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From: turpin@ut-sally.UUCP (Russell Turpin)
Newsgroups: sci.lang,comp.ai
Subject: Re: Langendoen and Postal (posted by: Berke)
Message-ID: <9445@ut-sally.UUCP>
Date: Mon, 2-Nov-87 15:23:50 EST
Article-I.D.: ut-sally.9445
Posted: Mon Nov  2 15:23:50 1987
Date-Received: Fri, 6-Nov-87 04:16:46 EST
References: <8941@shemp.UCLA.EDU>
Organization: U. Texas CS Dept., Austin, Texas
Lines: 31
Summary: Seems to me all natural languages are finite.
Xref: mnetor sci.lang:1638 comp.ai:1043

In article <8941@shemp.UCLA.EDU>, berke@CS.UCLA.EDU writes:
> I just read this fabulous book over the weekend, called "The Vastness
> of Natural Languages," by D. Terence Langendoen and Paul M. Postal.
> ...
> 
> Their basic proof/conclusion holds that natural languages, as linguistics
> construes them (as products of grammars), are what they call mega-collections,
> Quine calls proper classes, and some people hold cannot exist.  That is,
> they maintain that (1) Sentences cannot be excluded from being of any,
> even transfinite size, by the laws of a grammar, and (2) Collections of
> these sentences are bigger than even the continuum.  They are the size
> of the collection of all sets:  too big to be sets.

Let me switch contexts. I have not read the above-mentioned book,
but it seems to me that this claim is just plain wrong. I would
think a minimum requirement for a sentence in a natural language
is that some person who knows the language can read and
understand the sentence in a finite amount of time. This would
exclude any infinitely long sentences. Perhaps less obviously, it
also excludes infinite languages. The reason is that there will
never be more than a finite number of people (ET's included), and
that each will fail to parse sentences beyond some maximum
length, given a finite life for each. (I am not saying that
natural languages include only those sentences that are in fact
spoken and understood, but that only those sentences that could
be understood are included.)

In this view, infinite languages are solely a mathematical
construct.

Russell