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The key feature here is that "reading" apparently has no object (reading what?) but its object is assumed to be the book in question. The properties of the construction are quite subtle, for example
is generally considered ungrammatical by most native English speakers.
Parasitic gaps are an important topic of study in syntax, especially in the framework of Transformational grammar. It has been argued (controversially) by some linguists working in this framework that speakers' intuitive knowledge of the construction can only be explained by an innate universal grammar. The question of how these sentences should be analysed is still very much open.