From: jmu@uhunix.uhcc.Hawaii.Edu (James M. Unger)
Newsgroups: sci.lang
Subject: Re: Written and Spoken Language(s)
Date: 12 Apr 92 18:01:24 GMT
Organization: University of Hawaii

In article <44973@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1992Apr11.174155.665@news.Hawaii.Edu> jmu@uhunix.uhcc.Hawaii.Edu (James M. Unger) writes:
>
>>The point is that you cannot express using mathematical notation everything
>>you can express using, say, English.  Strings of mathematical symbols are
>>logographic inasmuch as they can be "read" differently in different
>>(spoken) languages, and the set of all well-formed strings may be
>>"infinite"; they obviously are not, however, coextensive with the
>>permissible strings of any natural language.  In order to merit being
>>called a writing SYSTEM, it is necessary that the entity in question be (1)
>>coextensive with a natural language and (2) practically learnable/usable by
>>ordinary individuals.  Military codes (NOT ciphers) come close to meeting
>>condition (1) but certainly not condition (2).  Compared with Mandarin
>>writing, they are far closer to being genuine logographic writing SYSTEMS.
>>The fact that thousands of Chinese do learn how to read Mandarin whereas
>>few human beings (if any) ever succeed in memorizing codebooks that
>>approach the size of complete lexica shows that Mandarin writing is NOT a
>>good example of a lographic writing SYSTEM even though any one particular
>>Chinese character may, in a given orthographic context, may be legitimately
>>said to function as a logogram.
>
>In principle or in practice?  

In practice.

>The converse problem is essentially true,
>also.  The only way one can express mathematics (or physics or chemistry)
>in English is to use a symbolic essentially literal trascription of the
>notation of these fields into English, and to operate on them with the
>grammar rules of those fields, not English grammar.  

This shows a complete misunderstanding of what "grammar" means in linguistics.
Formalisms of various scientific bodies of knowledge are by no means
comaprable to the grammars of natural languages. 
 
>Now nobody has tried
>to do this with expressing natural languages in mathematics, although a
>small amount of this has been attempted in producing logic systems, but
>the same thing can be done, at least for written English.  The translation
>of characters into ASCII (or other) strings of bits, or the earlier use
>of telegraph symbols, is such.  But the use of English to express 
>mathematics is much more transliteration rather than translation.

You evidently believe that mere transliteration suffices or should suffice
to render any possible well-formed utterance of English into an equivalent
mathematical form.  You've got to be kidding.  Incidentally, in the 17th
century, several savants DID try to reduce language to mathematical
formalism--and naturally failed.

>As for being learnable by "ordinary" individuals, I claim that mathematical
>ideas are far easier to learn if they are not forced to be expressed in the
>clumsy and imprecise "natural" languages, and they can be learned by ordinary
>individuals more easily than the so-called "natural" linguistic ideas.  It is
>probably easier to teach mathematical ideas to first graders than to graduate
>students.  I would even go so far as to say that mathematics is essentially
>pure grammar, and that the understanding of mathematical notation and 
>precision, the linguistic aspects of mathematics, are what non-mathematician,
>including linguists, should know about it.
>
>What is a natural language?  Restricting the notion of natural language to
>the existing spoken systems is a great mistake.  

Do you know any children who have acquired, say, plane geometry by age 4 or
5 without formal instruction?  English is an example of a natural language;
group theory is not even language.  I suggest you read _Visible Speech_ by
John DeFrancis (Hawaii, 1989) re so-called pictorial writing systems before
proceeding with this string.

--
J. M. Unger, Chairman
Department of E. Asian Languages & Literatures
University of Hawaii