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SYNTAX: Principle which keeps an element A from entering a syntactic operation unless it satisfies a need of A itself. EXAMPLE:

(i) seems to [NP a strange man] [that it is raining outside]
According to Chomsky (1992), a strange man cannot raise to check the case feature of matrix T; since a strange man has already been case-marked by to, movement of a strange man to check case on matrix T would not satisfy a need of a strange man itself, and therefore this movement would violate Greed.
In chapter 4 of the Minimalist Program, Greed is incorporated into the definition of Attract.
LIT. Chomsky, N. (1993)