As a historical culture, a civilization, the West is to be distinguished not only from the East but also from "pre-Western" cultures to which it "returned" in various periods of "renaissance." Such returns and revivals are characteristics of the West. They are not to be confused with the models on which they drew for inspiration. "Israel," "Greece," and "Rome" became spiritual ancestors of the West not primarily by process of survival or succession but primarily by a process of adoption: the West adopted them as ancestors. Moreover, it adopted them selectively -- different parts at different times. Cotton Mather was no Hebrew. Erasmus was no Greek. The Roman lawyers of the University of Bologna were no Romans.
I viscerally disagree with this statement, but I've been unable to find a real flaw with it. The best response I can come up with is that even if we emphasize some parts of our past over others for social, political, or aesthetic reasons our past is still our past. If one emphasizes Great-Great-Great-Great-Etc-Grandpa John who came over on the Mayflower over Crazy Uncle Bobby the Ex Con, it doesn't mean that either was chosen as an ancestor. They simply were ancestors.
The family-resemblance argument is difficult to sustain if only because of the very different shape European intellectual life had between, oh, 400 and 1300. There is almost no Aristotle until the end of that period (the bishop of Paris did ban the teaching of Aristotle twice); only one Platonic dialogue in wide circulation; no Greek drama to speak of (Petrarch, if I remember, assembles the dialogues we have today); no work with Biblical texts in the original; and law itself tends to be commentaries on commentaries (or glosses) of Roman law rather than the law itself.
This is not to make the argument that intellectual life was dead in the period mentioned: there's still Anselm and Boethius and the sometimes very interesting work done by the commentators, especially after the Papal Revolution ('interesting' is not coterminous with 'correct'). But it's also not the case that there's a simple line that can be drawn from the ancient past to be medieval or modern worlds--certainly not so easy a line as an 'Athens and Jerusalem' storyline would make it sound.
The interesting question that comes out of this, then, is whether it makes sense to think of humanism/renaissance/the reformation as historically continuous or discontinuous--a case could be made either way (it also raises the possibility that discontinuity may actually be a more faithful representation of the past than continuity).