Title: On status of concept for a "problem" in linguistics.
Author: Valery Solovyev.
One could rarely find a problem description for future research in
publication in linguistics, while it has become usual to set unsolved
problems in mathematical publications. Some of most famous problems
in mathematics such as Fermat theorem or Cantor's continuum hypothesis
stayed in the center of attention of mathematicians for tens and even
hundreds years. A lot of new mathematical theories have been
raised as a result of attempts to resolve them. Thus, emphasis on important
problems, their formal definition and concentration of efforts for
solving, has important methodological influence in development of mathematics
as a whole. The same one could see in development of theoretical physics, especially in such a formalized branches as field theory.
We meet rather different situation in linguistics. And one obvious reason
of it is insufficient level of formalization. Still some sections of
linguistics, generative grammar at first, can be characterized as
formal enough, and the methodology noted above seems to be applicable
to them.
Of course, one cannot disagree with Martin Everaert that the problems
are observed and solved on frame of concrete theory. But a problems itself
can be set both in frame of some theory, and without any theory. It is quite
enough for a theory to be formalized in intuitively clear (for researchers
working in the field) terms and be sensible.
In the latter case an appropriate theory can be found (or created) based
on the same term apparatus. Otherwise the comparison of different theories
was completely impossible. When considering (discerning) examining some problem
in a context of concrete theory three variants are possible. First of all
the problem can have no common points to the theory given, since it cannot be
defined in the same notions (terms) in which the theory is built. It also
possible that a problems has different solutions in frames of different
theories. Thus in the example noted above Cantor's continuum hypothesis
is true in some variants of set theory and false in another! More
than that in most popular version of the Sets Theory - axiomatic theory of
Zermelo-Frenkel the hypothesis is nither provable nor refutable (although
it can be expressed in the theory).
In this case the problem is called theory-independent. Such a variability does not diminish status of a problem. Anyway the problems stay an important
mean to test a theory. How do we compare different theories with the same
term apparatus? Obviously one of the main parameters of comparison is what
problems (and how) can be solved within frames of given theory.
Now let's look at metaproblems. Those metaproblems mentioned by
Andrew Carstairs-McCarthy do not seem to me to be real metaproblems.
They are just usual problems, that must be viewed, say, not in GB-theory,
but in some other (linguo-cognitive-historical) theory, that issues the
causes of formation languages in the shape they currently have.
Is it possible to find direct analogy in Physics. Along with different
theories that study some particular properties of a matter, there is also
so called super-string theory that tries (besides other questions) to
answer why the matter of our Universe has exactly the properties that
we obeserve.
I propose to use term "metaproblem" in another sense. Metaproblem is a
problem concerning not an object of research in linguistics - language,
but concerning tools of investigation i.e. term apparatus, theories.
In such a sense the questions like the following can be called metaproblems:
-is a theory A more strong than theory B
-is a theory logically contradictory (consistent)
-is a problem solvable in frame of theory B
Finally I'd like to note that distinct, accurate setting of
problems important to linguistics must become significant factor
of it's development. This refers especially to generative grammar.
Modern communication media allows to organize operative discussion
on problems, and thus provide an effective support for this methodology
of science development.