Re: Universal grammar


Hans Aberg wrote:

There is no problem dealing with that, as in metamathematics, one
introduces the notion of a theory with equality.

Well then, let us go a step further. Mathematics relies on the basic
formula a equals a, while nature, life and art follow Goethe's formula
"all is equal, all unequal ..." Mathematical logic is entangled with
every part of the world, while covering only half of the world. You
must always secure it against the wilderness of the equal unequal.
For example one is not allowed to divide a number by zero. Why?
When I asked my teacher, he knocked me on the head with a large
iron key. Not a very mathematical argument, I thought. Years later
I found a logical answer: when I divide a number by zero, I get an
infinite number as result. One times infinite equals two times
infinite,
three times infinite, and so on, hence I am in the realm of the equal
unequal, forbidden for mathematicians. The division by zero, one may
say, is a "wormhole" between mathematics ruled by the basic formula
a equals a, and the real world, where a equals a unequals a.

Also language follows Goethe's formula. Language is full of vital
ambiguities. They make words resound, store plenty information
on life and nature, and allow us to speak on more than one level.
You find them everywhere, even where you would expect them
least. You may have read parts of Homer's Odyssey in school.
What did you make of beautiful Helen, allegedly the cause of
the Trojan war? You may consider her a historical figure, or,
more probably, a fictitious woman. But no, she is no woman.
In my opinion, Helen symbolizes the then rare and precious
metal tin, which came from the Ore Mountain and from Central
Asia and was bound to pass Ilium, where the Trojans laid hands
on it. Her glittering long robes she made herself are shiploads
of the glittering tin ore cassiterite. Her thread is tin wire, cut from
tin foil. Her husband xanthos Menelaos symbolizes copper, the
color xanthos covering all shades of copper ores, yellow, brown,
red. Their daughter, lovely Hermione who resembles golden
Aphrodite, symbolizes the alloy bronze, of a golden shine when
freshly cast ...

Language and poetry are full of ambiguities, on every level.
Drive them out and you kill them both.

All you can possibly achieve, in my opinion, is to reduce ambiguity
in mathematical logic. In order to get a more universal grammar
for your software. Some clever compromises.

The situation may change with neuronal networks - genuine
neuronal networks, not just simulated ones on Von Neumann
computers. I could imagine that such a machine of the near (?)
future may allow to find a path from A to B - say, in the case of
a mathematical problem -, whereupon a classical computer may
broaden the pathway, miraculously found by the network, into
sort of a highway.

Sorry if I talk nonsense. I am a computer moron. But the
discussions about programming remind me of discussions
of turntables in the late 1970s: how can one possibly improve
them? And all of a sudden there were CD players that made
all those endless discussions superfluous.

My advice: prepare yourself for a new era, be open for new
possibilities, adopt your work and reasoning to the future task
of accompanying neuronal network computing, and don't hope
to ever free language from ambiguities that make it so rich
and lively! Ambiguities are emanations of the formula a equals
a unequals a, and thus testify to the logic of nature and life.

Other forms of computing appear on the horizon as well: quantum
computing, DNA computing. Also they may once be embedded
in classical computing, and each one will excel at a different task.
Consider how the brain works. Vision occupies a third or even half
of the brain and involves thirty areas, each one performing a special
task. Also grammar of the future may be a combination of grammars:
classical grammar, generative grammar, Rupert Ruhstaller's grammar
of functors and arguments, visualized in budding circles (the only
grammar I know that finds meaning in seemingly free word order),
and so on.

Grammar of the future will achieve more than artificial language
of today, however, you can never really tame language. Consider
what language is. Here you are with my definition from 1974/75:
Language is the means of getting help, support and understanding
from those we depend upon in one way or another --- and every
means of getting help, support and understanding may be called
language, on whatever level of life it occurs. What is special about
human life? the use of artificial things we made ourselves. What is
special about human language? the use of words, which name
things and make us see a world full of things ... The more things
we use, the more specialized our lives become, and the better we
must be able to explain our specific situation before we can hope
to get our needs satisfied and our wishes fulfilled, and so it comes
that most of our language describes the world, nevertheless,
language serves needs and wishes.

You can never really tame language. Already Rupert Ruhstaller
told me that. Speakers will always find a way to get around
rules. You can perhaps deal with some tame forms of language,
but you can never tame language per se. I say this to the
computer people, and to the grammar fans in sci.lang as well.

Regards Franz Gnaedinger

"All is equal, all unequal": www.seshat.ch/home/equal.htm

Rupert Ruhstaller's grammar: www.seshat.ch/home/grammar.htm

.

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