From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.lang
Subject: Re: Written and Spoken Language(s)
Date: 12 Apr 92 21:10:28 GMT
Organization: Purdue University Statistics Department

In article <1992Apr12.180124.21175@news.Hawaii.Edu> jmu@uhunix.uhcc.Hawaii.Edu (James M. Unger) writes:
>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:

			.................

>>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. 

Grammar is not the same as axiomatization.  The notion of a grammatically
correct statement in other fields is not that different from grammar in
"natural" languages, only more restricted.

>>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.

What do you think you are doing when you are producing your posting to
electronic form?

As for 17th century attempts to reduce everything to mathematical form,
they did not know anything yet about the foundations of mathematics, and
they assumed it would be an easy matter.  In fact, they even assumed that
the real world (such as physics and chemistry) obeyed simple mathematical
laws, this continuing even to this century.  There was no satisfactory
consideration of the foundations of mathematics until the middle of the
19th century, any more than there was a satisfactory consideration of
the grammar of natural languages before the early grammarians looked at
their languages and decided that it was not a hodgepodge, but that there
was a structure.  I notice that linguists have a tendency to ignore the
grammar in favor of vocabulary, but is this correct?

An attempt to use mathematics to model natural language would have to
be a major undertaking, and even physics and chemistry have not been
satisfactorily modeled.  The term is modeled, not incorporated.  The
use of models is purely linguistic, and the power of this use is that
the very grammar of mathematics allows conclusions to be drawn in the
model, which appear to apply to the "real world."

>>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.

If you think that plane geometry is basic in mathematics, you are mistaken.
The structure of the number system, not developed until late in the 19th
century, is much simpler.  

Children learn English from instruction, even if it is not formal.  They
even learn grammatical rules in English or other languages before they
have much vocabulary.  Grammar is the structure of language; the rest is
data hung on the structure.  In other fields, this is noticed more easily,
but it is still not appreciated enough.

As someone who encounters non-mathematicians with problems, the difficulty
is not that they do not know the mathematical analog of vocabulary, 
namely, mathematical facts, but that they cannot use mathematics as
a language to carry out the necessary translation.  The introduction 
of the purely grammatical notion of variable is essential to teaching
this to the "typical" person, just as simplification of writing from
purely pictorial was needed to the use of writing to cummunicate well.
-- 
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)