[language] Re: [evol-psych] Bushman click languages
H.M. Hubey
hubeyh at mail.montclair.edu
Mon Sep 9 02:24:45 UTC 2002
<><><><><><><><><><><><>--This is the Language List--<><><><><><><><><><><><><>
Steven D'Aprano wrote:
>And language is too important to let the essential meaning of the word
>be diluted by those who would talk about the language of art. Art does
>not communicate, any more than words use language. Art is the medium of
>communication, not the body that communicates.
>
>
I wrote earlier that language is very-well-defined. I am copying this
out of a book. I think
it should be read carefully, and saved and referred to regularly by
anyone who has
an interest in this topic. I am copying from this book because it is
short, concise and
has other wonderful applications which will interest the readers.
The relevance of this will be shown below. If I am going thru all this
trouble of typing
it seems those who want to comment should at least read carefully and
think a while
about what all this means.
{Note": The set inclusion sign is denoted by @, or I use the word
"is-in" to mean the
same thing. The symbol "->" and "=>" are both arrows, and used differently.
The notation P(i+1) used once means P subscript i+1. Elsewhere the subscript
is simply lower case e.g. Pi is P sub i except where integers are used
e.g. P2, P3, etc) )
From page 331 of Banks, Signal Processing, Image Processing and Pattern
Recognition, Prentice-Hall, 1990.
----------------------------------start here
-----------------------------------------
[1] We begin by abstracting the basic elements of an ordinary (written)
language. An alphabet
is a finite nonempty set V whose elements are called letters. A word w
(over V) is a finite
string of zero or more letters of V, and its length is |w| being the
number of letters in the string.
... The set of all words over V is denoted by W(V) or just W if no
confusion over the set of
letters is likely.
[2] If P, Q @W [mine: e.g. P,Q is-in W) then PQ (or P*Q) denotes their
concatenation. Note that
concatenation is associative ... P is a subword of Q if Q=P1*P*P2 for
some P1,P2 @W.
Subsets of W are called languages (over V).
[3] A generative grammar (or phrase structure grammar is a quadruple
G=(Vn,Vtm,S,F) where Vn and Vt
are disjoint alphabets, S at Vn, and F is a finite set of ordered pairs
(P,Q) such that P,Q at W(V),
where V=Vn.union.Vt and P contains at least one letter of Vn. The
elements of Vn are called
nonterminals, and those of Vt terminals, while S is called the initial
letter. If (P,Q)@F we write
P ->Q
[4] Such an element (P,Q) is called a rewriting rule or production. We
say that P generates Q directly
and write P=>Q is there exist words R,T and a production P1->Q1 @F such
that P=R*P1*T and
Q=R*Q1*T. Similarly, we say that P generates Q and write P=>*Q if there
exists a finite
sequence of words P0,..., Pk such that Po=P, Pk=Q and Pi=>P (i+1) for
0<=i<=k-1. Thus
P=>* Q = P= P0=>P1...=>Pk=Q.
[5] The language L(G) generated by G is then defined by
L(G) = {P: P at W(Vt), S=>*P}
....
The rules of production (i.e. elements of F) defined above are very
general and without
some restrictions lead to significant problems in formal language
theory. A hierarchy of grammars
is therefore introduced, each being more general than the following
grammar. The four main
types may be defined as follows:
[6] Type 0 or unrestricted grammar allows productions as defined above.
Type 1 or context-sensitive grammar allows only production of the form.....
Type 2 or context-free grammar allows productions of form A -> P where
A at Vn,
and P at W(V).
Type 3, or finite-state or regular grammar allows productions of the
forms A -> BP,
or A -> P, where A,B @Vn, P at W(Vt).
---------------------------------------------end here -----------------
Before Larry gets boringly pedantic, we should notice that the
restriction to
"letters" is for simplicity. We can assume that we use a phonemic or
phonetic
alpahbet ( and that there are no extra monstrocities such as English
"two, too, to"
etc. These certainly make things more complicated but do not add to the
discussion.
Now the real problems are elsewhere. (I numbered the paragraphs to make
it easier for later discussion and referral, but I will not put
comments here now
because it will get too long.)
Arguments against this from linguists (not all linguists) are various
kinds. Probably
the most common one (and the most confusing one) is this one:
THIS LANGUAGE PRODUCES ALL KINDS OF THINGS! WHAT
KIND OF A LANGUAGE IS THAT?
Yes it does, and so it should. Indeed, I give an example right from this
book, on page 339, and I will quote.
--------------------------start here --------------------
In this section we shall describe some of the more widely used pattern
languages and their primitives. The first was developed to deal with
two-dimensional picture type objects which do not link together naturally
at single points. This means that simple concatenation of symbols cannot
be applied without some simplification of picture primitives. In order to
reduce the problem to a concatenation language the picture description
language (PDL) is defined in terms of primitives, each of which has only
two points (head and tail) which can be joined to other primitives.....
-----------------------end here-----------------------------------
Note: No circularity. There are primitives.
Now, here is the main problem. And it is a very general one. Some linguists
want to know why these grammars can be used for things other than
natural language such as English. The answer is quite simple. Did they ask
their teacher why there are no integers for counting only apples? Did they
ask their physics teachers what kind of physics uses equations for
electrical
circuits (e.g. TV tuner) the same equation that can be used to model the
sugar-insulin cycle ? Did they ask why the equation for the propagation of
sound waves after an integral transform happens to be the same equation
as that of a pendulum? There are many many such examples.
The best answer is yet another question:
Why should the mathematical formulation of language not be able to
also model other things?
I deleted many things but they are all trivially non-germane. What is really
required is what is called "maturity" (mathematical maturity). That is the
crux of the problem. The rest is boring detail.
The historical explanation is simply that because of the development of
digital computers, the field suddently went on a trip on a super-highway
and it is much
different than riding on a donkey cart. There is a book called "Thirty
Years That
Shook Physics" (about the relativistic and quantum explosion). That also
lost a lot of
old-time physicists. That is how life is. The same thing happened to
economics. So now
it is the time of linguistics.
--
M. Hubey
hubeyh at mail.montclair.edu /\/\/\/\//\/\/\/\/\/\/http://www.csam.montclair.edu/~hubey
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