A Note on the Posting of Tara W. Mohanan

[Sebastian Shaumyan]

              A NOTE ON DIMENSIONS OF THEORETICAL RESEARCH

Tara W. Mohanan and KP Mohanan have proposed to distinguish various
dimensions of theoretical research. No matter in which terms we
formulate them, these distinctions reflect essential aspects of
theoretical research which must be recognized explicitly. The
different dimensions of theoretical research are real and it is
important to understand the interrelations of these dimensions.  The
different dimensions of theoretical research are not on a par. There
is a certain hierarchy between them. Mohanans' posting contains a lot
more than I am able to discuss here in detail. I will only make some
comments on the relation of the dimension of the formal framework to all the 
other dimensions of theoretical research which I will denote by the cover
term "core dimensions of theoretical research".

How the dimension of the formal framework relates to the core dimensions
of theoretical research?  These two aspects of theoretical research
are not on a par: the essential aspect is the core dimensions of theoretical
research whereas the formal framework is important for ensuring rigor
and precision in the formulation of the results of the core dimensions of
theoretical research. Furthermore, a properly constructed formal
framework reflecting the concepts and laws of the core theoretical
research may also have a heuristic function; a fruitful deduction, a
fruitful calculus may lead to new insights into the essential
properties of the empirical object under investigation, it may
stimulate our imagination. The goal of the formal framework is an
adequate mathematical description of language. But to attain this goal
one must know what is language. To say that language is a formal
object is to say nothing: every object of mathematical description in
every science is a formal object. To make a proper mathematical
description of language, one must know what is language as an
empirical entity, one must understand concepts and laws characterizing
the essential empirical properties of language. The formal framework
depends on the core theoretical research whereas the core theoretical
research is independant of the formal framework.

There is a wide-spread belief that the formal model in itself
determines a correct analysis of language. This belief is a fallacy
that has pernicious consequences. Understanding language has nothing
to do with mathematics. My linguistic theory, Applicative Universal
Grammar (AUG), uses a sophisticated mathematical formalism based on the
Variable-Free Semantics of Combinatory Logic. But it does not appeal
to mathematics in support of its fundamental concepts and laws. On the
contrary, the function of the formal framework of AUG is to express
the concepts and laws of AUG in rigorous mathematical terms. The
formal framework of AUG relies on the core theoretical research of
AUG. The conceptual problems have nothing to do with
mathematics. Conceptual analysis is independent of any
mathematics. Mathematics is a tool of deduction. Deduction from what?
The value of deduction depends on the value of the initial ideas to
which deduction is applied. Deduction must be applied to right
concepts. In this connection I would like to quote mathematicians as
impartial judges on the value of mathematics in science. Thus, after
giving striking examples of the abuse of mathematics in different
sciences, V. Nalimov concludes:

"The use of mathematics in itself does not eliminate absurdities in
publications. It is possible to `dress scientific brilliancies and
scientific absurdities alike in the impressive uniform of formulae and
theorems' (Schwartz, 1962). Mathematics is not the means for
correcting errors in the human genetic code. Side by side with the
mathematization of knowledge, mathematization of nonsense also goes
on; the language of mathematics, strange as it seems, appears fit for
carrying any of these problems" (Nalimov, 1981).

And now let me quote a passage from Chapter V "Linguistic Methodology"
of my book: A SEMIOTIC THEORY OF LANGUAGE:

"As an instrument of cognition, mathematical language has a special
function-to be a tool of deduction. The word DEDUCTION is
important. The use of mathematical language as a tool of deduction
makes sense when the initial ideas from which we deduce their
consequences have cognitive value. If, on the contrary, the initial
ideas do not have cognitive value or, worse than that, are absurd,
then the use of the mathematical language as a tool of deduction
causes harm. In this case, mathematical language turns from an
instrument of cognition into an instrument of obfuscation. Deduction
is neutral to the cognitive value of ideas: mathematization of
nonsense is equally possible."
 
"Successful application of mathematics in various sciences has caused
an aura of prestige about scientific works that use mathematical
symbolism. There is nothing wrong with that, since the right use of
mathematics is really important in any science.  A well-motivated use
of mathematical formalism can enhance the value of a mathematical
paper or a book. In case of an abuse of mathematics, however,
mathematical symbolism acquires a purely social function of creating
an aura of prestige about works whose cognitive value is null or, at
best, very low. In this case, the manipulation of mathematical
symbolism, the play with symbols, belongs to phenomena of the same
order as the ritual dances of an African tribe. The manipulation of
mathematical symbolism becomes a sign of affiliation with an exclusive
social group. The magic of the play with symbols can have an effect
comparable to the effect of drugs. The participants of the play get
high and then fall into a trance that makes them feel they are in
exclusive possession of God's truth.  (Shaumyan, 1987: 321).


                          REFERENCES

Shaumyan, S. (1987). A Semiotic Theory of Language. (Indiana
       University Press:Bloomington,Indiana)

Shaumyan, S. (1980). "Semantics, The Philosophy of Science, and
       Mr. Sampson". In FORUM LINGUISTICUM, Volume V, Number 1. pp. 66-83.
       Published by Jupiter Press for Linguistic Association of Canada
       and the United States. Adam Makkai, Editor, P.O.B. 101. Lake Bluff,
       Illinois, 60044.

Shaumyan, Sebastian & Segond, Frederique (1994). "Long-Distance Dependences
       and Applicative Universal Grammar". In COLING 94. Kyoto, Japan.

Descles, Jean-Pierre (1990). Languages applicatifs,langues naturelles
       et cognition (Hermes: Paris).
           
Nalimov, V.V. (1981). In the Labyrinth of Language: A Mathematician's
       Journey. Philadelphia: ISI Press.

Schwartz, J. (1962). "The Pernicious Influence of Mathematics on
       Science". In Logic,Methodology, and the Philosophy of
       Science. Proceedings of the 1960 International Congress. Palo Alto,
       Calif.: Stanford University Press.



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