From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.lang
Subject: Re: Written and Spoken Language(s)
Date: 12 Apr 92 14:50:23 GMT
Organization: Purdue University Statistics Department

In article <1992Apr11.174155.665@news.Hawaii.Edu> jmu@uhunix.uhcc.Hawaii.Edu (James M. Unger) writes:
>In article <44833@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>>Mathematics uses an essentially infinite set of pronouns,
>>which can even be restricted, and one can even have difficulties at
>>a lecture because the spoken expression of these, and of standard 
>>notation, is quite different from language to language.  A chemist
>>can write down a structure which is quite clear to another chemist,
>>even en if they might have difficulty introducing themselves. Greektch
>>typesetter could set this in type without understanding a word of it
>>orally.  

>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?  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.  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.

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.  
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)