Generative Grammar
Proponent
Noam Chomsky
Purpose
Produce well-formed sentences
Reject ill-formed sentences
Pointers
Concept of Infinity
Finite rules on a language
Infinitely new utterances
Pointers
Grammaticality is not defined by people, but just a principle waiting to be discovered.
Used
Constituency grammar or the grammar that is applicable to all languages
Transformational grammar or the grammar that is exclusive to a language
Reasons for infinite production
Human Creativity
Recursion
Another aim
To find the 'natural' languages of human
Mathematical Analogy
Circles
A certain language is like a circle on a graphing paper.
Inside and outside the circle, there are points which we can label as the 'grammatical and ungrammatical, respectively.
Points
All these points are infinite.
Even there are infinite points, we are ought to find the grammatical ones.
Formula/Rules
A certain mathematical formula or rule can satisfy the search for these grammatical sentences.
Generative grammar works like this.