Linguistics theories

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The main theoretical approaches to linguistics are generative (derivational and non-derivational), functionalist, and cognitive. They can be characterized as follows.

Generative linguistics
This paradigm was founded by Noam Chomsky, attempts to find the basic underlying rules that underlie any given language, and all languages. The term "generative" is a mathematical term that means to fully describe, account for, and explain a system (it has nothing to do with generating in a mechanical or mechanistic sense, like a machine cranking out grammar patterns or sentences). Chomsky's theories began with a complex set of transformations in the original Transformational Grammar framework, which have been simplified in later theories - Principles & Parameters, Government & Binding Theory, and the current Minimalist paradigm. These have been reduced to a smaller set of so-called movements, but to make this simplification possible, the syntactic structure has been made more complex by adding abstract categories in the syntactic trees or syntactic structure.
Constraint-based generative linguistics
Some generativists do not favor the use of transformations, derivations or movements, and in response, non-derivational constrain-based theories have emerged, particularly Optimality Theory in phonology. Instead of movements or derivations, universal constraints are proposed, which are present in all languages, but work differently in various languages. This has also been applied to syntax, e.g., Optimality Syntax.
Functionalism
This approach is an attempt to ground language on pragmatic or usage-based and communication-based principles and categories. It focuses on surface forms rather than abstract structure. It has advantages in application to language pedagogy and the study of pragmatics.
Cognitive linguistics
This paradigm began with the insights of Gestalt psychology, and later, schema theory in cognitive psychology. It assumes that language is a cognitive domain that is grounded in cognitive psychology and other mental faculties, and that language must have arisen from cognitive faculties rather than just on its own, and hence, language is crucially connected with cognition - be it natural semantic categories in our world, or human social cognition. It combines these psychological insights with the key insights from the study of metaphor - that metaphor is a key element of meaning in language, and hence, a whole field of cognitive semantics exists for exploring this.