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This question already has an answer here:

why recursive languages does not come under Chomsky hierarchy ? why Chomsky did not classified it? any real life resemblance of recursive language something that i can connect it with like regular language are ones which needs finite memory or context free languages are those which can be parsed using single stack .something like that .

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marked as duplicate by Raphael May 8 '14 at 7:33

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The hierarchy is defined in terms of grammars. It is still an open question whether there is a natural grammar formalism for recursive languages (check out this question), and certainly no such formalism had been known at the time Chomsky wrote his paper.

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