Re: Negation?

I'm not sure this'd be particularly useful to anyone, but in case it
is....

There's this intriguing book out by Gilles Fauconnier, called _Mental
Spaces_ (translation of a French original).  It does away with
traditional 'referential' semantic analyses of sentences in favor of a
'cognitive' analysis.  He sees sentences not so much as "carriers of
meaning", where a sentence or a word "has" a meaning, but as minimal
sets of instructions, which tell the hearer how to construct a meaning
by manipulating, adding to, and subtracting from configurations of
mental entities.

Basic to the theory is the idea that meaning is distributed across
sets of "mental spaces," so called because they are usually (in
ordinary conversation) spoken of in metaphorical terms borrowed from
physical spaces.  Any situation where meaning is compartmentalized is,
in this theory, represented by different mental spaces: different
times, different places, different contexts, different social spheres,
reality and possibility, antecedent and consequent, and so on, all use
exactly the same mechanisms.

Ex. "In baseball, you use a smaller ball than you use in football."
"In 1843, we had a different president than we have now."  Note the
use of "in" to mark mental spaces.

Also basic to the theory is the idea that entities in one mental
space may be linked to entities in another mental space (or in the
same one!) via _connectors_ of different kinds.  Generally it is
possible to use the name or description of an entity in one space to
refer to an entity to which it is _connected_.  Identity is one
connector among many.  Different kinds of analogy are also connectors,
and so are well known functional relationships like those between
authors and books -- "Plato is on the third shelf from the left."
Connectors of another kind link roles and values.

Note that one interpretation of one of my sentences above, "In 1843,
we had a different president than we have now," uses a word which is
felicitous describing the present American populace (1st plural) but
not in describing the past American populace (I am not a part of that
populace).  But it works due to a connector between the two, and the
connector hovers close enough to the border between identity and
analogy that it's difficult to say if I am speaking analogously of
them as "we" or postulating a greater "we" consisting of all Americans
who ever lived, so this is a case of true identity and "we" is in fact
felicitous.  In mental space theory, the distinction is irrelevant to
the mechanics of sentence disambiguation, which explains why it seems
such a fiddly detail to bring up and analyze.

Definite and indefinite descriptions are easily explicated in mental
space theory: a definite description identifies an entity already
existing in a mental space; an indefinite description is an
instruction to set up a new entity in a mental space.  (Broadly
speaking.)

Anyway, in mental space theory, negations are instructions to set up
a mental space which contains the negated material, and to block the
focussed entities from the negative space from being allowed into the
reference space.  ("Reference space" is a relative term meaning
something like the "parent" space with reference to which the
negation-space is set up as a "daughter.").

According to this theory, I suspect that any word whose semantics
include a negative presupposition, including "avoid," "fail to",
"other than," and so on, would work the same way.  It would be fairly
simple to make a language which avoids simple "nots" but it would be
very difficult and perhaps not very useful to make a language with
*no* words whose semantics involve setting up a negative space.


Ed Heil ------------------------------- edheil@postmark.net
"Facts are meaningless! You can use facts to prove anything
   that's even _remotely_ true!"           -- Homer Simpson