Re: Satire? Who said satire?

[cbmvax!uunet!PRC.Unisys.COM!dave]

nsn@ee.mu.OZ.AU

Ronald Hale-Evans <EVANS@binah.cc.brandeis.edu> writes:

> Besides being a brilliant satire of the planned language movement (and I
> think we can see a little bit of Esperanto, Loglan/Lojban, BABM, the "a
> priori" languages of Descartes and friends, Solresol, maybe even Lincos, in
> here), this piece raises some interesting philosophical questions. *Why*
> can't we create a language where grammatical correctness implies factual
> correctness? (Douglas Hofstadter is great for this stuff; see *Goedel,
> Escher, Bach*.) 

There are three excellent reasons.

First, anyone acquainted with general semantics will recognize the
slogan, "The map is not the territory."  Anything which we say about
reality is an *abstraction* of reality; it does not, and inherently
cannot, say all there is to know.  The closest we could come would be
an extremely lengthy dissertation on how to build a highly accurate
simulation of the real situation.  And if we tried to make the
simulation too accurate, down to the level of individual atoms, the
Heisenberg Uncertainty Principle comes into play, telling us that it is
*theoretically* impossible to ever form a completely accurate
description of physical phenomena.  Thus, while we can tell the truth,
we are forever limited from telling the whole truth.

Now, in general, I think our abstractions are very good ones.  Maybe
extremely good.  Embodied in the languages we use, they are powerful
tools for helping cope with the world in which we live.  However, they
aren't perfect (hmmm..."perfect abstraction" is literally an
oxymoron).  Since they are not perfect they will, when pushed too far,
inevitably lead to error.

Although in principle we can't build a language that exactly reflects
reality, we can at least attempt to reason correctly with those
concepts we *can* express in the language.  Formal logic, for example,
starts with *premises* that are taken to be true, and defines correct
reasoning from those premises.  In a sense, mathematical proofs in
formal logic follow a "grammar" that ensures their correctness.

So suppose we fall back from a language that grammatically enforces
"truth" to one that grammatically enforces correct reasoning?  Well,
the fact is, we *can* design such a language.  It isn't even too hard,
actually; the language description merely requires the use of a
recursively-enumerable grammar.  This brings us to the second reason
we cannot build such a super-language as is suggested above:
computational intractability.

The traditional classification of grammars is into regular grammars,
context-free grammars, context-sensitive grammars, and
recursively-enumerable grammars.  These are in order from
computationally cheapest to computationally most expensive.  Anyone
attempting to use a grammar for any practical purpose is limited to
regular or context-free languages, with occasional forays into
context-sensitive grammars.  Beyond that, it is possible *in
principle* to use the more high-powered grammars, but it is not
practical to do so.  Furthermore, no conceivable super-duper
futuristic computer will ever make this practical (if you want
evidence for this claim, check out any decent textbook on formal
grammars; I'm not going to try to make the case).

Arthur W. Protin Jr. cites a third reason, Godel's Theorem.  A
somewhat simpler statement of Godel's Theorem is:

	If a language is powerful enough to talk about itself,
and
	If you can prove (within the language) that the language
	is consistent,
then
	The language is not in fact consistent (i.e. it lied to you
	when it said it was).

This is indeed a lovely and elegant theorem.  What it says about our
alleged super-language, in which only true statements are grammatical,
is that either (1) you cannot express within the language the fact
that only true statements are grammatical, or (2) you can express it,
but it ain't so.


  -- Dave

P.S.  I agree with lojbab regarding the posting of copyrighted texts :-(

-- Dave Matuszek (dave@prc.unisys.com)  I don't speak for my employer. --
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