# Theory

A **theory** is formed by a system of laws and hypotheses and of some other items such as concepts and conventions(definitions, operations and rules of deduction).

The construction of a theory is the highest and most demanding goal of scientific research and can be undertaken only if and when a number of interrelated laws has been found. There is much confusion about the term theory, especially in linguistics, where all kinds of formalisms, thoughts, approaches, descriptive tools, definitions, and concepts are called theories.

Theories have two functions: (1) they represent the body of scientific knowledge in a scientific discipline and (2) they are the only means to scentifically explain (and predict) facts and phenonema.

## Kinds of theories

The philosophy of science distinguishes two kinds of theories:

- the axiomatic theories of logics and mathematics, and
- the empirical theories in the factual sciences.

While the first ones make statements only within a given axiomatic system and can be used only to construct analytical truths, the latter ones make statements about parts of the world. The truth of an empirical theory and of its elements, the laws, does not only depend on internal correctness but also on the correspondence with the facts of reality – although every empirical theory must have an axiomatic kernel.

## Theory construction

Currently, there are two approaches to the construction of a linguistic theory (in the sense of the philosophy of science): (1) synergetic linguistics and (2) Altmann’s and Wimmer’s unified theory.

The basic idea behind synergetic linguistics is the aim to integrate the separated laws and hypotheses which have been found so far into a complex model which not only describes the linguistic phenomena but also provides a means to explain them.

The other approach at theory construction in linguistics is Wimmer’s and Altmann’s unified theory. Integration of separately existing laws and hypotheses starts from a very general differential (alternatively: difference) equation and two also very general assumptions: (1) If y is a continuous linguistic variable (i.e. some property of a linguistic unit) then its change over time or with respect to another linguistic variable will be determined in any case by its temporary value. Hence, a corresponding mathematical model should be set up in terms of its relative change (dy/y). Consider, as an example, the change of word length in dependence on its frequency. We know that words become shorter if they are used more frequently but a long word will be shortened to a higher extent than an already relatively short one. (2) The independent variable which has an effect on y has to be taken into account also in terms of its rela-tive change (i.e., dx/x). In our example, it is not the absolute increase in usage of a word that causes its shortening but the relative one. The discrete approach is analogical; one considers the relative difference ?yx/yx. Hence, the general formulas are dy/y = g(x)dx and ?yx-1 / yx-1 = g(x). Based on various results in linguistics it could be shown that for the continuous case it is sufficient to consider

or

and for the discrete case

or

Both are well interpretable linguistically and yield the same results as the synergetic approach. The great majority of laws known up to now can be derived from the above equations (e.g. Menzerath´s law, Zipf-Mandelbrot law, Frumkina´s law, all laws of length, diversification laws, TTR, synonymy, polysemy, polytextuality laws, morphological productivity, vocabulary growth, Krylov´s law, the law of change, etc.). The discrete and continuous approaches can be transformed into one another (cf. Mačutek, Altmann 2007) and yield all discrete probability distributions used in linguistics. The parameters are interpreted as specific language forces as known from synergetic linguistics.

Both models, the unified one and the synergetic one, turn out to be two representations of the same basic assumptions. The synergetic model allows easier treatment of multiple dependencies for which in the general model partial differential equations must be used.

## References

- Altmann, Gabriel. 1980.
*Wiederholungen in Texten*. Bochum: Brockmeyer.

- Bunge, Mario. 1967.
*Scientific Research I, II*. Berlin, Heidelberg, New York: Springer.

- Mačutek, Ján & Altmann, Gabriel. 2007. Discrete and continuous modeling in quantitative linguistics.
*Journal of Quantitative Linguistics*. (to appear).