) There is no metalanguage (unless you're a Chomskyan).

SR> Huh?  Methinks this is a confusion.

That depends on what you mean by a difference in language.  In formal
language theory (as practiced by logicians and computer scientists),
the syntax of a language is defined by a collection of formal grammar
rules G and a vocabulary V.  If you change one rule in G or one symbol
in V, then you get a totally different language.

Linguists who deal with natural languages recognize that there is
a vague boundary between languages, dialects, and idiolects (dialects
that are spoken by a single individual).  Strictly speaking, no two
individuals ever speak exactly the same dialect, and even a single
person will change idiolect as he or she learns new words, habits of
speaking, etc.

On a larger scale, there are languages such as Swedish, Danish,
and Norwegian, which are mutually intelligible.  Then there are
dialects of Chinese, which is called a single language, even though
many of the dialects are not mutually intelligible to speakers who
have not spent some time learning each other's dialect.  In countries
such as the fragments of Yugoslavia, the distinctions between languages
and various dialects of each depends more on religion than on choice
of words, grammar, or pronunciation.

For reasons such as these, linguists have a half-serious, half-jocular
definition of the difference:  "A language is a dialect with an army."
In other words, where you draw the line is at least as much a political
decision as a scientific decision.

The distinction between "object language" and "metalanguage" was most
sharply drawn by the logician Alfred Tarski, who defined a stratified
hierarchy of "metalanguages":  you can start with a language L0 that
talks about a domain of individuals D.  Then a language L1 would be a
metalanguage with respect to L0 if it can talk about the individuals
in D, the symbols in L0, and the relationships between the symbols
of L0 and the individuals in the domain D.

To avoid paradoxes, the language L1 would not be allowed to talk about
its own symbols.  For that, you would define a metametalangauge L2,
which would be able to talk about D, the symbols in L0, the symbols
in L1, and the relationships between all three of these kinds of things.
You could keep going up the hierachy of metalanguages to L3, L4, etc.

The languages that Tarski was considering were all dialects of
first-order predicate calculus, but you could apply his distinctions
to any language, including English.  You could distinguish a subset
of English L0 that would have words for talking about a certain
domain D.  Then L1 would be a larger subset of English with words
for D plus words for talking about the words and syntax of L0 and
their relationship to D.

If you want to, you could say that all those metalevels are
dialects of "the same language" or you could say that they are
distinct "languages".  Either definition is OK, but you have to
specify exactly what you mean by "language" or "metalanguage".

John Sowa
Received on Friday, 27 April 2001 20:13:53 GMT

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