Re: Universal grammar

In article <1161593335.080182.129420@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Franz
Gnaedinger" <frgn@xxxxxxxxxxx> 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.

One important (meta-)scientific development coming after Goethe, was
moving away from positivism, where one believed one would develop theories
identified with reality, towards merely describing theories. Developments
in physics such as QM, GR, etc., forced that development.

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.

So, if one should make 1/0 mathematically usable, one will have
to introduce some axioms, and show consistency. Under some circumstances,
this might be useful, but mostly not.

But you see the principle: one does not speculate over what does "1/0",
but merely develop s a formal description of it.

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 ...

In fact, most ancient Greek mythology have foundations in reality, either
as symbolism, or a distortion of reality. For example, the story about
Jason and the golden skin describes a real life Greek prince who went from
Greece through the Bosporus, to Armenia, where sheep skins still today are
used for washing gold. To pay for the trip, one bought beautifully dyed
skins at some Greek island. The story about Achilles' heal tells the dyers
to not leave a spot where the skin held while being dipped. A certain
percentage of the babies are born cyclops, but they are still-born. And so
on.

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

Ambiguity just mean "multiple possibilities". So keep track of them, to
the extent needed for the task at hand. If you take a sentence like
  Time flies like an arrow.
at one level, there will result in multiple ASTs. If one wants to pin down
word ambiguity, one will have to develop the logical model further,
resulting in even more splitting.

All you can possibly achieve, in my opinion, is to reduce ambiguity
in mathematical logic.

This is not really ambiguous.

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.

These are already around, up and working - in the form of humans. :-)

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.

More seriously, if one wants to develop machines, that is usually because
one wants to do something different from what humans already can. Or at
least, machines do it differently.

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.

Well, progress in AI has been slow over the last couple of decades, and
there is no sign of a quick change there. The more powerful PCs available
nowadays may though speed up developments.

Other forms of computing appear on the horizon as well: quantum
computing, DNA computing.

For something like that to take off, it really needs to go into
mass-production first.

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.

I think one will have to think carefully at the objectives at hand, not
just trying to combine inputs.

Grammar of the future will achieve more than artificial language
of today, however, you can never really tame language.

The problem is really trying to cope with human cognition. It does not
really matter what the human means of expression are, if it now is human
language, math, or something else.

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 ..

A philosopher mentioned a funny story about a kitten getting stuck into a
tree. Then the mom climbed up the tree, demonstratively past the kitten,
and then down again. So after awhile, the kitten realized: so that is how
to do it, and climbed down. So cats, by your definition, have a language.
:-)

--- 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.

The idea is not to tame human language, but merely to get some aspects of
it into the computer. This is surely possible, as it is possible to write
stuff like this. :-) So one just attempts to upper the simple
character representation somewhat.

--
Hans Aberg
.

Relevant Pages

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  • Re: Universal grammar
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    ... A footnote said that the basic formula of mathematics, ... q equals q, ... each having its own formal language. ... I don't see any way to get rid of such ambiguities, ...
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  • Re: Universal grammar
    ... q equals q, ... all of it has an equality, at least on the set level. ... not part of the language. ... Mathematics does not just mimic nature. ...
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  • Re: Universal grammar
    ... A footnote said that the basic formula of mathematics, ... q equals q, ... each having its own formal language. ... I don't see any way to get rid of such ambiguities, ...
    (sci.lang)