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We all know that language uses finite means to get infinite number of sentences. We can create sentences almost freely. Sometimes they don't make sense, true, but they still remain a possibility.

 

However, language in general also has the property of recursion. By its definition "recursion" is the repetition of something. In language, things can be repeated almost infinitely. Take for example the following sentence:

I am very tired.

If I feel extremely tired, I might (instead of using the adverb phrase extremely) put another very in front of very tired as a premodification:

I am very very tired.

Grammatically, this is allowed even one hundred times. So sentence I am very very very very very very very very very tired. is perfectly grammatical, although it is not used simply because its not economical or practical. This is the example of recursion: the repetition of the adverb / adverb phrase very.

One other way in which recursion is realised is via coordination. Consider the following:

Mary was in school.

If we wanted to name all the children who were in school, that would be allowed, so we might get a very very very long sentence (I just love recursion), for example:

Mary and John and Jane and Joseph and George and Steve and Tina and Josh were in school.

Coordination allows me to name as many children as I want. Same is with adjectives:

I am tired and sleepy and frustrated...

And finally, there is one more structure I can think of: embedding! Also known as : subordinate clauses.

He says that I know that Mary thinks that John believes that ....

 

So, this is recursion. I used the examples from English simply because we all understand it. However, recursion is present in other languages as well. The only reason why it doesn't function is the memory limitation. We forget what we'd wanted to say or we forget what we'd already named - things like that. Still, these sentences remain grammatical. We cannot call them ill-formed, merely impractical. 

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